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Full text of "Raman centennial"

C . V . RAMAN 

1888 CENTENNIAL 1988 

Journal of the 


Vol . 68 . Nos 11-12. Nov. Dec. , 1988 

Editorial Committee 

M. Vijayan 

Associate Editor: 
R. Narayana Iyengar 

Executive Editor: 
P. R. Mahapatra 

Technical Officer (Editorial): 
K. Sreenivasa Rao 


Ami Kumar 
R K. Kaul 

S. S. Krishnamurthy 
B. G. Raghavendra 
M. R S. Rao 

A. P. Shivaprasad 
J. Srinivasan 
N. Viswanadham 
R Vittal Rao 

Guest Editors: 

N. Mukunda 

T. V. Ramakrishnan 

D. P. Sen Gupta 

ISSN No. 0019-4964 

Enquiries to: 

The Executive Editor. 

Journal of the Indian Institute of 

CO IlSc Library, Bangalore 360012. 


is available in 
microform v 

from University 

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ZnfaRmd. Am Arbor. MJ 4B10G. 

Cover design: D P Sen Gupu and N. Mukunda 

Special Issue 


Country- T. M. K. Nedung*da 

Chandrasekhara Venkata Raman 
November 7 t 1888-November 21. 1970 


Last year *as the birth centenary of the mathematical genius Srinivasa Ramanujan. This 
vem »e celebrate the centenarv of the scientific colossus Chandrasekhara Venkata 

Raman is the greatest ph. skim and experimental scientist this country has so far 
produced He was totally self-made and self-taught, his only true "teachers' being 
Rayleigh and Helmholtz through their writings. In some ways he may be viewed as the 
Usi in their line of classicists, though his own work, in the words of R. W. Wood, gave 
'one of the most convincing proofs of the quantum theory of light". Raman was blessed 
mith supreme self-confidence, boundless curiosity to understand Nature, infinite sensiti 
la her nuances, and a deep sense of patriotism, In addition to these remarkable 
qualities, he was able to inspire those around him to achievements of an order they could 
not have reached on their own, 

With indefatigable energy and a "European intensity" no other Indian scientist exhi- 
bited, in the period 1907 to 1933 Raman created and sustained a school of physics in 
Calcutta that in Sommertelds words made this country "an equal partner with her 
European and American sisters". Even before the discovery of the Raman Effect in 1928 
which led to the award of the Nobel Prize in 1930, Raman had done outstanding work in 
acoustics and light scattering recognised by his election to Fellowship of the Royal 
Society in 1924 

We at this Institute remember Raman as our first Indian Director from 1933 to 1937. 
and thereafter as Professor and Head of the Department of Physics (set up by him in 
i until his retirement in 1948. Here too he created an outstanding school of physics 
with memorable contributions such as the Raman-Nath theory of diffraction of light by 
ultrasonic waves and the Raman-Nedungadi discovery of the "soft mode", among 
others. U was also in the Bangalore period, in 1934, that Raman established the Indian 
Academy of Science! 

In our one-day symposium arranged to pay tribute to Raman, we have invited a group 
of distinguished scientists to speak to us of Raman's life and work, the contributions of 
his school in Bangalore, and the present scope and applications of the Raman Effect. 
This special issue of the Journal of the Indian Institute of Science brought out on this 
occasion contarns the texts of these talks, some rare photographs, and reprints of some 
of Raman's most significant papers. 

On Ramans birth centenary it is appropriate that we remind ourselves of the great 
qualities that he possessed, and the ideals and dreams of self-reliance and independence 
that he cherished 


C. N. R. Rao 
Bangalore Director 

November 1988 Indian Institute of Science 

ra Venkata Raman Centenary 1988 

A. Vsswramitra 

G Venkata raman 

A. K. Sood 

A Special issue of the 
Journal of the Indian Institute of Science 


Professor C. V. Raman and the Department 
of Physics, Indian Institute of Science, 

Some reflections on the life and science of 

Sir C. V. Raman 

Light scattering from condensed matter- 
Contributions of the Raman school 

Sudhanshu S. Jha 
Herbert L Strauss 

A. K. Ramadas 

T. V. Ramakrishnan 

Some recent trends in Raman spectroscopy 

The resonance Raman spectrum of l 2 in 

Inelastic light scattering in crystals 

Selected papers of Raman: An introduction 

Selected papers of Raman 

(i) Contents 

In) Reprinted papers 







W fct «M> -Dec 196*. «S, 445-447. 

C. V. Raman and the Department of Physics, 
Use. 1933-1948 

Dcfwnmcni of Pliyaict, Indian Institute of Science, Bangalore 561) 012. 

Raman joined the II Sc as Director on 31st March 1933. The Department of 

was inaugurated in July 1933 with Prof. C. V. Raman as the first head of the 

inment and with eight students; namely. R. S. Krishnan, S, Jagannathan, R. 

Aaaathakrishnan, G. Narasimhaiah, D S. Subbaramaiah, N. S. Nagendra Nath, P. S, 

Snmvasan and P, Pattabhiramaiah. Later in the year, B. V. R. Rao and C S 

Yenkateswaran joined. 

Research was initiated in the following subjects: Doppler Effect in light scattering, 

oottotd optics, diffraction of light by ultrasonic waves, and Raman spectroscopy. This was 

bfiowed in subsequent years by crystal physics, dynamics of crystal lattices, e .#., the soft 

■ode. phvsics of diamond, second-order Raman spectra of crystals. X-ray topography, 

md Brilloum scattering. 

The total number of research scholars during the period 1933-1948 was 98. Among 
them in addition to those already mentioned, are: K. Venkatachala Iyengar, P. 
NBakantan. B. V. Thosar. S. Ramaswamy. T. M. K. Nedungadi, B. D. Saxena, Vikram 
hai, Anna Mani, P. Raman Pisharoty, G. N. Ramachandran. D. D. Pant, S. 
Ramaseshan, K. G. Ramanathan. V, Chandrasckharan. T, Radhakrishnan and 
P S. Narayanan. 

Several distinguished scientists spent considerable periods of time here. In particular. 
P- Max Born spent six months as a Visiting Professor in the Department in 1936. Dr. 
H J- Bhabha joined the Department as a special Reader in Theoretical Physics, to 
deliver 25 lectures, in 1940. In 1942, he became a special Reader with the status of a 
Professor as a personal distinction, and was at the IISc till 1945. 

Raman stressed in his students, the desire for excellence in research as a prime 
wqtm t uient and also encouraged them to develop a strong initiative for independent 
research. His presence and the intellectual environment he provided, brought out their 
best and resulted in some significant contributions from the laboratory during his tenure 
here. Some of these are the following: 

I. The reciprocity theorem in colloid optics - R. S. Krishnan 

Proc. Indian Acad. Set,, 1935, 1, 782, 



2. The diffraction of light by high frequency sound waves. Parts I, II, III, IV and 
V. -C. V. Raman and N. S. Nagendra Nath 

Proc, Indian Acad. Set., 1935, A2, 406, 413; 1936, A3, 75, 119, 459 

3. A new technique of complementary filters for photographing the Raman spectra of 
crystal powders - R, Ananthakrishnan 

Curr. Set., 1936, 5, 131. 

4. 1 tiering and fluid viscosity - C. V. Raman and B, V, Raghavendra Rao 

ure, 1938. 141, 242. 

5. Effect of temperature on the Raman spectrum of quartz - T. M. K. Nedungadi 
Proc. Indian Acad. 3d., 1940. All, 86. 

6. Raman Effect and crystal symmetry - B. D. Saxena 
Proc. Indian Acad, Set., 1940, All. 

7. The a-p transformation of quartz - C. V Raman and T, M. K. Nedungadi 
Nature, 1940, 145, 147. 

8. Intcrferomelric studies of light scattering - C S. Venkateswaran 
Proc. Indian Acad. Sci., 1942 U5, S16\ 322 -1. 

9. New con C. V. Raman 
Cm Sci., 1942, II, 85. 

10. The physics of diamond - C. V. Raman 
Curr Set., 1942. II, 261 

11. The Raman spectrum of diamond - R. S. Krishnan 
PrOC. Indian Acad. Sci.. 1944, A 1 9, 216. 

12. X i i\ topographs of diamond - G. N. Ramachandran 
Proc. Indian Acad. Sci.. 1944, A 1 9, 2 SO 

13. The photoconductivity of diamond - D. D. Pant 
Proc, Indian /t , 1944, AI9, 315, 325. 

14. The crystalline forms of the Panna diamonds - S. Ramaseslian 
Proc, Indian Acad. Sci., 1944, A 19, 334. 

1 5. Raman spectra of second order in crystals: calcite gypsum, quartz - R. S. Krishnan 
Proc. Indian Acad. Sci., 1945, A22, 182, 274, 329. 

16. The Faraday Effect in diamond - S. Ramaseshan 
Proc. Indian Acad. Sci., 1946. A24, 104. 

17. Infrared spectrum of diamond - K. G. Rarnanathan 

Nine, 1945, 156, 23. 

18. A Theory of the crystal forms of diamond - S. Ramaseshan 
Proc Indian Acad. Sci., 1946, A24, 122 

19. The phosphorescence of diamond - V, Chandrasekharan 
Proc. Indian Acad. Sci,, 1946, A24, 193. 

i home made infrared spectrometer - K. G. Raman a than 

Cnrr Set., 1946. 15, 184. 

21, The vibration spectra of the alkali halides - R. S. Krishnan and P. S, Narayanan 
Proc. Indian Acad. Sci. 1949, A2S, 296. 

22. The influence of optical activity on light scattering in quart/ V. Chandrasekhaian 
Proc. Indian Acad. Sci.. 1949. A28, 409. 


The Raman spectrum of ammonium dihydrogen phosphate - P, S. Narayanan 
F*oc. Indian Acad. Sci.. 1949, A28, 469. 

Many of these are superb contributions and measure up to the best published 
anywhere at that time in the areas of optics and crystals. The list given also tells us how 
Raman not only inspired his students to take up forefront research problems but also 
encouraged them to publish the results by themselves, 

Opening new lines of experimental physics research goes much beyond manipulation 
of available equipment. Raman stressed the determining role played by our ability to 
create our own instruments and newer techniques. He created departmental workshops 
in addition to the central workshop and produced some excellent results with a home- 
made spectrometer and a three-metre spectrograph. No less was Raman's emphasis on 
developing experiments in close interaction with theory. 

After Prof, Raman's retirement, the main course of research in our Department 
continued on the lines set by him, for several years. But the decades that have now 
followed naturally have brought about many changes, with some research activities 
withdrawn and some recast and strengthened Out major efforts are in condensed-matter 
physics, experimental as well as theoretical. We have also taken up some newer areas 
like the physics of biomolecular systems. Many of the boundaries between conventional 
sciences disappear when biological systems are studied to their end. To the physicists 
concerned with understanding the way nature works, biology offers a unique scope and 
some most fascinating and challenging problems. Raman himself in his later years took 
up some of these studies and was deeply concerned with questions related to vision and 
colour. Everything that involved light fascinated the great scientist. Our own studies on 
DNA, 1 hope, will one day lead to exploring problems involving the effect of light; like 
how the genes function under light. 

It is with pride and pleasure that the Department of Physics remembers its founder in 
the centenary year of his birth. 

My own contact with Prof, Raman was years after he retired from the Department. 
There were a few occasions when 1 was fortunate to meet and talk to him in person. They 
were great moments. I also like to recall here his lectures at the Raman Research 
Institute which we used to attend, when we were students of the Department. It was not 
just that Raman narrated brilliantly. He assumed no prior knowledge and yet we came 
out with the feeling that we understood everything he said, very clearly. When Raman 
spoke there never was any communication gap. We are far away from those days but 
Raman s achievements continue to inspire our progress as in the past. 

J I*bm bet. So., Nov.- Dec. 1*W, 68, 449-460 
c iadtta hrfwM* of Science . 

Some reflections on the life and science of 
Sir C. V. Raman 

I i Vfnkataraman 

RAG. RC'l Campiu, Mumidipally P.O. Hyderabad 500065, India 

Received on Sept em Kf 13, |4#H, 

It is a privilege to speak about Raman, especially in this Institute where he spent a cru- 
cial period of his life. This being the year of his birth centenary, the essential tie I ails of 
arc now better known than before, in view of that and the fact (hat on an earlier 
Prof Ramaseshan has delivered a memorable lecture on Raman here in this 
I shall not discuss Raman's life in the usual sense of the word. Instead. 1 shall 
on some of the lesser-known aspects, m particular those associated with the 
spent here. Nevertheless, the requirement of completeness demands that I 
m least a rapid thumb-nail sketch of Ramans life, which I shall now proceed to 

was born near Tiruchirapally on November 7, 1888. At the age of four, 

s father moved to Visakhapainam to serve in a college there. Thus the early 

of Raman was spent in what is now a pari of Andhra Pradesh and not surpri- 

Raman could speak Telugu fluently, a fact that is hardly known. Being an un- 

£\ gifted student, Raman raced through school and college and. at eighteen. 

erred not only with an MA. degree topped I hut also with a passion 

for physics. But in those days* a career in science for Indians was unthinkable and 

did what was expected of him namely, enter government service as an adrninis- 

Thai was in the year 1907. 

The government job took Raman to Calcutta which was then the capital of India. 
There working in his spare time, Raman studied many problems in physics, particularly 
■ dK area of acoustics and optics. The pursuii of science was made somewhat eas\ fot 
HBO* the facilities provided by the Indian Association for the Cultivation of Science. It 
sj nutter of history that though the Association was founded on the model of the Royal 

ammon in London, it did not function in thai stj le. at least during the life time of its 
Fhe Association sprang to life only after Raman joined it and took charge. 

A major turning point came when, in 1917, Raman resigned from the government 
to accept the Palit Chair for Physics in the University of Calcutta, an act which 
hailed by all lovers of science, particularly by Sir Asutosh Mukherjee who publicly 



applauded the sacrifice Raman had made in giving up a highly lucrative career in 
government. The second decade of Raman's stay in Calcutta was truly a glorious period. 
No longer had he to work alone in the Association for he now had a big gathering of 
highly talented students drawn from all over the country. In fact the reputation of the 
Association spread even overseas, so much so the great Arnold Sommerfeld once 
remarked thai 

India had suddenly emerged in competitive research as an equal partner with 
hei European and American sisters. 

The high point of this period was undoubtedly the discovery of the Raman Effect, 
which brought fame and glory both to the discoverer as well as the institution he worked 

Success also breeds envy and Ramans success was no exception. As a result of several 
painful incidents, Raman had to leave the Association. Fortunately for him. precisely at 
this time there was an invitation to become the Director of the Institute of Science, 
When Raman left Calcutta, it was said by the noted geologist Sir L. L. Fermor: 

Calcutta's loss will be Bangalore's gain. At present < Calcutta may be regarded as 
a centre of scientific research in India but with the transference to Bangalore of 
one of our leading investigators, she will have to guard her laurels 

Bangalore was no bed of roses as I shall shortly describe in detail. Nevertheless, 
Raman made many important contributions both as a scientist and as a leader. Unfortu- 
nately these are hardly remembered because the controversies chat he was involved in 
eclipsed his accomplishments. In 1948 Raman retired and adjourned to the Institute he 
himself had founded, viz., the Raman Research Institute where he spent the remaining 
years of his life. This last phase was also rather a sad one. md will receive some attention 
later in this lecture. 

1 now go back to the early thirties, that is the period just before Raman took charge as 
the Director of this Institute. At that time he was a member of the Institute Council, 
having been nominated as a representative of the Eastern Group of Universities Twice 
during this period he was warmly felicitated by the Council, once when the Knighthood 
inferred upon him. and later when he won the Nobel Prize. Sir Martin Forster was 
the Director then, and his term a is coming to a close on April 1 , 1933. In anticipation of 
that, the Council appointed in July 1931, two committees which would submit names of 
suitable candidates for a successor 1 he committee in England was convened and chaired 
by Sir William Bragg and had Sir William Pope and Sir Robert Robertson as the other 
two members. The Indian committee consisted of Sir Samuel Christopher, Sir T. Vijaya- 
raghavachariar and Sir M. Visweswarayya, the last mentioned being the Chairman and 
the Convenor. Both the committees unanimously favoured Raman for the post, and in 
July 1932 the Council recommended to the Viceroy that Raman be appointed the 

There was trouble right from the beginning when Sir P. C. Ray and Mcghnad Saha 
opposed some appointments proposed by Raman. Although the opposition was ROtio- 


►. historically speaking one sees an extension of the animosity 
Raman's Calcutta period. 

office in April, 1933 Raman did three things, namely, bring a new 
into existence, restructure some of the existing departments, and 
he workshop. According to Raman, all these were for the better of 
t unfortunately for him. every one of these actions boomcranged. 

a new department, one needs money, staff and students. Raman had no 
attracting students but he did have difficulties in finding money and in 
If appointment. 1 be seed money he had been given was woefully inadequate 
salaries studentships, cost of journals books, equipment, etc. Raman therefore 
some of the Institute budget to aid the fledgeling Physics Department, an 
later invited charges of embezzlement! 

was firmly wedded to the view that excellent work comes from excellent 

He was quite dissatisfied with the performance of the existing departments, and 

felt that the Institute needed fresh blood, luckily, an opportunity for inducting 

alent was presenting itself, since many eminent scientists were fleeing Hitler's 

German) just then. Why not bring some of them over to the Institute 7 As we shall toon 

ice. one particular appointment which he pursued with enthusiasm created a huge 

problem . 

The reorganisation previously referred to antagonised both the Professor of Chemistry 
as »ell as the Professor of Electrical Engineering. Raman found that the Physical 
Cbemisir} Section was engaged mainly in studies relating to magnetism Hack at the 
Association, magnetism was one of the strong points of his research group. Feeling that 
the Physical Chemistry Section was somewhat isolated in relation to the other activities 
the Chemistry Department. Raman decided to strengthen it by making it a part of the 
ae* Physics Department .specially since the merger would provide the chemists con- 

..-- .. *nh opportunities fof oonsi ml and profitable interaction with other colleagues 
having allied interests. Prof. Watson, under whose care the Physical Chemistry Section 
■ad functioned earlier, was deeply offended and he resinned, Likewise, Prof. Mowda* 
wafta ol" the Electrical Technology Department opposed Ramans idea that the Institute 
Workshop, instead or mcrcK training students, also bshsI research workers by building 
equipment for them. Mowdawala also became resentful and chose to leave. The sleepy 
caatpus was coming alive with controversy, and pretty soon it would be time for the 

Cornell to sit up and take notice, which is exactly what the opposition wanted. 

The Born episode brought things to a boil I ike many others. Max Born left Germany 
■a lie early thirties and found for himself a temporary beith in Cambridge. At that time 
he re letter from Raman asking for the names of bright theoretical physicists 

■anting to leave Germany and who could be considered lor appointment at the Institute 
Bom replied that he could not recommend name ig about the conditions 

m India. Raman understood Horn's position: so why could not Born come to Banc 
lor a while and see things for himself? The Institute Council approved a temporary 
Readership for Max Born (as it also did for Prof. Hevesey). Born accepted the offer. 


especially as his Cambridge appointment was drawing to a clow. Further, Rutherford 
advised him to try out Bangalore as the salary was better! 

In the autumn of 1935 Born and his wife Hedi sailed for India. Soon after they arrived 
in Bangalore, a professor of Electrical Engineering named Aston came from England. 
He was Mowdawala's replacement. The Astons stayed with the Borns till their own 
bungalow was ready. Later, Aston actively worked against Raman and also attacked 
Max Born, 

Raman developed a great liking for Born, despite the difference of opinion he had 
concerning theories of lattice dynamics. He was very keen that Born should continue in 
the Institute as a permanent member but first he had to persuade the Faculty to accept 
the idea. Accordingly he proposed to the Senate that it recommend the appointment of 
Max Born as the Professor of Mathematical Physics. In his speech supporting the 
motion, Raman strongly eulogised Born but nevertheless the motion was not received 
well by many, As Born describes, 

Aston went up and spoke in a most unpleasant way against Raman*! motion, 
declaring that a second-rank foreigner, driven out of his country, was not good 
enough for them. This was particularly disappointing uj been kind to 

the Astons, I was so shaken that when I returned to Hedi 1 simply cried. 

Meanwhile the turmoil on the campus continued to grow, and in July 1935 the Council 
recommended to the Viceroy that a Review Committee be appointed. Unlike in the 
past, the Council this time spelt out in detail the various items the proposed Committee 
should address itself Do. The list was heavily loaded against Raman and his protests were 

Unmindful of all this, Raman continued to steadfastly campaign for Born's appoint- 
ment and in fact in November 1935 the Council even accepted his suggestion that a 
professorship in Mathematical Physics be created. But then the Irvine Committee came 
in the way. 

The Review Committee appointed by the Viceroy or rather the second Quinquennial 
Review Committee as it was officially called, consisted of Sir James Irvine, Vice- 
Chancellor of St. Andrew's University. Dr. A. H. Mackenzie. Pro Vice-Chancellor of 
Osmania University and Prof. S, S, Bhatnagar. Irvine was born in Glasgow in 1877 and 
practically grew up with St. Andrew's University having been associated with it succes- 
sively as a student. Lecturer. Professor, Dean of the Faculty of Science, Principal and 
finally Vice-Chancellor Bhatnagar was at that time in Lahore as the Professor of 
Chemistry in the Punjab University. As for Mackenzie, he seems to have been included 
mainly on the strength of his administrative background. 

I do not have the time to analyse the findings of the Irvine Committee; those inte- 
rested in such details may find the same in my book. It suffices to observe that the Irvine 
Committee did what it was supposed to do, namely, slay Raiti m 

That this is not an idle accusation becomes evident when one reads a letter written by 
Max Born to Lord Rutherford in October 1936. After returning to England, Born 


quite silent about the affairs in Bangalore, and it was only when Lord Rutherford 
insisted that Born decided to speak out. Let me now quote a few passages from Bom's 
letter. Borrowing from Richard Feynman, one can describe this letter as an outsider's 
inside view of the Institute affairs! This is what Born says in part: 

Raman came to the Institute with the idea of making it a centre of science of 
international standard. What he found was a quiet sleepy place where little 
work was done by a number of well-paid people, M> wife and I met an English 
couple — the man was a retired official in Ootacamund. When 1 said 1 was at 
the Indian Institute of Science, Bangalore, this man said laughing "Ah! That is a 
nice sinecure where people draw high salaries'. Similar expressions we have 
heard on other occasions. Ramans mere speeding up of the entire pace at the 
Institute was bound to look like criticism on the former work. Add to this that 
he made 9 heavy mistake in not waiting a year or two before starting actual 
reforms. Naturally he got into troubles with the professors who were at the 
Institute before him. Two of them left the Institute during the first year — an 
Indian Mowdawalla, Professor of Electrical Engineering and Watson, 
Professor of Physical Chemistry. The latter case seems to me one of the main 
sources of difficulty Raman was to encounter later. Watson's friends and he 
himself may have expected thai he was to be the new Director after Sir Martin 
retired. Certainly Watson did not like to continue as a Professor under an 
Indian Director. I was told this by some of his English friends. It is easy now to 
make the loss of Prof. Watson a point against Raman but it is certainly not just. 
Openly the real reasons for Watson's leaving the Institute were not known; 
only the given reason was known, namely, that Raman's manners had driven 
him away. I know that Raman's manners can cause serious grievances but in 
Watson's case they were but a pretext. 

Elsewhere in the letter Born says: 

1 want to show you by a few examples that all this is not a matter of mere 
.^sumption. Three weeks after us arrived the new Professor of Electrical 
Engineering Aston at the Institute. Immediately after his arrival the open 
revolt amongst staff and students began and he became a centre lor collecting 
ever so silly complaints against Raman. We wondered very much till one day 
Mrs Avion said to my wife that her husband had been made to accept the post 
by his English colleagues in charging him with the definite mission to clear up 
the Institute. Aston had been received in Bombay by the Tatas. had been their 
guest and got instructions. 

Incidentally, Born also points out that Aston failed to get a Professorship in England. 
About the Irvine Committee, Born observes: 

1 have no right to criticise the attitude and proceedings of the Committee but I 
must say that it seemed to me rather surprising. Instead of visiting the Institute 
and studying the work done in the laboratories, they sat in a government 
building some four miles away where they behaved like a law court. It was 


evident to me from the beginning that they had received instructions before- 
hand. They examined chiefly Raman's opponents, even students. All the dirty 
affairs were treated in detail but no voice was raised to take into account the 
good intentions of Raman 01 his achievements at the Institute. 

Let me now continue with the narration. The Irvine Committee submitted its report in 
I he middle of IWft and when it was discussed in the Council. Raman was severely 
attacked for his alleged infringem. .ni o: rules and procedures. Only three people namely, 
the Dewan of Mysore, Prof. B. Venkatesachar and Dr. Bawa Kauai Singh spoke on 
behalf of Raman. Hncou raged by the support given by the Council and the adverse 
report of the Irvine Committee. Raman's opponents now stepped up the campaign Mid 
finally on June 1. 1937 Raman wrote lo the Chairman of the Council: 

Having considered all the circumstances, I feel it would be best that I offer to 
terminate my contract of service with the Institute as its Director. 

Along with his resignation letter, Raman submitted a lengthy memorandum regarding 
his work at the Institute and defending his actions. The Council resolved that Raman's 
resignation be accepted, and acceded to his request tor a speck] retirement allowance. It 
also recorded that the settlement should be regarded as final and amicable. As events 
transpired, neither was true? In Ins capacJtJ as the Director, Raman forwarded the 
Council resolution to the Viceroy and along with it sent a letter of his own. This infuri- 
ated the Council which then summoned Raman and revoked its earlier offer. It declared 
thai Raman was unfit to continue am longer as Director and offered him two Choi 
Eithei to continue as Professor of Physics or resign with effect from April 1 , 1938 on such 
allowances as he might be entitled to according to standard rules. Raman was also 
warned that if he declined both options, he would be suspended! There was practically 
no support from any quarter. 

Soon after Raman stepped down, it was widely remarked, including by people well 
disposed, that while Raman was a brilliant scientist he was a poor administrator. Similar 
statements were aired in the press during 'he earlier showdown in Calcutta. These 
comments do not make ait) sense when one considers the rich encomiums paid to 
Raman for his administrative ability while he was in government service. No less a 
person than the Member for Finance in the Viceroy's Council had written: 

We find Venkataraman is most useful for the Finance Department being, in 
fact, one of our best men. 

The truth is not that Raman was a bad administrator but that he was a strong one, a fact 
not liked by his opponents. 

From a historical perspective, I see Raman's struggle as a battle between excellence 
and mediocrity. Raman championed the cause of excellence but. unlike in fairy tales, he 
lost. The Council lie laced no doubt had men of eminence but alas, they were the legal 
types who understood little about academic matters or scientific creativity. The handful 
of people that did, were mostly opposed to Raman on personal grounds. 


It is sometimes said that the battle of Kurukshctra is a symbolic representation of the 
inner conflict we often face. In a similar vein I venture to suggest that Raman's struggle 
is the paradigm of the battle between excellence and mediocrity which is still going on in 
most of our laboratories and academic camp*;ses. And alas, as before, excellence is 
generally continuing to lose. 

One of the charges levelled against Raman was that he was antagonistic to applied 
science. In fact, the Irvine Committee went to town on this subject claiming that while 
I imshedji Tata wanted a close association of scientific research with industry, Raman 
came in the way. In his defence, Raman drew attention to the consultancy he had been 
offering to the Railways, to his role as an adviser to many princely stales concerning their 
industrialisation programmes, etc. At the same time, he firmly declared that as far as the 
Institute itself was concerned, it should not become the front-end for industry solving its 
day-to-day problems like : how to extract more oil, how to make better soap or how to 
make a particular industrial process more efficient. The Institute was an academic centre 
aiming to become world-renowned and as such should engage only in those problems 
which would stimulate the keenest minds. Superior skills are developed only by facing 
basic challenges. However, the exercise would not be in vain, for such abilities are always 
useful and available on tap when applications are demanded. Back in 1924, Raman had 
spent a semester, at Caltech as the guest of Robert Millikan and it would seem that he 
was trying to model the Institute along those lines whereas the Irvine Committee and the 
Council both wanted it to go in exactly the opposite direction. The crying irony is that 
after Raman was removed, the Institute did not rath do much to promote the 
industrialisation of the country. As Homi Bhabha pointed out years later, when after 
Independence we started setting up steel plants, we went abroad shopping for techno 
logy although steel plants had been established decades earlier by Tata and by Viswes- 
warayya. Even today we are importing technology left and right. All that has happened 
is that we have established a string of premier institutes which process our human 
resources into a commodity called NRIs. 

Let me now turn to the scientific contributions which Raman made during his 
Bangalore period. After he ceased to be the Director. Raman focussed all his attention 
on research and on building up his Department. Not surprisingly, the prophecy about 
Bangalore becoming a centre for scientific excellence soon became true. If today 
Bangalore has emerged as the Science City of the Nation, it is in no small measure due to 
the seeds sown by Raman half a century ago. Since subsequent speakers are likely to 
discuss Ramans work in detail. I shall restrict myself to calling attention to a few hardly 
noticed facts. 

