USE OF THE DIFFERENTIAL REFLECTOMETER IN THE STUDY
OF THIN FILM CORROSION PRODUCTS ON COPPER

By
CHARLES WILLIAM SHANLEY

A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF

THE UNIVERSITY OF FLORIDA

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS OF THE

DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA
1977

ACKNOWLEDGEMENTS

The author wishes to express his sincere appreciation
to his advisor, Dr. Rolf E. Hummel, for his guidance and
confidence throughout this work. Special thanks are
extended to Dr. J. B. Andrews for his help in the design
and construction of much of the apparatus used in this
work, and to Dr. R. J. Nastasi -Andrews for numerous
stimulating discussions.

Special thanks are also extended to
Dr. E. D. Verink, Jr., for his advice concerning the
electrochemical aspects of this research, and to
Drs. J. J. Hren, R. Pepinsky, D. B. Dove, and
E. D. Verink, Jr., for serving on the author's supervisory-
committee .

The author wishes to express his appreciation to
Dr. B. Cavin, who performed the X-ray analyses mentioned in
this work, and to Mr. Patrick Russell, who performed the
ellipsometric measurement.

The National Science Foundation provided financial
support for this research, which is gratefully acknowledged.

TABLE OF CONTENTS

Page

ACKNOWLEDGEMENTS i i

LIST OF TABLES v

LIST OF FIGURES vi

ABSTRACT x

SECTION

I INTRODUCTION 1

II LITERATURE REVIEW 11

Introduction 11

Related Techniques 12

Cuprous Oxide 28

Band Structure Calculations 28

Optical Spectroscopy 31

Growth and Kinetics 37

Summary 41

III EXPERIMENTAL PROCEDURE 46

Introduction 46

Sample Preparation 47

Metallographic Preparation 47

Special Procedures for In Situ Samples. 50

Electrolyte Solutions 54

The Differential Reflectometer 54

Introduction 54

The Instrument 56

Advantages and Disadvantages 59

Other Equipment 62

Operating Conditions 66

Other Considerations 67

Summary 70

TABLE OF CONTENTS - continued.

SECTION

Page

IV RESULTS AND DISCUSSION 72

Introduction 72

Theory of Differential Ref lectograms

of Thin Films 74

Non-7n Situ Experiments 95

In Situ Experiments 10 7

Further Discussion 116

V CONCLUSIONS AND SUGGESTIONS FOR

FURTHER WORK 124

REFERENCES 127

BIOGRAPHICAL SKETCH 131

LIST OF TABLES

Table Page

1 Comparison of Peak Positions for

Absorption and Reflection Spectra 32

2 Major Peak Positions in C112O Optical
Spectra Compared to Transitions

Calculated from the Band Diagram 45

3 Composition of Electrolyte Used in

Nil Chloride Experiments 55

4 Optical Constants ft = n+ik for Copper
and Cupric Oxide (CuO) as a Function

of Wavelength 83

5 Major Structure in CU2O Spectra Obtained
from Other Techniques Compared to
Differential Ref lectometry 120

LIST OF FIGURES
Figure Page

1 Typical experimental arrangement for
ellipse-metric measurements. The angle

<{> is the angle of incidence 13

2 Schematic diagram of a modulated
ellipsometer developed by Jasperson

et al. 14 The detector (DET) sends the

modulated signal to two lock- in amplifiers

tuned to 100 KHz and 50 KHz and to a low

pass filter. The data is reduced by the

computer, C, and displayed on a digital

meter, DV. Q' or A' is an additional

polarizer used to calibrate the instrument... 17

3 Electrochemical modulation apparatus used
by Mclntyre.22. The HIS 60 70 is a

computer used to reduce the data 22

4 Schematic diagram of a rapid scanning
spectrophotometer used by Mclntyre

et al . See text for details 25

5 Band structure diagram for cuprous oxide

(Cu20) calculated by Dahl and Switendick 30

6 Reflectivity spectrum of polished and

polished and etched Cu?0 crystals 33

7 Electroref lectance spectrum of single
crystals of CU2O for various AC voltages
superimposed on a 1 KV DC bias 36

8 Electroref lectance spectrum of CU2O at
85 K and no DC bias. The modulating

electric field was 60 KV/cm 38

9 Schematic diagram of the differential

ref lectometer 57

10 Schematic diagram of the standard

corrosion cell used for non-in situ

experiments 63

LIST OF FIGURES - continued.

Figure

11

12

Schematic diagram of the corrosion
cell used for in situ experiments.
Details of the sample holder are not
shown for clarity

Theoretical (Figure 12A) and experimental
(Figure 12B) Pourbaix diagrams for copper
in nil chloride solutions

65

73

15

14

15

Differential reflectogram of a sample
prepared in the CU2O region of the
Pourbaix diagram (-225 mv SCE, pH 9.2,
66 hours)

Differential reflectogram of a sample
prepared in the CuO region of the
Pourbaix diagram (+200 mv SCE, pH 9.2,
18 hours)

Typical compositional modulation
differential reflectogram. One sample
is pure copper, the other copper with
1 at . % aluminum in solid solution

75

76

77

16

17

19

Schematic representation of a typical

sample with an oxide film covering half

the exposed surface 79

Variation in AR/R as a function of film

thickness for a CuO film on a copper

substrate. The wavelength of light

used is assumed to be 600 nm 82

Theoretically constructed differential
reflectogram of a CuO film 100 A thick
on a copper substrate. A = 600 nm 85

Theoretically constructed differential

reflectogram of a CuO film 35 A thick

on a copper substrate. X = 600 nm 87

LIST OF FIGURES - continued

Figure Page

20 Theoretically constructed differential
reflectogram of a CuO film 500 A thick
on a copper substrate. A = 600 nm 88

21 Theoretically constructed differential
reflectogram of a CuO film 7500 A
thick on a copper substrate. X = 600 nm.

22 Variation in AR/R as a function of film
thickness for a CuO film on a copper o
substrate over the range d = 0 to 200 A.
The wavelength of light is assumed to be

600 nm 91

23 Comparison of the differential reflectogram
of an experimentally prepared CuO film
(potentiostated at +500 mv SCE at pH 9.2
for 18 hours) to a theoretically
constructed reflectogram of a CuO film

25 A thick 93

24 Differential reflectogram of a sample
prepared by immersion in distilled water
for eighteen hours, with a continuous
stream of oxygen bubbled through the
water. The structure is characteristic

of a mixed oxide of CU2O and CuO 100

25 Differential ref lectograms of three areas
of the same sample, which had been
potentiostated near the CU2O/C11O equilibrium
line (-50 mv SCE at pH 9.2) for eighteen

hours 102

26 Differential reflectogram of a sample
potentiostated in the CuO region (A) of
the Pourbaix diagram, and of the same
sample after the potential has been changed
to the CU2O region (B) . Curve C is the
same sample potentiostated for a longer
period of time in the CU2O region. The
baselines of the curves have been shifted

for clarity 105

LIST OF FIGURES - continued.

Figure Page

27 Differential ref lectograms of two samples
potentios tated under the same conditions
(5.5 hours at -200 mv SCE, pH 9.2). The
first was run in the non-in situ cell and
measured in air, while the second was

prepared and run in situ 108

28 Differential ref lectograms of a sample
half covered with a Cu20 film, showing
the sample as measured in air (A) , in
the empty in situ cell (B) , and in the

in situ cell filled with electrolyte (C) Ill

29 In situ differential ref lectograms of a
copper sample potentiostated at -200 mv
SCE, pH 9.2, which is in the Cu20 region

of the Pourbaix diagram 113

30 Continuation of the in situ experiment
of Figure 29. Note the change in scale.
Since the curves do not change appreciably
during these times, the zero lines have

been shifted for clarity 114

Abstract of Dissertation Presented to

the Graduate Council of the University of Florida

in Partial Fulfillment of the Requirements for the

Degree of Doctor of Philosophy

USE OF THE DIFFERENTIAL REFLECTOMETER IN THE STUDY
OF THIN FILM CORROSION PRODUCTS ON COPPER

By

Charles William Shanley

December 1977

Chairman: R. E. Hummel

Major Department: Materials Science and Engineering

An investigation was undertaken to examine the

feasibility of using the technique of differential

ref lectometry to identify and study thin film corrosion

products on metal substrates. Differential ref lectometry

is a form of modulation spectroscopy which measures the

normalized difference in reflectivity between two samples,

or two adjacent areas of the same sample. In these

experiments, one half of each sample was protected by an

insulating lacquer while the other half was allowed to

form a thin film corrosion product. When the lacquer was

subsequently removed, the normalized difference in

reflectivity as a function of wavelength was measured over

the range A = 800 nm to 200 nm (1.55 eV to 6.20 eV) . The

use of a transparent lacquer permits monitoring of the
film in situ. Because of the differential nature of the
technique, the effect of the metal substrate is subtracted
out, so that the resulting differential reflectogram is
related to the absorption spectrum of the corrosion
product. The similarity in the structure between
reflection, absorption, and differential reflectivity
spectra substantiates this viewpoint.

In these experiments, copper was chosen as the
metal on which the thin film corrosion products were
grown. Characteristic spectra for the copper oxides Cu~0
and CuO were obtained, and were used to help define the
boundaries of the regions of stability of the copper-water
Pourbaix diagram. In addition, the evolution with time of
a Cu?0 film was monitored in situ.

It was established that in the thickness range of

o

passive and semipassive films (d = 0 to 200 A) dif-
ferential ref lectometry produces a unique spectrum for
each corrosion product, and that the intensity of the
structure in the differential reflectogram is related to
the thickness of the film. A method is described for
calculating the differential ref lectograms of thin film
corrosion products for various film thicknesses if the
optical constants of the film and substrate are known.

Sample spectra are calculated for various thicknesses of a
CuO film on a copper substrate. These spectra compare
favorably with experimental curves.

XII

SECTION I
INTRODUCTION

Although metallic corrosion is a familiar phenomenon,
many aspects of the process remain poorly understood. The
reason is not that there is some fundamental bit of in-
formation which is lacking; rather, it is that corrosion
itself is not a single process. Generally speaking, there
are eight basic forms of corrosion, any one or more of
which may be present at the same time. The effects may be
additive, as when pitting and uniform corrosion attack a
holding tank, or even synergistic, as when erosion corro-
sion and selective leaching attack a brass pipe. In addi-
tion, matters taken to eliminate one form of corrosion may
inadvertantly introduce new problems, as when the painting
of the inside of a tank with a protective coating to
eliminate uniform corrosion induces pitting in spots where
the coating is imperfect. Altogether, the cost of corro-
sion in the United States alone is estimated to be in

2
excess of eighty billion dollars annually.

In order to correct a corrosion problem, an engineer
must know what kind of corrosion process is present. Fre-
quently, the answer to this question is based on the

identification of the corrosion product. For bulk speci-
mens with massive corrosion, x-ray diffraction techniques,
perhaps supplemented by wet chemical analysis, are ordi-
narily sufficient. Many such bulk corrosion problems are
long familiar to the corrosion engineer and may be identi-
fied by inspection. For thin films the identification of
the corrosion products is considerably more difficult.