One observes that in the Bangalore period, Raman has become more preoccupied 
than before with natural phenomena. No longer does he seem to set up controlled 
experiments to test specific principles or theories of physics. Instead aesthetics domi- 
nates his attention, and he explores things such as the colour of plumage, the iridiscence 
of shells and of ancient glass, and so on. Even his style seems different. Consider, for 
example, how he opens his very first paper from Bangalore. He starts: 


Great interest naturally attaches to the investigation of the colours that form a 
striking feature of the plumage of the numerous species of birds. Even a 
cursory examination, as for instance the observation of the feathers under 
microscope, shows that the distribution of colour in the material and its optical 
characters are very different in different cases, indicating that no single expla- 
nation will suffice to cover the variety of phenomena met with in practice. 

ing whether the problem of the origin of colours belongs to the realm of 
chemisrn or physics, Raman directs his attention to the feathers of one particular bird 
namely, Camcm indica. About this bird he says: 

This is a species of jay, very common in Southern India, which furnishes readily 
accessible material for the investigation of this type of colouration of birds 
Seen sitting with its wing folded up. Caracas indica is not a particularly striking 
bird, though even in this posture its head, sides and tail show vivid colouration. 
It is when in flight that the gorgeous plumage of this bird is more strikingly seen 
and museum specimens of the bird are therefore best mounted with the wings 
outstretched. The wings then exhibit a succession of bands of colour alternately 
a deep indigo-blue and light greenish-blue; the tips of the wings show a delicate 
mixture of both colours 

Raman wrote two papers on shells, the first of which is largely descriptive, being in the 
style of a naturalist. The papers abound in Latin names seldom seen in a physics journal, 
and there are delightful descriptions of the shells. 

Most people today would tend to conclude that such work is not physics and thai 
Raman had started rambling. My own view is quite different, being based on a deta 
study not only of Raman's papers but those of his students as well If one reads Raman's 
papers carefully, one will observe a connecting link which is that all these studies relate 
to the optics of heterogeneous media. While Raman focussed on the natural moni- 
tions of such media, his students explored the more technical aspects The study of 
the optical properties of heterogeneous media is highly developed at the present tin. 
and has many practical applications. Unfortunately, the pioneering contributions made 
hy the Bangalore school to the development of this subject ire hardly known. It has also 
escaped notice that these studies are a vindication of Raman's point of view that good 
applied science is born out of high-class basic research. 

During the final phase, Raman spent a good deal of time studying gems and minerals. 
I have read many of Ramans papers on this subject, and I must confess they left me a bit 
disappointed on first reading. Some mighl even wonder whether such papers would gel 
past a referee. Perhaps they might not but that would be too clinical an analysis of the 
matter, Viewed in a larger perspective, it would appear that during this phase Kim in 
uas no longer interested in explaining to others. He had seen, he had understood and he- 
had enjoyed — that was all that mattered. As the poet Keats wrote: 

To understand and so become aware. 

And. thus, mine beauty from the crystalled air. 


It would be too hasty to dismiss these papers as lacking physics. On the contrary, these 
ligations raised several important questions which were left for Raman's protege 
Pancharatnam to answer. Crystal optics might have not been Eashionable in an age when 
parity non-conservation was the in thing. But there were certain subtle questions relating 
to coherence which Pancharatnam exposed and succinctly answered, almost at the same 
time when others came to similar conclusions via the newly emerging topic of quantum 
Optics. Here in Bangalore. Raman and Pancharatnam did not need the mascr. good old 
crystal optics was jusl as effective, 1 should also call attention to several papers Raman 
wrote on internal conical refraction. It thai sounds like a topic belonging to the 19th 
century, then let me mention that Bloembergen investigated precisely ihis phenomenon 
in the lale seventies, several years after Raman had passed away, Of course. Bloem- 
bergen was in t crested in the nonlinear aspects 

I do not warn you to carry the impression that it was all feathers, shells and gems. The 
Raman -Nalh theory and the soft mode about which you will undoubtedly hear later 
offer adequate proof that at least till the forties, Raman did contribute directly to main- 
stream plnsics. ]i is, hi unfortunate that even these contributions did not alwa\s 
receive the recognition they deserved. I have, fbf example, seen books on acousto-optics 

hi h make no mention of the Raman -Nath papers, although the theory due to them is 
discussed! There are others who make it appear as if the last word on the subject was 
said by Brillouin. which is not true 

Why did Raman continue with optics after leaving Calcutta, especially when nuclear 
physics was the new rage? This is an interesting question. Actually Raman was greatly 
excited by what was going on at Cavendish and very much wanted to pursue nuclear 
physics. But alas, he had no money* When Bhabha joined the Institute Raman doped 
that the Tatas would make a small grant. The Tatas eventually did. not to Raman but to 
Bhabha so that he could found the 1 II R! However, that is another story. Nevertheless, 
for a moment one does wonder what might have happened if nuclear physics had struck 
roots in Bangalore instead Ol in Bombay. It is said that later in his life Raman often 
lamented that he should have spent his Nobel Prize money buying a gram of radium 
instead of investing it on diamonds. 

During the last decade. Raman spent much time studying the physiology of vision, a 
to which his boyhood hero Helmholtz had contributed very much- It is an accepted 
fact that from a scientific point of view, this work of Raman is of no consequence 
Raman is often summarily dismissed for having produced theories of dubious value like 
this one. i do not wish to defend the indefensible but would at the same time like to ask 
whether it is not conceivable for a person to lose his creativity when repeatedly trampled 
upon? If this seems far fetched, consider what Abraham Pais says about Einstein: 

After that, the creative period ceases abruptly, though scientific efforts 
continue unremitting lv for another thirty years. Who can gauge the extent to 
which the restlessness of Einstein's life in the I920's was the cause or the effect 

of a lessening ol creative powvi 


The reference is to the violent attacks made on Einstein as a part of Hitlers anti- 
Semitic campaign. Thus we have here one more famous example of the loss of creativity 
caused by intemperate personal vilification. 

The Raman Institute phase should have been a happy one for Raman as he was now in 
his own laboratory with independent means and totally free from outside control. 
Besides, there were interesting problems to study, there were the affairs of the Academy 
to manage, and last but not the least, there was the wonderful garden to tend lo. And yet 
were some of the most painful years that Raman spent. Prof. Ramaseshan has 
given us a poignant description of Ramans agony, comparing his emotions to those of 
Mahatma Gandhi during the Noakhali disturbances. Why was this so? 

In the yean immediately after Independence, one witnessed a remarkable scene. We 
had at the helm of our affairs a great visionary whose centenary we shall be celebrating 
next year. Unlike the run-of-the-mill leader of the Third World, Jawaharial Nehru 
pm found thinker and held the view thai India must emulate the Soviet Union in 
adopting science and technology as the means of solving her numerous problems. Such a 
dream had been forming in his mind since the thirties, and now was the time to give 
shape to those dreams. Thus, science became the magic wand and everybody rallied to 
Nehru's clarion call Those were exciting times, thrilling beyond words. Laboratories 
established, buildings built, equipment bought, and people hired in large numbers. 
In no other countl o much sought to be accomplished so rapidly. I vividly recall 

the magic spell cast on us by Bhabha. 

Wasn'1 this t greet experiment and wasn't it to be supported? i es, thought the whole 
country, swepl as it was 03 a sense of euphoria. But Raman was troubled. He 100 wanted 
poverty banished, he also was in favour of technology and industrialisation, and he was 
behind no one in his desire to see his country emerge as a powerful nation. However, 
science was not created merely b\ spending money, starting laboratories and by 
ng orders. More important was the human element, and if in the name of hurry 
quantity replaces quality then disaster would inevitably follow. To him it seemed that the 
policies pursued by the government were fraught with danger, however good intcntioned 
they might be. Besides, they appeared to be a negation of all that he had stood 
and wo] ked lor, And so in a characteristic manner he made his objections be known. He 
was brief, blunl and brusque. As was to be expected, especially in the mood that 
prevailed, Raman was ignored in official quarters, although his comments made good 
copy I myself used to wonder in those days vs hv Raman was objecting to something that 
appeared to be good. After all he himself had worked for the development of science So 
is he now vigorously protesting? Three-and-a-half decades of service in govern- 
ment have made me wiser and 1 am now able to see clearly the logic behind Raman's 
arguments, although he himself chose not to elaborate on it. 

As m all countries, funding for science and technology in India has necessarily to come 
from the government but thai does not mean it should come with strings attached. [| 

ted fact that the existing governmental framework is not conducive to 
creativity. Science is a creative endeavour and yet for four decades we have been 
compelled to work with a totally incompatible system. Government control not only 


inhibits creativity, hut more disastrously, it encourages sloth and intrigue, besides 
rewarding non-performance. 1 1 is not as if the government and the bureaucrat 
composed of ignorant or stupid people. On the contrary, there are many many ck 
and talented persons in government. And yet we see this amazing contradiction of the 
government spending a sizeable amount of money in the name of science, etc.. on the 
One hand and preventing achievement In slipping an outmoded system on the other. I 
have come to the conclusion that barring isolated individuals, the governmental machi- 
nery as a whole is indifferent and insensitive to whether our science achieves excellence 
or not. If specific individuals achieve excellence bj overcoming obstacles like 
Ramanujan and Raman did. for example, they arc applauded by the society and the 
government alike; otherwise scientists as a community are either criticised or ignored. 
This is a great tragedy, considering the high place given to talent and creativity in our 
society in earlier eras. Richard Feynman has pointed out in his celebrated report on the 
Challenger enquiry, that if there is ;i Kiss of common interest between the scientists and 
the management, then calamities are possible. Calamities do not always have to be in the 
form of a crash; being saddled with a millstone is an equal disaster 

Raman was one of the first to raise his .nee against the bureaucratic approach in the 
post-Independence era, and he did this even though he himself was not subject to the 
pinch. It is curious that no less a person than Nehru complained about bureaucracy in 
sevenij of his addresses to the Science Congress, Homi Hhabha did the same in his List 
public lecture. But bureaucracy has survived, thrived and grown to even more ominous 
proportions. And there is nobody left now to raise a word of public protest. 

I belong to the generation which saw Raman as a fading giant. And our impressions 
wen based on the misconceptions and the biased folklore we were fed with. Having 
carefully researched his life. I now see how misguided 1 was I am sure there must be 
many other misguided persons like me Raman was and still is orten portrayed as one 
who did not understand physics. It heats one's imagination how then he coutd have 
commanded the respect of giants like Rutherford and Bragg, long before he discovered 
the Raman Effect. Again, how was he elected a Fellow of the Royal Society as earl v as 
\92A although he did his work in a place so far away from London? Horn was it that h 
was asked to open a discussion meeting in Toronto in the earl) twenties and how come 
Millikan invited htm as a Visiting Professor at Callech, a post earlier adorned by 
Lorentz, Sommerfeld and Einstein'' When he was appointed to the Paiit Chair, it was 
Bested that Raman should first visit England to receive training He indignant lv 
refused to visit Hngland for that purpose, although he had not gone abroad even once a't 
thai lime, How many would pass lt p :| foreign trip today? When he had to step down 
from the Directorship of this Institute, the press w;is full of rumours that Raman was 
planning to settle abroad With a Nobel Prize in his pocket that should have been quite 
easy and yet Raman chose to stay behind in his darkest hour. Today, on the other hand, 
people ire dreaming ol a green card even while entering college! After retirement, the 
government offered funds but Raman rejected it even if it meant hardship, so that he 
could preserve his independence. Can we find such a spirit today? And finally, when he 
was sounded out for the high office of the Vice Presidentship, he declined, How many 
would turn down power and position? 


It seems to me that this gauntry has been most fortunate in producing such a spirited 
scientist who, by his shining example, showed that given courage and tenacity one can 
achieve against the greatest odds. On the occasion of the Silver Jubilee of the Raman 
effect, Homi Bhabha wrote that the only purpose of celebrating the anniversary of a 
great event is to derive inspiration from it. Today we are celebrating another anniversary 
and I submit that wc should derive inspiration from all that this Noble Son of India stood 
and worked for. Raman made Mahendralal Sircar's dreams come true but unfortunately 
tits op* n dreams did not. Should we not on this occasion dedicate ourselves to the reali- 
sation of that ideal? 

i tadim fast. Set., Nov.-Dec. 1988. f& 461-481. 
* Indian Institute of Science. 

Light scattering from condensed matter — Contributions 
of the Raman school 

A. K, Sood 

1>l-| MfUBeol of Physics. Indian Institute of Science, Bangak>re 560012, India, 

Received on September 29, 1988. 


An attempt has been made to highlight some «f the contributions of Raman and his coworkers to the field of 
light scattering from condensed matter. The topics reviewed cover Rayleigh, Brillouin and Raman scattering 
from a variety of systems— pure liquids, liquid mixtures, colloids, crystals and glasses, 

Key words: Lighr scattering, condensed matter. Raman. 

L Introduction 

Light scattering which encompasses Rayleigh, Brillouin and Raman scattering has play- 
ed a key role in the understanding of static and dynamic properties of condensed 
matter — be it liquids, crystals, glasses, colloidal suspensions, emulsions or polymers. 
Professor C. V. Raman published more than 70 papers and his students, collaborators 
and those who were inspired by him published about 400 papers on various aspects of 
light scattering from a wide variety of systems'. The remarkable and pioneering results 
are too many to be reviewed in this paper, and hence we attempt to highlight only a few 
of them. All the results presented here are from the pre-laser era. It will be seen that 
even without lasers which have completely revolutionized and rejuvenated the field of 
light scattering, Professor Raman and his school made notable contributions- the fore- 
most one, of course, being the discovery of the effect which bears his name. 

The scattering of light, in general, occurs due to optical inhomogeneities in the scatter- 
ing medium These inhomogeneities can arise due to different reasons, the most obvious 
case being of gross inclusions of one substance in the other as in colloidal suspensions. 
The thermodynamic fluctuations of density and temperature (or pressure and entropy), 
orientations of anisotropic molecules, the fluctuations of concentrations in mixtures or 
the vibrations ol atoms about their equilibrium positions produce fluctuations of dielect- 
ric constant of the medium and hence scatter light. The temporal behaviour of different 
fluctuations is different with time and therefore they modulate the scattered light in 
different ways, 




The entropy fluctuations at constant pressure or the concentration fluctuations do not 
propagate in the medium and hence result in the Rayleigh scattering unshifted in fre- 
quency. The Rayleigh line is. of course, broadened due to the dissipation of the fluctua- 
tions. The temperature fluctuations will damp out due to thermal dissipative processes 
which depend on thermal conductivity and the concentration fluctuations are governed 
by translational diffusion of the molecules. The orientational fluctuations of the aniso- 
tropic molecules dissipate due to rotational relaxation processes. 

The fluctuations of density or pressure at constant entropy (adiabatic) represent local 
compressions or rarefactions which can travel in the medium with velocity of clastic 
waves. The incident light is scattered due to the grating formed by the periodic stratifica- 
tions of a particular wavelength governed by the well-known Bragg condition. The pro- 
pagation of the "grating 1 produces Doppler shift of the incident frequency. This view was 
first put forward by Brillouin 2 and hence the Doppler-shifted components on either side 
of the Rayleigh line due to waves travelling in opposite directions but with the same 
speed are called Brillouin lines. These lines are broadened due to thermal dissipative 
processes which damp out the elastic waves (sound waves or acoustic phonons). 

The fluctuations in the dielectric function can also arise due to the time dependence of 
some excitations of the medium. These excitations which can be the vibrational modes of 
e molecule or optical phonons in solids, electronic excitations or magnons in magnetic 
systems cause inelastic scattering of light called Raman scattering. This was first dis- 
covered by Professor C. V. Raman on February 28, 1928 when he pointed a direct-vision 
spectroscope on to the scattered track in many pure organic liquids and observed the 
presence of another colour separated from the incident colour \ This was the culmina- 
tion of seven years of intense research by Raman and his many coworkers on light 

The above discussion points out that the spectrum of scattered light contains valuable 
information on the imprints of different forms of fluctuations in the medium. The four 
quantities which contain the knowledge of the fluctuations and can be determined 
experimentally are: (1) the frequency shift (2) the intensity of the scattered radiation (3) 
spectral linewidth and (4) polarization. 

The plan of the paper is as follows. In Section II, we present the important contribu- 
tions of the Raman school to Rayleigh-Brillouin scattering from liquids, crystals and 
glasses. Under this heading, the topics to be briefly reviewed are: 

i) Intensity of the total scattered light from the liquids. 

ii) Brillouin scattering from liquids, deviation of intensity ratio of Rayleigh to Brillouin 

lines from the Landau- P I ac/ek ralio, 
mi Brillouin scattering from viscous liquids and glasses. 

iv) Light scattering from glasses — the concept of 'frozen-in' fluctuations, depolariza- 
tion of scattered light in terms of Krishnan ratio, and Brillouin scattering, 
v) Brillouin scattering from crystals. 

Section III deals with Raman scattering. A very large number of systems were studied 
for the first time by Raman and his coworkers to probe structure, symmetry and 
dynamical properties. We shall not give a catalogue of all those investigations but briefly 


discuss only the following: (i) use of Raman spectroscopy in chemical analysis, (ii) reso- 
nance Raman scattering, (iii) symmetry and Raman selection rules, (iv) crystal dynamics 
and (v) phase transitions and the soft mode, 

2. RaykiRh-BrillcHUn scattering from liquids, crystals and glasses 

2.1 Scattering from liquids 

Historically speaking, Smoluchowski 5 invoked the idea of density fluctuations to explain 
the phenomenon of critical opalescence. Later, Einstein 6 developed the statistical theory 
of light scattering based on fluctuations in density for a pure liquid along with concentra- 
tion fluctuations in multi-component systems. 

Let J be the intensity of incident light of wavelength A. The total scattered intensity by 
a volume element v reaching the detector at a distance L is given by 

h = ±l£ J* <(& fl ) 2 > (1+cof**) (1) 

where Se q is the qth Fourier component of fluctuations in dielectric constant. The wave- 
vector q = Jc,-i s and is the angle between Ii and Jc s which are the waveveetors of the 
incident and scattered light. The brackets, { ), denote the average over the equilibrium 
Taking e to be a function of pressure P and entropy 5, 

«K*-(S£ ««■>*> + (S£ mf) (2) 

where subscript q has been dropped for the sake of convenience. We can write 

(SJ **>'{wt <(ar)I>: (3 > 

HT}** VBp) 1 \dTfp 

From the theory of thermodynamic fluctuations 

C p pv 



Here p and Tare density and temperature, ft the adiabatic compressibility, C,. the speci- 
fic heat at constant volume, a v the volume thermal expansion coefficient and k p the 
Boltzmann constant. Using eqns (2)-(4) in eqn (1), one gets (for ft = 90*) 

'-* 4 HI *»•' 

♦*fH('*M«)l : 

It can be shown" that if 




+ [p 

— ) 

4p) T 

eqn (5) goes over to the Einstein formula: 

h = 



P%1 f*Tk*T. 

9 5> 



where p r is the isothermal compressibility. 

So far (Se) is taken to be a scalar which is the case when molecules comprising the 
medium are optically isotropic. On the assumption that molecules arc freely rotating, 
Raylcigh and Cans have shown that the optical anisotropy makes an additional contribu- 
tion (6 4- 6r)/(6 - 7r) to the scattering where r is the depolarization ratio given by r - l H t 
/, , Inih -2) is the scattered intensity with polarization parallel (perpendicular) to the 
scattering plane. The total scattered light due to density and anisotropy fluctuations is 
given by 


i — " 



(6 + 6r) 


In order to compare eqn (8) with experiments, it is necessary to know {pdtidp) T . 
Einstein used the Lorentz-Lorenz formula connecting e and p: 


e + 2 

= C'p 


where C is a constant. Differenting (9), 





After substituting (10) in (9) to get i a , it was found that the computed scattered intensities 
are appreciably Ln<vr than the measured values. The discrepancy was reduced by 
Ramanathan y . He used the relation, t— 1 - (constant)p by arguing that (e + 2) in cqn 
(9) arises due to the action of molecules located outside the small sphere (the Lorentz 
phcrt | surrounding the motecule under observation. The influence of fluctuations of e 
in the material outside the Lorentz sphere on the change of field inside the sphere will be 
small and hence the term (e + 2) can be regarded as constant. Then one gets 

] he agreement of eqn (11) with experiments, though satisfactory for a number of liquids, is 
still not good. Venkateswaran 1 " suggested that the limitation involved in adopting any 
relation between * and p is removed by using the experimentally determined values of 
ad i aba tic piezoelectric coefficients (pd/i/dp), (p. = refractive index = VI) obtained 
by Raman and Venkataraman 11 . The contributions of Krishnan 12 , Raman and Rao '\ 
Ramanathan 14 and Ananthakrishnan 15 are noteworthy for the measurements of scatter- 
ed intensities in a number of liquids. Rao 16 investigated the dependence of the scattered 
intensities on temperature for liquids and interpreted his results in terms of eqn (11). 
Raman and Krishnan 1 ', and Cabannes and Daure l!H discovered that a depolarised 
continuous background appears which extends out - 150 cm - ' from the unshifted line 
and even further. This arises as result of the rapid temporal changes of the fluctuations of 
the anisotropy. In recent times, this broad wing has been investigated extensively to 
study rotational-relaxation mechanisms, 

2,2 Briilouin scattering from liquids and Landau- Placzek ratio 

As mentioned in the introduction, the density fluctuations at constant entropy give rise 
to Briilouin lines shifted by frequent 

at B = ± v e q (12) 

where v t is the appropriate sound velocity and q = (4irp sin 0/2J/A. Here p is the refrac- 
tive index of the medium. 

The sum of the intensities {21b) of the two Briilouin components is given by the first 
term in eqn (5) and the other terms in the equation contribute to Rayleigh line intensity 
(In), Landau and Placzek 19 showed that, under certain assumptions. 

21b ft C, 

= Y-1 (13) 

Even though the prediction of the shifted lines was made by Briilouin 2 in 1922, the 
first experimental observation was made by Gross 20 in liquids after the discovery of the 
Raman Effect. Krishnan 21 in his review article on Briilouin scattering mentions that the 



most satisfactory patterns of the Doppler-shifted Brillouin components in liquids were 
recorded by Rao 22 . Extensive work was done by Venkateswaran 23 and Sunanda Bai 24 . 

Venkateswaran 23 was the first to demonstrate the failure of Landau-Placzek relation, 
eqn (13). in many liquids. Cummins and Gammon 25 attributed this discrepancy due to 
the neglect of dispersion of the thermodynamic quantities in the hypersonic region. The 
quantities involved in the expression for /* correspond to the static value (o» = 0) where- 
as the quantities in 21 B should be those in the hypersonic frequency range (at ~ 10 10 Hz). 
The correction for the dispersion does not remove the discrepancy completely, the 
observed /«/2/ w is always higher than the theoretical values 25 . For example, the 
observed value of /r/2/ h in benzene is 0,84, eqn { 13) gives 0.43 and after correction for 
dispersion, it is 0.66. 

The relatively small calculated values of /#/2/ ff point out that there are other mecha- 
nisms contributing to the Rayleigh intensity. These can be understood in the hydrody- 
namic theory of light scattering by Mountain 2 * 1 , He pointed out that the spectral distribution 
contains a non-propagating mode in addition to the usual thermal and phonon modes 
which give rise to the central and two shifted-Brillouin components. This new mode 
called the fourth component arises from the exchange of energy between the internal vibra- 
tional modes and translation modes of the molecules and dissipates with relaxation time 
7. it gives rise to the appearance of a broad line of unshifted frequency with a w«dth 
Aa>rc =• t" 1 and integrated intensity (1 - v$tvi )y~ l , where v and v B are the low- and 

high-frequency sound velocities. The fourth component is polarised in the same plane as 
the Brillouin components. Figure 1 shows a schematic of the spectrum of scattered light. 
The presence of the fourth component also makes Brillouin lines asymmetric, and this 
can depend on temperature due to the dependence of the relaxation time t (and hence 
Aa>/r C ) on 7 . Since the fourth component is mainly present over the central component, 
the measured ratio of I R f2I B will be higher than that estimated from eqn (13) even after 
applying correction for the dispersion. 












Fig. 1. Schematic illustration of (he spectrum of the 

scattered light from a liquid. R and B Ma nil for Ray- 

Icifh and Brillouin components, A is the background 

10 oncniational fluctuations and FC is the fourth 

ncnt proposed hy Mountain 2 *, 


Knapp el al 21 have argued that in addition to the thermal relaxation process intro- 
duced by Mountain in frequency -dependent hulk viscosity, other relaxation processes 
described by frequency -de pendent shear viscosity or elastic modulii would give rise to 
velocity dispersion and hence to the presence of the fourth component. Their experi- 
ments on glycerine as a function of temperature show that the broad intense background 
arises due to the structural relaxation occurring predominantly in associated liquids 
(which tend to form ordered molecular aggregates over various volumes), 

2.3 Brillouin sea tie ring from viscous liquids and glasses 

A finite damping ol the sound waves in a viscous medium contributes to the linewidth, 
Auj#, of the Brillouin lines"' 19 : 

&w ff - iy - 2av t (14) 


r.i [}%+*+ ^ (T-i)]. 


Here ij, and i) v are the shear and bulk viscosities, tr the thermal conductivity and a the 
absorption coefficient for the sound waves in the medium. The term u(y~ l)'C p is 
usually very small as compared to viscosity terms in eqn (15). The peak of the Brillouin 
line is also shifted from uig given by eqn (12) as 

^ = (V* " 2« 2 v*)" 2 . (16) 

ft appears that when n, and r?, are large (in viscous liquids), ±a># will be very- 
large and the shift &'& will go to zero, suggesting that the Brillouin lines should not be 
seen in viscous liquids and glasses. Contrary to this, Venkateswaran" observed the 
Brillouin lines in a number of viscous liquids, including glycerine and castor oil. The 
shifted components were seen in glycerine up to a viscosity of 120.4 poise and for castor 
oil, up to 6.04 poise (for comparison, the viscosity of water at room temperature is 
- 0.(11 poise i 

A number of unsuccessful attempts were made before 1950 by Gross. Ramm, Raman 
and Rao, Venkateswanm. VelicJtkina, and Rank and Douglas to detect Brillouin lines in 
glasses. The first successful observation was reported by Krishnan"* in fused quartz by 
using 2536 A excitation from mercury vapour lamp. The Brillouin shift was ±1.5 cm -1 
which agreed well with the calculated ±1,65 cm -1 from the elastic constat 

Let us now see how we can qualitatively understand Venkateswarans obsen 
viscous liquids and Krishnan's result on fused quartz. The argument that the absorption 
coefficient a is proportional to the viscosity v cannot be valid for the entire range of n 
because, if this were the case, the glasses lor which -q - 10 13 poise) cannot be good 
conductors of sound. In reality, glasses are good conductor of sound >r M high 
quencies. This happens because of the relaxation processes due to which a increases *«] 
increase in viscosity up to a definite maximum, after which it fall*; off with continued a*- 

4™ A, K. SOOD 

crease in tj. The difficulty in delecting Brillouin lines in earlier observations can be 
understood by realising that I B * ft [see eqn (5)] and ft - ( pVfls ) ] where v m is the 
hypersonic velocity. In relaxation theory, at higher frequencies (an > 1) when a system 
with a large value of q relaxes, v . - v will also be large i.e. , the liquid will behave like a 
solid at high frequencies. The large dispersion in velocity will make ft and hence In small 
as compared to that in the low-viscous liquids. 

2.4 Light scattering from giu 

In this section, we shall highlight the fundamental contributions in the following: 
i) Concept of Trozen-in fluctuations in glasses; and it) Krishnan Effect. 

2.4./ 'Frozen-in' fluctuations in glasses 

Young Rayleigh 2 " (John William Stnitt) conjectured that accidental inclusions and inci- 
pient crystallization occurring within the glass were responsible for scattering the light. It 
was first shown by Raman" that light scattering from glasses has its origin in true mole- 
cular scattering arising from local fluctuations of composition and of molecular orienta- 
tion, as in a liquid. He arrived at this important conclusion after measuring scattered 
intensities tor fourteen different types of silicate glasses with refractive indices varying 
from 1.4933 to 1.7782. The measured intensities relative to liquid benzene varied from 
0,11 to 0.63 while the depolarization ratio ranged from 0.045 to 0.295. Raman's conclu- 
sions were reinforced later by Krishnan", Krishnan and Rao 12 , Rank and Qouglas". 
Debye and Bueche^ and Maurer' 5 . 

In all these studies, ii was found that the value of the measured scattered intensity is 
almost an order of magnitude larger than the calculated intensity on the basis of equili- 
brium density fluctuations. Raman"' proposed that the increased measured intensity was 
due to the freezing-in' (thermal arrest) of concentration fluctuations. Later. Muller 36 
extended this idea to the frozen-in" density fluctuations. Fabclinskii* has quoted the 
work of Vladimirskii (in 1940) which suggested the possibility of freezing of orientation 
fluctuations. In order to amplify the above point regarding the discrepancy between the 
red and calculated intensities, we shall quote the results of Velichkina on fused 
quart/ as reported by Fabelinskii 8 . 

The measured scattering coefficient /?, defined as R = I s L 2 /t v. for fused quartz In 
transverse direction (0 = 90°) at a temperature of -70*C was 1.86xlO~ A em '. In 
order to calculate the scattered intensity, glass was considered either as a liquid or as a 
crystal with an infinite number of symmetry axes. Using eqn (8) and taking Fto be the 
temperature of measurements, Velichkina estimated R = 2.3 x 10 -7 cm -1 . The scatter- 
ing coefficient for the cubic crystal for the transverse scattering, when incident light is 
un polarized, is given by 8 


n 2 

l?k B T 

P 2 n 


i l 


t (Pu-Pn) 2 < 

)] <17) 

4C„ HCn-C a ) 

This expression was obtained by Leontowitsch and Mandelstamm in 1932. Here Q are 
the elastic constants and p tl are Pockel's eiasto-optical constants. The First term,pi 2 /Cu , 
arises due to density fluctuations and the other terms are due to anisotropy or orienta- 
tion scattering. For isotropic solid, pu-Pu - ^-P^ and " Qj - C i2 = 2C44. Using eqn 
(17), Velichkina calculated R = h&x \0 cm -1 for fuscd-quartz. Therefore, the calcu- 
lated scattering coefficients for fused quartz using either liquid state theory or based on 
crystals are an order of magnitude larger than the measured value, 

2,4 J A Freezing-in density fluctuations 

Applying this idea to fused quartz, Velichkina assumed that the scattering in fused 
quartz is determined by the density fluctuations close to the glass-transition temperature 
Tg ~ 2100 K. Then, using eqn (8) and taking T = Tg, R = 1.5 x MF* is in good agree- 
ment with the experiment. 
The density fluctuations can be either isobaric or adiabatic: 

<(w2> -(ar? «Mtf> + (£)E <(8S)J> - m 

The isobaric density fluctuations are dissipated with a time-constum 

where x = vfpCp is the thermal diffusivity. For visible light and 9 = 90°, q - 5 x 
10 5 cm -1 and taking for glasses,* ~ 3x 10" 3 enr/s, r p - 10" 9 s. Hence the isobaric 
fluctuations of the density are quite fast and it is likely that such fluctuations may or may 
not freeze during cooling. 