It is not uncommon for thin, semipassive layers of
corrosion products to form on metals such as aluminum,
copper, or silver. Such layers, whether they be oxides,
hydroxides, chlorides, or something more complex, are in
general insulating or at best semiconducting. Since the
aforementioned metals are extensively used by the elec-
tronics industry, these thin corrosion films, which form
insulating or rectifying contacts on electrical equipment,
are of great concern. As in the case of bulk corrosion,
the identification of the corrosion product is the first
step in solving the corrosion problem.

Unfortunately, such films are frequently difficult to
analyze. X-ray diffraction techniques, which probe as
much as a millimeter into the surface of a specimen, will
often not show up an oxide layer on the outer one hundred
thousandth millimeter of the surface. A more surface sen-
sitive, less penetrating form of spectroscopy is called for.

Electron spectroscopy techniques seem to provide the
answer. Auger Electron Spectroscopy (AES) and Electron
Spectroscopy for Chemical Analysis (ESCA) are the most
commonly used techniques. Both have certain advantages
over x-ray techniques for the study of thin films. Auger
analysis and ESCA penetrate only a few atomic distances

o

(typically around 25 A) into the sample. This makes them
well-suited for thin film analysis. Auger spectroscopy is
not particularly well-suited for the identification of
specific compounds, but ESCA, as its name implies, can
identify compounds as well as elements. If the AES or
ESCA apparatus is equipped with an ion milling device, the
evolution with depth of the thin film corrosion product
may be also studied. Both techniques are precise, well-
known, and the apparatus is readily available.

No technique is without its limitations, and AES and
ESCA are not exceptions to this rule. The equipment for
either is expensive and complex, and requires trained
operators. They are both destructive techniques, in that
an electron or ion beam abrades away the sample. They are
not particularly fast. However, their most fundamental
problem is that they require the sample to be placed in a
vacuum.

Removing a sample from its normal environment for
study is a common research technique, but it is never done

without a certain amount of misgivings. The boundary
conditions are changed, and the results may not be the
same as if the study were performed in situ. If a ti-
tanium or aluminum specimen with an oxide coating is
placed into a vacuum chamber, there will probably be no
change in the oxide layer. However, if a sample with a
fragile hydroxide layer or a complex compound containing
water of hydration is removed from an electrolyte and
exposed to air for a few hours, it is likely that the

compound will not remain the same. If the sample is

- 7
placed in a vacuum chamber and evacuated to 10 torr,

the probability of changes in the sample approaches
certainty. Some analytical technique which does not
require a vacuum, and can hopefully be used for in situ
analysis, is clearly needed.

Optical techniques may provide a solution in such
cases. Many of these thin film corrosion products are
semitransparent to the eye. This implies that the films
preferentially absorb certain wavelengths of light in the
visible region of the spectrum. This absorption could be
the basis for the analysis of the thin films. In addi-
tion, optical techniques have other advantages over x-ray
or electron spectroscopy.

A light beam penetrates typically fifty atomic dis-
ci
tances (around 100 A) into a metal. It penetrates a much

further distance through a semitransparent film, making it
suitable for examining the entire depth of the film with-
out penetrating extensively into the metal substrate. In
addition, optical techniques are non-destructive tech-
niques. But the greatest advantage of optical techniques
is that they do not require a vacuum; indeed, the proper
technique can study a sample in situ.

Traditionally, ellipsometry has been the optical
technique used to study thin films on substrates. This
technique measures the degree to which a film changes
plane polarized light into elliptically polarized light,
and the phase difference between the two components of the
elliptically polarized light. Using this information,
ellipsometry can calculate any two of the three para-
meters n, k and d, where n is the index of refraction, k
is the index of absorption, and d is the thickness of the
film. Computerized iteration techniques permit the
determination of all three parameters, but the process is
not rapid. High speed computer -controlled ellipsometers ,
although expensive, have improved this situation some-

what .

4
One technique, differential ref lectometry , provides

fundamentally different information when compared to

ellipsometry, or for that matter, to AES or ESCA. By

monitoring the difference in reflectivity between two
samples as a function of wavelength, a series of peaks is
obtained, each of which represents a transition from one
energy band to another in the sample. If one sample is
clean metal and the other sample metal with a thin film of
corrosion product on it, measurement of the difference in
reflectivity should show only the effect of the corrosion
product. Since each compound is presumed to have a unique
set of energy levels, this technique can identify the
presence of a corrosion product, its identity, and its
evolution with time. The measurements may be performed
in situ, if need be. In addition, it is nondestructive,
fast, and does not require a vacuum.

In addition to studies on existing corrosion prob-
lems, the technique of differential ref lectometry is use-
ful to corrosion engineers in other ways. Pourbaix dia-
grams are often used to represent a large amount of
thermodynamic data concerning corrosion in an easy-to-
interpret form. Such a diagram is a plot of potential
versus pH, and shows regions of thermodynamic stability
for metals and their associated corrosion products. A
Pourbaix diagram may be constructed from thermodynamic
data on the metal and corrosion products with the aid of
the Nernst equation,

0 nF Ti^dJ

where E is the half-cell potential, En is the standard

half-cell potential, R is the gas constant, T is the

absolute temperature, n is the number of electrons

transferred, F is the Faraday constant, and [a 1 and
' ' ' L ox

[a j] are the activities (concentrations) of the oxidized
l fed

and reduced species.

This equation is used to define regions of thermo-
dynamic stability in the Pourbaix diagram. It is well-
known, however, that many real physical processes do not
take place under equilibrium conditions. Hence the equi-
librium diagram may not apply. Therefore it is of great
interest to the corrosion engineer as well as the thermo-
dynamicist to construct experimental Pourbaix diagrams to
which the thermodynamically correct Pourbaix diagram may
be compared. This experimental diagram is a practical
guide which may be useful in engineering applications as
well as being a comparative measure of how closely experi-
mental conditions approach equilibrium conditions.

Experimental Pourbaix diagrams are normally con-
structed using the potentiodynamic method. At a fixed
value of pH, the potential of the sample relative to some
convenient reference is slowly varied while the current

through the sample (which is directly proportional to the
corrosion rate) is monitored. A plot of applied potential
versus the logarithm of the corrosion current is normally
obtained on an x-y recorder. If the potentiodynamic scan
is begun with the potential applied to the sample well
into the immunity region of the Pourbaix diagram, the
corrosion current should be essentially zero. As the
potential becomes more cathodic and the sample moves out
of the immunity region, the corrosion current should in-
crease. Any abrupt change in the corrosion current sig-
nals the formation or dissolution of a corrosion product.
For example, a sudden decrease in the corrosion current of
several orders of magnitude as the potential is made more
cathodic may indicate the onset of passivity at that po-
tential and pH. Numerous scans at different values of pH
serve to establish the experimental Pourbaix diagram.

One difficulty with this technique is that although
the formation of a corrosion layer may be observed, the
identity of that corrosion product is not determined. If
the corrosion product forms in or near a region of the
Pourbaix diagram where a certain product is expected it
is not unreasonable to assign that product to that area of
the experimental Pourbaix diagram. However, borderline
cases or conflicting results are not uncommon, as is a

good deal of experimental scatter. Independent verifica-
tion of the corrosion product is essential. Specimens
prepared potentiostatically are inherently closer to
equilibrium than potent iodynamically varied samples, and
may be analyzed to determine the identity of the corrosion
product. Since many of these films are too thin for x-ray
analysis, optical methods represent the only simple
techniques for examining these films without resorting to
a vacuum. Because differential ref lectometry seems to
produce a unique set of peaks for each corrosion product,
it should be possible to identify corrosion products pre-
sent in various regions of the experimental Pourbaix
diagrams. In addition, in situ techniques make possible
the study of kinetics of film dissolution or formation.

Initial studies of any new technique must be made on
carefully selected samples. Copper was chosen as the
metal upon which the films would be formed, since copper
has fairly well- characterized corrosion products, most of
which have a visible color which implies absorption bands
in the visible region. In addition, theoretical and
experimental Pourbaix diagrams have been established.

It is the purpose of this work to investigate the
feasibility of using the technique of differential reflec-
tometry to identify and characterize thin film corrosion

10

products on metal substrates. In addition, the concept of
using potentiostatic electrochemical techniques in con-
junction with differential ref lectometry to delineate
areas of stability in experimental Pourbaix diagrams is
to be investigated. To this end, the advantages of dif-
ferential ref lectometry , such as speed, freedom from
vacuum requirements, and, most importantly, the possi-
bility of true -in situ measurements , are used to supplement
conventional potentiostatic and potentiodynamic research
techniques. Differential ref lectometry provides a techni-
que for the direct observation of corrosion phenomena,
thereby supplementing the indirect technique of potentio-
dynamic scans. In this respect it is similar to x-ray
diffraction, which can provide a direct way of studying
phase changes in materials which are indirectly indicated by
res is tometric or differential thermal analysis (DTA)
techniques .

No single technique, or combination of techniques,
can be applied to the study of all corrosion phenomena.
It is believed, however, that differential ref lectometry ,
by supplementing the information obtained using more con-
ventional techniques, will provide a rapid, reliable, and
more complete means of studying thin film corrosion
phenomena.

SECTION II
LITERATURE REVIEW

Introduction

In the development of a new analytical technique, two
problems must be considered— the mechanics of the technique
itself and the interpretation of the results of that
technique. Therefore, this review will be divided into
two major parts. The first is a discussion of several
optical methods which have been developed for the study of
thin films. Their chief advantages and disadvantages, as
well as how they relate to differential ref lectometry ,
will be discussed. Most of these techniques are useful
primarily for the study of very thin films and seek to
find the optical constants n and k and the thickness, d,
of the film. Differential ref lectometry seeks only the
identity of the film and its thickness, without regard for
the particular optical constants.

The second part of this review will concentrate on
optical studies of cuprous oxide, Cu^O. In order to
identify thin film corrosion products with the dif-
ferential ref lectometer , one must know the absorption
spectra or optical constants of each corrosion product as

11

12

a function of wavelength. This initial study has con-
centrated on the oxides of copper, Cu?0 and CuO. Of the
two, C^O has been more extensively studied since it
possesses an intrinsically interesting electronic struc-
ture. Cuprous oxide, Cu20, has a rich exitonic spectrum
as well as a fundamental energy gap in the visible area of
the spectrum. (An exiton is a bound electron-hole pair
produced by some semiconductors by the absorption of an
appropriate wavelength of light.) Cupric oxide, CuO, has
not been as extensively studied. Fortunately, one study
which has been done provides the optical constants as a
function of wavelength, something which has not been done
for Cu?0.