The adiabatic fluctuations of density move with the speed of hypersound (giving rise to 
Brillouin scattering). From the fad that Brillouin components exist in glasses 28 , the 
freezing of adiabatic density fluctuations is clearly ruled out. 

2,4,1.2 Freezing-in concentration fluctuations 

The time constant associated with the concentration fluctuations is 



where D is the diffusion coefficient. For ordinary liquids, D — 10~ 5 cm 2 /s and hence 
t c ~ 10" ' s. But near (he n nion temperature, D decreases by many orders ml 

magnitude (recall Da l/tj). Taking D - HT* cm 2 /s, r c - 10" 8 s and hence one can 
expect the arrest of the concentration fluctuations in liquid to glass transition. 

2.4. i J Fictive temperature' in a glass 

The concept of frozen -in fluctuations proposed by Raman is one of the key points in glass 
physics. The introduction of a 'fictive temperature' ,73s is a useful concept, At a fictive 
temperature 7), density fluctuations are arrested so that upon lowering the temperature 
further no structural rearrangement is possible. Therefore, T f becomes the governing 
temperature for the molecular structure of a glass. Another fictive temperature T} is 
associated with thermally arrested concentration fluctuations, and in general, T} * T f . 

Typically r, % - 10P and therefore T' f may be taken to be the temperature at which the 
liquid viscositv is — 10 7 — 10 s noise*'. 

liquid viscosity is — 10- 10 8 poise 

2,4.2 Krishnan Effect 

The Krishnan Effect, discovered by R. S. Krishnan, relates to the state of polarization of 
the scattered radiation by condensed matter in a direction normal to the incident beam. 
As shown in fig. 2, four possible scattering intensities can be measured: /,{VV), /,(VH), 
/,(HV) and /,(HH), where H and V refer to the polarization parallel and perpendicular 










Fig. 2. Schematic representation of the polarized 
components of the scattered light. 


to the scattering plane, respectively. The first letter in brackets (e.g., V in / 5 (VH)) refer 
to the polarization of the incident radiation and the second one corresponds to the 
polarization of the scattered radiation. The depolarization ratios are defined by 

PH ~ T?hh) (2l) 


f>v = 

/,(VH) (22) 


The relation /, (VH) = /*(HV) is true for all materials (not optically active) ind is called 
Rayleigh- reciprocity relation as was shown by Krishnan 40 . 

For isotropic fluids consisting of molecules with dimension much less than wavelength 
of light, 

/(VH) = /(HV) = /(HH). 

The Krishnan Effect is the observation that in "a number of liquids and solids, 

Ph < 1 C 23 ) 

The Krishnan Effect has been demonstrated for critical liquid mixtures, associated 
liquids like formic and acetic acids, emulsions, colloids, proteins 40- * cholesteric liquid 
crystals 47 and a number of glasses 31 - 39 - 48 **. The effect observed in colloids could be 
explained with Mic theory of light scattering from medium consisting of non spherical 
particles (or 'clusters) with linear dimensions of the order of wavelength of incident light 
wherein the phase differences between the waves emitted from different points of the 
particle must be taken into account. It may be noted that the intensities referred to in p N 
are for the unshifted component (Rayleigh) as the Briltouin components are very weak 
in these systems. 

There have been a number of attempts to understand Krishnan Effect in glasses. 
Prompted by the effect in colloids, Krishnan proposed that there are 'clusters' of dimen- 
sion ~ A in glasses which scatter light. Gans 50 gave a theory based on the optical aniso- 
tropy of clusters which have to be necessarily strongly aspherical. dans' theory 50 usually 
predicts p H > 1 in contrast to the observation that p H < I, The next theoretical work 
was that of Miillei 36 who questioned the cluster hypothesis of Krishnan in light of the X- 
ray investigation of Warren. Miiller proposed a theory of Krishnan Effect based on strain 
scattering in glasses in which it is assumed that the equipartition of energy is not obeyed. 
The strain energy is stored more in the longitudinal modes than in the transverse modes 
The Krishnan ratio becomes 

Uj Cu_ Vj (i-«r, ) _ 

pH U L 2C<4 U L (l-2<r P ) 



where U T and U L are the energy densities of the transverse and the longitudinal strain 
waves and a> the Poisson ratio. If the equipartition energy principal is used. £/ r - U L = 
2v then p„ = C U /2C U which is the same as in an isotropic solid. To explain p„ < 
I, Muller argued that U L = k B T^2v and U T < U L . This assumption is definitely un- 
appealing because the transverse waves should as well play an important role as the 
longitudinal waves in the glass transition. Further, for glasses like fused quartz™. p„ ~ 
1 Mueller theory does not specify on what grounds one expects p„ - I in some glasses. 
Further, according to theory 3 *, 

= i El ( 

Pv = T 

1 - (Tp 
1 - 2(7 r 



where q and p are Neumann's constants related iop tl by p u = 2q/p, t p n 
eqns (23) and (24), 



Ipip.. From 


In general, q < p and, therefore, the maximum value of p v !p H is 0.25 in Miiller's 
theory. The experimental results on many glasses 48 - 49 do not agree with eqn (25). 
Schrocder 1 " has established a connection between concentration fluctuations and the 
Krishnan Effect by measuring p, { in a number of xK 2 O(100-x)SiO 2 and jrNa 2 O(100- 
x)Si0 2 glasses. Figure 3 shows his data on pu versus x. The minima in p» mostly arises 
from announced maxima in / T (HH) rather than any anomalous behaviour in 
/,(VH) The above silicate glasses undergo phase separation as a function of 

temperature and it has been observed that ph is the minimum at those concentrations of 
alkali oxides which are close to the critical composition. This establishes that A(HH) 
reflects some aspect of the critical phase -separation process. This is further corroborated 

U/ I \.*Kj0.(I00-r)S«0j 
\ i - xNa t Q(i0O-*)Si0 

02- \ 

O 20 30 40 


Fin. 3, Krixrman ratio p,, versus concentration of 
alkali oxides in glasses Data are taken from Schro- 
der's work", 


by Schroeder by observing that p\\ increases from — 0,2 to — 0.5 as ( T- T,) is increased 
from 5<> to 150X (here 7 is the temperature at which each particular sample was heat- 
treated and T, is the spinodal temperature). Schroeder has suggested that the isotropic 
composition fluctuations (described by a scalar) which increase near the critical tempera- 
ture must be coupled to the longitudinal "frozen-in* fluctuations of the dielectric suscepti- 
bility (a tensorial quantity) and a mode-mode coupling approach may provide the Id 
the Krishnan Effect. 

The effect in the tie of polvbutadiene and polypropylene glycol has been attri- 

buted to the frozen-in fluctuations of the anisotropy 4 * 44 . 

2.5 Briiloum scattering from crystals 

In a crystal, three pairs of Doppler-shifted components can occur due to three types of 
elastic waves which can propagate- with different velocities in any general direction. For a 
symmetry direction the waves can be pure longitudinal or pure transverse. The Brillouin 
lines were first observed in a solid like quartz by Gros> ' and later by Raman and 
Venkateswaran 52 in gypsum. Chandrasekharan 5 * showed that for a birctringent crystal. 
there should be twelve Doppler components, A number of crystals like diamond, calcite 
and alkali halides were studied by Krishnan and coworker 

3. Raman scattering 

Contributions of Indian scientists to Raman spectroscopy have been reviewed recently 
by Krishnan 5 " 4 . We shall mention here only a tew of them. 

3.1 Use in chemical analysis 

The extensive use of Raman spectroscopy in chemical analysis is based on the fact that 
every chemical bond in a molecule has its characteristic Raman Fingerprints which are 
not affected much by the other parts of the same molecule. By examining a homologous 
series of compounds commencing from its earlier member, it is possible to trace the 
development of Raman spectra with increasing complexity of the molecule and to locate 
these frequencies which are characteristic of particular groups or linkages. This impor- 
tant conclusion was reached by Bhagavantam, Venkateswaran and Ganesan along with 
others like Dadien and Kohrausch (for detailed noes, see the review article by 

Bhagavantam 55 ). 

3.2 Resonance Raman scattering 

When the incident radiation is close to an electronic transition in the medium, the 
Raman cross-section shows an enormous enhancement, defying the usual v* taw. This is 
called resonance Raman scattering and was discussed by Placzek in his masterly theory 
of Raman scattering 56 . With the advent of tunable dye lasers, resonance Raman scatter- 
ing has become an important technique to understand electron-phonon interactions in 
crystals, especially semiconductors 57 , and in conformational analysis of biomolecules. 

474 A. K. SOOD 

The first observations which gave clear indication of resonance enhancement were made 
by Sirkar 51 * in CCI 4 and nitrobenzene. He also showed that the depolarization character- 
istics of the Raman lines also change as the incident radiation frequency approaches the 
absorption frequency In liquids. 

3.3 Symmetry and Raman selection rules 

A vibration is said to be Raman active when it produces a change of poiarizability in the 
vibrating system. The deformations produced by the vibrations in the poiarizability ellip- 
soid of the crystal depend upon the symmetry of the given vibration and the symmetry of 
the crystal. Placzek 5 * has given tables of selection rules for various types of vibrations 
belonging to any of the 32 point crimps of crystal symmetry. However. Saxena 5 " gave a 
lucid exposition of the subject based on the geometrical reasoning and cleared up certain 
discrepancies between the theoretical works of Plae/ek and Cabannes who give different 
tensors for degenerate vibrations in systems possessing only one axis of three-fold sym- 
jf, Pioneering work was done by Bhagavantam and Venkatarayudu who gave a clear 
group-theoretical analysis of vibrations in crystals based on the unit-cell approach* 0,61 . 

3.4 Crystal dynamics 

Due to wavevector conservation, phonons near the Brillouin-zone centre (q - 0) can 
participate in the first-order Raman spectra and hence the detailed nature of the 
phonon-dispersion curves is not probed. In the second-order Raman scattering, how- 
ever, two phonons of equal and opposite wavevectors. anywhere in the Brillouin zone, 
can participate. Hence Ihc second-order spectra (SORS] » insisting of a continuous 
background extending over a wide frequency range with sharp peaks superimposed on it 
arc much more rich in information and have an important bearing on the theories of 
lattice dynamics. High-quality SORS were recorded by Krishnan for diamond, rock salt 
and alkali halides 62-65 . Prompted by this. Born and Bradburn 66 applied ihc Born -von 
Karman theory of lattice dynamics to calculated SORS of rock salt. Later, Birman 67 and 
Loudon 6 ** have pointed out the importance of van-Hove singularities in the one-phonon 
densities of states to explain the peaks in the intensity distributions of SORS. 

Another important observation is in SORS of diamond by Krishnan" 5 . Figure 4 shows 
the microphotometer record of the Raman spectra of diamond 65 . The peak at 1332 cm - ' 
is the first-order Raman mode. What is of significance is that the sharp peak ai 
2666 cm -1 observed in the second-order Raman spectra lies higher than twice the first- 
order line. Later, Solin and Ramdas 69 reexamined the Raman spectra of diamond with 
improved experimental accuracy using lasers and confirmed the results of Krishnan and 
also obtained temperature and polarization characteristics of 2666 cm -1 mode. These 
results prompted Cohen and Ruvalds 70 to propose the existence of two-phonon bound 
state which can be split off the top of the two-phonon continuum by an harmonic phonon- 
phonon interactions. 



Freq. Shift (cm 

Fit,. 4. Micfophotomctcr record of ihe Raman spec- 
trum of diamond (after Knshnan)''" 

3,5 Phase transitions and 'soft mode' 

The study of phase transitions has been one of the most pursued branch in condensed- 
matter physics. The concept of 'soft mode 1 , formally proposed by Cochran 71 in 1959 but 
discovered much earlier by Raman and Nedungadi 72 in 1940, has played an increasingly 
dominant role in the understanding of solid-state phase transitions 71 . What is a soft 
mode? A soft mode is a collective excitation which may be either propagating or diffu- 
sive, whose frequency decreases substantially as the transition temperature To (or 
pressure) is reached from above or below. Figure 5 shows the schematic behaviour of the 
soft mode for first- and second- order phase transitions. The static atomic displacements 
occurring in going from one phase to the other represent the frozen-in mode displace- 
ments of the unstable phonon. 

The question of structural phase transition as the limit of stability against a particular 
mode of vibration was formally discussed by Cochran 71 . The basic idea and the first 
observation of the soft-mode were made by Raman and Nedungadi 72 in their Raman 
investigations of a solid-state structural phase transition from a (trigonal) to ^(hexa- 
gonal) phase at — 573°C in crystalline quartz, They observed thai The 220 cm 
line behaves in an exceptional way, spreading out greatly towards the exciting line and 
becoming a weak diffuse band as the transition temperature is approached". Realising 
the importance of their results, they proposed that "The behaviour of the 220 cm 
line clearly indicates that the binding forces which determine the frequency of the 
corresponding mode of vibration of the crystal lattices diminishes rapidly with rising 
temperature. It appears therefore reasonable to infer that the increasing excitation of 
this particular mode of vibration with rising temperature and the deformations of the 
atomic arrangement resulting therefrom are in a special measure responsible for the 
remarkable changes in the properties of the crystal as well as for inducing the transfor- 
mation from the a to the /? form". This is an exceedingly beautiful description of a soft 



Second Order 


Fie. 5. Schematic representation of variation of soft- 
mode frequency with temperature for first- and second- 
order phase transitions. 

mode, almost twenty years ahead of Cochran's work. Saxena 74 carried out a lattice 
dynamic calculation of quartz and showed that one particular mode was unstable. 

Figure 6 shows the data of Nedungadi" for a-quartz for two modes. The bars indicate 
the lower and upper limits of the Raman lines. Earlier it was confusing that the two modes 
at ~ 220 cm -1 and — 147 cm -1 show anomalous temperature dependence. Also, the 
147 cm 1 was present in polarized or^-Raman spectra, in addition to the four modes 
predicted by group theory. The unambiguous assignment of this extra mode as the 
second-order (two-phonon) process was made by Scott and Porto 77 . Scott 76 showed that 
the soft-mode at - 220 cm ' interacts very strongly with the two-phonon state via 
anharmonic interaction (Fermi -resonance). The soft-mode in quart/, is then the feature 
at - 40 cm - 1 close to T . The temperature dependence of the uncoupled mode deduced 
by Scott along with his data on quartz are shown in fig, 7. The soft-mode behaviour 
goes as to ~ A (To- T) 03 . 

The concept of soft-mode initially given for the displacive phase transitions has been 
extended to order-disorder transitions like in hydrogen-bonded ferroelectric*. The soft- 
collective excitations in order-disorder transitions are not phonons but rather unstable 
rJo-spifl waves which occur in addition to all the phonon modes predicted by har- 
monic theory of crystal lattices. Further, the idea of lattice-vibrational soft-mode has 
been generalised by Schneider el al 7 * to several other phase transitions (like superfluid 
transition) by combining the static aspects of phase transitions with the dynamic 


250 1 1 1 1 — r 


1 1 1 1 1 1 1 




^«=A(T -T) OJ 
1 1 1 . I . 1 


200 400 

GOD 800 

50 100 

300 800 

Fw 7 Temperaiurc dependence in a-quartz from 
Fig. 6. Temperature dependence or modes in a- the work of Scott" The solid lines show the tempera 
quartz. Data are taken from Ncdungadf turc dependence of uncoupled modes. 

response of the system To summarize, the concept of the soft-mode provides a unified 
View of the phase transitions and hence the early work of Raman and Nedungadi assumes a 
significant place in the study of the phase transitions, 

4. Conclusion 

We have attempted to bring out a few important contributions of Raman and his co- 
workers in all the fields of light scattering from condensed matter. Limitations of space 
did not allow us to include the interesting work of Raman and Ramdas on the scattering 
of light at the interface between two media and the famous Raman-Nath theory of dif- 
fraction of light by sound waves. Nor could we include post-laser work on the Raman 
study of ferroelectric phase transitions by P. S. Narayanan and his group. 

To conclude, the work of Raman school on light scattering remains a guiding spirit in 
many of the present-day researches in condensed-matter physics. 


1. Raman. C, V. 

2. Bkiluhjin, L. 

3. Raman, C. V. and 
Kkishnan, K. S, 

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6. Einstein, A, 

7. Landau, L. D. and 
Lifsmtz, E. M. 

8. Faselinskii, 1, L. 

9. Ramanathan, K. R, 

10. Venkateswaran, C. S. 

11. Raman, C. V, and 
Venxataraman, K, S. 

12. Krishnan, K. S. 

13. Raman, C, V. and 
Rao, K. S. 

14. Raman a than, K. R. 

15. Ananthakkishnan. R. 

16. Rao, R. 

17. Raman, C. V, and 
Krishnan, K. S. 

18. Cabannes, J. and 
Daure, P. 

19. Landau, L. D. and 
Lifshjtz, E. M. 

20. Gross, E. 

21, Krishnan, R. S 

22 Rao. B V, R. 

23. Venkateswaran. C S. 

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29. Strutt, J.W. 

(Lord Rayleigh, Vouho) 

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31. Krkhnan, R, S. 

32. Krismnan, R, S. and 
Rao, P. V 

33. Rank, D. H and 
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34. DOBVB, P, and 
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35. Maurer. R. D. 
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37. Tool, A. Q, 
3*1, Rjtland, H. N. 

39. ScHROEDER, J. 

40. Krisknan, R. S, 

41. Krishna*, R. S, 

42 Krishna n, R, S. 

43 Krishnan. R, S, 

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45- Subbaramaiva, D. S. 
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47. Wano. C. H. and 
Ht ano. Y. Y. 

48. RtMMG, Y Y. and 
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49. Huang, Y, Y. and 

Wano, C H 

50. Cans, R. 

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52. Raman, C. V. and 
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56. Placzek, G. 

57, Cardona, M. 

58, SmKAK, S. C. 


60. Bhacavantam, S. 

61. Bmaoavantam, S. and 
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62. Krishnan, R, S. 

63. Krishnan, R 5, 


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64. Krishnan, R, S. and 

Narayanan, P. S. 

65. Krishnan. R. S. 

66. Born, M. and 

Bradburn. M. 

67. BlRMAN, J. 

68. Loudon, R, 

69. Solin, S, A, AND 
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70. Cohen, M. H. and 
Ruvalds, J. 

71. Cochran, W. 

72. Raman, C. V. anp 
Nedungadi, T. M K. 

73. Scott, J F 

74. Samm. B. D. 

75. Neditngadi. T. M. VL, 

76. SODTT, J. F. AND 

Porto, S. P, S. 

77. Scott, J, F. 

78. Schneider, T. , 
Srinivasan, G. and 
Enz, C P 

The vibration spectra of the alkali halkfcs, Proc. Indian Acad. ScL , 
1948, A28, 296-306; Nature, 1949, 163, 570-571. 

The second order Raman spectrum of diamond, Proc. Indian Acad. 
Set., 1946, A24, 25-32. 

The .theory of the Raman effect in crystals, in particular rock-salt, 
Proc. R. Soc. Land., 1948, AIRS, 161-178. 

Theory of infrared and Raman processes in crystals— Selection rules 
in diamond and zincblendc, Phys. Rev., 1963. 131, 1489-1496. 

Theory of the first order Raman effect in crystals, Proc. R. Soc. 
Land., 1963, A275, 218-232. 

Raman spectrum of diamond, Phys. Rev., 1970, BI, 1687-1701, 

Two phonon bound states, Phys. Rev. Lett., 1969, 23, 1378-1381, 

Crystal stability and theory of fcrroelectricitv, Phys. Rev. Lett., 1959, 
3, 412-414. 

The a-fi transformation of quartz. Nature, 1940, 145, 147. 

Soft-mode spectroscopy — Experimental studies of structural phase 
transitions, Rev. Mod. Phys.. 1974, 46, 83-128. 

Analysis of the Raman and infrared spectra of a-quartz, Proc. Indian 
Acad. Set.. 1940, A 12, 93-139 

Effect of temperature on the Raman spectrum of quartz, Proc. 
Indian Acad Sci., 1940, All, 86-95. 

Longitudinal and transverse optical lattice vibrations in quartz, Phys. 
Rev., 1967, 161, 903-910. 

Evidence of coupling between one- and two-phonon excitations in 
quartz, Phys. Rev. Lett., 1968, 21, 907-910. 

Phase transitions and soft modes, Phys, Rev., 1972, AS, 1528-1536, 

/ Indian inst. Set., Nov.- Dec, 1988, 68, 483-491. 
c Indian Institute of Science, 

Some recent trends in Raman spectroscopy 


Tata Institute of Fundamental Research, Bombay 400 005, India. 

Received on September 21, 1988. 

1. Introduction 

Even after sixty years since the discovery 1 2 of the Raman fcffect in 1928, Raman spectro- 
scopy continues to be an exciting field of research, covering an increasingly wider spec- 
trum of extremely important problems in physics, chemistry, biology and other branches 
of science and technology. Ordinarily, this should not be surprising because the 
frequency -shifted Raman lines, corresponding to inelastic scattering of incident photons 
by a material medium, directly give the most basic information about the possible excita- 
tions in the system. This is obviously very useful in determining the structure and the 
nature of the material medium at the microscopic level. However, the spontaneous 
Raman scattering is a very weak second-order electronic process; the scattering cross- 
section for the Raman process involving vibrational excitations in a typical liquid being 
only of the order of 10 _3o cm 2 per molecule. The signal is extremely small, if the 
scattering volume is small or the observation time is very short. Moreover, in most cases, 
while detecting the Raman signal one is faced with a large unwanted fluorescence back- 
ground arising from the two-step real absorption and emission of photons by impurities, 
etc., in the sample. In spite of these difficulties, the reason for Raman spectroscopy to 
remain so popular and extensive is, of course, due to major revolutionary developments 
which arc taking place in optics since the discover} of lasers in the early sixties. These 
not only relate to the availability of powerful laser sources which can be tuned in a wide 
range of frequencies and also generated as ultrashort picosecond and femtosecond 
pulses 3 , but also to the development of extremely sensitive optical photon-detection 
systems and multi-channel analysers 4 . They have indeed opened up a vast range of new 
possibilities in the field. 

The main aim of this presentation is not to attempt an exhaustive review of all the 
recent important developments in the field, but to select an illustrative list of some of 
these topics for discussing their importance as well as typical results obtained so far. 
Hopefully, this would bring out, at least partially, the flavour of present trends in re- 
search in modern Raman spectroscopy. 

In recent years, there has been a greater emphasis on the use of Raman spectroscopy 
to study the dynamics of a given system and its excitations, instead of just its structural 


484 \NSHU S fHA 

properties. This is best accomplished by using the so-called time-resolved Raman 
Spectroscopy 3 , with pulsed-laser sources in the appropriate temporal range. This tech- 
nique will be discussed in some detail in Section 2 In the conventional CW experiment. 
this information is buried in the shape and the width of the Raman line which, very 
often, can not be analysed easily tor obtaining the relevant dynamical parameters. 

The increasing role being played by Resonance Raman S copy* (RRS) in the 

i on of various biological, chemical and other delicate systems like molecules 
adsorbed on surfaces will be discussed in Section 3 Next, we will consider various types 
of new studies involving high-vibrational overtone spectroscopy, nonlinear Raman 
spectroscopies and K>urier-Transfbrm (FT) Raman spe py. Before concluding, 

we will also mention briefly some recent work on superlattice structures as well as 
theoretical calculal intensities for vibrational excitations in molecules 

2. Time-resolved Raman studies 

The time-domain optical study of fast dynamical processes at the microscopic level 

requires ultrashort light pukes, during which the temporal property of the system must 
not change appreciably. Vibrational energy relaxation in liquids and solids as well i 
excited-state chemical reactions and energy transfers at the chemical-bond level from 
one part of a biological molecule to another, represent dynamical processes on the pico- 
second and subpicosecond time scales, Highly excited nonequilibrium carriers (electrons 
and holes) in semiconductors can exchange energy among them id with lattice 

phonons on similar ultrashort time scales. In fact, in man) cases, the nature of elec- 
tronic-excited states can chang iabl} even in a few femtoseconds. In principle. 
lived Raman spectroscop) in which vibrational (ionic) oi electronic excita- 
tions ol "h bort pulses at different time-delays with respect to the 
initial time at which the system is prepared in the required state, is an ideal technique for 
such temporal studies because the intrinsic time of such Raman scattering | 
themselves is less than 10 : seconds. !n actual practice, the application ot the Raman 
technique for ultrafast time-resolved studies has been slow, mainly because of the 
culties m detecting extremely small Raman signals and m synchronising vario 
including the preparation of the system in the required initial stale. However, with the 
introduction of position-sensitive mi innel plate photo-multipliers, CCD cameras. 
powerful monochromators, new pulsing techniques, and various optical data acquisition 
and processing systems, this situation is changing fast. In the years to come, time-resoh t J 
Raman measurements are expected to be a substantial part of the activity in Raman 
Spectroscopy. This is mainly because, in the conventional Raman experiments, one 
serious difficulties in separating various dynamical processes responsible for the line 
Deluding inhomo! rienijs broadening due to a distribution of mode 
frequencies Measurements in time-domain directly determine relevant relaxation rates 
or temporal evolution (whether exponential or not), e.g. of mode population, vibra- 
dephasi ncentratton of different transient species, etc. 

In the earliest time-resolved Raman experiments 7 , the studies were made mainly of 
the dynamics of vibrational modes in the electronic ground state 


medium- Usually, a strong optical pump-pulse was used to prepare the initial state of the 
system by exciting coherent vibrational modes in liquids like CHjCQj or phonons in 
solids like diamond, through the stimulated Raman scattering process or resonant infra- 
red absorption. A series of weak probe pulses at different time delays was then used to 
measure the vibrational dephasing time (TV) or the population life-time (T|), using 
coherent Raman scattering or the usual incoherent anti-Siokes Raman scattering. In 
chemistry, it is extremely important to determine the flow of energy between different 
degrees of freedom in a chemical solution, t.e. the complete pathway* for T t -relaxation. 
Molecules in solutions can remain in nonequilibrium (hot) for hundreds of picoseconds, 
For proper understanding of chemical reactions in solutions, one has to study the % r ibra- 
lional mode frequencies and their dynamics by determining the changes in the potential 
function for the nuclear motion due to the presence of solvent and other molecules. In 
general, the investigation of chemical reaction dynamics and the decay of transient 
species is very important for time-resolved Raman studies in chemistry"*. Recent in- 
coherent pump-probe Raman experiments, with picosecond-time resolution, have 
shown thai it is indeed possible to obtain such information in a wide range of systems, 
including pyrrole, haemoglobin, etc. In such a pump-probe technique, the pump beam 
merely acts to prepare the system far from equilibrium involving incoherent super- 
position of various excitations, and the weak probe beam monitors their population as a 
function of time via Raman scattering from these excitations. 

A tvpical pump-probe set-up is shown in fig. 1, in which both the strong pump and the 
weak-probe pulses are generated by the same laser beam, but the probe beam is delayed 
with respect to the pump beam by introducing an additional variable optical length in its 
path. Ideally, one would like to avoid the detection of the Raman signal arising from the 
pump beam by choosing the probe frequency quite different than the pump-laser fre- 
quency. However, because of technical difficulties, it may not be possible to do so in 
many situations. In such a case, the real Raman signal from the probe beam is discrimi- 
nated against the pump scattering by using different polarizations for the pump and 
probe beams dictated by appropriate polarization selection rules for the excitations'". 
The dependence of Raman scattering signal from the probe beam on the delay time t d at 
which the probe beam is switched on for a short time t p . arising from a given excitation 
mode A of frequency to A decay constant F A and occupation number n A (/h is approxi- 
mately determined by the temporal functions 

Gsiohnf = O + 'j.) - 

the * w ' "•■-' ,r * lT K<'d + ' P -r)+lF 


t'A Sloke&(' - 'rf + { P ) _ 

tire '<"'" "" "■ tl * }r [n x (t d + t p -r)] 2 



where w s and w, are scattered and incident frequencies, respectively" l2 . If one assumes 
that during the short-probe pulse width, the system properties including n x {t) do not 
change appreciably, the above expressions lead to the signals proportional to n K {t^) +- 1 
and « A (/ d J, with Raman lines of width irlt p at the frequencies ta s = m^ u> x , respectively, 
for 1/T A large compared to the pulsewidth t p . This implies that for spectral restitution of 



microchannel plate photomultiplier/CCD 



<^TV^P sample I delay line 

/. 3k — .> 

beam splitter 

Compression . j j L ^ j_ 1/ SLfTS 


fib or 








Frr; I Typical pump-probe R;tm,in sthenic 

at least 100 cm - \ one can not use pulses shorter than 200 femtoseconds 12 . For shorter 
pulses, one can only monitor much higher frequency vibrational modes or electronic 
excitations, because of the uncertainty principle. 

Recently, dynamics of nonequilibrium carriers and LO-phonons have been studied 1314 
in several polar semiconductors like GaAs. InAs. Al s Gai_ x As and ln R Ga]_,As, using 
subpieosecond pump-probe Raman technique. A very short laser pulse, with photon 
energy above the band gap of the intrinsic semiconductor, pumps electrons from its 
valence bands to the conduction band with carrier densities in the range of 10 16 to 
10 18 cm~ 3 t depending on the total pump-laser energy. Because of the strong Frohlich 
interaction of carriers with LO-phonons, electrons and holes relax towards band extrema 
by emitting long-wavelength LO-phonons on a time scale of 15(1 to 200 femtoseconds. 
Since the lifetime of the generated LO-phonons is much longer (several picoseconds), 
their occupation number first increases from its equilibrium value as a function of time 
t d , before decreasing towards the equilibrium value. The Raman signal of the probe 
beam, either on the anti -Stokes side or on the Stokes side, directly monitors this 
temporal evolution as a function of the time delay t d . The initial rising slope gives the 
electron-LO-phonon scattering time (about 160 femtoseconds in GaAs) and the later fall 
determines the LO-phonon decay time, for different lattice temperatures of the sample. 
Because of the current interest in fabricating fast electronic devices, these studies are 
also being extended to quantum-well and superlattice structures of GaAs and AlAs. 



3. Resonance Raman Spectroscopy (RRS) 

The advent of powerful lasers in the early sixties, allowed increased source intensity with 
an extremely narrow spread of incident frequencies, and the resulting increase in signals 
for the spontaneous Raman scattering. However, this ease in detection was not very 
useful for investigating many delicate biological and chemical systems or for studying 
processes at solid surfaces involving very small scattering volumes. In such systems, one 
faces severe limitations in increasing the incident laser intensity because that can heat 
and alter the nature of the system itself, which is under study. On the other hand, with 
easy availability of tunable lasers in the late sixties and early seven lies, it was realised 
that one could enhance the basic Raman scattering process itself by several orders of 
magnitude by tuning the incident laser frequency close to one of the electronic inter- 
mediate states of the medium under study. Since Raman transition polarizabihty is a 
second-order perturbation process involving the interaction of the electrons in the 
system with the incident photons (<*>/) and the scattered photon (w.s), the cross section 
has also a resonance structure when w/or w. v is close to an electronic intermediate state 
of the system. The essential point is that in the so-called Resonance Raman Spectroscopy 
(RRS), the signal can be increased by a factor of approximately [At&t) '{Wnd * where 
hr„, is the transition width of the intermediate electronic state n. 

The extension of RRS up to the ultraviolet (UV) region of the incident frequency has 
allowed the study of many important biological molecules and processes. Prosthetic 
groups such as heme, flavin, retinal and metal-ion centres, and aromatic chromophores 
in complex environments have been recently investigated using visible and UV excita- 
tions 15 . Apart from other studies of nucleic acid structures, lipids and related systems, 
new studies of benzene, benzene derivatives, ammonia, oxygen, etc., have also been 
made using far UV-RRS to determine changes in the excited-stale geometry and highly 
excited vibrational levels of the ground electronic state 16 . By pulsing the incident laser, it 
has also been possible to couple RRS with the time -resolved studies of protein dynamics, 
In RRS, partial depolarization of the resonance Raman signal from molecular vibrations 
is present if the molecules could rotate during the time interval between the absorption 
and emission steps. In fact, the measurement of the depolarization ratios in RRS can 
give very important data on fast collisional processes in liquids, because the efficiency of 
RRS depends essentially on the dephasing time of the intermediate electronic state. The 
excited-state rotation and collisions with solvent molecules give a value of the dephasing 
time of the order of 10 -13 seconds, which leads to a partial depolarization of RRS. 

The study of adsorption and reaction dynamics of a very small number of layers of 
molecules on the surfaces of metals and semiconductors has become possible in recent 
years, because of the development of the so-called Surface-Enhanced Raman Spectro- 
scopy (SERS) and the new highly sensitive optical-detection techniques. For many mole- 
cules adsorbed on metals like Ag, Au, Pt, Al, etc., there is a large enhancement of 
Raman cross-sections for various vibrational modes of the molecules 1 , due to resonance 
of the incident and/or scattered frequencies with the electromagnetic surface-plasmoo- 
polariton modes of the medium or with the charge -transfer band of the surface complex 
formed by the molecule and the solid substrate. SERS has been used to study 



important processes at electrodes and in biological molecules. Of course, new optical- 
detection techniques have now allowed observation of very weak Raman signals from 
adsorbed molecules, even without any apparent resonance enhancement. 

4. Vibrational otertone, KT Raman, and nonlinear Raman spectroscopies 

In polyatomic molecules, anharmonicity of nuclear motion on a potential energy hyper- 
surface becomes increasingly important with increasing amplitude of vibration. In fact, 
small amplitude normal-mode picture collapses as the amplitude of vibration approaches 
bond dissociation. Because of the lowering of the restoring force at the outer turning 
points, the separation between vibrational levels in a diatomic molecule decreases with 
increase in vibrational energy. In general, bond-stretching vibrations decouple from 
other molecular motions and get localized, if we increase vibrational energy in that 
bond. The measurement of overtone vibrational frequencies in the region of very high 
vibrational energies gives essential information in constructing the complete potential 
energy hypersurface which is important in understanding the mechanism of any chemical 
reaction involving such molecules. With increased sensitivity of optical detectors, it is 
expected that the observation of Raman scattering from high vibrational overtones will 
complement similar studies using infrared spectroscopy. 

The use of Raman scattering technique for analytical purposes has always been slow 
because of the need to eliminate background fluorescence signal which can sometimes be 
much stronger than the Raman signal. This problem is more severe, if one is not ana- 
lysing samples of single-component compounds. With the development of Fourier-trans- 
form (FT) infrared spectroscopy in recent years, it is now possible to obtain FT Raman 
spectra with almost no fluorescence background. When samples are irradiated in the 
near infrared, there is only weak absorption due to excitations of overtones and 
combinations of fundamental vibrations, and fluorescence is almost absent with the 
usual energy of infrared laser being used in Raman experiments. Instead of the disper- 
sive elements used in detecting optical signals in the conventional Raman spectroscopy, 
a Michelson interferometer, or other interferomctric method is used to detect signals in 
FT- Raman spectroscopy, This results in very high resolution and allows measurement 
of even very small -frequency shifts, with the possibility of a belter accuracy in absolute 
frequency measurements. The optimization of various systems in FT- Raman instru- 
mentation is still continuing, but its application to various interesting systems in future 
seems very promising. 

Development of intense tunable lasers with high spatial and temporal coherence has 
also allowed the use of nonlinear Raman spectroscopies to solve problems which can_not 
be tackled otherwise. These arise because of the third-order term involving # H, F.EE in 
the induced-polarization P of the medium. When incident radiation fields at frequencies 
W| and <u 3 (let gj, > <*>;) are present in coincidence in space and time in the medium, such 
that <i>, - tt> 2 is equal to the frequency <t>„ of a Raman-active excitation, because of the 
\ r 'Iwi , - u>2*ut\) term one can study the gain in the amplitude of the wave at the lower 
frequency u> 2 (Raman-gain spectroscopy), or a loss at the higher-frequency wave at w, 
I Inverse Raman spectroscopy), or the growth of the amplitude of a new wave at 2a», - tt> 2 


(CARS). Whereas the changes in intensities of the waves at *», and w? are related to the 
imaginary part #{?*, the CARS intensity is related to jrgU s | 3 = IaTr* + *nr + 
Vr ' : Here, the signals in these nonlinear spectroscopies are background free because 
of the special need for temporal and spatial coincidence of beams in these processes. 
However, due to the nonrcsonant contribution vsr in CARS, there are distortions in 
the line shapes in CARS as opposed to, e.g. Raman-gain (amplification) spectroscopy 
Since gases can withstand very high power needed in these spectroscopies, they have 
been applied ver> successfully in recent years for very high-resolution Raman studies in 
such systems. Using picosecond -pulsed lasers. Raman amplification technique can also 
be used in the condensed phase, e.g., in a single crystal of ion-exchange resin which is 
otherwise extremely fluorescent In high-order processes beyond \ n> , one can generate 
new waves when W| - ui 2 is equal to a subhaimonic of the active Raman mode w,,. For 
example, with Vr' («!• — «2.Wi,-»z,tt|). one creates waves 21 at (o l -u> 2 = w u /2. 
However, these signals may not necessarily contain any more information than that 
obtained in the lower-order nonlinear spectroscopies. 

5. Concluding remarks 

Before concluding, let us emphasize here that in this article we have touched upon only a 
very small sub-set of present interesting topics in Raman spectroscopy. Among many- 
other important investigations like high-pressure Raman experiments, etc., we have not 
said anything about the beautiful Raman studies of acoustic phonons in periodic semi- 
conductor lattices as well as non-periodic (Fibonacci quasi-periodic, random, etc.) 
lattices. These structures consist of sequences of two building blocks of GaAs and AlAs 
layers of thickness of the order of 20 to 40 A or so. Because of zone-folding in the q- 
space. in the direction of the supcrlattice structure, acoustic phonons have many 
different sets of longitudinal and transverse branches, starting from q = 0. with a much 
shorter first Brillouin-zone in the q-space Long-wavelength (q-*0), finite-frequency 
modes can then be observed via Raman scattering. This provides extremely useful 
information about the structural and elastic properties of these layered materials 22 . In a 
sense. acoustic-Raman scattering studies in a periodic supcrlattice can approximately 
map the acoustic phonon dispersion relations of the original bulk materials up to the 
targe original Briltouin-zone in the q-space. in the direction of the supcrlattice structure. 

Substantial progress has also been made in calculating Raman-scattering intensities for 
vibrational excitations in various molecules, from first principles. Since the computation 
of absolute Raman cross-sections has always been a troublesome theoretical problem, 
one is often content with only relative comparisons of experimental results with theoreti- 
cal predictions However, recent ab initio calculations 23 of the polarizability derivatives 
in molecules like H 2 0, etc., via direct computation of electronic energy derivatives, 
have been quite promising. 

The present activity in the field of Raman spectroscopy is quite vast and very exten- 
sive. Since it covers many diverse disciplines in science, it has been difficult to do justice 
to various exciting developments taking place in the field, in an article like this. The vita- 
lity of the field is proved by the exciting proceedings of biennial international confe- 



rences on Raman spectroscopy, and by the increasing number of interesting papers 
being published in the field in a large number of research journals. With the rapid 
growth of sophistication and sensitivity in optical detection and data-processing tech- 
niques, and the progress made in controlling and generating tunable optical sources 
which can be pulsed to the level of a few femtoseconds, different forms of Raman 
spectroscopy arc expected to remain in the limelight for decades to come. 


1. Raman, C. V. and 

Krishnan, K, S, 

2 Raman. C, V 

J. [PFEN, E. P. AND 

Shank, C. V. 

4. Chaw.. R. A. and 
Long, M. B. 


6. Hudson, B. 

7. Raker, W. and 

l.AI'HI-KE-At', A. 

8. Yelsko, S. and 


9. Hamaglciii. H. 

10. Kasii, J. A., 


It. Jha, S. S. 

12. Jiia, S. S.. 
Kash, J. A. AND 
TSANG, J . C. 

13. Tsani., J C, 


Jha, S S 

It. Kami, J. A., 
Jha, S. S- and 
TsANti, J. C. 


16. Hudson, B. and 

Si wsjon, R. J. 

17. a- MosnovrTs, M. 

b. Jha, S S 

c. Otto, a 

,\ature {Land.), 1928, lit, 501. 

Indian J. Phys , 1928, 1, 387. 

In Ultrashort light pulses, 1977 and 1984. Topics in. Allied Physics. Vol. 18, 
ed. S. L. Shapiro. Springer- Vcrlag, Heidelberg. 

In Light scattering in solids II. 1982, Topics in Applied Physics. Vol. 50, cd, 
M Cardona and G. Gunihcrodt, Springer- Vcrlag, Heidelberg, 

see, e.g.. Time-resolved vibrational spectroscopy , 1985. cd. A, Laubcrcau 

,ind M. Stock burger. Springer- Vcrlag, Heidelberg. 

Spectroscopy, 1986, I, 22. 

Rev. Mod. Phys., 1978. SO, 607, 

/ Fhys. Chem.. 1985, *9, 2240. 

In Vibrational spectra and structure. Vol. 16, 1987, ed. J. Dung, Elsevier. 

New York 

Pit vs. Rev. Lett., 1985, 54* 2151. 

Indian J Pure Appt. Phys , 1988, 26, 192. 
Fhys. Rev.. |9Kn. BJ4, 5498. 

Pkysica, 1985. B134, 184 

Fhys. Rev. Lett . 1987. 58, 1864; ibid, 1988. 60, 864. 

ite, e.g . Spectroscopy of biological molecules. Vol, 13, 1984. cd. R. J H. 
Clark and R E Hcsicr. Wiley, Chichester 

In Vibrational spectra and structure. Vol. 17, 1988, cd JR. Dung, Else- 
vier. New York. 

AY i Mod. Phys., 1985, 57 f 783 
Surf. Oct., 1985, 15*. 190. 
Surf. Sir., 1987, 188. 519. 



IB. Chase, B. J. Am. Chem. Sac., 1986. tOS, 7485. 

19. Chase, B. Anal Chem.. 1987, 59, 881 A. 

20. NlBLER, J. W. and In Advances in nonlinear spectroscopy. Vol. 15, 1984, ed. R. J. H- Clark 
Pubanz. G. A. and R. E. Httier. p. 1, Wiley, Chichester. 

2 1 . Tar an. J. P. In Proc. XI int. Cong, on Ramon Spectroscopy . 1988, ed. R. J. H. Clark arid 
Joni-v W. J. D. A. Long, p. 31. Wiley, Chichester; sec also, ibid, p. 35. 

22. Mi- run. R., /. Phys.. (Pans). 1987. 4M, C5-509. 
Bajhma, K., 

NAtil.l-., J. AN1J 

Ptjooc, K. 

23. Amos, R D. Adv. Chem. Phvs., IW7, 60, 241. 









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Professor Ranum with Pandit Nehru. 

J Indian Inst. Sci., Nov.-Dec. 1988, 68, 493-504. 
• Indian Institute of Science. 

The resonance Raman spectrum of I 2 in solution 

Herbert L. Strauss 

Department of Chemistry, University of California. Berkeley. California 94720, U.S.A. 
Received on August 26. 1988. 


An extensive set of resonance excitation profiles and the corresponding depolarization dispersion profiles of 
the vibrational bands of iodine in solution were determined. The results of the experiments are compared to 
the results of detailed calculations. The calculations are based on the gas phase potentials of iodine. Overall 
agreement is good for the noninteracting solvents considered here. However, there are a number of discre- 
pancies, which suggest that higher iodine states — perhaps charge transfer states involving the solvent — 
contribute to the Raman cross section in the visible region of the spectrum. A number of other small effects, 
such as rotation of iodine in the excited states, also contribute. 

Key words: Resonance excitation profiles, resonance Raman spectrum, iodine properties. 

One day in the Spring of 1969, I knocked at the door of C. V. Raman's residence in 
Bangalore. I had come despite the warnings of my friends at the I.I.Sc. and the 
forbidding sign that Raman had erected beside his front gate. However, the Ramans 
greeted me with enthusiasm and Raman showed me his latest work, while Mrs. Raman 
made tea. We spent a very enjoyable few hours together. Raman was eager to discuss 
both his recent work and that of years past. He continued to relish his older work and 
restate his sometimes controversial positions from long ago. A month later I met with 
Professor Charles Coulson in Oxford. When I recounted some of Raman's conversation. 
he said, "That's just what he said to me at a meeting in 1937!" One of Raman's lifelong 
interests was the color of things, especially his prized flowers. It is with this in mind that I 
discuss in this paper the effect of changing the color of the excitation on the Raman 
Effect of the well-known colored solutions of I 2 , 

Two observations led to this investigation. The first is the profound changes in the 
relative intensity of the iodine fundamental and its overtones as the frequency of the 
exciting laser is changed throughout the visible band. The second and more unusual 
observation is that the Raman bands apparently shift as the color of the laser is changed 

(fig. D l - 

The visible spectrum of I 2 is one of the spectra most thoroughly studied by molecular 
spectroscopy. The electronic states of L 2 have been particularly well characterized in the 
spectral region that contributes to the visible absorption and fluorescence spectra" - 
The potential energy curves for the states that contribute to the visible absorption are 













390 410 

Aw (em"') 

Fig. 1. High-resolution Raman spectra of the fundamental (A) and first overtone (B) of l 2 in /i-hexane. Each 
spectrum is labeled with the laser excitation wavelength. The changes that occur in the band shapes and posi- 
tions are due to the relative resonance enhancements of the hot bands. The frequency scale for each spectrum 
of the overtone was calibrated relative to the n-hexane band at 370cm '. The band at 402cm ' is another 
solvent band. 

shown in fig. 2 6 . The low-resolution spectrum of I 2 vapor is shown in fig. 3. The total 
absorption band is composed of three parts. About 5% of the total absorption is due to 
the A<— X transition, which gives rise to the weak low-frequency wing. At the high- 


1 1 



JT 20550- 

| B 0* 

3 n) 


^. 1 esso- 



1 \B"iu( 1 n) 


U 12550- 

l\ \ — _ 

g 8550 - 


I i yAAiu( 3 n) 



\ | /xOflVl) 



r i i i 



2 3 4 5 6 7 

Internuclear Distance (A) 

Fig. 2. Potential energy curves for the electronic 
states of I 2 that contribute to the visible absorption 
spectrum. The dashed line at 2.67 A represents the 
equilibrium internuclear distance for ground state 
I, (redrawn from ref. 6), 

825 . 

" 550 

_i 275 . 

■ 1 

/ ^ 


. _/ .s*~ 


v, (cm" 1 ) 


Fig. 3. The low-resolution absorption spectrum of 
I 2 vapor. The solid line is the total absorption, the 
contribution of the A ♦— X transition is represented 
by the dashed line, the contribution of the B"«-X 
transition is represented by the dot-dashed line, and 
the contribution of the B«-X transition is repre- 
sented by the dash-dashed line. Note that the diffe- 
rence between the A*-X and the total absorption 
is negligible below 14,500cm" '. The total spectrum 
and the breakdown into contributing transitions are 
plotted from the table of values in ref. 2. The 
Dumpiness in the B <— X spectrum is the result of 
residual vibrational structure. 


frequency side the B"*-X transition appears, and this accounts for 22% of the absorp- 
tion. The main B<— X transition accounts for 73% of the absorption. 

The properties of iodine in solution have been of interest to scientists for at least a 
century 7 . Most spectral studies of iodine in solution have dealt with the charge-transfer 
interactions between I 2 and the solvent 8 . Recently, much attention has been focused on 
the effect of solvents on the predissociation of I? and subsequent recombination of the I 
atoms 910 . 

Theory predicts that, in the resonance region, the Raman spectrum of I 2 will depend 
on the frequency of the laser and on the interaction of the solvent with the excited states 
of the spectroscopically active molecule. The differential cross section for the Raman 
cross-section of a randomly oriented gas phase molecule is given by" 


d^r bc-r^ 

X ts P a pa {vLJ*F)l<rL 


where the elements of the polarizability tensor, a (ttr , are given by 

^ ( „„ ,, F) = V <F\rS\EXE\^\l> 
P e » E -v,-v,-iY E 

Here / and Fare the initial and final states of the molecule and the summation over E is 
over all the states of the molecule. i> s , v L , v E and v t are the energies (in cm -1 ) of the 
scattered light, the incident laser, the intermediate state E and the initial state /, respec- 
tively, r is the width of the intermediate state. The polarization vectors of the scattered 
photons. e p and the incident photon. €„, are referred to the molecular-fixed frame. The 
direction cosines Isp and i aL covert this frame to the laboratory frame of reference. A 
number of steps are required to convert this formula to usable form. The averages over 
the direction cosine elements are taken and lead to expressions involving specific 
components of the a-tensor. The dipole matrix elements such as <F| /a | /> are separated 
into electronic and vibrational parts by invoking the Born-Oppenheimer approximation. 
Finally, the appropriate index of refraction corrections for the presence of the solvent 
are made. 

The results of the calculations are formulas for the total differential cross-section and 
for the polarization ratio in terms of the components of the polarizability. For I 2 there 
are two such components, a yy where y is the molecular axis, and a^ where is an axis 
perpendicular to y. For the B <-X transition the only non-zero terms are in a yy . and for 
the A <-X and B"*-X transitions only the a pfi survive. As a consequence, the depenali- 
zation ratio would be 1/8 if only the A and B" states contribute to the Raman cross- 
section and 1/3 if only the B state contributes. 

We have made four types of measurements and compared the results to 
lations 13-16 . In doing this, we had two goals in mind. The first is to provide 
hensive test of the theory of the resonance effect and to resolve various cootr 



the literature. The second is to determine the properties of the excited states of I2 in solu- 
tion. As we shall see, the information available from resonance Raman spectroscopy is 
complementary to that from absorption spectroscopy. 

The four types of measurements are: (1) The resonance excitation profile, REP; that 
is, the change of intensity of the various I 2 Raman bands as a function of the frequency of 
the exciting laser. This measurement was done in w-hexane, a rather non-interacting 
solvent. (2) The depolarization dispersion profiles which we call DDPs; that is, the varia- 
tion of the depolarization ratio versus frequency of the exciting laser. (3) The REPs in 
other non-interacting solvents. (4) The variation of the band shapes of the I 2 Raman 
spectrum with laser frequency. 

It is worthwhile to digress to consider the theory of the resonance Raman Effect 
further. In eqn (2), the F in the denominator is the lifetime of the excited state for a gas 
phase molecule. For a molecule in condensed phase, the correctness of using F to 
account for interactions with the surroundings is not so clear. We followed the formu- 
lation of Mukamel 17 which shows that Y is \IT 2 for the intermediate state. Mukamel's 



1 1 ' 

1 Mi ■ 

1 1 













_. — -?-- 

1 1 1 


1 ^-> 









Fig. 4. The experimental (dashed line) and calculated (solid line) visible absorption spectrum of I 2 in n- 
hexane. The anharmonic ground state, discussed in the text, was used for all calculations of I 2 in n-hexanc. The 
calculation parameters are: J" - 20cm" 1 ; 8. the inhomogeneous width. = 400cm" 1 ; and T = 300K. The 
calculated spectrum is fairly insensitive to T< 100cm '. The intensity of the B state absorption was matched 
using L 2 = 1.75 as a solution correction factor. The width of the spectrum was matched by adjusting 0. The 
calculated spectrum fits less accurately in the high and low frequency wings where the A and B" states 


4 00 


Fir.. 5. Calculated and ex peri mental RbPs lor the I 2 funda menial »n n-hcxartc plotted cm an absolute scale. 
The data points with errot hats are our experimental values (the error bars shown are ± 10%). The results of 
repealed experiments are shown .is multiple data points. The open circles represent data points from Rousseau 
ttal 1 "*. These points were scaled to our value of the absolute cross section at 5145 A. The homogeneous line- 
widths, oi damping factors, are as follows: T= (a) Won" '. (b) 15 cm '. (c) 20cm ', (d) IScm ', (ef 
50 cm ' . (f ) 100 cm" 1 , and (gj 200 em " The in homogeneous linewidth and the solvent effect on the transition 
strength ate both determined In the absorption spectrum. 

formulas contain separate terms for the resonance Raman scattering and the resonance 
fluorescence. The latter is very broad and we ignore it in what follows. 

The total resonance Raman intensity varies with T in si ark contrast to total intensity of 
an absorption spectrum, which is of course invariant to the width of the states. 1'hus a 
measurement of the absolute intensity of the Raman Effect determines l\ provided we 
have a model of the vibronic stales that allows us to calculate the matrix elements of eqn 
(2). To determine these, we assume that ihc electronic states of I 2 are the same in hcxane 
as they are in the gas phase. However, we do modify the ground state vibrational states 
in hexane and the other solvents we have used to match the observed anharmonicity for 
each one 1 *. Our calculations match the observed absorption spectrum well, as shown in 
fig. 4 1 *. 

We take up the Raman Effect experimental results in order. Figure 5 shows the reso- 
nance excitation profile for the I-. fundamental. Also on the figure are the results of 
calculations which we discuss in a moment. Figure 6 shows the data tor the first and 
second overtones of I 2 - In applying the gas phase electronic data to the solution spectra, 
we chose a value of 1 to gjve the best fit. The best choice for F is about 20 cm" ' atid gives 
an excellent overall tit, but there are a number of discrepancies. Note that the experi- 
mental points are higher than calculated ones at the high-frequency side of the REP of 
the fundamental and at the peak of the REP of the first overtone. 





3 00 

£ 2.00 


b C? 

"o|"o 2,00 


t p r — i i 



Fit-. 6. Calculated and experimental RHPs for the I . first (A ) and second (B) overtones in rr-hcxane. The error 
bars on the experimental points are r |W% ;is in fig. S. The parameters for J he calculations are I" = 20 cm ' 
(dashed lines) and 1" = J 5 crn 1 (solid lines). Note thai I is the only adjustable parameter and the ordinate 
scale is absolute 

To obtain a better fit, we consider the depolarization dispersion profiles and also vary 
the calculations systematically to test various effects of the solution excited states. 
FigUCC 7 shows Ihe new calculations with Ihe same data lor the REP of the fundamental, 
Also shown is the DDP of the fundamental. Near the center of the absorption bands the 
DDP is almost 1/3, the value for the B slate alone, as expected. Ai ihc low- and high- 
frequency wings of the band the DDP changes away from 1/3 as the A. B", and other 
degenerate states participate. We show similar information for the first overtone in 
%. 8- In an attempt to resolve the discrepancies mentioned, we included the contri- 
bution from the D stale in the calculation . The D stale is at much higher energy in the 
isolated U molecule — at about 54 ,000 cm" '. It contributes to the Raman spectrum near 
the I> visible absorption band through the B-D cross term that appears in the expression 
for the polarizability squared. As seen in figs 7 and 8, the fundamental REP is still in 
disagreement as before, but the overtone REP is in rather better agreement. This is 
partly due to a recalibralion of the absolute intensity, which is based on comparison with 




w r.o . 

a jc _ 

•-! m 



Fuj 7. (A) Calculated and experimental REPs for the I., fundamental in hcxanc plotted on an absolute scale, 
as sn tic.. 5 but with more data points and 15% error bars. These points were rcscalcd lo our value of the 

absolute cross section al 5145A. The homogeneous linewidths, or damping factors, art as follows: 

1 2 rm -1 — 15 cm" l , 20 cm '. 30 cm ', and + + + 30cm" 1 . The in homogeneous unewidth and the 

solvent cffeci on the transition strength are both determined by the absorption spectrum. The D stale is 
included in the calculation. (B) The calculated and experimental depolarization dispersion curves of the l 3 
fundamental in hcxanc. The circled data point*, between 17,000 and 21,300cm l represent the raw data at 
those frequencies. The triangles represent normalized data. Belo* 17.000cm ' and above 21 ,500 cm ' there 
was no need to normalize the data The error bars arc drawn to ± 10%. The calculation parameters arc as in 
(A | with I" = l5cm~ J The solid line includes the 1) state contribution, while the dashed line neglects this 
contribution The horizontal lines at 1/3 and 1/8 represent the depolarization ratios if only nondegencrate or 
doubly degenerate slates, respectively, contribute to the Raman cross-sections. 

the benzene 992 band. The calculated DDPs are in better agreement for the fundamental 
than for the first overtone (fig. K) or the second overtone (not shown). 

Various possibilities were tried to resolve the discrepancies between theory and calcu- 
lation. Perhaps the most interesting of these considers the addition of an iodine-solvent 
charge -transfer slate to the set of Raman- active states in order to raise the REP in the 

high-frequency wing. This possibility is subject to experimental test. We repeated our 
RKP measurements in perfluomhexatte and in chloroform 15 . Hexane is thought to have 
a contact charge -transfer stale with l : in contrast to perfluoro hexane, which is not 

•HKSl l*W 


\ *-r- ; 

;---- L r- 

Fie, S. The calculated and experimental REPs for the first overtone of I 2 in hcxanc. 1 

lo ± 15%. The parameter* arc the same as in fig.. 7 cscepi (hat (he curve * 

Ifkin '. 




J»*SO. ZZSOO. 2I2M. 34000. 


Fiti. 9. The UV-visihlc absorption sped rum of 1 2 

in n hexatte and irv pcrfluorohcxane. '["he lop spec- 
trum i* ]_. in n he.\;.uie which has been offset by 0.08 
absorbancc units to distinguish the tsvo specira. 
Note the strong absorption band appearing in the 
UV spectrum of l> in hcxane but not in the spec- 
trum of I; in perfluorohexanc. 

Fici. 10. Ine calculated and experiment a] RLPs of 
the l z fundamental in pcrfluorohcxane The error 
bars are drawn to ± 10% . '["he curves were all calcu- 
lated with I = 15 cm '. I Tie dashed line was calcu- 
lated with the D state contribution with Imxp-' 2 = 
40 D", the solid line was calculated with |uxo ' = 
25 D-, and the dot-dashed line was calculated with 
no D state contribution 

i n I l | I — < — i — » — i- 






Fig. II. Raman spectra of the I 3 fundamental fit 
with Lorenlzian lines spaced according to the 
known anharmonicity of I : in hcxanc. The diffe- 
rence between the experimental spectrum and the 
total fit is plotted to scale beneath each spectrum. 
The contributions from the various initial states arc- 
as follows: i = ( — ), i = 1 ( }, 

I = 3 ( ) and i = 4 ( ) The excitation 

frequencies are (A) 4579 A (21 ,840cm" 1 ), (B) 5145 A 
< 19.435 cm '). and (C) 5945 A (16,810 cm -1 ). 



thought to have one 211 . Chloroform should, of course, have a stronger charge-transfer 
complex than hexane. Figure 9 shows the UV-visible absorption spectrum of I 2 in both 
n-hexane and in perfluorohexane. It shows the absorption from the charge-transfer 
complex in hexane and the lack of such art absorption in perfluorohexane. 