Related Techniques
The traditional method for investigating thin films
on substrates has been ellipsometry . In a typical experi-
mental arrangement, shown in Figure 1, a monochromat ic
light beam passes through a polarizer to produce plane
polarized light. This light is reflected from the metal
or metal/film surface at the angle of incidence, $ , pro-
ducing elliptically polarized light. This elliptically
polarized light may be visualized as two perpendicular
plane polarized waves of amplitude ratio 4> and phase dif-
ference A. These ellipsometric parameters are determined

13

bfl

C

o

H

c

CD

<D

f-l

U

Sh

C

oj

a;

T)

T— 1

• H

rt

U

+->

C

C

■H

0)

e m-i

■ H

O

M

<D

a;

P<iH

X

to

<D

C

03

t— i

o3

CD

U X

•H

4-J

P,

X t/1

H

•H

r— 1

<D

M

3

14

by the optical constants of the metal and film, as well as
the thickness of the film. The phase difference, A, be-
tween the two plane polarized waves can be brought to zero
by appropriate adjustments of the compensator, producing
a single plane polarized wave again. The analyzer is then
rotated so as to extinguish the plane polarized light, and
the resultant values of A and \p determined from the com-
pensator and analyzer settings. The values of A and \\> are
then used to calculate the optical constants n and k.
The situation is not quite as simple as this, of
course. The values of A and \p by themselves are insuf-
ficient to uniquely determine n, k, and d for the film.
Until recently, the film thickness, d, had to be deter-
mined independently, by coulometry, interf erometry , or
a series of ellipsometric measurements. None of these

methods are particularly easy, and all are time-con -

7 8

suming . However, Paik and Bockris have shown that

the ratio of the intensity of the light reflected from

the film parallel to the plane of incidence (ri i) to that

polarized perpendicular to the plane of incidence (ri) can

be used in addition to ijj and A to determine the unknowns

n, k and d. Unfortunately, only a few existing automatic

ellipsometers , such as those of Paik and Bockris and

Cahan and Spanier, can easily measure these quantities.

15

9 in

A new approach by O'Handley and O'Handley and Burge

calculates the effective reflectivity from A and ip and

uses this quantity in addition to A and v/j to find the

three unknowns, n, k, and d, for the film. As O'Handley

points out, two possible values of the film thickness, d,

can be produced using this analysis, but since they often

differ by an order of magnitude, only a general idea of

the thickness of the film is necessary to unambiguously

determine all three parameters.

Another feature of the classic ellipsometer which has
made it less than ideal for thin film investigations is
its lack of speed. In electrochemical investigations,
many reactions occur very fast, and the determination of
A and ty for a classic ellipsometer may require many
minutes. Modifications to the normal operation of an
ellipsometer, such as off -null techniques, can increase
the sensitivity to transients and facilitate the moni-
toring of known films, but more exotic techniques are
required for unknown films of very rapid film formation.

One approach to the problem is to speed up classical
ellipsometry . Such an approach has led to a series of

automatic ellipsometers , such as that of Cahan and

3 \2

Spanier, and recently to a commercial instrument.

These instruments, which often use a continuously rotating

16

analyzer and a dedicated minicomputer, can analyze a film

1 2
for n, k, and d in four to ten seconds. Their chief

drawback is their expense, since a commercial automatic

ellipsometer costs approximately $20,000, or about four

1 3
times the cost of a conventional ellipsometer.

Various kinds of modulation techniques have also been
employed to speed up ellipsometry . The modulated para-
meter is ordinarily the polarization of the light beam,
which is varied by a photoelastic crystal or by a
Faraday cell. Alternately, an oscillating analyzer
or polarizer may be used. Figure 2 shows one such modu-
lated ellipsometer developed by Jasperson et al . It is
similar to a standard ellipsometer except that instead of
a normal compensator it uses a piezoelectrically -driven
quartz crystal to modulate the phase shift of the light
beam. The detector uses two lock-in amplifiers to
simultaneously monitor the reflectivity at the modulation
frequency (50 KHz) and at twice the modulation frequency
(100 KHz). In addition, the DC reflectivity is also
monitored using a low pass filter in order to take into
account changes in source intensity, detector response,
and so on. The 50 KHz and 100 KHz signals contain in-
formation from which n and k for the film may be derived
if the. thickness , d, is known. If it is not, the method

17

-SH

Figure 2. Schematic diagram of a modulated ellipsometer
developed by Jasperson e t a 1 . 1 4 The detector
(DET) sends the modulated signal to two lock-in
amplifiers tuned to 100 KHz and 50 KHz and to a
low pass filter. The data is reduced by the
computer, C, and displayed on a digital meter,
DV. Q' or A' is an additional polarizer used
to calibrate the instrument.

9
of O'Handley may be used to find n, k, and d simul-
taneously. The instrument is said to be an order of
magnitude more precise than standard ellipsometers and
can measure A and >p in less than thirty seconds.

Differential ref lectometry , as used in the study of
thin film corrosion products, is similar to the related

technique of differential reflection spectroscopy used by

17-19
Mclntyre and others. Differential reflection spec-
troscopy, however, uses polarized light and seeks to find
the optical constants ft = n + i k for the film, while
differential ref lectometry does not require polarized
light and seeks only the reflection spectrum of the film
to identify it.

As in differential ref lectometry , the differential
reflection spectroscopy technique of Kolb and Mclntyre
measures the normalized difference in reflectivity,

AR = R1'R2
R R,

where R-^ is the reflectivity of the metal and R? the re-
flectivity of the metal/film composite. The difference
in reflectivity is normalized by dividing by the re-
flectivity of the metal rather than the average reflec-
tivity. Additional information may be obtained by
polarizing the light beam parallel to [(y),,] and per-

19

AD

pendicular to [ (—} , ] , the plane of incidence. Mclntyre

18
and Aspnes have shown that if the film thickness is very

small relative to the wavelength of light being used, then

and

rAR
(TTJJ_

!tt d n„ costf) t, - e7
r ImC-Ur^)

(1)

(AR
1 R J

0
Itt d n0 cos* /V^x-^Y^CV^sin2^^
Imi- — 5—! 1 =s — ]}(2)

A

G0^2 l-(^_)(en+g9)sin"

•0 2-

where t)> is the angle of incidence. The surrounding phase
(either air or electrolyte) has a real dielectric con-
stant, en, and index of refraction, nn , while the thin

absorbing film and substrate metal have complex dielectric
constants, e, and &~, respectively.

Using these equations, there are two methods for
measuring the optical constants of the film.

1. Measure the two quantities {—) , and (y) , , at
a single angle of incidence.

2.
angles of incidence.

The details of each kind of measurement have been
given by Kolb and Mclntyre. Method 2 is not used be-
cause of mathematical difficulties in extracting the

Measure either (^-) , or (^) , , at two or more

R

20

optical constants n and k. Method 1 has been used suc-

° 19
cessfully to study adsorbed layers on gold 6 A thick.

This technique has certain advantages over conven-
tional ellipsometry which are similar to the advantages
of differential ref lectometry , such as easily performed
measurements in situ, fast response time, and measure-
ments over a range of wavelengths. However, it is a dif-
ference technique rather than a differential technique
because the reflectivity of the metal and the metal/film
composite is not measured at the same time. The reflec-
tivity of the clean metal surface is measured in air,
rather than in situ. The sample cell is filled with
electrolyte and the sample potentiostated in the desired
region of the Pourbaix diagram. After an appropriate
amount of time, the reflectivity is again measured as a
function of wavelength for both polarizations of light.
The normalized difference in reflectivity is then calcu-
lated point by point by computer.

Several points need to be considered when comparing
differential reflectance spectroscopy to differential
ref lectometry . In differential reflectance spectroscopy,
two scans over the entire wavelength range are necessary
to determine the complex dielectric coefficient of the
film, in addition to the reflectivity measurements and

21

Kramers -Kronig calculation necessary to obtain the optical

1 o

constants of the substrate. ' Secondly, the output is
not a continuous curve, but only a series of points.
Sharp changes can be missed. Thirdly, if the film is
absorbing, the thickness must be determined independently
before n and k for the film can be obtained. Finally,

I o

equations 1 and 2 are only accurate if d/X < .003. For
A = 250 nm (approximately the lowest wavelength used in

o

this work) d must be less than 7.5 A. Hence the technique
is useful mainly for studying adsorbed monolayers. Semi-

o

passive films such as CuO or Cu?0 are often over 100 A

20

thick," and even passive layers such as those found on

° 21

stainless steel are often around 30 A in thickness.

In addition, since in most cases the absorption coef-
ficient, k, is greater than zero, the thickness, d, of the
film must be independently determined before the optical
constants n and k can be found. However, this technique
does measure the optical constants of the film, which is
something differential ref lectometry does not do.

Another popular technique is that of electrochemical

72
modulation spectroscopy (EMS)." Here, the modulated

parameter is the electrode potential, cell current, or

the surface charge of the sample. In its most common

form (Figure 3) it is used to measure adsorption on metal

22

Figure 3. Electrochemical modulation apparatus used by

Mclntyre.22 The HIS 6070 is a computer used to
reduce the data.

2 3

substrates, such as hydrogen on rhodium or iridium, '
or oxygen on gold, platinum, or nickel electrodes. * '
Light from a Xenon arc lamp passes through a monochromator
and polarizer and into the optical cell, where it is re-
flected from the metal surface and collected outside the
cell by a photomultiplier tube. The potential of the
sample is controlled by a potentiostat which can be
modulated by an external waveform generator. At a signal
from an on-line minicomputer, the waveform generator
imposes a triangular pulse on the voltage supplied to the
sample. The reflectivity as well as the cell current and
the electrode potential are digitized and recorded by the
minicomputer at 256 time intervals. A number of sweeps
(typically 64) are made to increase the signal to noise
ratio, and the data is reduced by computer to a plot of
-=- versus A. As in the case of differential reflectance
spectroscopy, the output is in the form of a series of
points rather than a smooth curve.

Although electrochemical modulation appears to be an
excellent method of studying adsorbed layers, two limita-
tions should be noted. First, the reaction must be truly
reversible. The formation of an oxide which does not
readily dissolve, for example, must be avoided. Second,
the reaction must be fast enough to be affected by the

2 4

modulation. (Typical modulation conditions are a sawtooth

9 7

wave, 44 mv peak to peak at 43 Hz." ) For fast, reversible
reactions, however, this technique works well.

Internal reflection spectroscopy has been used to

study adsorption on thin film substrates such as gold28 or

29
platinum. ' In internal reflection spectroscopy, a light

beam is internally reflected in a transparent substrate.
At the point of reflection, the light beam interacts with
the film on the other side of the substrate, and the re-
sultant changes in the light beam may be used to charac-

2 Q

terize the film. For example, Hansen has observed the

o

adsorption of molecular dyes on thin (100 A) layers of
gold. In addition, electrochemical modulation techniques
may be used with internal reflection spectroscopy to

study fast, reversible reactions. Such a technique was

2 9
used by Mclntyre and Peck to observe the adsorption of

0

hydrogen on platinum films 100 A thick in .5 M H, SO..
The beauty of the technique is that the observations are
made from the electrode side of the interface.

Rapid scanning spectroref lectometry is a new develop-
ment which permits the continuous measurement of reflec-
tion spectra over a wide wavelength range. A recent
instrument used by Mclntyre is shown in Figure 4.
A rapidly scanning galvanometer mirror (GM) sweeps a high

25

Figure 4. Schematic diagram of a rapid scanning spectro-
photometer used by Mclntyre.24 See text
for details .

2 6

intensity beam of white light across the surface of a
spherical mirror (SM) . The reflected beam is focused by
the spherical mirror onto a diffraction grating (GR) at a
fixed position, but at a variable angle of incidence.
This produces a wide beam of quas i -monochromatic light
which is scanned across the exit slit at speeds up to
1000 A/ms . A beam splitter (BS) permits the simultaneous
measurement of the incident light intensity via photo-
multiplier A (PMT A) and the reflected intensity via
photomultiplier B (PMT B) . The signals are sampled in the
time domain (which is related to the wavelength by the

oscillation frequency of the mirror) by a minicomputer.

AR
The normalized difference in reflectivity, -5-, of the

film free surface (obtained earlier and stored in the

computer) and the film covered surface is calculated and

displayed. Normally a signal averaging technique is

used, wherein typically 512 wavelength scans are used to

enhance the signal to noise ratio. Rapid reflectivity

changes can be observed, since even with signal averaging

a typical scan takes less than one minute. One important

advantage of the technique is that surface roughening,

such as is possible with electrochemical modulation

spectroscopy , is avoided since the electrode potential is

not modulated. However, since the scan is so rapid, the

27

high voltage supplied to the photo-multiplier tubes cannot
be easily adjusted to maintain the average output voltage
at an optimum level. As a result, precision may suffer
when the light intensity is low.

One final effect common to all these techniques is
the possibility of electroref lectance effects complicating
the reflectance spectra of the film/metal surface of

samples measured in situ. For such samples, the electro-

2 2
reflectance effect can arise from two sources: changes

in the dielectric constant of the metal at the surface due

to the capacitance of the electrical double layer between

the bulk metal and the bulk electrolyte; and, a change in

the refractive index of the solution at the ionic double

layer. High DC as well as AC potentials can produce these

2 7
effects. The electroref lectance effect can be a

valuable probe of the metal surface, or an unfortunate
complication of the thin film absorption spectra, de-
pending on what is being investigated. The effect does
not subtract out of the reflection spectrum when the dif-
ference techniques described in this section are employed
because the reflectivities of the samples are measured
under different conditions. Evidence will be presented in
Section III which indicates that the technique of dif-
ferential ref lectometry may not produce electroref lectance

peaks because the reflectivities of the samples are mea-
sured at the same time and under similar conditions.

Cuprous Oxide
Band Structure Calculations

Theoretical studies of the band structure of Cu?0

have been made by Zhilich and Makarov, Elliot, and

32
Dahl and Switendick. The early work of Zhilich and

Makarov treated only the r^5 •* r, transition, where

T^5 is assumed to be the top of the valence band, and r ,

the bottom of the conduction band. This is generally

agreed to be the fundamental energy gap of Cu20, and gives

the oxide its red color. This band gap, calculated

according to the method of Kohn and Rostoker was found

to be 2.38 eV, in good agreement with the experimentally

30
determined 2.2 eV.

31
Elliot did not calculate transition energies, but

instead presented a simple, qualitative band structure
derived from symmetry conditions of the cuprous oxide
lattice. Both direct and indirect transitions were con-
sidered .

By far the most ambitious attempt at the calculation

of the energy levels of Cu?0 has been by Dahl and

32
Switendick. They calculated the energies of a very

2 9

large number of energy levels, using the augmented plane
wave (APW) method proposed by Slater,3 with muffin tin
potentials. Their band calculations show the T' + r,
transition to have an energy of 1.77 eV, somewhat below
the experimental 2.2 eV. Figure 5 shows the calculated
band structure. Not all the possible transitions are
allowed, and of those which are permitted, many are in-
sufficiently intense to be observed. For information on
which transitions do occur, one must investigate the
optical spectra of Cu20 and attempt to correlate observed
structure with possible transitions. The major difficulty
here is that while band structure calculations are often
qualitatively correct, the assigned energies for favorable
transitions are frequently rather imprecise. As mentioned
previously, in the calculations of Dahl and Switendick,
the r^5 -*• r, transition, which is generally agreed to be
the transition defining the fundamental gap in Cu70, is
found to have an energy of 1.77 eV. Experimentally, the
gap is found to be 2.2 eV — a difference of half an elec-
tron volt. Hence while band structure calculations can
provide a useful qualitative picture of the structure of a
thin film differential ref lectogram, quantitative data
is best obtained from optical spectroscopy.

30

\_ i. V N 1_ \

TA R MITAX

Figure 5. Band structure diagram for cuprous oxide (CU2O)
calculated by Dahl and Switendick . 32

51

Optical Spectroscopy

35
Brahms and Nikitine have measured the absorption

and reflectance spectra for single crystals of Cu90 in the
2.5-6.5 eV region. Absorption was measured at 77 K and
295 K, and reflection at 77 K. A good deal of peak
sharpening occurs in the absorption spectra at low tem-
peratures. The correlation between peak positions for
absorption spectra and reflection spectra as shown in
Table 1 is quite good, as it must be. The authors
associate the transitions at 2.58, 2.62, 2.71, 2.74, and
4.33 eV with exiton formation. The strong peak at
5.5 2 eV is attributed to a maximum in the joint density
of states .

Balkanski, Petroff, and Trivich have measured the
reflectivity of Cu20 in the ultraviolet (2-25 eV) at
300 K, and the reflectivity in the visible (200-500 nm)
at 30 K. They then use the Kramers -Kronig relationship
to determine e- for the 2.5-6 eV region of the spectrum at
30 K. The reflectivity data for Cuo0 at 30 K corresponds

L

35
well to the earlier work of Brahms and Nikitine. Both

mechanically polished as well as polished and etched
samples were measured, as shown in Figure 6. It is evi-
dent that most of the structure, including all of the
exiton peaks, is dependent upon the surface state of the

32

Table 1

Comparison of Peak Positions for Absorption
and Reflection Spectra^S

Absorption

Reflectivity

Peaks [eV]

Peaks [eV]

2.61

2.58

2.62

2.71

2. 71

2. 75

3.62

3.62

3.9

4. 33

4. 33

4.48

4.48

4. 74

4. 74

4.86

4.86

4.94

4.94

5.08

5. 36

5. 39

5.52

5.53

5. 79

5.84

6.45

33

3500 I

M<chaniullr pol,lht4 thw cUmuli,
tUM

-— WilhsuL iliniil lUhn)

-K--

4000 4500 5000A X

Figure 6. Reflectivity spectrum of polished and polished
and etched Cu?0 crystals. 36

54

sample. No exitonic structure appears for unetched speci-
mens. This point is very significant since it implies
that exitonic structure might not be observed in the current
experiments, or that at least the structure may not be
sharp and well-defined. Thus only two areas of structure
would remain from which to identify the oxide Cu?0: the
broad transitions at 340 nm (3.64 eV) and at 225 nm
(5.51 eV) . The 3.64 eV structure may be due to a

transition at a high symmetry point, such as X,T -* X,f.

32
The theoretical value calculated by Dahl and Switendick

for this transition is 3.5 eV. The broad peak around

5.56 eV is thought to be due to another transition from a

high symmetry point, such as R.

Zouaghi, Prevot, Carabatos , and Seiskind mea-

37 38

sured the infrared absorption and photoconductivity of

Cu^O after annealing in oxygen for different times and
temperatures. They observed changes in the absorption and
photoconductivity with different oxygen concentrations and
annealing times, which implies that the method of forma-
tion of Cu70 may influence its optical spectra. Hence the

3 S
reflection and absorption spectra of Brahms and Nikitine

and of Balkanski et al. , which were thermally grown, may

not be identical with the spectra of electrochemically

prepared specimens.

3 5

In addition to reflectivity and absorption measure-
ments, some electroref lectance data has been obtained for
Cu20. Shestatskii and Sobolev have examined the elec-
troref lectance of polycrystalline Cu?0 from 3.3 to 4.5 eV
(375-275 nm) . Even in this short range, two strong peaks
were observed, at 3.6 eV (344 nm) and 4.25 eV (292 nm) .
These agree fairly well with the reflectivity data in that

interval of Brahms and Nikitine and Balkanski et al .

41
Shestatskii, Sobolev, and Likhobabin measured the

electroref lectance of Cu?0 single crystals at 77 K. The
thin, etched samples were studied at various modulation
voltages and DC bias voltages. Peaks were observed in the
2.5-2.8 eV(496-443 nm) range which were identified as
exiton peaks. Unfortunately, no measurements were per-
formed on unetched samples. Both the shape of the peaks
and their polarity were found to be dependent on modu-
lating voltage and DC bias. A representative set of
spectra is shown in Figure 7, for various AC voltages and
a constant 1 KV DC voltage.

A somewhat larger spectral region, from about 2.5 to

6.0 eV (500-200 nm) , was measured by Daunois, Deiss, and

42
Nikitine. ~ They measured the electroref lectance of bulk,

polished, and etched samples at 85 K. A large number of

peaks were observed, most of which agree well with re-

36

^ -i

1500

5000 i,}00

— i(h

tivlel/)

2.600

2 700

'J-

5000 WOO

Figure 7. Ele'ctroref lectance spectrum of single crystals
of Cu20 for various AC voltages superimposed on
a 1 KV DC bias.41

3 7

flectivity data. Figure 8 shows the electroref lectance
spectrum at 85 K. The structure is well-defined and very
rich.

Growth and Kinetics

The preparation of standard films of various copper
oxides is an important step in calibrating the dif-
ferential ref lectometer for corrosion studies of copper.
When the band structure of the oxide is known, it should
be possible to identify the oxide by the optical prop-
erties as recorded by the differential ref lectometer . In
other cases a standard film of known composition is needed
to determine the standard spectra. One method of ob-
taining a standard film is to potentiostat the base metal
under specific corrosion conditions which, according to
the Pourbaix diagram, might be expected to produce the
correct corrosion film. In the case of oxides, heating

the base metal in oxygen may be sufficient.

43
Ebisuzaki prepared large single crystals of Cu?0

from large slices of single crystal copper. The technique
involved high temperatures (980°C) and low partial pres-
sures of oxygen (3.1 mm tig in a nitrogen atmosphere).

Other thermally grown oxides were made by Wieder and

44
Czanderna. Most oxides were mixtures of Cu?0, CuO, and

CuO 67 (which is apparently a defect structure Cu?0) .

38

R"

x(A)

CUjO 8b K

fi +

y>(cm')i_

Figure 8. Electroref lectance spectrum of CU2O at 85 K and
no DC bias. The modulating electric field was
60 KV/cm.42

39

X-ray investigations showed that in the early stages of
oxidation the crystals produced were amorphous. This
implies that thermally grown oxides may not have a well-
defined crystal structure and hence not a well-defined
band structure during early stages of growth.