Figure 10 shows the REP of l 2 in perfluorohexane together with the results of the 
appropriate calculations. Calculations were again tried both with and without including 
the possible contribution of the D stale. As the figure shows, the experimental points are 
higher than the theoretical ones, just as for the data in hexane. The results for chloro- 
form are very similar. 

It is remarkable that the lit of theory and experiment are so similar for the REPs of I> 
in n -hexane, ^-perfluorohexane and chloroform. All of these give a width of about 
15 cm l for the levels of the upper electronic states. This suggests that the width is due to 
simple thermal fluctuations of the solvents since the three solvents do noi differ much in 
the magnitude of these fluctuations. 

Let us go back and consider the curious phenomenon we mentioned at the beginning: 
the 1 2 Raman bands shift with a change in exciting frequency. In all (he work mentioned 
so far, we took spectra fet relatively low resolution and ignored any small shifts. Now we 
consider spectra taken at higher resolution (fig. 1). Each Raman band is made up of 
both a transition to the ground vibrational state (for example. 1 «-0) but also hot bands 
(2-*— 1, 3«— 2, 2— >3, etc.). Figure 11 shows a fit of such a hot band sequence to the 
observed bands taken with different exciting frequencies. It shows that the components 
(hat make up an individual vibration shift drastically with excitation and 50 appear to 
shift the vibrational band. 

The observed bands can be resolved Into components at each exciting frequency and 
so we can derive REPs for each component. Again we can compare with the results of 
calculations; such a comparison for Ihe fundamental over a part of the frequency range is 
shown in fig. 12. Discrepancies between experiment and calculation are obvious at the 
low frequency side of the data. Agreement is good in the middle and high-frequency side 
(not shown) and for the first overtone (not shown). 

It is difficult to appreciate the details of the small shifts in the calculated REPs and 
DDPs due to a variety of causes and to compare all of these to the experimental results. 
Much more detail is available in the original papers 13- "\ Here, we summarize the high- 
lights of our studies. 

We have measured the REPs of the fundamental and first two overtones of F in 
n-hexane and placed these profiles on an absolute intensity scale. We have also 
measured the absolute REP of the I 2 fundamental in perfluorohexane and placed the 
previously reported REPs of chloroform on an absolute intensity scale. We have mea- 
sured both the depolarization dispersion profiles and relative intensities of the hot bands 
in the F bands in hexane. We have compared all of these to calculations, based on gas 
phase values of the excited slate parameters. 

In all three solvents, the REPs fit best with an excited state homogeneous width of 
about 15cm ', which translates into 0.3 ps. For each fundamental REP. the majo 


Fks. 12. The calculated and experimental b-inilshapes fur l he inotropic pari ul the !_■> lundiimentat. The inten- 
sity of the strongest iraniiiion ai each listed excitation frequency is assigned a value of one. and the other trail- 
si t ions are drawn 10 (hi*, scale. The transitions arc numbered In indies ting the Lowci vibrational stale, I = 
I5cm ' and the l> *>ijte is in.luded in the calculation 


si r; 

discrepancy between calculation and experiment is in the high-frequency wing of the I; 
visible absorption band 

The calculated and experimental depolarization dispersion profiles are in good agree- 
ment, if it is assumed that the B" state is blue shifted about 100cm - ' relative to the B 
state. We note that this small shift' may well be due to inaccuracies in the gas phase 
values or to a solution shift. The consistently high experimental depolarization ratios are 
also explained, in part, by rotation of the I 2 molecule in the excited electronic state, The 
intensity distributions of the ground and hot band transitions show good agreement for 
the first overtone, but again there is disagreement for the fundamental 

It appears that there is a contribution missing from the calculation for the funda- 
mental. Although the addition of another state to the calculation would tend to increase 
the intensity in the wings as needed to approve agreement, it would all decrease the peak 
of the REF. This would result from the effect of the cross term between the new state 
and the B state. Such a decrease is not observed. However, the addition of contributions 
from a number of further states plus small shifts in the 1 2 potentials from those that occur 
for the isolated molecule will undoubtedly fit our data. More data are needed. The most 
useful would be in the UV region where the additional states are expected to lie. 
Another interesting direction is to consider the REPs and DDPs of much stronger 
I ..-benzene complexes, a direction we are now pursuing. 


Dr. Roseanne J. Sension and Mr. Takamichi Kobayashi did the many painstaking 
experiments presented here. Dr. Sension developed and carried out the extensive calcu- 
lations and put theory and experiment together. The National Science Foundation 
supported this work. 


1. ShSSION, R. J., 

Snydhh, R. G. and 
Strauss, It. L. 

2. Tellingirjisen, J 

3. MVLLlKt-N, R. S. 

4. COXON, J. A. 

5. Luc, P. 

6. BuRttSMA, J. P., 
liF.RF.NS, P. H., 

Wilson, K, R., 
Fredkin, D. R- and 

HELLfcK, E- J. 

Proc. Ninth Int. Conf. Raman Spectroscopy , Tokyo. Japan, 1984. 
pp 646-647. 

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/ Chem. Phys . 1971, SS, 288 309. 

Mot. Spectrosc, 1973, I, 177. 

/ Mot. Spectrosc. , 1980, 80, 41-55 

J, Phys Chem., 1984, 88. 632-619. 



7. a, Beckmann, E. 


and Glascock, B. L. 


Hlt-Dl-HRANn, J. H. 


Person, W B, 

Sf HtNLS, J. 'I 

HI. a. Bi kg, M . 

Harris, A. L. and 
Harris, C B. 
b. Harris, A, L-, 


Harris, C. B. 

11. Sam.rai, J. J. 
12 Yariv, A, 

13. Sension. R. J. an]? 
Strauss, H. L. 

14. Sension, R. J-, 


Strauss, H. L, 

15. Sension, R. J . 
Kobayasht, T. and 
Strauss, H. L. 

16. SensiOh, R- J. AND 
Strauss, H. L. 

17. MlJKAMliL, S. 

lft. KlF.Ft-.K. W. AND 
Bl-.RNSftlN, H. J. 

19. Rousseau, D. L., 
Friedman, J. M. and 


20. Evans. D. F. 

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Ann Rev. Pkys. Chem., 1985, 3*, 573-597. 
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Ann. Rev. Phys Chem , 1988, 39, 341. 

Advanced quantum mechanics. Addison- Wesley.. Reading, Mass,, I9n7, Ch. 2 
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/. Chem. Phys., 1987, 87, 6221-6232. 
J. Ckem. Phys., 1987. 87, 6233-6239, 

/. Chem. Phys.. 1988, 88, 2289. 

/. Chem. Phys., 1985, 82, 5398 5408. 
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Topks in current physics. Springer, Berlin, 1979, Vol. II, Ch. 6, 
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/ Indian Inn Set., Nov.-Dec. 1988, *S, 505-507, 
c Indian Institute of Science. 

Inelastic light scattering in crystals 

A. K. Ramdas 

Department of Physics. Purdue University. West Lafayette. IN 47907 USA. 

Received on September 26, 3988, 

(Extended Abstract of the talk, given at the Raman Centenary Celebrations at the Indian Institute of Science. 

Bangalore on November 10, 1988) 

In 1988, the year of the Raman birth centenary and ihe diamond jubilee of ihe discovery 
of the Raman Effect 1 , it seems appropriate to recall Lord Rutherford s statement in his 
presidential address to the Royal Society": "'The Raman Effect* must rank among the 
best three or four discoveries in experimental physics of the last decade. It has proved. 
and will prove an instrument of great power in the study of the theory of solids." 

The nature of the one-phonon and multiphonon-Raman spectra (Rasetti & Fermi 3 ; 
R. S. Krishnan 5 ; Raman-Born controversy 5 ); the LO-TO splitting of polar modes 
(Mathieu & Couture* 1 ); Brillouin scattering and elastic elasto-optic constants (Krishnan 7 ; 
Krishnan Sl Chandrasekharan*; Chandrasekharan 9 ); symmetry (Bhagavantam & 
Venkatarayudu IU ); and soft modes and phase transitions (Raman & Nedungadi 11 ) 
represent some of the major contributions to inelastic light scattering in crystals during the 
pre-laser period. 

The invention of the laser in 1960 and its application to Raman spectroscopy in 1962 
have made inelastic light scattering a powerful tool in condensed- matter physics. With 
major innovations in techniques (photoelectric detection; optical multi-channel detector 
systems; holographic gratings; piezo-electrically scanned Fabry- Perot interferometers; 
tunable dye lasers, etc.), the scope of the field is now vastly extended. Collective and 
localized excitations of vibrational, electronic or magnetic nature have become accessi- 
ble with Raman and Brillouin spectroscopy. Extreme physical conditions — high-magne- 
tic fields, ultrahigh pressures — are experimentally tractable. Time-resolved Raman 
spectroscopy has profound applications lor systems evolving with time scales as small as 
a Femto-second . 

Personally 1 have thoroughly enjoyed the applications of Raman and Brillouin 
spectroscopy in semiconductor physics. Since the first report on the 'Raman scattering in 
silicon' by Russell 13 , Raman scattering by polar phonons in compound semiconductors 
as well as their coupling with plasmons have been observed. Raman scaitcring from local 
modes; polaritons; donors and acceptors; free carriers in a magnetic field — all of these 
have extended and deepened our knowledge of semiconductor physics. Raman spectra 
of novel semiconductors like 'diluted magnetic semiconductors' and novel hetero- 



structures (superlattiees and multiple quantum wells) provide some of the must spectacu- 
lar and delicate illustrations of the power of Raman spectroscopy. 
In my talk I will focus on: 

(1) First and second-order Raman spectrum of diamond as well as the Rrillouin 
components'* M : Interpretation in terms of the dispersion curves for the lattice vibra- 
tions determined by Warren et al** using inelastic neutron scattering; absolute cross 
section of the Raman scattering; elastic and elasto-optic constants — these are the signi- 
ficant aspects of the phonon spectrum of diamond, a crystal of fundamental importance 
in condensed -matter physics. 

(2) Pi ezo- spectroscopy" 1 and the unusual aspects 1 of the zone center optical phonons 
in rt-quartz cr-quartz has a rich Raman spectrum exhibiting one of the sharpest lines in 

Raman spectroscopy along with linear-t| effects characteristic of polar phonons in 
crystals free of improper symmetry. Uniaxial stress effects piezospeetroscopy — is a 
powerful tool in the study of Raman spectra of crystals; this is illustrated with examples 
from the Raman spectrum of rt-quartz. 

(3) Phase transition, mode softening, and /one-folding in crystalline benzil 1 ": Crystal- 
line benzil (CJIsCQCOC<sHs ) is an isomorph of «-quartz at room temperature, It 
undergoes a phase transition to a monoclinic (Ct) symmetry below 7" 4 = 84 K. Associa- 
ted with this phase transition the unit cell enlarges. The external modes of benzil show 
striking effects in the Raman spectrum. 

(4) Magnetic excitations in diluted magnetic semiconductors 1 ": Raman: electronic 

paramagnetic resonance and Raman: anti-ferromagnetic resonance are exhibited by the 
novel, tctrahedrally co-ordinated diluted magnetic semiconductors (e.g. Cd, _ x Mn x Tc). 
Mutual exclusion of Stokes and anti-Stokes spectrum; magnetically and temperature- 
tuned resonance Raman Effect — such unusual, striking phenomena are displayed by 
these semiconductors. 


1 Rama'-. C V. 
.v Fhkmi. T-. -\M> 

Rasxtti. F. 

A. KftliHNAN, R. S 

6 Couture Maihih . L. and 
Mathieu, J. P. 

7 KRISHNA**, K s. 

8. Krisunam, R. S. an» 


Indian J Pttyx.. I, W1X. -W. 

h'mr. R. Site.. 143 L. 130*. 239 The quotation appears on p. 2W. 

I Phyx., 1931. 7t. 6S» 

Pwc Indian Acad. in.. I"M7. A 26. 3s*J 

For Raman -Born controversy see R Loudon. Adv Fkys.. I%4. 13. 

Comptea Rendu*. 1953. 236. 371. 

Pna India* Acad. Sd , 1955, A41, VI. 
Prot Indian Acad. Set., 1950, A3I, 427. 


4 Chandrasekharan, V. 
10 Bhaoavaniam. S. AMD 


11. Raman. C V. and 
Neixtmiadj, T. M K- 

12. Russeu-, J. P. 

13. Soi.in. S- A. and 
Ramdas, A- K. 

14. Crimsditch, M. H. and 
Ramdas, A, K. 

15. Warrj-N, J. L., 
Yaknf.i.l. J- L, 
Doi.lino, G. and 
Cowley, R. A. 

16a. Tekiffe. V. J.. 

Ramdas, A. K. and 

RonRUrllk/-, S. 

b. Brioos, k. J- AND 
Ramdas. a. K. 

17. Grimsdit<-h, M. H.. 
Ramdas, A. K., 
Rodriguez, S. and 

Tfkivph, V. J. 

18. MofWF, D- R.. 
TrKippF, V. J., 
Ramdas, a. K. and 
Toledano, J. C, 

19. Ramdas, A K. ani> 

Kc)[)KKiUC2. S 

Proc Indian Acad. ScL, 1950, AJ2, 379. 
Proc. Indian Acad. Set . 1939, A9 t 224. 

Nature, 1940. 145, 147. 

Appl- Phys Leu., 1965. 6, 223. 
Phys. Rev., 1970, Bl, 1687. 

Phys. Rev.. 1975. Bll, 3139. 

Phys. Rev., 1%6, 158. 805. 

Phys. Rev., 1973, W> 706. 

Phys. Rev.. 1977. Bl*. 3815. 
Phys. Rev., 1977. B15, 5869. 

Phys. Rev.. 1983. BJ7, 7676. 

in Diluted magnetic semiconductor 1 :. Vol. 25 of Semiconductors and 
semimetals, cd. J. K. Furdyna and J. Eto&ut, Academic Ptcss, 1988. 
pp. 345-411. 

J. Indian Inst Sci. Nov. Dec. 19R8, 68, 509-515. 
r - Indian Institute of Science. 

Selected papers of Raman: An introduction 

T. V. Ramakrishnan 

Department of Physics, Indian InslituSc di Science, Ban^uluie 5-60 012. 

A small selection of papers by Professor C. V. Raman follows this introduction, Some 

have been selected for their immediate as well as lasting impact, others for their 
prescience. They ill list rate his characteristically direct and incisive approach, his interest 
in natural phenomena, his concern for basic questions and implications, and his eye (and 

ear) for beauty. 

Raman's writing style is direct, clear and has a characteristic literary flavour. For these 
reasons annotating his papers is often an undesirable intrusion. However, many of them 
are very brief, and were written in a certain intellectual milieu lor a particular audience, 
Several papers hint at areas of physics which have seen growth much later. In this 
introduction. 1 try therefore to expand on the matter condensed in a few lines, to set out 
the background, or to point out how the work foreshadows present concerns in physics, 

The very first paper [PI J is an extremely brief and incomplete summary of one of 
Raman's two major contributions to musical acoustics, namely his work on the 
Mfdangam (and the Tabla). These Indian drums are true musical instruments, the 
musical quality being due to the harmonic overtones and their relative intensities, as well 
as to the clarity, duration and volume of sound. Now in a simple circular drum, the 
overtones are not integral multiples of i\ fundamental or lowest frequency mode of 
vibration, It is therefore not musical. Raman guessed that the Indian drum is designed 
(with its nonuniform black centre and an auxiliary circular leather strip) to produce 
harmonic overtones, to damp out high-frequency harmonics and to produce clear long- 
lasting notes. He showed this by exciting various harmonics, and determined their 
vibration patterns by noting the places where sand, spread on the drum, collects. (It 
collects at places which do not vibrate, called nodes; their number and shape are 
diagnostic of the frequency and nature of the mode of vibration). This note does not 
detail or even describe these results. They were written up much later, in 1934 (The 
Indian musical drums, Proc. Indian Acad. Set., 1934, I t 179-188]. though all the major 
results had been obtained before 1921. The reason for this delay was Raman's increasing 
preoccupation with light and its scattering, the beginnings of which can be seen in the 
next paper. Anyone interested in the area of musical acoustics should read his 1934 
paper. It describes Ramans discoveries in detail, with pictures of the drum in various 
'pure' modes of vibration. 


The second paper, on The colour of the sea" [P2] is a Raman classic. A great scientist. 
Lord Ra\ leigh (whom Raman particularly admired) said, perhaps without thinking much 
about it, that the blue of the sea is just the reflected blue of the sky. Raman, on his first 
\o\.age abroad, disposed, of this suggestion quickly with a few deckside observations 
using a Nicol prism analyzer. The idea is the following: the tight reflected from water is 
partially polarized, the polarization being nearly complete for a certain angle of 
incidence. The Nicol prism, if oriented in a particular direction, will completely block out 
polarized light. By this simple arrangement, reflected light can be eliminated. Raman 
found, under these conditions, that the blue of the sky instead of disappearing was 
"wonderfully improved*! I lis belief that the blue of the ocean had the same physical cause 
as the blue of the sky (explained by Lord Rayleigh!) was reinforced by two observations. 
The first is that when the reflected light is cut out, the colour of the sea depends on the 
angle between the incident sunlight and the sea-scattered light reaching the eye. Further. 
the track of sunlight in water could be seen under certain conditions out to considerable 
depth. Now, Lord Rayleigh had argued that the blue of the sky is due to scattering of 
sunlight in the following way. Purely statistically, at a given instant some regions of air 
are denser, some others rarer. Since the refractive index of air depends on density, these 
spontaneous density fluctuations mean that the refractive index fluctuates randomly. 
This scatters sunlight; the extent or intensity of scattering depends on angle as well as on 
light wavelength, increasing inversely as the fourth power of the latter. Thus the blue 
part of sunlight is scattered much more than the longer wavelength parts. There is every 
reason to expect that similar fluctuations in density should occur in water as well and so 
the same scattering process should be operative. Raman pursued this idea vigorously, 
and produced a fairly detailed analysis of the colour of the sea rather soon (Proc. R. 
Soc, 1922, A101, 64-80. and a monograph entitled 'Molecular diffraction of light' 
published by the Calcutta University in 1922). The point is that this scattering is due not 
to extraneous causes such as dust or other substances, but is due to density fluctuations. 

Ramans sustained efforts at observing this Rayleigh scattering in dust-free fluids in 
the laboratory originate with this experience. These bore fruit in several spectacular 
ways. Some of these are subjects of the next few reprints. 

Raman was probably the first person to appreciate the implications of light scattering 
from glassy or amorphous solids, and viscous liquids. Glasses are generally made by 
rapidly cooling melts or liquids, the cooling rate being large enough to prevent 
crystallization or formation of the crystal. If the arrangement of atoms in the glass is just 
the same as in the melt, but is frozen-in. then light would be scattered from the frozen-in 
density fluctuations appropriate to that for the melt i.e. the liquid. Another possibility is 
that atoms in a glass are positionally well ordered, almost as in the corresponding crystal, 
but that the constituent anisotropic molecules are not orientattonally ordered, i.e. there 
are considerable orientational fluctuations (frozen-in again). A third possibility is that 
especially in chemically complex glasses (e.g. optical or window glass) there are sizeable 
compositional fluctuations. In general, things tend to separate out at low temperatures 
(entropy is less at lower temperatures!) so that these compositional fluctuations tend to 
increase on cooling. In a particular glass, all these effects could be present to different 
degrees at different length (and time) scales. 



In the very first brief paper on the subject [P3] Raman argued, from the radi 
Rayleigh-like scattering of light in glasses, that there are sizeable fro ze* m 
fluctuations in them, comparable to those in liquids. Thus a quasici ystaJfal 
the glassy state, with sizeable crystallites, is ruled out. To confirm for himself eke 
thesis that the scattering of light from glasses is due to intrinsic fluctuations and mo 
dental inclusions' and inhomogeneities. Raman took a dozen optical glasses with srtttz 
refractive indices and studied the intensity and the depolarization of light scattered fwam 
these [PI 1J. He found that the former increases and the latter decreases as the refractr** 
index increases. This systematic dependence suggests that the scattering process at »ort 
is intrinsic, related to their "op'tical density' and is not extrinsic, These contnbuwms 
mark the beginning of a powerful way of probing a class of systems and phenomena not 
fully understood yet. 

Glasses are strange systems which have fallen out of thermal equilibrium in regard to 
some degrees of freedom (or configurations) and are in equilibrium as far as other 
degrees of freedom {e.g. local atomic vibrations) are concerned. That is, the distribution 
of energy in some arrangements of atoms or molecules cannot be described by a 
temperature, while for some other arrangements it can be! The dynamics of this process. 
i.e. how it occurs, is an area of great current interest. Light-scattering techniques are 
much more sophisticated now and time-dependent processes are routinely studied 
Fascinating very slow relaxation processes have been uncovered. However, one still does 
not have a deep understanding of these phenomena which are common to all glasses. 

Another contribution in the same general area is light scattering from viscous liquids 
[P9]. Raman was fascinated by the following idea, due primarily to Britlouin. The 
thermal (temperature-induced) agitation of atoms in a liquid (more clearly in a solid) can 
be thought of a sum (or superposition) of. sound waves of different wavelengths, 
amplitudes and directions of propagation. Scattering of light from one such wave will 
lead to a light wave with a slightly different (shifted) direction of propagation and nearly 
the same frequency just as happens when light is incident on a diffraction grating. This 
Brillouin line was looked for by Raman and coworkers. Now if the sound wave damps 
out quickly, such a distinct line won't be seen. The damping is due to viscous friction in a 
liquid, and will thus decrease as temperature increases (and fluid viscosity decreases). 
Thus on increasing the temperature of a liquid, the Brillouin line should appear: this 
was exactly what Raman and Raghavendra Rao found. This also is an active current area 
of research: one would like to probe and understand the way the Brillouin line 
disappears as one approaches the glass transition marked by a catastrophic viscosits 

The paper on optical behaviour of protein solutions [P5] is again well ahead of its time. 
Whereas large protein molecules in solution were thought of as particles of dust leading 
to haze or light scattering, Raman considered them to be a gas of particles with a 
temperature, compressibility, etc. It turns out that this gas or fluid changes its nature 
(e.g. from gas to liquid) as its density, or the medium in which the molecules arc 
suspended, changes. At such a transition point, fluctuations in density are »«iy 
prominent, and we expect the same excess scattering of light as occurs for example at the 


liquefaction point of carbon dioxide. The study of phase changes in polymers, colloids 
and gels has emerged as. a major field and light scattering is an important tool for 
monitoring molecular movements, arrangements and cooperative changes. This was 
probably the first paper in which one such object (protein solution) was thought of as a 
thermodynamic system. 

Raman's interest in understanding the arrangement of molecules in dense systems such 
as liquids led to the pioneering use of X-ray scattering (diffraction) for probing their 
structure. Raman and Ramanathan had realized in 1923 that since X-rays have 
wavelengths of molecular dimensions, small-angle scattering is related to the statistical 
density fluctuations described earlier but large-angle scattering is a direct probe of local 
molecular arrangement. This large-angle scattering shows up as haloes [P4]. Raman and 
Sogani compared the haloes for two organic compounds, hexane and cyclohexane, and 
argued that the differences are due to specific differences in molecular shape. This is the 
first work on X-ray diffraction as a structural tool in liquids. The work would have been 
complete if the authors had realized that the Fourier transform g(r) of the observed 
intensity S(q) (as a function of wavevector change q) gives the two-particle correlation 
function or the probability of finding two molecules a distance r apart, a quantity of 
direct physical appeal. This was done by Zernicke and Prins in 1927. 

The papers P6, P7 and P12 describe the most celebrated contribution of Raman to 
science, namely the Raman Effect. Raman, his students, and coworkers had been investi- 
gating the scattering of light from liquids since 1921 or so. Most observations, some of 
which have been described above, could be explained by assuming light to be a classical 
wave scattered by spontaneous fluctuations in the medium. However one persistent 
phenomenon did not fit into this pattern; it was dubbed 'weak fluorescence' to begin 
with. Clues about its nature and evidence for its general occurrence, were obtained over 
the years. One such is the following. By using a pair of complementary filters, i.e. , filters 
such that one filter blocks the colours that the other transmits, Raman and Krishnan 
found the following: When both the filters are placed in the path of the beam incident on 
the pure fluid no scattered light is seen. However, if one filter is placed in the path of the 
incident beam and the other in the path of the scattered beam, some weak fluorescence 
could be seen. This clearly means that the colour (or wavelength) of the light transmitted 
by the first filter changes on scattering by the fluid so that it is no longer exactly comple- 
mentary to the other filter and is therefore not fully blocked by it. Raman was reinforced 
in this belief by the then recently discovered Compton Effect in which the wavelength of 
X-rays hitting a 'free' electron is changed. He reasoned that there could be an optical 
analogue of the Compton Effect, namely that a light wave changes its wavelength (or 
frequency or energy) on being scattered by an atom or molecule. To check this", a source 
emitting light of a single colour or wavelength is needed. An intense mercury vapour 
lamp with proper filters is such a monochromatic source. When the scattered light was 
viewed by a spectroscope (in which light of different wavelengths shows up as differently 
placed lines) Raman found, in addition to the line corresponding to the original wave- 
length, another line with a shifted (increased) wavelength. In some substances, more 


than one line was seen; there were also lines with reduced wavelength. The spectra ««e 
recorded, and the papers reprinted here show some of them. 

Why is this "new radiation' important? With his uniquely well-prepared mind. Raniar 
understood it all. Firstly, it is striking evidence for the quantum nature of light A W*e 
quantum hits a molecule, and excites one of its internal modes. The rtmam 
electromagnetic energy comes out as a light quantum or photon of reduced eaesgj 
increased wavelength. If the light quantum absorbs a quantum of internal moieadm 
excitation, the ©incoming photon has higher energy or shorter wavelength 
Einstein's ideas (put forward to explain the photoelectric effect) that light energy i 
carried in quanta, and that this energy is equal to (hcfX) where h is a constant called 
Planck's constant, c the velocity of light and A the wavelength, are strongly supported. At 
a more detailed level, Raman realized that the polarizability of the molecule was 
involved in the mechanism. (This is the same property which causes the refractive index 
of the liquid to differ from unity and to depend on light wavelength). Indeed, he realized 
that a detailed theory of molecular and atomic polarizability, due to Kramers and 
Heisenberg. suggested the possibility of such an effect 

The other major implication, clear to Raman, was that here was a tool of great 
convenience, precision and power for studying internal excitations of molecules, e.g. 
their vibrations, rotations, and electronic-excited states. Instead of studying the former 
by direct absorption in the infrared and far-infrared, one could conveniently investigate 
them in the optical region, as energy differences. Now molecular structure and binding 
are the backbetne of chemistry, so he foresaw that this new branch of spectroscopy would 
be important for chemistry. With the advent of lasers (monochromatic light sources of 
great intensity and coherence) Raman spectroscopy became a standard physico-chemical 

The availability of lasers has brought about an explosive increase in the number of 
light-scattering experiments, as several articles in this volume describe. In his Nobel 
lecture. Raman said: The universality of the phenomenon, the convenience of the 
experimental technique and the simplicity of the spectra obtained enable the effect to be 
used as an experimental aid to the solution of a wide range of problems in physics and 
chemistry. Indeed, it may be said that it is this fact which constitutes the principal 
significance of the effect. The frequency differences from the spectra, the width and 
character of the lines appearing in them, and the intensity and state of polarization of the 
scattered radiations enable us to obtain an insight into the ultimate structure of the 
scattering substance. As experimental research has shown, these features in the spectrm 
are very definitely influenced by physical conditions, such as temperature and state c 
aggregation, bv physico-chemical conditions, such as mixture, solution, mofccmbr 
association and' polymerization, and most essentially by chemical constitution I: fatal 
that the new field of spectroscopy has practically unrestricted scope m the snad; 
problems relating to the structure of matter. We may also hope that it will lead ■ 
fuller understanding of the nature of light, and of the interactions between 
light". The prophecy has been fulfilled, I think even beyond the dreams of i 



The paper in this collection on anomalous diamagnetism [P8] is an example of 
the quickness and richness of Raman's scientific imagination. Diamagnetism is due to 
electrons circulating in "closed (atomic) orbits. Ehrenfest had suggested that the large 
diamagnetism of bismuth implied that in crystalline Bi electron orbits are specially large. 
Raman argues in this paper that many facts e.g. large change of electrical resistance in 
magnetic field, anomalous Hall Effect, large change of stee in a magnetic field, change 
of these properties with temperature, are all connected with this. Now with hindsight (as 
well as the idea of holes and an extremely detailed knowledge of electronic states in Bi) it 
appears that many of the suggestions are not correct, but let us just look at the quick 

The paper with Nagendra Nath [P13] is one of a series of five, in which a phenomenon 
first observed by several others, was analyzed in a characteristically direct fashion. A 
high-frequency sound wave propagates in a liquid, and on being reflected by a plane 
boundary wall, forms stationary waves, or fixed sinusoidal patterns of lower and higher 
liquid density (and hence refractive index). Now suppose a plane light beam is incident 
on this. It will be diffracted. The pattern of intensity of diffracted light is observed to be 
very complex, with a large number of maxima and minima, and considerable wandering 
of their relative intensities as the angle of light incidence or sound wavelength are varied. 
Raman and Nath assumed to begin with that the periodic change in refractive index 
affects only the phase of the plane wavefront sinusoidally. Thus the outcoming wavefront 
is no longer planar, but corrugated. They calculated diffracted beam intensities, and 
showed that the complex observations are explained simply. In further work, the 
assumption that only the phase changes (valid if the light wavelength is much shorter 
than the sound wavelength) was given up, and amplitude modulation also considered. 
This whole work is remarkable for its perfection (a well-defined, interesting and rich 
phenomenon was completely explained theoretically), for its prototypical nature, and 
because it is a primarily theoretical contribution from a great experimenter. (Contrary to 
popular belief Raman not only had a sure and creative grasp of theoretical concepts and 
principles, he was also conversant with theoretical methods, and of course in detail with 
the great masters e.g. Rayleigh, Helmholtz, as well as with the theoretical papers of rele- 
vance to his interests). 