In most of these cases of thermally grown Cu?0, the
aim was to produce bulk samples, rather than thin films.
Electrochemical methods are probably better suited to
growing thin films on copper substrates than thermal
methods, since electrochemical methods tend to produce
films which are more dense and compact. Characterization
of the film is, as usual, the major problem.

The growth of oxide films of spherical single

crystals of copper in distilled water was studied by

20 45 46
Kruger." ' '' Using a special oscillating crystal

technique he was able to establish that Cu„0 was the film
formed on copper in distilled water exposed to air. This
is the same oxide which is slowly formed when copper is
exposed to air. Further, when pure oxygen was bubbled
through the water, the film initially produced was Cu?0.
This is not unreasonable since any CuO which begins to
form would tend to be reduced to Cu20 by the copper sub-
strate. These Cu20 films were observed to form very
rapidly and reach a limiting thickness after about two

4 0

hours. The precise film thickness, as measured by
standard ellipse-metric techniques, varied with the
crystallographic orientation of the copper, but averaged

o

about 90 A for this case. After long times a porous,
loosely adherent CuO layer was observed to form on the
Cu20 layer. The formation of the CuO overlayer apparently
did not prevent the continued growth of the Cu?0 under-
layer. One variable was found to influence the growth of
Cu^O, however: light.

Cuprous oxide is a p-type semiconductor. Since its
band gap of 2.2 eV is in the visible part of the electro-
magnetic spectrum (about 560 nm, or yellow- green) it is
not unexpected that light might have some effect on its
electronic properties. That these electronic properties
affect the kinetics of growth is somewhat more surprising.
When Cu20 films are illuminated by the appropriate wave-
length of light, electrons are transferred from the
valence band to the conduction band, where they can mi-
grate to the copper electrode. This process inhibits the
growth of the Cu20 film by a process not completely under-
stood. Whatever the exact mechanism may be, inhibition of

Cu20 growth has been observed by Kruger on single crystals

45 46
of copper. ' Similar results were obtained by Ives and

47
Rawson for polycrys talline copper. Kruger 's work with

41

single crystals showed a decrease in Cu?0 film thickness
of about one-third for samples illuminated by a 500 watt
tungsten light over similar samples which were not
illuminated. No effect on the film growth rate was ob-
served if the distilled water was kept saturated with
oxygen. Attempts to employ a monochromator with the
light source to determine the spectral response of the
inhibition of film growth were not successful due to the
lack of light intensity. This implies that monitoring
film growth with the differential ref lectometer or an
ellipsometer probably would not inhibit the growth of a
Cu^O film.

Summary
Of the several methods related to differential re-
flectometry which may be used to investigate thin film
corrosion products, ellipsometry is the most common. In
its basic form, ellipsometry can determine the optical
constants n and k to a high degree of precision if the
thickness of the film is known. Recent advances have
eliminated even that requirement, provided the absolute

o

reflectivity can be measured, or if a reasonable guess

9 10
can be made as to the thickness of the film. ' Very

precise values of n, k, and d may thus be determined from

42

a classical, well-established instrument. The only re-
maining drawback is the slow speed of the classical
ellipsometer , and even this barrier is being overcome
through the use of automatic and modulated
ellipsometers .

For thin adsorbed films, many spectroscopic techni-
ques are available. Differential reflection spectro-

17-19 .
scopy is very similar to differential ref lectometry ,

but employs polarized light and measures the reflectivity
before and after film formation rather than concurrently.
Although it can determine the optical constants, it can
only do so for very thin monolayer films.

For the study of fast, reversible reactions in situ,
electrochemical modulation ' " is ideal. Here an
adsorbed film is induced to form and redissolve by modu-
lations of the electrode potential. Its only real dis-
advantage is that the number of possible applications is
small. Also somewhat limited in application is internal
reflection spectroscopy, which has the unique advantage of
observing film formation from the electrode side of the
interface. Its chief limitation is that light must pass
through the electrode. Finally, for very fast reactions
or transient phenomena, rapid scanning spectroref lectivity
can be a useful method of measuring changes in reflectivi-
ty.

4 3

Some such techniques have the advantage over dif-
ferential reflectometry in that they can determine the
optical constants of the thin film corrosion product.
Some, such as electrochemical modulation or rapid scanning
spectroreflectivity, can study very rapid reactions.
However, all except ellipsometry are more or less limited
to very thin (monolayer) films. Such films are important
in studies of catalysis and adsorption, hut passive and
semipassive layers are too thick to be analyzed for n and
k using these techniques. Differential reflectometry is
well-suited to the study of these films in the 5 A-500 A
range, but requires some way other than the optical con-
stants to identify the film.

Several avenues are open to one wishing to identify
thin film corrosion products with differential reflecto-
metry. Some, such as x-ray or various forms of electron
spectroscopy, were discussed in Section I. Other methods
include the correlation of peak position with either band
structure data, or reflectivity spectra.

The most complete band structure study of Cu?0 is
that of Dahl and Switendick. " While it agrees well
qualitatively with observed structure in the reflectivity
spectrum, the energies of transitions do not. More de-
tailed calculations are required before band structure

44

data alone may be used to identify corrosion products
without additional data from reflectivity curves.

Several techniques have been used to record the
optical spectra of Cu20. Most agree on the major struc-
ture, but various techniques differ in their sensitivity
to exiton structure and to complications from electro-
reflectance effects. The data of Balkanski et al . is
most important since it shows that structure due to
exiton formation may not be visible in unetched specimens.

Table 2 summarizes the reflectivity data and band
structure calculations discussed in this section. Only
room temperature data are shown . The calculations of Dahl
and Switendick are shown shifted so that the fundamental
gap occurs at the experimental energy, with the original
data in parentheses. This translation may not be correct,
but probably results in more accurate values than the
original calculation. It is given here as an approxima-
tion only. Agreement between the different experimental
techniques is good, which implies that peaks at similar
positions should be visible in differential ref lectograms
of Cuo0.

4 5

Table 2

Major Peak Positions in C112O Optical Spectra Compared
to Transitions Calculated from the Band Diagram
(see text)

Reflect ivity

36

e2

Electrore
Ref. 40

f lectance
Ref. 4 2

3?
Calculated

2. 5

2.7

-

2. 59

2.73

2.25 (1.77)

3.4

-

3.35
3.60

3.66

3.77

3.84 (2.86)

3.7

3. 7

3. 78
3.95

-

3.74 (3.26)

4. 3

4.4

4.08
4.25

4. 35
4.90

4.41 (3.63)

4. 7

4. 8

-

4. 72
4.76
4.92

4.83 (4.35)

5.0

5.3

-

5.03
5.21

5.07 (4.59)

SECTION III
EXPERIMENTAL PROCEDURE

Introduction

Any analytical technique must be capable of consis-
tent results. Frequently this is the most difficult
aspect of the development of a new technique, since un-
expected variables in the experimental process may produce
inconsistent results. The application of differential
ref lectometry to corrosion studies is particularly sus-
ceptible to this problem for three reasons— it involves
thin films, electrochemistry, and a new analytical techni-
que .

One reason thin films of corrosion products are
difficult to study is because they are difficult to de-
tect. They are known to be delicate, often easily al-
tered, and frequently nonuniform, either across the
specimen or in depth profile. Electrochemical techniques,
being thermodynamic in nature, are easily influenced by
small changes in experimental conditions. For example,
unexpected temperature changes or power interruptions may
produce anomalous results. Finally, the analysis techni-
que, differential ref lectometry , while well-established

4 6

47

for compositional modulation studies of alloys, " has
never been applied to electrochemical studies.

It is therefore of the utmost importance that the
sample preparation and experimental procedure be carried
out in a careful and consistent manner, in order that the
results be as reproducible as possible.

Sample Preparation
Metallographic Preparation

Copper samples were prepared from a 3/4" (19 mm)
diameter bar of 99.999% pure copper.* Each sample was
lathe cut from the bar to form a dish 3/4" (19 mm) in
diameter and approximately 3/8" (9 . 5 mm) thick . In order
to eliminate any possible contamination by the cutting
operation, each dish was immersed in 20% nitric acid for
fifteen hours. A small, 1/16" (1.6 mm), hole was drilled
in the back of the sample to a depth of about 3/16"
(4.8 mm) to facilitate the attachment of the electrode
wire .

Each sample was then ground flat with a succession
of 180, 320, and, finally, 600 grit silicon carbide
papers. Grinding was accomplished on a metallographic

*0btained from the A. D. McKay Corp., New York, New York.

4 8

polishing wheel while the papers were lubricated with
liquid soap and water. Due to the fact that the silicon
carbide particles tend to become embedded in soft mate-
rials such as copper, the minimum amount of polishing
necessary to properly finish the specimen was performed.
Since it was found that even these measures did not
eliminate silicon carbide embedding, further polishing was
performed using Microcut paper.* Microcut paper is a
mildly abrasive , napped paper which produces a surface
finish similar to 600 grit silicon carbide paper, but
contains no silicon carbide or other particulate abra-
sives. The cutting action is a product of the nap of the
cloth alone. By polishing each sample for a sufficiently
long period of time on several pieces of Microcut paper
lubricated with liquid soap and water, it was found that
virtually all silicon carbide contamination could be
eliminated, as confirmed by microscopic examination.
Fortunately such elaborate measures were found to be
necessary only during the first polishing of the as-cut
specimens. Used specimens with mild amounts of corrosion
in the form of thin film layers could be cleaned with
Microcut paper alone. As mentioned above, this produced

'Microcut paper, trademark of Buehler, Ltd., Evanston,
I 1 lino is

4 9

a sample with a finish similar to that produced with 600
grit silicon carbide paper, but without the silicon car-
bide contaminants. Such a finish completely removed all
traces of the thin films studied in this work.

After polishing with Microcut paper, each sample was
fine-polished with 6 micron followed by 1 micron diamond
paste on a felt cloth using Metadi* fluid as a lubricant.
This polishing technique produced a uniform, mirror-like
finish on the sample.

In order to fasten the sample wire to the specimen,
a tiny brass fitting was constructed. The fitting was in
the form of a truncated cone with a maximum diameter of
about 1/16" (1.6 mm). The sample wire, which was insu-
lated with Teflon** to ensure freedom from attack by the
electrolyte, was soldered to the end of the fitting.
This assembly could be attached to the sample by means of
a press fit. Finally, the fitting and most of the sample
were covered with a special lacquer (Miccrof lex***) which
previous experience had indicated would not be affected by

^Metadi fluid, trademark of Buehler, Ltd., Evanston,

111 inois
**Teflon, trademark of E. I. DuPont , Wilmington, Delaware
***Miccroflex, trademark of Michigan Chrome and Chemical
Co., Detroit, Michigan

50

the electrolyte and would prevent the covered section of
the sample from corroding.

Special Procedures for In Situ Samples

Samples prepared for in situ analysis require an
optically transparent layer for the insulating coating,
since the light beam must be able to see a corroded and
an uncorroded part of the sample at the same time while
the sample is in the electrolyte. It was eventually
established that collodion provided the most satisfactory
coating .