The latest paper reprinted here [P10J reports a discovery: the soft mode. Many 
crystalline solids change their structure as a function of temperature, pressure, or both. If 
the change or transition is continuous, one can imagine a particular distortion or 
movement of atoms leading to the new structure. Now in a crystalline, harmonic solid, all 
arrangements of atoms can be described in terms of normal modes of atomic oscillations 
about a mean position. Thus as the point of transition is approached, that mode of 
oscillation which corresponds to the displacements leading to the new structure becomes 
soft, i.e. easily excited or of low frequency. This was exactly what Raman and Nedungadi 
observed in quartz. The particular lattice-vibration mode corresponding to the symmetry 
change (a^»/3 quartz) was seen to become softer and softer as the transition temperature 
T is approached. In the 1960s Cochran as well as Anderson showed that the square of the 
soft mode frequency is proportional to (T- T c ). The subject of structural transitions and 



soft modes saw considerable activity in the two decades 1960-1979; the pioneering work 
of Raman and Nedungadi was noted to be the beginning of it all. 

I am thankful to Professors P. S. Narayanan, S. Ramaseshan, and C. N. R. Rao for 
help and advice about the selection of papers, and to Professor Ramaseshan for a 
conversation regarding Raman's contributions as well as style. 

Selected papers of Raman 


[PI] Musical drums with harmonic overtones, Nature. 1920. 104, 500 519 

(with Sivakali Kumar) 

[P2] The colour of the sea. Nature, 1921, 108, 367. 519 

[P3] Molecular structure of amorphous solids, Nature. 1922, 109, 520 


[P4J X-ray diffraction in liquids. Nature, 1921, 119, 601 (with 521 

C M. Sogani). 

[P51 Optical behaviour of protein solutions. Nature, 1927, 120, 158. 521 

[P6] A change of wave-length in light scattering, Nature. 1928, 121, 619. 522 

[P7] The optical analogue of the Compton Effect, Nature, 1928. 121, 522 

711 (with K. S. Krishnan). 

[P8] Anomalous diamagnetism. Nature. 1929, 124, 412. 523 

[P9] Light scattering and fluid viscosity, Nature, 1938, 141, 242-243 523 

(with B. V. Raghavendra Rao). 

[P10] The a-p transformation of quartz. Nature, 1940, 145, 147 (with 525 

T. M. K. Nedungadi). 

[Pll] The scattering of light in amorphous solids, J. Opt. Soc. Am., 526 

1927, 15, 185-189. 

[P12] A new radiation, Indian J. Phys., 1928, 2, 387-398. 531 

[P13] The diffraction of light by high frequency sound waves: Parts 544 

I & II, Proc. Indian Acad- Set, 1935, A2, 406-420 (with 
N. S. Nagendra Nath). 

The Journal of the Indian Institute of Science is grateful to Nature, the Journal of the Optical Soaety 
America, the Indian Journal of Physics, the Proceedings of the Indian Academy of Sciences for grinta* 
permission to reproduce the above papers. 




January 15, 1920 
no. 262o, vol. io4] 5oo 

Musical Drums with Harmonic Overtones. 

It is well known that percussion instruments as a 
class give inharmonic overtones, and are thus musically 
defective. We find on investigation that a special 
type of musical drum which has long been know n and 
used in India forms a very remarkable exception to 
the foregoing rule, as it gives harmonic overtones 
having the same relation of pitch to the fundamental 
tone as in stringed instruments. Five such harmonics 
(inclusive of the fundamental tone) can be elicited 
from the drumhead in this type of instrument, the 
first, second, and third harmonics being special I v 
well sustained in intensity and giving a fine musical 
effect. The special method of construction of the 
drumhead which secures this result will be understood 
from the accompanying illustration (Fig. i). It will 

properties have been investigated by us. It is found, 
as might have been expected, that the fundamental 
pitch and the octave are derived respectively frorn the 
mode a of vibration of the .membrane without any 
nodal lines and with one nodal diameter.- The third 
harmonic, vye find, owes its origin to the fact that the 
next two higher modes of vibration of the drumhead 
(those with two nodal diameters and with one nodal 
circle respectively) have identical pitch, this being a 
twelfth above the fundamental. There is reason to 
believe- that the fourth and fifth harmonics similarly 
arise from some of the numerous more complex modes 
of vibration of the drumhead becoming unified in 
pitch in consequence of the distributed load at the 
centre and round the periphery of the membrane. The 
central load also improves the musical effect bv in- 
creasing the energy of vibration, and thus prolonging 
the duration of the tones. C. V. Raman. 

Sivakah Kumar. 
210 Bo\\b;iz;iar Street. Calcutta, India, 
December lo. 

KlC- i.— Drumhead gi»ing harmonic Overtones. 

be noticed (1) that the drumhead carries a symmetrical 
distributed load, decreasing in superficial density from 
the centre outwards (this appears as a dark circle in 
the middle of the membrane, the load consisting of a 
firmly adherent but flexible composition, in which the 
principal constituent is finely divided metallic iron) ; 
and (2) that a second membrane in the form of a 
ring is superimposed on the circular membrane round 
its margin. 

The character of the vibrations of this heterogeneous 
membrane which give rise to its remarkable acoustic 

Printed by permission from Nature, Copyright ©, Macmillan Magazines Limited. 


November 17, 1921] 

no. 2716, vol. 108J 3 6 7 

The Colour of the Sea, 
The view has been expressed that " the much- 
admired dark blue of the deep sea has nothing to 
do with the colour of water, but is simply the blue of 
the sky seen by reflection" (Ravleigh's Scientific 
"Pers," vol. S , p. 54 o, and Nature, vol. 83, p. 48, 
1910). Whether this is really true is shown to be 
questionable by a simple mode of observation used by 
the present writer, in which surface-reflection is 
eliminated, and the other factors remain the same. The 
method is to view the surface of the water through a 
Nicol's prism, which may for convenience be mounted 
at one end of a tube so that it can be turned about 
us axis and pointed in any direction. Observing a 
tolerably smooth patch of water with this held in 
front of the eye at approximately the polarising angle 
with the surface of the sea, the reflection of the sky- 
may be quenched by a suitable orientation of the 
Nicol. Then again, the sky-light on a clear dav in 
certain directions is itself stronglv polarised, and an 
observer standing with his back 'to the sun when it 
is fairly high up and viewing the sea will find the light 
reflected at all incidences sufficiently well polarised 
to enable it to be weakened or nearly suppressed bv 
the aid of a Nicot. 

Observations made in (his way in the deeper waters 
of the Mediterranean and Red Seas showed that the 
colour, so far from being impoverished bv suppres- 
sion of sky-reflection, was wonderfully ' improved 
thereby. A similar effect was noticed, though some- 
what less conspicuously, in the Arabian Sea. It was 
abundantly clear from the observations that the blue 

52 h 


colour of the deep sea is a distinct phenomenon in 
itself, and not merely an effect due to reflected sky- 
light. When the surface-reflections are suppressed 
the hue of the water is of such fullness and satura- 
tion thnj the bluest sky in comparison with it seems 
a dull yrev. 

By putting a slit at one end of the tube and a 
grating over the Nicol in front of the eve, ih<- .spec- 
trum of the light from the water can be examined. 
It was found to exhibit a concentration of energy in 
tFie region of shorter wave-lengths far more marked 
thon with, the bluest sky-light. 

Even when, the sky was completely overcast the 
blue of the water could be observed with the aid of 
a Nicol. It was then a deeper and fuller blue than 
ever, but of greatly enfeebled intensity. The altered 
appearance of the sea under a leaden sky must thus 
be attributed to the fact that the clouds screen the 
water from the sun's rays rather than to the inci- 
dental circumstance that they obscure the blue light of 
the sky. 

Perhaps the most interesting effect observed was 
that the colour of the water (as seen with the Nicol 
held at the polarising angle to the surface of the 
water and quenching the surface-reflection) varied 
with the azimuth of observation relatively to the plane 
of incidence of the sun's rays on the water. When 
the plane of observation and the plane of incidence 
were the same, and the observer had his back to the 
sun and tooked down into the water, the colour was 
a brilliant, but comparatively lighter, blue. As the 
plane of observation is swung round the colour 
becomes a deeper and darker blue, and at the same 
time decreases in intensity, until finally when the plane 
of observation has swung through nearly 180 the water 
appears very dark and of a colour approaching indigo. 
Both the colour and the intensity also varied with the 
altitude of the sun. 

The dependence of the colour on the azimuth of 
observation cannot be explained on a simple absorp- 
tion theory, and must evidently be regarded as a 
diffraction effect arising from the passage of the light 
through the water, Looking down into the water 
with a Nicol in front of the eye to cut off the surface- 
reflections, the track of the sun's rays could be seen 
entering the water and appearing by virtue of perspec- 
tive to converge to a point at a considerable depth 
inside it. The question is : What is it that diffracts 
the light and makes its passage visible? An interest- 
ing possibility that should be considered in this con- 
nection is that the diffracting particles may, at least 
in part, be the molecules of the water themselves. As 
a rough estimate, it was thought that the tracks 
could be seen to a depth of too metres, and that the 
intensity of the light was about one-sixth of that of 
the light of the sky from the zenith. If we assume 
that clear water, owing to its molecular structure, is 
capable of scattering light eight times as strongly as 
dust-free air at atmospheric pressure, it is dear that 
the major part of the observed effect may arise in 
this wav. 

It is useful to remember that the reflecting power 
of water at normal incidence is quite small (only 
2 per cent.), and becomes large only for very oblique 
reflection. It is only when the water is quite smooth 
and is viewed in a direction neartv parallel to the 
surface that the reflected sky-light overpowers the 
light emerging from within 'the water. In other 
cases the latter has n chance of asserting itself. 

C. V. Raman. 

S.S. Narkmrda, Bombay Hnrbour, 
September 26. 


[February 2, 1922 

no. 2727, vol. 109] 138.139 

Molecular Structure of Amorphous Solids. 

A question of fundamental impoitance in the theory 
of the solid stale is the nature of the arrangement 
of the ultimate particles in amorphous or vitreous 
bodies, of which glass is the most familiar example. 
Is it to be supposed that the molecules arc packed 
together in more or less uniform distances apart, as 
in crystals, the orientation of individual molecules or 
of groups of molecules being, however, arbitrary? 
Or, on the other hand, is the spacing of the mole- 
cules itself irregular, the solid exhibiting in a more 
or less permanent form local fluctuations of densitv 
similar to those that arise transitorily in liquids owing 
to the movement of the molecules? The physical pro- 
perties of amorphous solids, notably their' softening 
and viscous flow below the temperature of complete 
fusion, would tend to support the latter view, but the 
possibility of n closer approximation to the crystalline 
state should not entirely be ruled out, especially in 
view of the very interesting recent work of Lord 
Kayleigh on the feeble double refraction exhibited 
by fused silica (Proc. Roy. Soc., 1920, p, 284). A 
good deal might be expected to depend on the nature 
of the material, its mode of preparation, and heat 
treatment. A material formed by simple fusion and re- 
solidification of comparatively simple molecules, such 
as silicon dioxide, might stand on a different footing 
from a material such as ordinary glass built up by 
Chemical action and formation of'complex silicates. 

If the arrangement of molecules in a vitreous bodv 
were irregular, the local fluctuations of optical densitv 
would result m a strong scattering of a beam of light 

Eassing through it, the intensity of such scattering 
eing comparable with that occurring in the liquid 
state at the temperature of fusion of the material (see 
note by the present writer in Nature of November 24 
last, p. 402). On the other hand, if the arrangement 
of the molecules approximated to Ihe crystalline state 
the scattering of light would be merely that due to 
the thermal movements of the molecules and would 
be much smaller. As a matter of fact, glasses exhibit 

Printed by permission from Nature, Copyright ©, Marmillan Magazines Limited. 




a very strong scattering of light, some 300 to 500 
times as strong as in dust-free air, the Tvndall cone 
being of a beautiful sky-blue colour and nearlv, but 
not quite, completely polarised when viewed in a 
transverse direction. (Some glasses exhibit a green, 
yellow, or pink fluorescence when a beam of sunlight 
is focussed within them, and cannot be used for the 
present purpose : the fluorescence, even when very 
feeble, can be detected bv the difference in colour of 
the two images of the Tvndall cone seen through a 
double-image prism. 1 Ravleigh, who observed the 
light-scattering in glass, attributed it to inclusions, 
some of which he assumed must be comparable in size 
with the wave-length (Proc. Rov. Soc., iqiq, p. 476V 
The closest scrutiny through the microscope under 
powerful dark-ground illumination fails, however, to 
indicate the presence of any such inclusions, and it 
seems more reasonable to assume, in view of the fore- 
going remarks, that the scattering is really molecular. 
Its magnitude is of the order that might be expected 
on „the basis of a non-uniform distribution of the 

Further observations with specially prepared glasses 
and with fused silica would be of great interest to 
Investigate the influence of the chemical constitution 
and heat treatment on the molecular texture of the 
solid. C. V. Rama*. 

ato Bowbazanr Street. CaTcutta, December 20. 


April 23, 1927] 

No. 2990, Vol. J ID] 601 

X-ray Diffraction In Liquids. 

In order to find experimental support for the theory 
of X-ray diffraction in liquids put forward some three 
years ago by C. V Raman and K, R. Ramanathon 
[Proc. Indian Assorintion fur (he Cultivation of Science, 
vol. 8, p. 1 2i. 1 '.n2a i. extensive studies have been 
undertaken in the authors' laboratory of the pheno- 
mena observed when h pem-il a{ 'monochromatic 
X-rays passes through a layer of fluid, particularly 
with the view of determining how the effects are influ- 
enced by the physical condition and the chemical 
nature of the substance, under investigation. The 
photographs here reproduced (Fig. ], n and b) were 
obtained in the cmirse of work on this line by one of 
ua (C. M. Sogani) and represent the X-ray liquid- 
haloes of hexane and cyclo-hexane respectively. The 
fluids were contained in cells with very thin walls of 
mica, and the it-radiation of copper from a Shearer 
X-ray tube was used, 

The differences between the two patterns are 
sufficiently striking ; cyclo-hexane shows a bright and 
sharply defined halo with a very clear dark space 
within, while hexane, on the other hand, shows a less 
intense and relmively diffu.se halo, the inner margin 

Fia. 1.— X-ray diffraction haloes of liquids. 
a, llexnnc; b, cyclo-hexane. 

of which is not sharply terminated but extends almost 
up to the direction of the incident ravs. These 
differences indicate very clearly the effect of the 
geometrical form of the molecules on the X-rnv 
scattering by a liquid. From an X-ray point of view, 
cyclo-hexane consisting of ring-formed — though arbi- 
trarily orientated— molecules has a nearly homo- 
geneous structure, while on the other hand the 
elongated shape and varying orientations of the mole- 
cules in hexane cause it to he much less homogeneous 
in X-ray scattering. This explanation is supported 
by the observation that the diffraction halo of benzene 
resembles very closely that of cyclo-hexane. 

It is very interesting to contrast these facts with 
the optica! behaviour of the three liquids with regard 
to the scattering of ordinary light. Opticallv, hexane 
and cyclo-hexane are far more nearlv similar to each 
other, and differ strikingly from benzene, the de- 
polarisation of the scattered light being small for 
hexane and cyclo-hexane and relatively large for 
benzene. Here, evidently, the geometrical form of the 
molecule is of much le«* importance than its chemical 

Further studies of the liquid-haloes for various 
organic substances of the aromatic and aliphatic 
series, and specially with the long-chain compounds, 
are in progress. C. V. Raman. 

„ „ C. 11. Sogasi. 

210 Bowbazar Street, 
Calcutta, India, Feb. 10. 


[July 30, 1927 

No. 3013, Vol. 120] 158 

Optical Behaviour of Protein Solutions 

A very remarkable increase in light -s 
power in exhibited by gelatine solutions 
hydrogen-ion concentration approaches I 
(about pH - S) corresponding to the in itn liii 
This effect, which (appears to have been 

Printed by permission from Nature, Copyright ©, Macmillan Magazines Limited. 



boiiio tii i Mi, has been recently studied in detail by 
Kraemor and }iis co-workers, who give interesting 
curves showing the manner in which the Tyndall effect 
varies with pil and temperature (" Colloid Sym- 
posium Monograph," vol. 4, and Journal of Physical 
Chemistry, May 1927). 

The phenomena are scarcely intelligible on tho view 
commonly adopted that tho Tyndall effect in a 
colloidal solution is simply proportional to the number 
of scattering particles of tho same kind present in it. 
Their explunution becomes clearer if we apply to 
colloidal solutions the general thermodynamic theory 
of light scattering, in which the Tyndall effect ia 
regurded as due to local fluctuations of optical density 
in the medium. According to tho latter theory, the 
scattering power of a colloidal solution would be con- 
nected with the osmotic pressure P of tho particles, 
by tho relation 

k*RT k{frlTk)*ptm ... 

2Nk* i'P'lck * ' ' " { ' 
whore k i-s the concentration of tho dispersed material, 
« is the optical dielectric constant of tho solution and 
p;m is practically unity for a dilute solution. It is 
well known from the work of Jacques Loeb that the 
osmotic pressure of a gelatine solution alters in a 
notable manner with pH t becoming very small at the 
iso-electric point. Equation (1) then enables us to 
see at once why the Tyndall effect becomes very large 
under the same conditions. 

A detailed discussion of colloidal optics on the ba«i£ 
of the thermodynamic theory of light scattering will 
be published in the Indian Journal of Physics. 

C. V. Raman. 


April 21, 1928] 

No, 3051, Vol. 121] 619 

A Change of Wave-length in Light Scattering. 

Further observations by Mr. Krishnan and myself 
on the new kind of light-scattering discovered by us 
have been made and have led to some very surprising 
and interesting results. 

In order to convince ourselves that the secondary 
radiation observed by us was a true scattering and 
not a fluorescence, we proceeded to examine the effect 
in greater detail. The principal difficulty in observing 
the effect with gases and vapours was its excessive 
feebleness. In the case of substances of sufficient 
light-scattering power, this difficulty was overcome 
by using an enclosed bulb and heating it tip so as to 
secure an adequate density of vapour. Using a blue- 
violet filter in the track of the incident light, and a 
complementary green-yellow filter in front of the 
observer's eye, the modified scattered radiation was 
observed with a number of organic vapours, and it 
was even possible to determine its state of polarisa- 
tion, ft was found that in certain cases, for example. 

pentane, it was strongly polarised, while in others, as 
for example naphthalene, it was only feebly so, the 
behaviour being parallel to that observed in the liquid 
state. Liquid carbon dioxide in a stoel observation 
vessel was studied, and exhibited the modified scatter- 
ing to a notable extent. When a cloud was formed 
within the vessel by expansion, the modified scatter- 
ing brightened up at the same time as the ordinary 
or classical scattering. The conclusion is thus reached 
that the radiations of altered wave-length from 
neighbouring molecules are coherent with each other. 

A greater surprise was provided ■ by the spectro- 
scopic observations. Using sunlight with a blue filter 
as the illuminant, the modified scattered radiation 
was readily detected by the appearance in the spectrum 
of the scattered light of radiations absent from the 
incident light. With a suitably chosen filter in the 
incident light, the classical and modified scatterings 
appeared as separate regions in the spectrum separated 
by a dark region. This encouraged us to use a 
mercury arc as the source of light, all radiations of 
longer wave-length than 4358 A. being cut out by a 
filter. The scattered radiations when examined, with 
a spectroscope showed some sharp bright lines addi- 
tional to those present in the incident li<rht, their 
wave length being longer than 4358 A. ; at least two 
such lines were prominent and appeared to be accom- 
panied by some fainter lines, and in addition a con- 
tinuous spectrum. The relation of frequencies between 
the new lines and those present in the incident light 
is being investigated by photographing and measuring 
the spectra. The preliminary visual observations 
appear to indicate that the position of the principal 
modified tines is the same for all substances, though 
their intensity and that of the continuous spectrum 
does varv with their chemical nature. 

C. V. Raman. 

210 Bowbazar Street, 
Calcutta, Mar, 8. 


May 5, 1928] 

No. 3053, Vol. 121] 711 

The Optical Analogue of the Compton Effect, 

The presence in the light scattered by fluids, of 
wave-lengths different from those present in the 
incident light, is .shown very clearly by the accom- 
panying photographs (Fig, I). In the illustration (1) 
represents the spectrum of the hgnt from a quartz 
mercury vapour lamp, from which all wave-lengths 
greater than that of the indigo line have been filtered 
out. This line (4358 A. ) is marked D in the speotrogram. 
and C is the group of lines 4047* 4078, and 4109 A. 
Spectrogram (2) shows the spectrum of the scattered 
light, the fluid used being toluene in this oase. It will 
be seen that besides the lines present in the incident 
spectrum, there are several other lines present in the 

Printed by permission from Nature, Copyright ©. Macmillan Magazines Limited. 



Fjo. 1. — (1) Spectrum of incident tight; (2) spectrum of scattered light. 

scattered spectrum. These are marked a, b, c in the 
figure, and in addition there is seen visually another 
group of lines which is of still greater wave-length 
and lies in a region outside that photographed. 
When a suitable filter was put in the incident light 
to cut off the 4358 lino, this latter group also dis- 
appeared, showing that it derived its origin from the 
4358 linw in the incident radiation. Similarly, the 
group marked c in spectrogram (2) disappeared when 
the group of lines 4047. 407S and 4109 was filtered 
out from the incident radiation by quinine solution, 
while the group due to 4358 A. continued to be seen. 
Thus the analogy with the Compton effect becomes 
clear, except that we are dealing with shifts of wave- 
length far larger than the.-* met with in the X-raj 

As a tentative explanation of the new spectral lines 
thus produced by light -scattering, it may be assumed 
that an incident quantum of radiation may be 
scattered by the molecules of a fluid either as a 
whole or in part, in the former case giving the original 
wave-length, and in the latter case an increased 
wave-length. This explanation iB supported by the 
fact that the diminution in frequency is of the same 
order of magnitude as the frequency of the molecular 
infra-red absorption line. Further, it is found that 
the shift of wave-length is not quite the same for 
different molecules, and tliis supports the explanation 
suggested, . , . 

Careful measurements of wave-length now being 
made should settle tins point definitely at an early 
date. £ V. Raman, 

K. S. Kmshnan.- 

210 Bowbazar Street, 
Calcutta, Mar. 22. 


[September 14, 1929 
No. 3124, Vol. 124J 412 

Anomalous Diamagnetism. 

In a letter in Nature of June 22 (p. 945), reference 
was made to the Ehrenfest hypothesis which ascribes 
the high diamagnetic susceptibility of bismuth to the 

existence of closed eiectr-^r. 
atomic dimensions in 

It may be pointed out that 
orbits appears to furnish a very 
of a variety of phenomena 
been obscure. In the first place, 
nounced diamagnetic anisotropy 
bismuth (and also of graphite) 
intelligible as a consequence of the 
of the assumed electronic circulatka* 
crystal lattice. Further, the large Hal 
changes of electrical resistance exhibited by 
and graphite when placed in a magnetic 
comprehensible, since the electronic? 
be modified by the field, and result i 
modifications of the flow of electricity 
substance under a simultaneously 
motive force. There would be every 
as is indeed the case, that the magnitude* a 
effect and the change of resistance wouid 
the orientation of the crystal in the 
and the direction of flow of electricity ihni^gh 

Then again, with rise of temperature and 
thermal derangements of the lattice, trm 
electronic circulations would tend to 
give place to chaotic electronic 
diamagnetic susceptibility would thendimin. 
its normal value for a non-crystalline 
substance, and corresponding changes 
the coefficients of the Hall effect and 
tion of electrical resistance. That liquid 
not, so far as I am aware, exhibit a measurable 
effect is significant in this connexion. 

In close analogy with the influence of 
ture, and presumably to be explained on very 
lines, is the remarkable fact that the 
diamagnetism of bismuth and of graphite 
diminish or disappear when the substances are 
to a colloidal condition. 

Finally, it may be remarked that the 
of the crystal lattice cannot be uninfluenced fa 
existence of such regular electronic circulai 
it or by modifications produced in them by 
agency. That the magnetostriction of 
strong fields discovered by Dr. Kapitza 
July 13, p. 53) is connected with the 
diamagnetism of the substance admits of little 
The notable increase in magnetostriction t 
temperatures observed by him appears to fit i 
well with the Ehrenfest hvpothesis. 

C. V. Raxay 


Feb, 5, 1938 

No 3562, Vol 141 242 243 

Light Scattering and F.ujd 

According to well-known b_ 
plane waves of sound propagated 

Printed by permission from Nature, Copyright g), Vfacmillan Magazines Limited 



r_z-; a diminution of amplitude in the ratio 
lji m traversing a number of wave-lengths given by 
the quantity 3Ca/8jc*v, where C is the velocity of 
aouad, X ia'the wave-length of sound and v is the 
kmematic viscosity. Taking X = 4358 A., this 
■ amber for various common liquids which are fairly 
csobile at room temperature ranges from about 3 in 
the case of butyl alcohol to about 30 in the case of 
carbon disulphide. For phenol at 25° C, the number 
b lees than 1, and for glycerine, it is a small fraction 
of unity. A consideration of these numbers shows 
that the theories due to Einstein* and L. Brillouin*. 
which regard the diffusion of light occurring in liquids 
an due to the reflection of light by regular and 
infinitely extended trains of sound-waves present in 
them, can only possess partial validity for ordinary 
liquids, and must break down completely in the case 
of very viscous ones. In an earlior note in Nature*. 
we reported studies of the Fabry-Perot patterns of 
scattered light with a series of liquids, which showed 
clearly that the Dopplor -shifted components in the 
spectrum of scattered light fell off in intensity rela- 
tively to the undisplaced components, with increasing 
viscosity of the liquid. 

We have now to report aome further results which 
illustrate in a striking way the part played by fluid 
viscosity in the diffusion of light by liquids. As 
mentioned in our previous note, the light scattered 
by liquid phenol at ordinary temperatures gives a 
Fabry-Perot pattern which is scarcely distinguishable 
from that of the incident light. When, however, the 
temperature of the liquid is raised, the viscosity falls 
off rapidly, and the number 3CX/8rc*v assumes a 






Fig. 1. 


Fig. 2. 
State or polarization ; above, 


value which is many times greater than at room 
temperature. Simultaneously, as can be seen from 
Fig. 1, the character of the Fabry -Porot pattern 
alters, and the Dopplor-shifted components come 
increasingly into evidence ; at 70° C. they are just 
as prominent as in ordinary inviscid liquids. The 
influence of temperature revealed by these studies 
for the case of the very viscous phenol is to be clearly 
distinguished from the broadening of the Doppler 
components with rise of temperature reported by us 
in an earlier note* for the case of carbon tetra- 

The four patterns reproduced in Fig. 2 show the 
remarkable difference in the state of polarization of 
the Fabry-Perot patterns of transversely scattered 
light for an inviscid liquid such as toluene and a 
viscous one such as phenol at room temperature. In 
the former case, only a continuous radiation is to be 
observed in the horizontal component ; in other 
words, both the displaced and the undisplaced com- 
ponents in the pattern are sensibly completely 
polarized with the vibrations vertical. In the case 
of phenol, however, the undisplaced radiation ia 
evidently partially polarized, as it appears both in 
the vertical and the horizontal vibrations ; a part ial 
polarization of the continuous radiation is also 

C. V. Raman. 

B. V. Raohavendra Rao. 

Department of Physics, 

Indian Institute of Science, 


Doc. 29. 


Lsnit>, "Hydrodynamics", fifth nljtkm, f. 013. 
Einstein, A., Ann. Phut., 32, 1275 (191(1). 
Brilloiiin, J„, Ann. 1'tiy*.. 17, 88 < 11)221. 
.Nature, ISO, 585 < April 3, 19371. 
XaTUMt. 135. 7ol (May 4. Ifi:t;,>. 


Jan. 27, 1940 

No. 3665, Vol. 145 147 

is the transition temperature is 
other hand, the other intense line* h 
and smaller frequency shifts oontiaH 
visible, though appreciably broadened 

The bohaviour of the 220 cm.-- line ciemrr. . 
that the binding forces which dete~ 
quency of tlio corresponding mode of 
the crystal lattices diminish rapidly with r 
temperature. It appears therefore reasonable to 
that the increasing excitation of this particular i 
of vibration with risinp temperature and the defo 

The *-# Transformation of Quarts 

As is well known, the ordinary form of quartz 
which has trigonal symmetry changes over reversibly 
to another form which lias hexagonal symmetry at a 
temperature of 575° C. Though the trans- 
formation does not involve any radical re- 
organi Tuition of the internal architecture 1 of 
the crystal and takes place at a sharply de- 
fined temperature, it is nevertheless preceded 
over a considerable range of temperature 
(200 i -o7. f >°) by a progressive change in the 
physical properties of 'low' quartz which pre- 
pares the way for a further Budden change, 
when the transition to 'high' quartz actually 
takes place. The thermal expansion co- 
efficients, for example, gradually increase over 
this range of temperature, becoming prac- 
tically infinite at the transition point and 
then suddenly dropping to small negative 
values 1 . Young's moduli in the same tem- 
perature range fall to rather low values at 
the transition point and then rise sharply to 
high figures 1 . The piezo -electric activity also 
undergoes notable changes*- 1 . 