From a theoretical point of view, quartz would seem
to provide the best coating. It is optically transparent,
insulating, and very resistant to chemical attack. How-
ever, quartz cannot be easily deposited on the copper
surface. Extensive attempts to sputter quartz on the
sample face were not successful due to the nature of the
sputtering process. When quartz, SiO?, is sputtered off
a quartz target, SiO- particles are not the only species
produced. The momentum transfer process which makes
sputtering possible partially dissociates the SiO? into
Si, 0, 0?, and SiO as well as the predominant Si02- The
resulting free oxygen in the chamber reacts with the
copper sample before a protective layer of SiO., can be

51

deposited. The result is oxidized copper, covered with an
insulating SiCL layer. The effect is enhanced by the high
temperature of the plasma and the high energies imparted
to the oxygen ions by the sputtering action. In addition,
in order to obtain SiO~ layers free from SiO contamina-
tion, the manufacturer* suggests adding additional oxygen
to the system and sputtering in an oxygen enriched argon
atmosphere. This only provides more oxygen to oxidize the
copper before a protective layer is formed. (The situa-
tion is no problem to the major user of quartz sputtering
equipment, the semiconductor industry, since they are
generally sputtering onto silicon.)

Silicon monoxide, SiO, was another unsuccessful can-
didate. Although it can be evaporated instead of sput-
tered, it is not entirely optically transparent. A SiO
coating has a yellow-brown tint which is readily detected
by the differential ref lectometer . Attempting to
evaporate SiO in an oxygen enriched atmosphere and deposit
Si02 on the sample produces only the oxidation and de-
struction of the boat used to evaporate the SiO.

Evidently some kind of mechanically applied chemical
compound similar to Miccroflex but transparent was

*Perkin-Elmer Co., Palo Alto, California

5 2

necessary. Miccroflex may be thinned out to a great
extent and still remain protective, but it also remains
purple. The color may not be apparent to the eye, but the
differential ref lectometer shows it quite clearly. Other
commercial compounds used in electroplating such as
Miccroshield* showed similar results.

It is known that Tygon tubing, noted for its chemical
resistance, can be liquified by the chemical Tetra-
hydrafluoran (THF) . This can then be readily applied to
specimens by a dip method, and subsequent air drying
restores the physical and chemical properties of the
original Tygon. Transmissivity studies showed it to be
transparent from 800 to approximately 350 nm, which en-
compasses much of the present range of the instrument.
Unfortunately, the dissolved Tygon would not dry to a
uniform thickness. This produced interference colors on
the film which completely obscurred any differential re-
flectometry data. Attempts to produce films of Tygon

o

thinner than about 2000 A in order to eliminate the inter-
ference effect produced films with no appreciable degree
of adherence to the copper sample. This led to a small

''Miccroshield, trademark of Michigan Chrome and Chemical
Co., Detroit, Michigan

53

gap between the copper and the "protective" film, causing
massive crevice corrosion.

Thus far the most satisfactory coating has been found
to be collodion, a waxy organic compound used to make
replica specimens for transmission electron microscopy.
It is available dissolved in either amyl acetate or
alcohol and may be thinned to any desired degree by the
addition of additional solvent. Since alcohol of extreme-
ly high purity is easily obtained, and has the advantage
of rapid drying time, it was chosen over amyl acetate as
the solvent for this work. Collodion layers may be
deposited on half the sample by the simple method of
dipping half the sample in the dissolved collodion. The
collodion then dries to a uniformly thick, fairly adherent
layer in about thirty seconds.

The physical properties of the collodion layer are
similar to the Tygon coatings. Thick layers will produce
interference colors due to non-uniformity of the film.
Extremely thin layers have little adherence to the copper
sample, and produce crevice corrosion. The advantage of
collodion over Tygon is that the collodion is more
readily dissolved, dries faster, and produces more uniform
films. Even so, a film sufficiently thin to minimize
absorption of the light beam and eliminate interference

5 4

colors will break down or loose adherence after twenty-
four to forty-eight hours in the electrolyte. Further
research in this area of transparent, insulating coatings
is clearly needed.

Electrolyte Solutions

Electrolyte solutions were prepared from reagent
grade chemicals and distilled water which had been passed
through two ion exchange columns. Typical resistivity was
on the order of 10 ohms-cm. Nil chloride solutions were
prepared according to Table 3.

Immediately before use electrolytes were deoxygenated
by vacuum deaeration. All beakers, flasks, and corrosion
cells used for nil chloride work were used only for nil
chloride work, and were periodically cleaned with nitric
acid to ensure freedom from chloride contaminants.

The Differential Ref lectometer
Introduction

The differential ref lectometer is a device which
measures the difference in reflectivity of two samples as
a function of wavelength. The technique is a form of
modulation spectroscopy where the modulated parameter is
the surface composition of the samples. Originally de-

55

Table 3

Composition of Electrolyte Used
in Nil Chloride Experiments

pH

Buffer

Na

OH

4

100 ml 1.0 M KHP

5

100 ml 1.0 M KHP

108

ml

.5

M

6

100 ml 1.0 M KHP

180

ml

.5

M

7

14 3 ml 0.7 M H BO

10

ml

.1

M

dilute to

8

14 3 ml 0.7 M H^BO

100

ml

.1

M

2000 ml

9

14 3 ml 0.7 M H BO

100

ml

.5

M

10

14 3 ml 0.7 M H BO

184

ml

.5

M

11

132 ml 0.7 M H BO

220

ml

.5

M

56

veloped to monitor changes in the band structure of metals
with alloying, it is used here to investigate the
growth of thin films of corrosion products on metal
substrates. In this case the differential ref lectometer
scans a light beam between two areas of the same sample,
one of which is clean and the other covered with a thin
film of corrosion product. The reflectivity of the copper
substrate, which is common to both sides of the sample,
does not contribute to the differential ref lectogram,
while the absorption spectrum of the corrosion product
does contribute.

The Instrument

A schematic diagram of .the instrument used in this
work is shown in Figure 9. Light from a high pressure
Xenon light source* is passed through a scanning mono-
chromator** and reflected by a flat mirror onto an
oscillating mirror. The oscillating mirror scans the
light beam across the two areas of the sample at a fre-
quency of 60 Hz. The size of the area to be scanned can
be varied by changing the voltage applied to the mirror.

*Xenon light source, Mc Pherson model 613, 75 W,

Mc Pherson, Inc., Acton, Massachusetts
**Grating monochromator , Mc Pherson model 218, Mc Pherson,
Inc., Acton, Massachusetts

57

- .*

i '<z

-x -Z
u a

.2 E
<

o
S

bo

03

e
u

CO

5 8

Normally the total area scanned is about 2x4 mm. In the
present work, one area of the sample is clean copper, and
the other copper with a thin layer of corrosion product on
top. The reflected light is focused on a frosted quartz
plate in front of the photomultiplier tube.* The purpose
of the frosted plate is to diffuse the light across the
face of the photocathode , since the response of the
photocathode normally varies across its surface. The
signal from the photomultiplier is of the form of a square
wave superimposed on a DC signal. This output signal is
split into two channels. The first passes into a lock-in
amplifier which is tuned to the frequency of the oscil-
lating mirror. This produces a slowly varying DC signal
whose amplitude is proportional to the square wave com-
ponent of the signal from the photomultiplier. The output
from the photomultiplier is also passed through a low
pass filter, which smoothes out the AC signal and produces
an output whose amplitude is proportional to the average
reflectivity, R. These two signals are then combined in
a divider circuit to produce the AR/R signal, which is
plotted on the y-axis of an x-y recorder. A voltage from
the monochromator supplies the signal to the x-axis of the

^Photomultiplier tube, EMI extended S-20 type, EMI, Inc.,
Middlesex, England

59

recorder proportional to the wavelength, A. In its
present form, the differential ref lectometer scans a
wavelength range of 200 to 800 nm (6.2-1.6 eV) in about
one and one-half minutes.

The differential ref lectometer used in this work is

an improved version of the instrument described else-

4
where. The chief improvements are the substitution of

mirrors for lenses in order to eliminate chromatic abera-
tion, and a new monochromator to improve resolution.
Improvements to the electronics have also been made to
maintain the average output voltage of the photomultiplier
at a constant level by varying the applied voltage auto-
matically .

Advantages and Disadvantages

Conventional optical studies of corrosion products
have typically been performed using ellipsometric techni-
ques. As mentioned in the introduction, this technique
can determine the thickness, d, of a thin film if its
optical constants n and k are known. Layered films,
however, may confuse the issue by giving anomalous values
for n and k. In addition, for in situ studies, the effect
of the absorption spectra of the electrolyte and windows
must be taken into account. Finally, conventional ellip-
sometry is not particularly rapid.

60

Differential ref lectometry , on the other hand, has
certain advantages over ellipsometry . Among these are the
speed of the analysis and the fact that each corrosion
product appears to have a unique differential reflecto-
gram. However, the most important advantage of the
technique is that it is a differential technique, so that
all factors contributing to the reflectivity which are
common to both sides of the sample cancel out. For
example, the electrolyte solution which the light beam
passes through during in situ measurements has an
absorption spectrum which is a function of wavelength. If
e^ and e~ are the voltage levels produced by the photo-
mulitplier tube when it is illuminated by the light re-
flected from the two halves of the sample, and a (A) is
the function describing the absorption of the electrolyte
as a function of wavelength, then

e1 = a(A) R-,(A)

and

where R, and R2 are the reflectivities of the first and
second half of the specimen, respectively.
Thus ,

e1-e2 a(A)R1-a(A)R2 Ri"R2

e1 + e2 a(A)R1 + a(A)R2 Rl + R2 ' R
( 2 ^ ( I ) C — 2 -*

^ (3)

61

The effect of the absorption spectrum of the elec-
trolyte cancels out. This argument also holds for other
"machine parameters" such as the spectral output of the
lamp and the response of the photomult iplier , both of
which are also a function of wavelength. In addition,
recent improvements to the instrument such as matching the
time constant of the AR and R channels have reduced the
effect of transients such as line voltage fluctuations.

The technique of differential ref lectometry is not
without its limitations, however. Since it requires a
"standard" or reference sample, it may be difficult to
implement in some cases. When compared to ellipsometry ,
it does not seem possible to determine the optical con-
stants of the film.

When compared to electron spectroscopy, differential
reflectometry lacks the ability to analyze the surface of
the thin film, since light penetrates the film to a
greater extent than an electron beam. This also implies
that no depth profile of the film may be made. In addi-
tion, the analyzed area is presently 2 mm square on each
half of the specimen, which eliminates the possibility of
analyzing microscopically small areas of the sample.
Finally, for in situ analysis, a transparent lacquer must
be used to cover the "clean" or reference half of the

62

sample. This is difficult to achieve in practice, and
even a seemingly transparent film will absorb a light beam
to some extent. This is acceptable if no additional
structure is added to the differential ref lectogram.

In conclusion, each experimental technique offers
certain advantages over the others. It is believed that
differential ref lectometry can compliment the better known
techniques of AES, ESCA, and ellipsometry .