Tn the hope of obtaining an insight into 
these remarkable phenomena, a careful study 
has been made of the spectrum of mono- 
chromatic light scattered in a quartz crystal at 
a series of temperatures ranging from that of 
liquid air to nearly the transition point. Sig- 
nificant changes are observed which are illus- 
trated in the accompanying illustration, re- 
producing part of the spectrum excited by the 
4358 A. radiation of the meroury are. A fully exposed 
spectrum at room temperature indicates fourteen 
different normal modes of vibration of the crystal. 
At liquid air temperature, the three most intense 
lines correspond to the frequency shifts 132, 220 and 
468 cm.- 1 and are all about equally sharp. As the 
crystal is heated over the temperature range 200°- 
530°, notable ohangee ocour, The 220 cm.-' line 
(marked with an arrow in the reproduction) behaves 
m an exceptional way, spreading out greatly towards 
thr excitinp tine and becoming a weak diffuse band 

Light scattering in quasxc 

tions of the atomic arrangement resulting t hert&aai 
are in a special measure responsible for lbs . 
able changes in the properties of the crystal 
mentioned, as well as for inducing the tra*Wc 
from the -x to the (3 form. 

C- V. Raju> 

T. M. K. Xedctecadl 

Department of Physics, 

Indian Institute of "Science. 


Dec. 11. 

'JBragg and Glbbs, Proc. Ho*. S<x.. A. 1M. 406 il«l. 
* Jay, Prix. RtrV. Sac., A, 14*, 237 (1833X 
Terrier and Mandrot, C.K., 17%. 822 UtSSi. 

4 Oaterberg and Cook»OD, J. Fmi. lmm.. BS 

' Pitt and Mckinley, Can*! J Km A 14 ie : 

Ml UStt). 

Printed by permission from Nature, Copyright ©, Macmillan Magazines Limited. 


[pin Journal 

of the 

Optical Society of America 


Review of Scientific Instruments 

Vol. 15 OCTOBER, 1927 Number 4 


By C. V. Raman 


Recent investigations have shown that when light traverses a dust- 
free liquid, an observable fraction of the energy is laterally scattered 
and that this effect is due to the local fluctuations of density and to the 
random orientations of the molecules which cause the fluid to be 
optically inhomogeneous. 1 In the case of a mixture of liquids, we have 
in addition a scattering due to the local fluctuations of composition 
which cause corresponding local variations of refractive index. Since 
the transverse scatterings due to density and composition fluctuations 
are fully polarized,*- while that due to the random orientation of the 
molecules is almost entirely unpolarized, the resultant scattering in 
a fluid is usually only partially polarized. When the temperature of a 
liquid is lowered, its compressibility usually diminishes and with it also 
the local fluctuations of density. Thus we may expect that when the 
liquid is cooled to such an extent that it passes into the amorphous 
solid condition, the density scattering would become very small. On 
the other hand, in liquid mixtures, the local fluctuations of composition 
usually tend to increase rather than to diminish with fall of tempera- 
lure. Thus they should certainly tend to persist or even increase when 
the mixture congeals into an amorphous solid. The effect due to random 
molecular orientations would certainly remain in the amorphous solid 
condition. Thus, we may anticipate that an amorphous solid such as 
glass consisting of a mixture of anisotropic molecules would exhibit 
^hen light traverses it, a partially-polarized internal scattering or 
opalescence of an order of intensity not greatly inferior to that ordinarily 
bserved in liquids or liquid mixtures. 

1 C. V. Raman, Molecular Diffraction of Light, Calcutta University Press, 1922. 


Printed by permission from J. Opt. Sac. Am., 1927. 15, 185-189. 


C, V, Raman 


An internal scattering of light in common glasses and abo 
glasses has actually been noticed. 1 Its nature has been a 
debate, 1 and owing to our insufficient knowledge of the 
state, is not fully understood at present. Judging, however, f: 
observations as are available, it is the opinion of the writer, thai 
effect observed in optical glasses is a true molecular scattering 
from local fluctuations of composition and of molecular orie-:i 
being thus of the same general nature as the opalescence observed 
in binary liquid mixtures such as phenol-water, carbon disulphide 
methyl alcohol and so on. In support of this view, it is proposed in 
this paper to give the results of the study of the light-scattering in a 
series of 14 different optical glasses manufactured by the firm c: 
Schott in Jena. 1 If the light-scattering in glass were due to accidenia. 
inclusions or incipient crystallizations occurring within it as has bee.- 
suggested by some writers, we should expect the intensity of the 
scattered light to show large and arbitrary variations depending on the 
circumstances of the particular melting from which the specimen was 
taken. On the other hand, if the phenomenon has a true molecular 
origin, we should expect to find the intensity of scattering to be defi- 
nitely correlated with the refractivity and chemical constitution of the 

Table 1. List of classes examined. 





index n 


No. 1 



Fluor crown 





U. V. 3199 

U, V. crown 






Botosilicate crown 






Prism crown 






Silicate crown 






Telescopic Hint 






Baryta light flint 






Densest Borosilicate crown 






Ordinary Light flint 


41 4 




Baryta light flint 






Ordinary flint 






Baryta flint 






Dense flint 






Densest flint 



•Lord Rayieigh, Proc. Roy. Soc., 95, p. 476, 1919, and C. V. Raman, "Molecular I>: 
fracUon of Light," p. 85. 

1 R. Cans, Ann. der Phys,, 77, p. 317; 1925. 

* The specimens were presented by Messrs. Schott to Prof. P. N. Ghosh, who kindly plat*: 
them at the writer's disposal for the work. 


October, 1927] 

Scattering in Solids 



Table 1 gives a list of the glasses examined and their description as 
furnished by the manufacturers, arranged in order of increasing refractive 
index. The samples were furnished in the form of slabs 7 cmX? cmX2 
cm, with one pair of end-faces polished. For the purpose of the obser- 
vation of light-scattering, the slabs were immersed in a trough con- 
taining benzene and a beam of sunlight focused by a lens was admitted 
through a side-face, the necessity of polishing the latter being thus 
avoided. The track of the beam as seen through the end-faces was 
perfectly uniform and appeared of a beautiful sky-blue color. 


When the scattered light was viewed through a double-image prism 
held so that the direction of vibrations in the two images seen were 
respectively perpendicular and parallel to the direction of the beam 
traversing the glass, it was seen that these were of very different 
intensities, showing that the scattered light was strongly but not 
completely polarized. The color of the stronger image was always a 
sky-blue. The color of the fainter image in the ordinary flint glasses 
was blue, but in the other specimens varied very considerably. The 
total intensity of the scattered light in the glasses was determined by 
comparison with that of the track in a bulb containing dust-free 
benzene immersed in the same trough as the block of glass under 
examination and traversed by the same beam of light. A rotating- 
sector photometer was used for the purpose. The ratio of the intensities 
in the parallel and perpendicular components of vibration in the 
laterally scattered light was also determined with the help of a double- 
image prism and nicol(Cornu's method) in the usual way. The measure- 
ments give us the ratio of the intensity of the faint image to the bright 
image seen through the double image prism, and this expresses the 
Ic-gree of depolarization of the scattered light. 

The results of the work are gathered together in Table 2. 


From a scrutiny of the figures in Table 2, several interesting facts 
emerge. In the first place, it will be seen that the crown glasses show 
uniformly a smaller intensity of light-scattering than the other varieties 
of glass. Both the ordinary flints and the baryta flints scatter light 
strongly, the latter more so than ordinary flints of equal refractive 
index. It will be seen also that considering each species of glass sepa- 


C, V, Raman 


[J,O.S.A. & R.S.I, 15 

rately, there is a progressive increase of the intensity of light -scattering 
with increasing refractive-index. The colors shown by the fainter 
components of the scattered light in the first four glasses in Table 2 are 
obviously due to a species of weak fluorescence, probably of the same 
kind as has been met with in investigations on light-scattering in 
liquids.' This fluorescence being unpolarized, the laige values of the 
depolarization found in the case of these glasses stands self-explained 
If the fluorescent light had been excluded by the introduction of 

Table 2 ExfimmtnkU malts. 


Color of 

Iaitui. - . ■ 



Color of 








to ben 




Koe = 1 

No. 1 

Fluor crown 







U. V. crown 







Borosilicate crown 







Prism crowa 







Silicate crown 







Telescopic flint 







Baryta light flint 







Densest borosilicate 


1 5726 






Ordinary light flint 

1 5774 






Baryta light flint 







Ordinary flint 




0.079 | 



Baryta flint 

1 6235 






Dense flint 







Densest flint 






suitable color-filters, the depolarization for these glasses would haw 
been much smaller. It is interesting to notice that in glasses Nds. 6. ~ 
and 8, we have a low value for the depolarization in spite of the obvious 
presence of a weak fluorescence; this is obviously due to the grei.:-. * 
intensity of polarized scattering appearing in the last column ol Tabk 
2 of these glasses. 

The several regularities to which attention has been drawn above, 
particularly the fact that the intensity of scattering is very clearly a 
function of the refractive-index and chemical composition of the glass, 
render it extremely improbable that the effect can arise from accidental 
inclusions or imperfections in the structure of the glasses. It is, in fact, 
clear from the data that the effect arises from the ultimate molecular 
structure of glass. 

« K. S. Kri&hnan, Phil. Mag., 50, p. 697; 1925. 


October, 1927] 

Scattering in Solids 


It would be very interesting to study the light-scattering in amor- 
phous solids having a relatively simple chemical constitution, e.g., 
transparent quartz-glass. Experiments on the scattering of light in 
liquids which can first be rendered dust-free and then supercooled into 
the amorphous solid state may also be expected to furnish important 
information. Further work on these lines is in progress. 

210 Bowbazae Street, 

Calcutta, India, 

May 11, 1927. 

[P12] 2 * 

A New Radiation 1 


Prof. C. V. Raman, F.R.S. 
(Plate XII). 

1. Introduction. 

I propose this evening to speak to you on a new kind of 
radiation or light-emission from atoms and molecules. To 
make the significance of the discovery clear, I propose to 
place before you the history of the investigations made at 
Calcutta which led up to it. Before doing so, however, a few 
preliminary remarks regarding radiation from atoms and 
molecules will not be out of place. 

Various ways are known to the physicist by which atoms 
or molecules may be caused to emit light, as for instance, 
heating a substance or bombarding it with a stream of 
electrons. The light thus emitted is usually characteristic of 
the atoms or molecules and is referred to as primary radiation. 
It is also possible to induce radiation from atoms and mole- 
cules by illuminating them strongly. Such light-emission is 
referred to as secondary radiation. The familiar diffusion of 
light by rough surfaces may be cited as an example of 
secondary radiation, but strictly speaking, it hardly deserves 
the name, being an effect occuring at the boundaries between 
media of different refractive indices and not a true volume- 
effect in which all the atoms and molecules of the substance 

1 Inangnra.1 Address delivered to the South Indian Science Association on Fria»y, 
the 15th March, 1928, at Bangalore. 

Primed by permission from Indian J. Phys., 1928. 2. 387-398. 






Fig 1 Llnniodifit 
\-"\g 2 Modified 

Fig 3 fl> 
Incident Spectrum 

Fig 3 (2> 
Scattered Spectrum 

Fig 4 <1) 

Incident Spectrum 

Fig" ■» <2) 
Scattered Spectrum 

388 C V. RAMAN 

take part. The first case discovered of secondary radiation 
really worthy of the name was the phenomenon of fluorescence 
whose laws Tvere elucidated hy the investigations of Sir 
George Stokes* This is a familiar effect which is exhibited 
in a very conspicous manner in the visible region of the 
spectrum by various organic dye-stuffs. I have here a bottle 
of water in which an extremely small quantity of fluorescein 
is dissolved. You notice that when placed in the beam of 
light from the lantern, it shines with a vivid green light, and 
that the colour of the emission is not altered, though its 
brightness is changed, by placing filters of various colours 
between the bottle and the lantern. A violet filter excites the 
green fluorescence strongly, while a red filter has bat little 

Another kind of secondary radiation whose existence has 
been experimentally recognized more recently is the scattering 
of light by atoms and molecules. It is this scattering that 
gives us the light of the sky, the blue colour of the deep sea 
and the delicate opalescence of large masses of clear ice. 
I have here a large bottle of a very clear and transparent 
liquid, toluene, which as you notice contains hardly any dust- 
particles, but the track of the beam from the lantern passing 
through it is visible as a brilliant blue cone of light. This 
internal opalescence continues to be visible even after the 
most careful purification of the liquid by repeated distillation 
in vacuo. A similar opalescence is shown, though much less 
brightly, by dust-free gases and vapours, and also by solid- 
A large clear block of ice shows a blue colour in the track of 
the beam when sunlight passes through it. The blue opales- 
cence of blocks of clear optical glass is also readily demons- 
trable. The molecular scattering of light is thus a pheno- 
menon common to all statei of matter. 

During the past seven years, the scattering of light in 
transparent media has been the subject of intensive experi- 
mental and theoretical investigation at Calcutta, and it is the 



researches made on this subject that have led to the discovery 
which I shall lay before you this evening. One important 
outcome of our researches has been to show that while light- 
scattering is in one sense a molecular phenomenon, in another 
sense it is a bulk-effect having a thermal origin. It is the 
thermal agitation of the molecules which causes them to be 
distributed and orientated in space with incomplete regularity, 
and it is the local fluctuations in t he properties of the medium 
thus arising which give rise to optical heterogeneity and 
consequent diffusion of light. The subject of light-scattering 
is thus a meeting ground for thermodynamics, molecular 
physics and the wave-theory of radiation. That the combina- 
tion of theories in such diverse fields of physics gives us 
predictions which have been experimentally verified, is one of 
the triumphs of modern physics. 

2. A New Phenomenon. 

While the quantitative investigations made at Calcutta 
have in the main substantiated the thermodynamic- wave- 
optical theory of light-scattering, indications appeared even 
in our earliest studies of a new phenomenon which refused to 
fit in with our pre-conceived notions. Thus, in some observa- 
tions made by me x with the assistance of Mr. Seshagiri Hao 
in December, 1921, it was found that the depolarisation of the 
light transversely scattered by distilled water measured with 
a double-image prism and Nicol increased very markedlv 
when a violet filter was placed in the path of the incident 
light. More careful investigations made with dust-free 
liquids 8 in 1922, confirmed this effect and showed it to exist 
also in methyl aud ethyl alcohols, and to a lesser degree in 
ether. It was also noticed that the colours of the scattered 
light from the different liquids studied did not match 

1 " Molecular Diffraction of Light," Calcutta University Press, Fobrnarv, 1922. 
• C. V. Raman and K. S. Rao, Phil. Mag., Vol. 40, p. G33, 1923. 

390 C. V. RAMAN 

perfectly. An important advance was made when Br, 
Ramanathan ' working at Calcutta in the summer of 1923, 
investigated the phenomenon more closely and discovered 
that it was not a true dependance of the depolarisation on the 
wave-length of the scattering radiation but was due to the 
presence in the scattered light of what he described as " a 
trace of fluorescence," This was shown by the fact that the 
measured depolarisation depended on whether the blue filter 
used was placed in the path of the incident beam or of the 
scattered light, being smaller in the latter case. Accepting 
the explanation of the effect as "weak fluorescence," it 
naturally became important to discover whether it was due to 
some impurity present in the substance. Dr. Ramanathan 
tested this by careful chemical purification followed by 
repeated slow- distillation of the liquid at the temperature of 
melting ice. He found that the effect persisted undimi- 

The investigation of this species of " weak fluorescence " has 
ever Bince 1923 been on our programme of research at Calcutta. 
Krishnan, 2 who investigated 60 liquids for light-scattering in the 
spring and summer of 1924, made systematic studies of the 
phenomenon, and found that it was shown markedly by water, 
ether, all the monohydric alcohols and a few other compounds. 
He pointed out that the liquids which exhibit the effect have 
certain family relationships amongst themselves, and that they 
are also substances whose molecules are known to be polar. 
The chemical importance of the subject led to Mr. S. Venka- 
teswaran attempting to make a fuller study of it in the 
summer of 1925, but without any special success. The re- 
search was discontinued at the time but was resumed by him 
later in the current year (January., 1928). The remarkable 
observation was made that the visible radiation which is excited 

1 K. R, Ramanathan, Proo. Ind, Assoc, Cultn. Science, Vol, VIII, p. 190, 1923, 
• K. 8. Kxiahnan, Phil. Mag,, Vol. L, p. 697, 1925. 



in pure dry glycerine by ultra-violet radiation (sunlight filtered 
through Coming glass G. 586) is strongly polarised. 

The possibility of a similar effect in gases and vapours 
was also borne in mind and repeatedly looked for by the 
workers at Calcutta. The feebleness of the scattering in 
gases and vapours, and the infructuousness of the earlier 
efforts in this direction, however discouraged progress, 

3. lis Universality. 

Though the phenomenon was described in the paper of 
Dr. Ramanathan and Mr. Krishnan as a " feeble fluorescence," 
the impression left on my mind at the time was that we had 
here an entirely new type of secondary radiation distinct from 
what is usually described as fluorescence. The publication of 
the idea was however discouraged by the belief then enter- 
tained that only a few liquids exhibited the effect and by the 
supposition that it was unpolarised in the same way as ordi- 
nary fluorescence in liquids. Indeed., h chemical critic might 
even have asserted that the effect was in each case due to a 
trace of dissolved fluorescent impurity present in the substance 
which our efforts at purification had failed to remove. Early 
this year, however, a powerful impetus to further research was 
provided when I conceived the idea that the effect was some 
kind of optical analogue to the type of X-ray scattering dis- 
covered by Prof, Compton, for which he recently received the 
Nobel Prize in Physics. I immediately undertook an experi- 
mental re-examination of the subject in collaboration with 
Mr. K.S. Krishnan and this has proved very fruitful in results. 
The first step taken in the research was to find whether the 
effect is shown by all liquids. The method of investigation 
was to use a powerful beam of sunlight from a heliostat 
concentrated by a 7" telescope objective combined with a 
short focus lens. This was passed through a blue-violet filter 
and then through the liquid under examination contained in 


392 C. V. RAMAN 

an evacuated bulb and purified by repeated distillation i=. 
vacuo. A second filter of green glass was used which was 
complementary in colour to the blue -violet filter. If it were 
placed in the track of the incident light, all illumination dis- 
appears, while, if it be placed between the bulb and the obser- 
ver's eye, the opalescent track within the liquid continued to 
be visible, though less brightly. All the liquids examined 
(and they were some 80 in number) showed the effect in a 
Striking manner. There was therefore no longer any doubt 
that the phenomenon was universal in character ; with the 
bulb of toluene on the lantern, you see that the effect is readily 
demonstrable. The cone of light vanishes when I place the 
violet and green filters together, but it appears when I transfer 
the latter to a place between my audience and the observation 

Now the test with the complementary filters is precisely 
that ordinarily used for detecting fluorescence and indeed was 
first suggested by Stokes in his investigations on the subject. 
You may therefore rightly ask me the question how does this 
phenomenon differ from fluorescence ? The answer to the 
question is, firstly, that it is of an entirely different order of 
intensity. A more satisfactory proof was however forth* 
ctming when Mr, Krishnan and myself examined the polari- 
sation of this new type of radiation and found that it was 
nearly as strong as that of the ordinary light scattering in 
many cases, and is thus quite distinct from ordinary fluor- 
escence which is usually unpolarised. 

This is shown for the case of toluene in Pigs. 1 and 2 
in Plate XII. Fig. 1 is a photograph of the scattering by 
toluene of sunlight filtered through a blue-violet glass. It 
was taken through a double-image prism of iceland spar with 
an exposure of 3 seconds, Fig. 2 is a picture with an addi- 
tional complementary filter of green glass interposed in front 
of the camera lens. The exposure necessary is now increased 
greatly by the insensitiveness of the plate to green light, and 



had to be as much as 25 minutes. It will be noticed that the 
polarisation of the track as shown by the difference in bright- 
ness of the two polarised images is quite as prominent in Fig, 
2 as in Fig. 1. 

I may also mention that Mr. Krishnan and myself have 
succeeded in detecting the new radiation and observing its 
partial polarisation in a number of organic vapours and also in 
the gases COj> and N 2 0, The problem in these cases is one of 
securing sufficient intensity of scattering for the effect to be 
detectable through the complementary filter. This can be 
secured by heating up the substance in a sealed bulb or by 
using steel observation- vessels for containing the compressed 
gases, so as to obtain sufficient density of the scattering mole- 
cules. The question of the background against which the 
track is observed is also of great importance. 

The new type of secondary radiation is also observable in 
crystals such as ice, and in amorphous solids. It is thus a 
phenomenon whose universal nature has to be recognised. 

4. Line-Spectrum of New Radiation, 

That the secondary radiation passes the complementary 
filter and yet is strongly polarised to an extent comparable 
with the ordinary molecular scattering, is clear evidence that 
we have in it an entirely hew type of secondary radiation 
which is distinct from either the ordinary scattering or the 
usual type of fluorescence. A striking and even startling 
confirmation of this view is furnished by an examination of 
its spectrum. Preliminary observations with sunlight filtered 
through a combination which passes a narrow range of wave- 
lengths, showed the spectrum of the new radiation to consist 
mainly of a narrow range of wave-lengths clearly separated 
from the incident spectrum by a dark space. This encouraged 
me to take up observations with a monochromatic source* of 
light. A quartz mercury lamp with a filter which completely 

394 c. y. RAMAN 

cuts out all the risible lines of longer wave-length than the 
indigo line 4,358. A. TL was found to be very effective. When 
the light from such a lamp was passed through the bulb eon- 
taming a dust-free liquid, and the spectrum of the scattered 
light was observed through a direct-vision spectroscope, it was 
found to exhibit two or more sharp bright lines in the blue and 
green regions of the spectrum. These lines are not present in 
the spectrum of the incident light or in the unaltered light of 
the mercury arc and are thus manufactured by the molecules 
of the liquid. 

Figs. 3 (1) and 3 (2), and Pigs. 4 (1) and 4 (2) show the 
phenomenon. They are spectrograms taken with a small 
Hilger quartz instrument of the scattering by liquid benzene. 
Tig. 3 was taken with the light from the quartz mercury arc 
filtered through a blue glass which allows the wave- lengths 
from about 3,500 A. U. to 4,400 A. 17. to pass through. Fig, 3 
(1) represents the incident-spectrum and Fig. 3 (2) the scatter- 
ed spectrum, and the latter shows a number of sharp lines not 
present in Fig. 3 (1). These are indicated in the figure. Fi<*s. 
4 (1) and (2) similarly represent the incident and scattered 
spectra with benzene liquid, the filter used being a potassium 
permanganate solution. Here again the new lines which 
appear are indicated in the figure. Visual observations were 
also made using a quinine sulphate solution together with the 
blue glass as a filter and thus cutting off all the radiations 
except 4,358 A,U. from the incident spectrum. Some of the 
modified lines then disappear, leaving only those of longer 
wave-length. It is thug clear that each line in the incident 
spectrum gives rise to at least two lines in the scattered spec- 
trum, one in the original or unmodified position, and a second 
in a shifted position of longer wave-length. There is thus a 
striking analogy with the Compton effect in the X-ray region. 

There has, as yet, not been sufficient time for photograph- 
ing the spectra from a large number of liquids, or even for 
measuring the photographs already obtained. Visual obser- 



vations have however been made with a large number of 
liquids There is an astonishing similarity between the 
spectra obtained with different liquids. When only the 4,358 
line was used, most liquids showed in the spectrum of the 
scattered light, a bright line in the blue-green region of the 
spectrum (about 5,000 A.U.), whose position was practically 
the same for chemically similar liquids such as pentane, 
hexane and octane for instance. There was, however, a recog- 
nizable difference in the position of the modified line when 
other liquids such as benzene or water were used. When the 
4,047 line of the mercury arc was let in by removing the 
quinine sulphate solution, a second modified line in the blue 
region of the spectrum was seen with most liquids. 

Photographs obtained so far with benzene and toluene 
suggest that there may be several modified lines, and that each 
modified line may be a doublet in some cases. In many 
liquids, the scattered spectrum shows in addition to sharp lines 
also an unmistakable continuous spectrum accompanying it. 
Carbon disulphide behaves in an exceptional manner, showing 
a diffuse band. 

Observations already made show that the new lines in the 
scattered spectrum are usually markedly polarised ; they also 
suggest that a continuous spectrum, when present, is less 
markedly polarised. 

5. Nature of the New Radiation. 

The discovery set out above naturally opens up an array 
of problems for investigation. The most pressing question is, 
how is the modified scattered radiation, as we may call it, 
generated by the molecules of the liquid p As a tentative 
explanation, we may adopt the language of the quantum 
theory, and say that the incident quantum of radiation is parti- 
ally absorbed by the molecule, and that the unabsorbed part is 
scattered. The suggestion does not seem to be altogether 


396 c. y. RAMAN 

absurd and indeed such a possibility is already contemplated 
in the Kramers-Heisenberg theory of dispersion. If we 
accept the" idea indicated above, then the difference between 
the incident and scattered quanta would correspond to a 
quantum of absorption by the molecule. The measurement 
of the frequencies of the new spectral lines thus opens a new 
pathway of research into molecular spectra, particularly those 
in the infra-red region. 

If a molecule can take up part of the incident quantum 

of radiation and scatter the remaining part, then it might 

also be capable of adding a quantum of its own characteristic 

frequency to the incident radiation when scattering it. In 

such a case we should expect a modified line of increased 

frequency. Such a result appears to he shown in Fig. 3 (2) 

of Plate XII, as a solitary line in the extreme left of the 

photograph. This result, however, requires to be confirmed 

by more photographs and with other liquids. So far it would 

appear that a degradation of frequency is more probable than 

an enhancement. It is too early to speculate at present on the 

origin of the continuous radiation observed in some cases, 

whether it is duo to changes in the molecule itself, or whether 

it arises from inelastic collisions of the second kind within the 

liquid resulting in partial transformation of the incident 

quantum of radiation into translatory kinetic energy of the 

molecules. "When further data are obtained, it should be 

possible to express a definite opinion on this point, and also 

on the role played by the solvent in the explanation of 

ordinary fluorescence. 

6. Relation to Thermodynamics. 

As explained in the introduction, the ordinary scattering 
of li ff ht can be regarded equally well as a molecular effect, 
and as a bulk effect arising from the thermodynamic fluctua- 
tions of the whole medium. The question arises whether the 



new type of secondary radiation is exclusively a molecular effect 
or not, and whether it is related in any way to thermodynamics. 
The question is obviously one to be answered by experiment and 
theory conjointly. The comparative study of the effect at 
different temperatures and in different states of aggregation of 
matter is obviously of great importance in this connection. It 
has already been remarked that the effect is observable in gases 
and vapours and indeed it is found possible to determine its 
intensity and polarisation in the gaseous state. It is also of 
great interest to remark that the solid crystal ice also shows 
the sharp modified lines in the scattered spectrum in approxi- 
mately the same positions as pure water. The only observa* 
tions made with amorphous solids are with optical glass, Here 
the modified scattered spectrum consists of diffuse bands and 
not sharp lines. Whether this is generally true for ail amor- 
phous solids, and whether any changes occur at low and high 
temperatures remains to be determined by experiment. 

1, Coherent or Non-Coherent Radiation ? 

An important question to be decided in the first instance 
by experiment is whether the modified scattered radiations 
from the different molecules are incoherent with each other. 
One is tempted to assume that this must be the case, but a 
somewhat astonishing observation made with liquid carbon 
dioxide contained in steel observation vessels gives us pause 
here. It was found on blowing off the C0 3 by opening a stop- 
cock, a cloud formed within the vessels which scattered light 
strongly in the ordinary way. On viewing the cloud through 
the complementary filter, the scattered radiation of modified 
frequency also brightened up greatly. This would suggest 
that the assumption of non-coherence is unjustifiable. 
Further, some qualitative observations suggest that the 
modified scattering by a mixture of carbon disulphide and 
methyl alcohol also brightens up notably at the critical 

39$ C V. RAMAN 

solution temperature. Quantitative observations are necessary 
to decide the very fundamental question here raised. 

8. Possible X-Ray Analogies. 

If a quantum of radiation can be absorbed in part and 
scattered in part in the optical region of the spectrum, should 
not similar phenomena also occur in X-ray scattering? The 
type of scattering discovered by Prof. Compton may possibly 
be only one of numerous other types of scattering with modi- 
fied frequencies, some with a line spectrum and some in the 
nature of continuous radiation. The extreme ultra-violet 
region of the spectrum may also furnish us with numerous 
examples of the new type of radiation, which clearly occupies 
a position intermediate between scattering and fiourescence. 

9. Conclusion, 

We are obviously only at the fringe of a fascinating new 
region of experimental research which promises to throw light 
on diverse problems relating to radiation and wave-theory, 
X-ray optics, atomic and molecular spectra, fiourescence and 
scattering, thermodynamics and chemistry. It all remains to 

be worked out. 

I have to add in conclusion that I owe much to the 
valuable co-operation in this research of Mr. K. 8. Krishnan, 
and the assistance of Mr. S. Venkateswaran and other workers 
in xny laboratory* 

The line spectrum of the new radiation was first seen on 
the 28th February, 1928. The observation was given publicity 
the following day. 

(Issued separately, 31st March, 1928). 




By C. V, Raman 


N. S. Nagendra Nath. 

{Prom the Department of Physics, Indian Institute of Science, Bangalore.) 
Received September 28, 1935. 