Other Equipment
Standard techniques were used for the electrochemical
parts of this study. Figure 10 shows a schematic of the
conventional corrosion cell used in this work. The body
of the cell is made of glass which had been cleaned with
Chromerge* and rinsed with concentrated nitric acid to
remove surface contaminants. A hard rubber stopper on
the top of the cell has ports for pyrex tubes which can
accommodate the sample electrode wire and bright platinum
auxiliary electrode wire. A Luggin probe, or salt
bridge, contains electrolyte and is connected to the small
electrode reservoir outside the corrosion cell where the
saturated calomel reference electrode is located. Pro-

*Chromerge , trademark Manostat, Inc., New York, New York

6 3

AUXILIARY
ELECTRODE

SAMPLE
WIRE

SALT
BRIDGE

H2
OUT

1 1
1 1

XT

SAMPLE

MAGNETIC
STIRRER

Figure 10. Schematic diagram of the standard corrosion
cell used for non-in situ experiments.

64

visions are also made for a thermometer and for a fritted
glass gas diffuser, whose purpose is to bubble hydrogen
through the electrolyte and keep it deoxygenated . A
Teflon encapsulated magnetic stirrer maintains circulation
in the electrolyte.

Figure 11 shows the corrosion cell designed for the
in situ examination of thin film corrosion products. The
major differences between the in situ cell and the con-
ventional corrosion cell are the addition of a quartz
window for the entering and exiting light beam and a
Teflon sample holder to keep the sample rigidly fixed at
the focal point of the oscillating mirror. In addition,
the auxiliary or platinum electrode is in the form of a
ring around the sample in order that it does not interfere
with the light path. The only materials which are in
contact with the electrolyte other than the sample are
made of quartz, Pyrex, Teflon, Tygon, or covered with
Miccrof lex.

The potentiostat used in these experiments was de-
signed and constructed in-house and was based on earlier
similar designs. The purpose of any potentiostat is to
maintain a constant potential difference between the
sample electrode and the reference electrode, which in
this case was a saturated calomel electrode. In order to

6 5

SAMPLE
WIRE

QUARTZ
NDOW

SAMPLE
TEFLON HOLDER

PLATINUM
ELECTRODE

MAGNETIC
STIRRER/

Figure 11. Schematic diagram of the corrosion cell used
for in situ experiments. Details of the
sample holder are not shown for clarity.

66

maintain the potential difference, sufficient current is
applied from the auxiliary (platinum) electrode to keep
the voltage drop through the electrolyte between the
sample and the reference electrode at the desired value.
The potentiostat constructed for this work can maintain a
potential within one millivolt of the desired value for
periods in excess of three days, and contains special
temperature compensating circuits to eliminate voltage
drift over all reasonable temperature fluctuations.

Finally, it presents an unusually high input impedance to

1 2
the reference electrode of 10 ohms.

Operating Conditions
Samples were prepared for normal or in situ analysis
as described previously. Approximately 700 ml of elec-
trolyte was deaerated by vacuum deaeration and trans-
ferred to the corrosion cell. In most cases, the sample
was placed in the cell and the potential between the
sample and reference electrode adjusted so as to put the
operating conditions in the immunity region of the
Pourbaix diagram (such as, 550 mv SCE at pH 9.2). Under
these conditions, the stable species is copper, and no
corrosion product should form. After approximately five
minutes, the potential was changed to the value desired

0 7

for the experiment in as short a period of time as pos-
sible. Hydrogen gas was bubbled through the electrolyte
at the rate of approximately 5 cc/sec. at all times to
keep the solution deoxygenated . In addition, the elec-
trolyte was continuously stirred by the Teflon encapsu-
lated magnetic stirrer. Only during actual in situ mea-
surements were these operations suspended, in order to
reduce mechanical vibration in the cell.

After potentiostating for the desired amount of
time, samples not to be measured in situ were removed
from the cell, rinsed with distilled water, and dried with
filtered, dry air. They were then immediately measured
with the differential ref lectometer . Time between re-
moval of the sample from the cell and measurement of the
differential reflectogram was typically two minutes.

Other Considerations

Any new analysis technique typically has a number of
problems which must be resolved before the technique can
be reliably applied. In this case, the problems may
conveniently be divided into two areas: those related to
electrochemistry and those related to the differential
ref lectometer .

It is well-known that electrochemical techniques have
certain problems associated with them due to the nature of

68

the techniques. For example, the saturated calomel
reference electrode must contain a truly saturated solu-
tion of potassium chloride (KC1) in the electrode
reservoir or it will not provide a stable reference
voltage. In order to assure this condition, a small
amount of KC1 crystals are kept in the electrode tip to
maintain complete saturation. A similar problem exists
with the salt bridge, or Luggin probe. If the resis-
tivity of the electrolyte solution is high, there will be
a voltage drop between the tip of the probe in the cor-
rosion cell and the calomel electrode at the other end of
the probe. This effect, which would lead to the incorrect
potential being applied to the sample, has been minimized
in this work by the careful design of a very high
impedance input to the potentiostat . This reduces current
drain from the calomel electrode to the picoamp range, so
that a relatively high resistivity in the electrolyte may
be tolerated without an appreciable voltage drop. How-
ever, the potentiostat is susceptible to both power
failures, which are generally detectable, and reductions
in line voltage, which are not so readily detected. If
the voltage to the potentiostat is sufficiently re-
duced, the potential supplied to the sample can shift in
unpredictable ways. If undetected, this may lead to

69

erroneous results. Continuous voltage monitoring and
multiple tests at each point in the Pourbaix diagram help
identify this problem.

Another difficulty which is difficult to resolve is
the possibility of film formation during the moments
between sample immersion and activation of the potentio-
stat, and the similar problem of film formation while the
potentiostat is being adjusted to the desired potential.
For example, after coating half the sample with
Miccroflex, approximately twenty minutes must pass before
the lacquer is completely dry. During this time, a thin
layer of air-formed oxide can form on the exposed half
of the sample. Attempts to observe this film using the
differential ref lectometer have not been successful,
which indicates that if the film does exist, it must be
very thin. Nonetheless, as was previously mentioned, it
has been general practice in this work to "pre -potentio-
stat" the sample in the immunity region of the Pourbaix
diagram for a few minutes prior to the actual experiment
in order to encourage dissolution of this hypothetical
film. Referring to the Pourbaix diagram of Figure 12,
however, it is clear that to adjust the potential from the
immunity region to the CuO region, the potential must pass
through the Cu?0 region. If a Cu?0 film forms rapidly, it

70

may interfere with the formation of the CuO film. This
transition time spent in the undesired region of the
Pourbaix diagram may be minimized but not eliminated. The
fastest rates obtainable are limited by the inherent time'
constant of the potentiostat to one to two seconds.

Experimental considerations concerning the dif-
ferential ref lectometer are relatively straightforward.
While a differential reflectogram is being made of an
in situ sample, the hydrogen being bubbled through the
electrolyte must be stopped and the magnetic stirrer
turned off to eliminate mechanical vibrations which
increase the amount of electronic noise in the system.
In addition, since it is well-known that light can affect
the growth of the thin film corrosion products, '4t)>4/
light from the monochromator must be blocked except when
actual measurements are being made.

Summary
The differential ref lectometer was used to measure
the difference in reflectivity between the corroded and
uncorroded areas of electrochemical specimens. The speci-
mens were prepared using standard metallographic techni-
ques, with extra care being used to eliminate carbide em-
bedding and sample contamination. Electrolyte solutions

71

were prepared from reagent grade chemicals and deaerated
before use. Normal as well as in situ corrosion cells
were designed to have only inert substances in contact
with the electrolyte. A plot of the normalized difference
in reflectivity of the clean half of the sample minus the
corroded half can be obtained as a function of wavelength
over the spectral range 800-200 nm.

SECTION IV
RESULTS AND DISCUSSION

Introduction

The purpose of this work was to investigate the pos-
sibility of using differential ref lectometry to identify
and study thin film corrosion products on metal sub-
strates. For this initial investigation, copper was
chosen as the base metal because it has easily formed
thin film corrosion products which are visible to the eye
This ensures that there are optical transitions which
would be detected by the differential ref lectometer ,
since the instrument can examine a wavelength range
greater than that visible to the eye. In addition, work
had previously been performed here on copper alloys using
the differential ref lectometer , so the mechanics of pre-
paring samples were known as well as the theory of inter-
band transitions in copper and their relation to peaks in

differential ref lectograms .

52
Both the theoretical or equilibrium (Figure 12A)

5 3
and experimental (Figure 12B) Pourbaix diagrams are

available for copper in nil chloride solutions. In the

basic half of the diagram (pH 7-14) three species are

72

73

X

CL

— • o
o | O

Q)

</)

LU

+

O

6

o
o
to

I

EU

c

o

s

•H •

Pi W

0 a

P. O

X -H

0) -M

3

H3t r-l

C o

03 co

CVJ

<N1 0)

r — N-H

o

Cs] o

1—1 I— t
p

CD

3 rH

X

•H p|

(0

O.

PL,

^ c

• H
t— 1

rt P

<fr

u <u

• H pi,

CVJ

O O

P U

o

<U Pi

^ o

74

shown to be stable depending upon the potential: copper;
cuprous oxide (Cu^O) ; and, cupric oxide (CuO) . Typical
differential ref lectograms , which will be explained in
detail later in this section, are shown in Figures 13 and
14. Figure 13 shows a differential reflectogram of a
sample prepared in the Cu?0 region of the Pourbaix diagram
(sixty-six hours at pH 9.2, -225 mv SCE) . Figure 14 is a
typical curve obtained from a specimen prepared in the
CuO region of the Pourbaix diagram (eighteen hours at
pH 9.2, +200 mv SCE). The structures are quite different
and easily distinguished. By way of comparison, a typical
compositional modulation differential reflectogram of a
copper versus copper/1 at . % aluminum alloy is shown in
Figure 15. Composition modulation spectra are not at all
similar to the differential ref lectograms of thin film
corrosion products and are therefore easily differentiated
from them.

Theory of Differential Ref lectograms of Thin Films
Thermodynamic predictions and x-ray analysis are two
methods by which differential ref lectograms of thin films
might be associated with particular corrosion products.
Another method is to predict the particular differential
reflectogram a given film would produce. In order to

7 5

O

- O

CVJ

+->

m
o

a

o

o

o

o

r
3

rO

u

CD

XJ

+->

P)

• H

O
O

<*

X

-d

h

(D

3

h

o

rt

X

Ph

<d

vD

fH

VO

PL,

a)

OJ

■— i

PhCT)

6

aJ X

(/)

fl<

rt

*

UJ

U-l

U

o

CO

ft

>

rci

e

H

Mld

o

CN

+->

OJ

u

1

o

v — '

l—l

Vj

ft

a;

rt

u

H

W>

i— i

tf

rt

•H

■H

T3

+->

c

X

o

• H

'm

nj

<D X)

<-H

h

^

3

7 6

CD

rC

o

*->

o

H-t

CVJ

o

c

o

■ H

W)

0)

O

!-.

o

o

rO

3

u

c/i

0) 3
U O
cU X
P.
CD 00

in a

ct3 -
W

m u

o CO

e >

in

o o

O +

t— I

CD rt

rt

■H

•H TJ

4->

fi

X

CD

•H

S-h

Oj

CD Xi

m

fH

m

3

•H

o

Q &.