7. Introduction. 
As is well known, Langevin showed that high frequency sound-waves of 
great intensity can be generated in fluids by the use of piezo-electric oscil- 
lators of quartz. Recently, Debye and Sears 1 in America and Lucas and 
Biqnard* in France have described very beautiful experiments illustrating 
the diffraction of light by such high-frequency sound-waves in a liquid. 
Amongst the experimenters in this new field, may be specially mentioned 
R, Bar 3 of Ziirich who has carried out a thorough investigation and has pub- 
lished some beautiful photographs of the effect. The arrangement may be 
described briefly as follows. A plane beam of monochromatic light emerging 
from a distant slit and a collimating lens is incident normally on a cell of 
rectangular cross-section and after passing through the medium emerges 
from the oppsite side. Under these conditions, the incident beam will be 
undeviated if the medium be homogeneous and isotropic. If, however, the 
medium be traversed by high-frequency sound-waves generated by intro- 
ducing a quartz oscillator at the top of the cell, the medium becomes stratified 
into parallel layers of varying refractive index. Considering the case in which 
the incident beam is parallel to the plane of the sound-waves, the emerging 
light from the medium will now consist of various beams travelling in 
different directions. If the inclination of a beam with the incident light be 
denoted by 6, it has been found experimentally that the formula 

sin 6 = ± -r~, n (an integer} > t\\ 

is in satisfactory agreement with the observed results, where A and A* are 
the wave-lengths of the incident light and the sound wave in the medium 

1 P. Debye and F. W. Sears, Proc. Nat. Acad. Sci. (Washington), 1932, 18, 409. 

2 R. Lucas and P. Biquard, Jour, de Phys. et Rod., 1932, 3, 464. 
* R. Bar, Helv. Phys. Acta, 1933, 6, 570. 


Printed by permission from Proc. Indian Acad. Sci., 1935, A2, 406-420. 


Diffraction of Light by High Frequency Sound Waves— I 407 

respectively. With sound waves of sufficient intensity, numerous orders 
of these diffraction spectra have been obtained ; a wandering of the intensity 
amongst these orders has also been noticed by Bar 8 when the experimental 
conditions are varied. 

Various theories of the phenomena have been put forward by Debye 
and Sears, 1 by Brillouin,* and by Lucas and Biquard." The former have 
not presented quantitative results and it is hard to understand from their 
theory as to why there should be so many orders and why the intensity should 
wander between the various orders under varying experimental conditions. 
In Brillouin's theory, the phenomenon is attributed to the reflection of light 
from striations of the medium caused by the sound waves. We know, how- 
ever, from the work of Rayleigh that the reflection of light by a medium of 
varying refractive index is negligible if the variation is gradual compared 
with the wave-length of light. Under extreme conditions, we might perhaps 
obtain the Brillouin phenomenon, but the components of reflection should 
be very weak in intensity compared to the transmitted ones. As one can 
see later on in this paper, the whole phenomenon including the positions of the 
diffracted beams and their intensities can be explained by a simple considera- 
tion of the transmission of the light beam in the medium. Lucas and Biquard 
attribute the phenomenon to an effect of mirage of light waves in the medium. 
In what way the relation (1) enters in their theory is not clear. The wander- 
ing of the intensities of the various components observed by Bar has not 
found explanation in any of the above theories. 

We propose in this paper a theory of the phenomenon on the simple 
consideration of the regular transmission of light in the medium and the phase 
changes accompanying it. The treatment is limited to the case of normal 
incidence. The formula (1) has been established in our theory. Also, a 
formula for the intensities of the various components has teen derived. It 
is found that the above results are in conformity with the experimental 
results of Bar.* 

2. Diffraction of light from a corrugated wave-front. 
The following theory bears a very close analogy to the theory of the 
diffraction of a plane wave (optical or acoustical) incident normally on a 
periodically corrugated surface, developed by the late Lord Rayleigh. 6 He 
showed therein that a diffraction phenomenon would ensue in which the 
positions of the various components are given by a formula similar to (1) 

< L. Brillouin, "La Diffraction de la Lumiere par des Ultra-sons", Act. Sci. et Ind., 1933, 


6 Lord Rayleigh, Theory of Sound (Vol. 2), page 89, 



C. V. Raman and N. S. Nagendra Nath 

and their relative intensities are given by a formula similar to the one we 

have found. 

Consider a beam of light with a plane wave-front emerging from a 
rectangular slit and falling normally on a plane face of a medium with a 
rectangular cross-section and emerging from the opposite face parallel to the 
former. If the medium has the same refractive index at all its points, the 
incident beam will emerge from the opposite face with its direction unchanged. 
Suppose we now create layers of varying refractive index in the medium, 
say by suitably placing a quartz oscillator in the fluid. If the distance between 
the two faces be small, the incident light could be regarded as arriving at the 
opposite face with variations in the phase at its different parts corresponding 
to the refractive index at different parts of the medium. The change in 
the phase of the emerging light at any of its parts could be simply calculated 
from the optical lengths found by multiplying the distance between the faces 
and the refractive index of the medium in that region. This step is justified 
for Jn(x, y, z)ds taken over the actual path is minimum, i.e., it differs from 
the one taken over a slightly varied hypothetical path by a differential 
of the second order. So, the incident wave-front becomes a periodic 
corrugated wave-front when it traverses a medium which has a periodic 
variation in its refractive index. The origin of the axes of reference is chosen 
at the centre of the incident beam projected on the emerging face, the 
boundaries of the incident beam being assumed to be parallel to the boundaries 
of the face. The X-axis is perpendicular to the sound-waves and the Z-axis 
is along the direction of the incident beam of light. If the incident wave is 
given by 

it will be 



AgSfriv {( - Lp{x)jc} 

when it arrives at the other face where I, is the distance between the two 
faces and ^{x) the refractive index of the medium at a height x from the 
origin. It is assumed that the radii of curvature of the corrugated wave- 
front are large compared with the distance between the two faces of the cell. 
If ^ be the refractive index of the whole medium in its undisturbed state, 
we can write /x{x) as given by the equation 


/*(*)— /*o-/* sm 


ignoring its time variation, p being the maximum variation of the refractive 
index from p . 

The amplitude due to the corrugated wave at a point on a distant screen 
parallel to the face of the medium from which light is emerging whose join 


Difjraction of Light by High Frequency Sound Waves-~1 409 

with the origin has its ^-direction-cosine I, depends on the evaluation of the 
diffraction integral 

f £iti{lx f fit, sin (2wx/A*)}/A fa 


where p is the length of. the beam along the X-axis. The real and the 
imaginary parts of the integral are 
j {cos ulx cos [v sin bx) — sin ulx sin (v sin bx)}dx 


/'" • • 

/ {sin ulx cos (v sin bx) + cos ulx sin (u sin bx)}dx 


where « — 2tt/A, 6 = 2tr/A* and v = w/*L = 2?r/xL/A. 

We need the well-known expansions 

cos (t> sin &t) = 227' J, r cos 2r&# 


sin (<y sin bx) = 2U ] ir+ i sin 2r + lta 

to evaluate the integrals, where J„[ — ]„{v)] is the Bessel function of 
the ttth order and a dash over the summation sign indicates that the co- 
efficient of Jo is half that of the others. The real part of the integral is then 

- ?' - r k — 

2£" Jtr I c °s ulx cos 2rbx dx— 227 J 2r+1 / sin ulx sin 2r + 1 bx dx 
-'A ° -*/. 



2' Jtr [{cos {ul+%rb)x + cos {ul - 2rb)x}dx 


+ ^ hr+i / (cos {ul + 2r + 1 b)x - cos (i#J- 2r+ 1 &)*}<** 

Integrating the above, we obtain 

« f sin ( w f+2ri)fl2 , sin (ul-Zrb)p\<l \ 
P c jtr { {ul+2rb)pl2 (ul-2rb)pj2 j 

« f sin (ul + WTlb)pl2 sin (ul-2T+l b)p j2 \ 
+ '{H («Z + 2r+l6)/»/2 (W-2r+l4)^/2 j '" v ' 

The integral corresponding to the imaginary part of the diffraction integral 


410 C. V. Raman and N. S. Nagendra Nath 

is zero. One can see that the magnitude of each individual term of (2) 
attains its highest maximum (the other maxima being negligibly small 
compared to the highest) when its denominator vanishes. Also, it can be 
seen that when any one of the terms is maximum, all the others have 
negligible values as the numerator of each cannot exceed unity and the 
denominator is some integral non- vanishing multiple of b which is sufficiently 
large. So the maxima of the magnitude of (2) correspond to the maxima 
of the magnitudes of the individual terms. Hence the maxima occur when 
ul±nb=0 «(an integer) >0 .. . . , , . . (3) 

where « is any even or odd positive integer. The equation (3) gives the 
directions in which the magnitude of the amplitude is maximum which 
correspond also to the maximum of the intensity. If 6 denotes the 
angle between such a direction in the XZ-plane along which the intensity 
is maximum and the direction of the incident light, (3) can be written as 

sin 6 = ± -^- .. .. -. .. .. (4) 

remembering that « = 2ir/A and b = 2-ir/A*. This formula is identical with 

the formula (1) given in the first section. The magnitudes of the various 
components in the directions given by (4) can be calculated if we know, 

J„ or J„(v) or J„(2^L/A). 
Thus the relative intensity of the ?nth component to the «th component is 
given by 

J'y'fo t where v = 2ttuI,/A. 
J« 2 (v) r ■ 

In the undisturbed state of the medium there is no variation of the refractive 
index, i.e., fi = 0. In this case all the components vanish except the zero 
component for 

J„(0) = for all m^O and J {0) - 1. 
In the disturbed state, the relative intensities depend on the quantity v or 
2-TTfj.hfX where A is the wave-length of the incident light, fj. is the maximum 
variation of the refractive index and L is the path traversed by light in 
the medium. We have calculated the relative intensities of the various 
components which are observable for value? of v lying between and 8 
at different steps (Fig. 1).' 

Fig. 1 shows that the number of observable components increases as 
the value of v increases. When v = 0, we have only the central component. 
As v increases from 0, the first orders begin to appear. As v increases still 
more, the intensity of the central component decreases steadily and the first 
orders increase steadily in their intensity till they attain maximum intensity 
when the zero order will nearly vanish and the second orders will have just 
appeared, As v increases still more, the zero order is reborn and increases 


Diffraction of Light by High Frequency Sound Waves — / 41 1 




i i 




, I 



(/) -to 



. . I ll 


, ! 

I I I 1 I 


l I I J l 

(.6)-* -7 

I , 

. I 


(p) -3-7 





II , , I I 


Fig. I. 

Relative intensities of the various components in the diffraction spectra. 
(For tables, sse Watson's Btsstl Functions and Report of the British Association^ 1915.) 

in its intensity, the first orders fall in their intensity giving up their former 
exalted places to the second orders, while the third orders will have just 
appeared and so on. 

Our theory shows that the intensity relations of the various components 
depend on the quantity v or 2?t/aL/A. Thus an increase of p. {i.e., an increase 
of the supersonic intensity which creates a- greater variation in the refractive 
index of the medium) or an increase of L, or a decrease of A should give similar 
effects except in the last case where the directions oi the various beams will 
be altered in accordance with (4). 

3. Interpretation of Bar's Experimental Results. 

(a) Dependence of the effect on the supersonic intensity . — Bar has observed 
that only the zero order (strong) and the first orders (faint) are present when 
the supersonic intensity is not too great. He found that more orders 
appear as the supersonic intensity is increased but that the intensity 
of the zero order decreases while the first orders gain in their intensity. 
Increasing the supersonic intensity more, he found that the first order would 
become very faint while the second and third orders will have about the 
same intensity. The figures la of his paper may very well be compared 



C. V. Raman and N. S. Nagendra Nath 

with our figures 1(c), 1(h) and l(A'). Thus, we are able to explain the appear- 
ance of more and more components and the wandering of the intensity amongst 
them as the supersonic intensity is increased, in a satisfactory manner. 

[b] Dependence of the effect on the wave-length of the incident light. — We 
have already pointed out that the effects due to an increase of /x caused by 
an increase of supersonic intensity are similar due to those with a decrease 
of A except for the fact that the positions of the components of the emerg- 
ing light alter in accordance with (4). Bar has obtained two patterns of 
the phenomenon by using light with wave-lengths 4750a and 3650a. He 
obtained, using the former seven components and using the latter eleven 
components in all. He also observed great variations in the intensities of the 
components. Not only is the increase in the number of components an 
immediate consequence of our theory, but we can also find the pattern with 
3650a if we assume the pattern with 4750a.. The pattern with the latter 
in Bar's paper shows a strong resemblance to our figure \{p) for which 2tt,uL/A 
is 3-7. Thus we can calculate 2t7^I v /A when A is 3650a. It comes to 
about 4-8. Actuallv our figure for which 2v^I,jX is 4 -8 closely corresponds 
to Bar's pattern with 3650a. 

(c) Dependence of the effect on the length of the medium which the light 

traverses. — It is clear from our theory that an increase of I v corresponds to 

an increase of v and that the effects due to this variation would be similar to 

those with an increase of the supersonic intensity. But the basis of our 

theory does not actually cover any large change in L. However, we should 

find more components and the wandering of the intensity amongst the various 


4. Summary. 

(a) A theory of the phenomenon of the diffraction of light by sound- 
waves of high frequency in a medium, discovered by Debye and Sears and 
Lucas and Biquard, is developed. 

(6) The formula 

sin 9 = ± -p- « (an integer) > 

which gives the directions of the diffracted beams from the direction of the 
incident beam and where A and A* are the wave-lengths of the incident light 
and the sound wave in the medium, is established. It has been found that 
the relative intensity of the mth component to the «th component is given bv 

J^(2^L/A) / JJ{ZvM\) 
where the functions are the Bessel functions of the mth order and the nth. 
order, ft is the maximum variation of the refractive index and L is the 
path traversed by light. These theoretical results interpret the experimental 
results of Bar in a very gratifying manner. 



By C. V. Raman 


N. S. Nagen'dra Nath. 

(From the Department of Physics, Indian Institute of Science, Bangalore,) 

Received October 4, 1935, 

/. Introduction. 
In the first 1 of this series of papers, we were concerned with the explanation 
of the diffraction effects observed when a beam of light traverses a medium 
filled by sound waves of high frequency. For simplicity, we confined our 
attention to the case in which a plane beam of light is normally incident 
on a cell of the medium with rectangular cross-section and travels in a direc- 
tion strictly perpendicular to the direction along which the sound waves are 
propagated in the medium. By taking into account the corrugated form of 
the wave-front on emergence from the cell, the resulting diffraction-effects 
were evaluated, This treatment will be extended in the present paper to 
the case in which the light waves travel in a direction inclined at a definite 
angle to the direction of the propagation of the sound waves. The exten- 
sion is simple, but it succeeds in a remarkable way in explaining the very 
striking observations of Debye and Sears 2 who found a characteristic varia- 
tion of the intensity of the higher orders of the diffraction spectrum when 
the angle between the incident beam of light and the plane of the sound 
waves was gradually altered. 

We shall first set out a simple geometrical argument by which the changes 
in the diffraction phenomenon which occur with increasing obliquity can 
be inferred from theTesults already given for the case of the normal incidence. 
An analytical treatment then follows which confirms the results obtained 


2. Elementary Geometrical Treatment. 

The following diagrams illustrate the manner in which the amplitude of 
the corrugation in the emerging wave-front alters as the incidence of light 
on the planes of the sound waves is gradually changed. In the diagrams, 

i C. V. Raman and N. S. Nagendra Nath, Proc. Ind. Acad. Sci., 1935, 2, 406—412. 
2 p. Debye and F. W. Sears, Proc. Nat. Acad. Sci (Washington), 1932, 18, 409. 




C. V. Raman and N. S. Nagendra Nath 

the planes of maximum and minimum density caused by the sound waves 
at any instant of time are indicated by thick and thin lines {e.g., AB and CD) 
respectively. The paths of the light rays are represented by dotted lines in 
Figs. 1 [b), £c) and (d). As we are mainly interested in the calculation of the 
phase-changes which the incident wave undergoes before it emerges from 
the cell, the bending of the light rays within the medium may, in virtue of 
Fermat's well-known principle, be ignored without a sensible error, provided 
the total depth of the cell is not excessive. 



FIG. 1. 

Considering the variation in the refractive index to be simply periodic, 
the neighbouring light-paths with maximum and minimum optical lengths 
AB and CI) respectively, in the case of normal incidence, are shown in Fig. 1(a). 
The lines AB and CD are separated by A*/2 where A* is the wave-length of 
the sound waves. The difference between the maximum and the minimum 
optical lengths gives a measure of the corrugation of the wave-front on 
emergence. Considering now a case in which the light rays make an angle <j> 
with the planes of the sound waves, we may denote the maximum and 
the minimum optical lengths by A'B' and CD' respectively. These would 
be symmetrically situated with respect to AB and CD, and would tend to 
coincide with them as «£ is decreased. The optical length of A'B' is less than 
that of AB, for the refractive index at any point except at is less than 
the constant maximum refractive index along AB, <£ being small. On the 
other hand, the optical length of CD' is greater than that of CD, for the 
refractive index is minimum along CD. A simple consideration of the 
above shows that the difference between the optical lengths of A'B' and 
C'D r Is less than that between those of AB and CD. As this difference 
gives twice the amplitude of the corrugation of the emerging wave-front, 
it follows, in the case shown in Fig. 1 (4>), that the amplitude of the 


Diffraction of Light by Sound Waves of High Frequency — // 415 

corrugation of the emerging wave-front is less than that in the case 

of Fig. 1 (a). 

Fig. 1 (c) illustrates a case when the maximum optical length is just 

equal to the minimum optical length. This occurs when the direction of 

the incident beam is inclined to the planes of the sound-wave-fronts at an 

R'B A*'2 

angle a, given by tan^ 1 ^rg- = tan" 1 — - = tan -1 (A*/L). That the optical 

lengths of A'B' and CD' in Fig. 1 (c) are equal follows by a very simple 
geometrical consideration. Thus, when light rays are incident on the sound 
waves at an angle tan -1 (A*/L), the amplitude of the corrugation of the 
emerging wave-front vanishes i.e., a plane incident beam of light remains 
so when it emerges from the medium. This result would also be true when- 
ever a„ = tan -1 («A*/L) t « =fc 0. The case when » = 2 is illustrated in Fig. 
1 (d). In all these cases the diffraction effects disappear. As the corrugation 
vanishes when <f> is o w+1 or a„, there is an intermediate direction which makes 
an angle jS w with the sound waves giving the maximum corrugation if light 
travels along that direction. We can take /3 (=0) to represent the case 
when the incident beam of light is parallel to the sound waves. 

Thus, we have deduced that the corrugation of the emerging ■ wave- 
front is maximum when the direction of light is parallel to the sound waves 
[fi 9 {= 0)], decreases steadily to zero as the inclination «£ between the incident 
light and the sound waves is increased to a 1( increases to a smaller maximum 
as j> increases from a x to j6 l( decreases to zero as ^ increases from fi x to a-, 
increases to a still smaller maximum as <f> increases from c^ to j8 2 , and so 
on. (I) 

As the variation of the refractive index is simply periodic along the 
direction normal to the sound-wave-fronts, it follows that the optical length 
of the light path is also simply periodic along the same direction when 
the incident light rays are parallel to the sound waves. This means that 
the corrugation of the emerging wave-front is also simply periodic. When 
the incident light rays ar£ incident at an angle «£ to the sound waves the 
optical length of the light path would be simply periodic in a direction 
perpendicular to the light rays. This means that the emerging wave-front 
would be tilted by the angle $ about the line of the propagation of the 
sound waves and that its corrugation would be simply periodic along the 
same line. 

We have shown in our previous paper that a simply periodic corrugated 
wave is equivalent to a number of waves travelling in directions which 
make angles, denoted by 6, with the direction of the incident beam given 


416 C. V. Raman and N. S. Nagendra Nath 

sin d = ± y- n (an integer) > ■ . . (1) 

where A is the wave-length of the incident light. In view of the Tesults 

obtained in the previous paragraph, the formula (1) would also hold good 
when the incident light is a small angle with the sound waves. 

The relative intensities of the various diffraction spectra which depend 
on the amplitude of the corrugation should obey a law similar to the one 
in the case of the normal incidence. 

Thus, we find that the results in the case of an oblique incidence would 
be similar to those oi the normal incidence with the amplitude of the corruga- 
tion modified. Hence, we deduce, in virtue of the statement I, the following 
results, assuming the results, in the case of normal incidence, obtained in 
our earlier paper. 

The diffraction spectrum will be most prominent when <f> = 0. The 
intensity of the various components wander when <f> is increased. When $ 
increases from zero to a lf the number of the observable orders in practice 
decreases and when <f> = a? all the components disappear except the central 
one which will attain maximum intensity. This does not mean that the 
intensities of ail the orders except the central one decrease to zero mono- 
tonically as <fi varies from zero to a u but some of them may attain maxima 
and minima in their intensities before they attain the zero intensity when 
<£ = <x t . This is obvious in virtue of the property that the intensity of the 
nth component depends on the square of the Bessel function ]„. As $ 
increases from a x to 0, the intensity of the central component falls and 
the other orders are reborn one by one. As j> increases from jS 1 to a?, the 
number of observable orders decreases and when j> = a a all the orders vanish 
except the central one which will attain the maximum intensity and so on. 

3, Analytical Treatment. 

In the following, we employ the same notation as in our earlier paper. 
The optical length of a path in the medium parallel to the direction of the 
incident light making an angle <$> with the sound waves may be easily calcu- 
lated. It is 

L sec <f> 


L sec <p 

/AqI, sec ^ — ^ / sin b{x — s sin <f>)ds. 

Diffraction of Light by Sound Waves of High Frequency— II A\7 
Integrating we obtain the integral as 

f^I, sec ^ — f^-J ( sin ( &L tan & sin 6* 4- [cos (61, tan <f>) - 1] cos bx). 

The last term can be written as 

— A sin bx -f B cos bx 

A = (* sin (6L tan <£) 
A Bin ^ v r ' 

B = - . ^ , [cos (&L tan i) -II 
b sin <p L r J 

Thus the optical length of the path can be written as 

MoL sec <f> - V(A* +B 2 ) sin bfx- tan" 1 ^\ 

Ignoring the constant phase factor, the optical length is 
t i 2u . (bh tan 6\ . , 

* L sec * " riiir? sm (, "2 ) sin **■ 

If the incident light is 

when it arrives at the face of the cell, it will be 

r 9 • / l sec <^ 

exp [-=%-(* - ffBin<£ - >(*)<**) : 

when it arrives at the face from which it emerges. 

The amplitude of the corrugated wave at a point on the screen whose 
join with the origin has its %-direction-cosine /, depends on the evaluation 
of the diffraction integral 

A [x>-- * + ^ « (^) - M] *• 

The evaluation of the integral and the discussion of its behaviour with respect 
to I may be effected in the same way as in our earlier paper. Maxima 
of the intensity due to the corrugated wave occur in directions making 
angles, denoted by 6, with the direction of the incident beam when 

sin (6 -f <f>) — sin tf> = ± -^ n (an integer) > • - (1) 

The relative intensity of the mth order to the wth order is given by 

JAv) ■■ ■' ■■ '• •■ ( 2 ) 


418 C« V. Raman and N* S. Nagendra Nath 


2tt 2u . / bL tan 4> 

v — — r- * -i— ■ — r sin ' 

/ bL tan tp \ 
TiinT 5m V 2 J 

27taL . sin * , t bL t an ^ 7r . Ij . ta .°. *ft_ 

T" sec * ~T~ w = a A* '• 

The expression for the relative intensities in our earlier paper, can be 

obtained from (2) by making <f> -> when v -> -^- = »,. So the 

expression for the relative intensities 

vw/ww •• -■ •• •• (3) 

in the case of normal incidence will change to 


v — v sec $ — - — . • ■ • • • - ■ (**) 

■nh tan <f> 

t - ■ ^ : 

Even if <£ be small so that sin <f> ^ tan 4> & <f>. it is not justifiable to write 
sin i**t unless nLf.'A* is also small to admit the approximation. As 
wL/A* is sufficiently large we should expect great changes in the diffraction 
phenomenon even if <f> be a fraction of a degree, v vanishes when 

t = mr n (an integer) > 0, 
that is, when L tan <j> — «A*, 


<f> =■■ tan" 1 -=- , n (an integer) > 0, 

confirming the same result obtained geometrically. Whenever v vanishes, 
it can be seen that, the amplitude of the corrugation of the wave-front also 
vanishes. The statement I in Section 2 and the consequences with regard 
to the behaviour of the intensity ' among the various orders can all be 
confirmed by the expression (3). 

In the numerical case when L = 1 cm., and A* = -01 era., the amplitude 
of the corrugation vanishes tan a y =0-01 or a x = 0° 34', This means that 
as <A varies from 0° to 0° 34', the relative intensities of -the various orders 
wander according to (2) till when </> = 0° 34', all the orders disappear except 
the central one which attains maximum intensity. This does not mean 
that the intensities of all the orders except the central one decrease mono- 
tonically to zero but they may possess several maxima and minima before 
they become zero. The intensity of the nth order depends on the behaviour 


Diffraction of Light by Sound Waves of High Frequency II 419 

^ t s I"., «« j. sin (wL tan i/A*) 1 , ,, 

or J„ I t' sec «£ 6 1^*) unrter t " e above numerical conditions 

as <£ varies from 0° to 0° 34'. As <f> just exceeds 0° 34', all the orders are 
reborn one by one till a definite value of <j> after which they again fall one 
by one and when <j> = ] ° 8', all the-orders disappear except the central one. 

The numerical example in the above paragraph shows the delicacy of the 
diffraction phenomenon. If the wave-length is quite small, the diffraction 
phenomenon will be present in the case of the strictly normal incidence 
as the relative intensity expression (3) does not depend on A* but will soon 
considerably change even for slight variations of <f> as the relative intensity 
expression (4) depends on A*. One should be very careful in carrying out 
the intensity measurements in the case of normal incidence, for even an error 
of a few minutes of arc in the incidence will affect the intensities of the 
various orders. 

4. Comparison with the experimental results of Debye and Sears. 
Deb} T e and Sears make the following statement in their paper : "Fixing 
the attention on one of the spectra preferably of higher order, one can observe 
that it attains its maximum intensity if the trough is turned through a 
small angle such that the primary rays are no longer parallel to the planes 
of the supersonic waves. Different settings are required to obtain highest 
intensities in different orders. If the trough is turned continuously in one 
direction, starting from a position which gave the highest intensity to one 
of the orders, the intensity decreases steadily, goes through zero, increases 
to a value much smaller than the first maximum, decreases to zero a second 
time and goes up and down again through a still smaller maximum." This 
statement very aptly describes the behaviour of the function 

ein {-ah tan ^,'A*) 

V [vo 

sec «£ 

(ttL tan $,A*) 

as <f> alters under the conditions imposed in the above statement. The 
zeroes and the maxima of the intensity of the «th order, as a function of A, 
correspond to the zeroes and the maxima of the above function. 

5. Summary, 
The theory of the diffraction of light by sound waves of high frequency 
developed in our earlier paper is extended to the case when the light beam 
is incident at an angle to the sound wave-fronts, both from a geometrical 
point of view and an analytical one. It is found that the maxima of 
intensity of the diffracted light occur in directions which make definite angles, 
denoted "by 6, with the direction of the incident light given by 

sin (0+4) — s'm <ft = ± -j*-, » (an integer) ^ 



C. V. Raman and N. S. Nagendra Nath 

where A and A* are the wave-lengths of the incident light and the sound 
waves in the medium. The relative intensity of the .mth order to the nth order 
is given by 

W (i^s^iifL) /!„•(*. sec *i£i) 

, , 2miL , ttL tan d> , 
where v =* — ^— , t — ^ — z -, 

is the inclination of the incident 

beam of light to the sound waves, p is the maximum variation of the 
refractive index in the medium when the sound waves are present and 
L sec <f> is the distance of the light path in the medium. These results 
explain the variations of the intensity among the various orders noticed 
by Debye and Sears for variations of ^ in a very gratifying manner, 

Published by P. R. Mahapatra; Executive Editor, Journal of the Indian Institute of Science, Bangalore 560 012. 
Typeset and printed at Phoenix Printing Company Pvt Ltd, Attibele Indl Area. Bangalore 562 107. 

Some important dates in the life of C. V. Raman 

November 7, 1888 






July 1917 

November 1919 



Feb. 28, 1928 

March 16, 1928 



March 31, 1933 






July 1948 

November 21, 1970 

- Born at Thiruvanaikkaval near Tiruchirapalli 

- Earlv education a: Vishakhapatnam 

- Matriculation Lsam 

- F.A. Exam 

Joins Presidency College, Madras 

- B.A.. 1st Rank. Gold Medal 

- First paper published in Phil. Mag., London 

- M.A.; Financial Civil Service Exam, 1st Rank 

- Marriage to Loka Sundari 

- Posted as Assistant Accountant-General, Indian Finance Deptt, Calcutta 

- Starts working at the Indian Association for the Cultivation of Science (IACS}, 

- Officer, Finance Deptt, at Calcutta, Rangoon, Nagpur. Calcutta 

- Palit Professor of Physics, Calcutta University 

- Secretary, 1ACS 

- First visit to England 

- Elected Fellow, Royal Society, London 

- Discovery of Raman Effect at Calcutta 

- First public lecture on the Raman Effect before the South Indian Science Associa- 
tion at the Central College, Bangalore 

- Knighthood of the British Government 

- Nobel Prize for Physics 

- Hughes Medal of the Royal Society 

- Director, Indian Institute of Science, Bangalore 

- Indian Academy of Sciences established 

- Raman -Nath Theory: Diffraction of light by ultrasonic waves 

- Resigns the Directorship of USc, continues as Professor 8t Head, Deptt of Physics 

- Raman- Nedungadi discovery of the soft mode 

- Franklin Medal 

- Retires from IISc, Raman Research Institute established; appointed National 

- Bharat Ratna 

- International Lenin Prize of the Soviet Union 

- Member, Pontifical Academy of Sciences, The Vatican 

- Passes away at Bangalore 




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