77

°<

P-CTi

*• — "

£*&

s<

LJ

1/)00

s c
o o

• H

+->
• 3

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Sh !/)

O id
+-> 'H
U rH

r-H

£

rt

3

■H

c

■P

■ H

c

£

0

3

in

r-H

0)

cti

4h

m

o\°

■H

1-1

4->

rt

c

o

r-H

•H

+->

rC

cd

+->

r-H

•H

3

£

T3

O

H

e

<D

d.

r-H

P.

rt

o

C

o

Cn

e

<u

O X

o

+->

rH

„

rt

rH

u

GJ

H

Ph

Ph ft

perforin these calculations, the index of refraction, n,
and the index of absorption, k, for both the film and the
metal substrate must be known as a function of wavelength.
The equations necessary to calculate the reflectivity

of the film covered metal surface have been described by

7
Heavens. Referring to Figure 16, n„ is the index of

refraction of the medium surrounding the sample, which

here is either air (nQ = 1.00) or electrolyte (n„ = 1.33).

The thin film corrosion product has optical constants n,

and k,, and the thickness d, while the metal substrate has

optical constants n? and k? . We have, then,

_ no2-nrki _ 2noki

' 2 — 2 1 ~ 2 7

(nQ+n1) +k1 (n0 + IV +kl

2 2 2 2
n"-n?+k, -k„ 2 (n, k? -n?k, )

2 " (n^n^^Ck^k^2 2 " (n1 + n2)2+(k1 + k2)2

2Trk,d 2Trn,d
a = — t — [radians] y = - — t [radians]

The reflectivity, R- , of the film/metal surface is

(gx + h2)e"2fX + (g2 + h2)e2a + Acos2y + Bsin2y
2 e2ci + (g2+h2) (g2 + h2)e"2a + Ccos2y + Dsin2y

where

A = 2(g1g2+h1h2) B = 2(g1h2-g2h1)

C = 2(g1g2-h1h2) D = 2(g1h2+g2h1)

79

n0 (AIR OR WATER)

Figure 16. Schematic representation of a typical sample,
with an oxide film covering half the exposed
surface .

8 0

The reflectivity of the clean copper surface is much

easier to calculate. Calling R, the reflectivity of the

copper surface and using the same notation for the optical

constants ,

2 2
(n?-n ) +k:

Rl = % 2 &

(n2+n0)-+k2

The normalized difference in reflectivity is easily
obtained :

AR R1~R2

~ r~Tr — (63

R ' 1 K2,

t— 2 — ]

These equations should reproduce the experimental
differential ref lectograms for non-in situ experiments if
nQ = 1.00 and if values of n and k are available in the
literature for copper and its oxide as a function of wave-
length. In addition, if the effect of collodion is
neglected, it should be possible to reproduce differential
ref lectograms of in situ experiments. In this case,
nQ = 1.33, the index of refraction of water, which is
approximately that of the electrolyte.

These calculations have been performed for the case
of a cupric oxide (CuO) film since the optical constants
for that compound have been published as a function of
wavelength. The optical constants for copper which were

used in these calculations are those of Schultz and

54 55
Tangherlini ' and are given in Table 4.

Figure 17 is the plot of the variation in AR/R for
CuO film on copper substrates as a function of film
thickness for a fixed wavelength of light. The particular
wavelength used in these calculations was 600 nm, but the
curve is similar to those calculated for other wave-
lengths. The curve shows a large increase in the dif-
ferential reflectivity for the first few hundred angstroms
of film thickness, followed by strong oscillations which
are gradually damped out. The oscillations are caused by
interference effects which occur when the film thickness
is of the same order of magnitude as the wavelength of
the incoming light. For constructive interference in this
case, the film thickness must be

d = Ji- (7)

2n, *- ■*

where n, is the index of refraction of the film, as be-
fore, and m is the order of the interference. The damping
effect is due to the fact that as the film thickness, d,
increases, less light penetrates to the underlying metal
surface. The reflectivity of the film/metal surface
slowly approaches the reflectivity of a bulk specimen with
the composition of the film. Further increases in the

82

c

o

e

e

i— i

c

■ H

4h

o

o

O vO

3

U

0

£

oj

o

h

4->

O

4h TJ

o

tfl

e

00

3

<U

to

G

t/l

r«

rt

6 <t>

4h M

O

U;

•H

g

r-i

o

•h 4^

+-)

o

u

G -G

3

+->

4-1

Cft

G

03

o

r-H

(/)

ID

cd

>

01

Iff!

V

Pi

0)

< X

H

C

■H

G

0

o

+J

> V)

8 3

Table 4

Optical Constants n = n+ik for Copper and
Cupric Oxide (CuO) as a Function of Wavelength^ , 54 , 55

A [nm]

Co]
n

jper
k

Ci
n

lO

k

450

.87

2. 20

2.45

.744

500

.88

2.42

2.59

.650

550

.72

2.42

2.57

. 539

600

.17

3.07

2.60

.449

650

.13

3.65

2.65

.345

700

.12

4.17

2.64

.236

750

.12

4.62

2.65

.170

800

.12

5.07

2.62

.132

84

thickness of the film do not change the reflectivity.
Since the clean copper surface has a constant reflectivity
at a given wavelength, the differential reflectivity does
not change after the film reaches a certain minimum
thickness. For the case of the CuO film this occurs at

o

roughly 7500 A, beyond which the differential reflectivity
is a constant 121% .

Other wavelengths of incident light show similar
oscillations with slightly different periodicity. This
interference can produce peaks in differential reflecto-
grams which are not due to interband transitions but
rather are due to the thickness and index of refraction
of the film. As a result, differential ref lectometer
spectra of thin films on metal substrates can have struc-
ture which varies as the film thickness changes. For
example, Figure 18 shows the theoretically calculated

o

differential reflectogram for a CuO film of 100 A thick-
ness. Two curves are shown, one for which the medium
surrounding the sample is air (nn = 1.00) and one for
which the surrounding medium is assumed to be electrolyte
(n~ = 1.33). Both curves are essentially the same, indi-
cating that there should be little difference between
spectra taken in situ or non-in situ if the effect of
collodion is neglected. These curves differ slightly from

8 5

u

• H

■M

O
U

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o

£
d

so
o

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o

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-G

G

H

)

86

the theoretical curve calculated for a 35 A thick CuO film
in air (Figure 19) but are significantly different com-

o

pared to the spectra of a 500 A film (Figure 20) .
Finally, Figure 21 shows the calculated differential re-

o

flectograms for a 7500 A CuO film surrounded by air or by

o

an electrolyte. Film thicknesses greater than 7500 A
should produce spectra similar to Figure 21, since in this
case the light beam will not be able to penetrate the film
all the way to the film/metal interface. As can be seen
by comparing Figure 21 with Figure 19, such curves bear no
resemblance to those of very thin films. Fortunately, as
will be described below, the thin film corrosion products
which were generated in this work have a thickness which
appears to be significantly smaller than the critical
thickness at which interference effects begin to distort
the differential ref lectograms .

o

Using Equation 7 with n-, = 2.1 and A = 2500 A, the

o

first interference maximum is at about d = 600 A. Wave-

o

lengths greater than 2500 A (which is the wavelength where
most differential ref lectograms begin) place the first
maxima at higher thicknesses. Therefore for thicknesses

o

up to at least 200 A the differential reflectogram should

u

o<

£

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g

W)

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u

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r<

0)

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O

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+-)

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TO

t/)

>H

Pi

+->

o

t/1

U ,Q

3

X

LO

I— (

1— 1

^

OJ

<d

U

a

■H

iX

+->

o

0)

u

fH

o

oj

0;

Xi

c

H

o

8 9

180

400

Figure 21. Theoretically constructed differential reflec
togram of a CuO film 7500 A thick on a copper
substrate. A = 600 nm.

90

not show an appreciable effect from interference. Film

o

thicknesses greater than 7500 A should also be free of
interference effects, since the light beam should not
reach the copper substrate under the corrosion product
film. Thus there may be defined three distinct ranges
relating film thickness to differential ref lectometry . In
the first range, where film thicknesses range from 0 to at

o

least 200 A, the structure in a differential reflectogram
is constant and unique for each kind of film. The thick-
ness of the film determines the intensity of the dif-
ferential reflectivity. In the second range, extending to

o

a thickness of about 7500 A, interference effects dominate
the spectra. Finally, in the third range, where the film

o

thickness is greater than 7500 A, the differential re-
flectogram will again be unique for each corrosion pro-
duct. However, peak intensities will be constant and
unaffected by increasing film thickness.

The differential ref lectometer should be most useful
in the first range, where intensity is related to film
thickness. Figure 22 shows the variation in AR/R with
film thickness for the same conditions as Figure 17 (CuO
film, copper substrate and reference, nfl = 1.00), but over

o

the more restricted film thickness range d = 0 to 200 A.
This curve may be fitted to either a power curve,

91

^ T3

CD (D

Oh e

PhS

0 w

0 i/i

o
o

03
(/)

CVJ

C, -H

O

1— 1 bO

•H -H

■4-1 rH

O <+-!
3 O

u

n3 +->

O

O CD

m

<d

w >

CO Oj

<u >

a

M CD

ox

• H H

X

4->

1 1

o<

rH

< »

•H O

o

(J)

<-H O
CM

o

to

0 0

UJ

+j

2:

a

0 0

*:

•H

0

■M II
CJ

X

3

H

4h cd
03 pj

>

03

_l

L0 rH

03

o
m

Li_

ariation in AR/R
ubstrate over the
0 be 600 nm.

o

o

o
o

o
00

o

o

o

OJ

<J

I ft:

9 2

AR/R = .03d ' , or an exponential curve, AR/R =

02d
2.45e' " , with correlation coefficients .99 and .92,

respectively. The curve is sufficiently steep that an
uncertainty in AR/R of 51, which is extremely conserva-
tive, produces an uncertainty in the film thickness of

o

only 5 A. This thickness is on the order of a monolayer
of atoms.

Figure 2 3 shows an experimentally ohtained dif-
ferential reflectogram of a sample potentiostated in the
CuO region of the Pourbaix diagram (+500 mv SCE, pH 9.2,
eighteen hours) and a theoretically calculated dif-
ferential reflectogram of a sample covered with a CuO film

o

25 A thick. The agreement is quite reasonable. The dif-
ferences which do exist can probably be attributed to the
fact that the optical constants of very thin films are
seldom precisely the same as those of thicker films or
bulk samples. The data of Ladelfe, Czanderna, and
Biegen, which were used here, were obtained from trans-

o o

mittance measurements on films between 350 A and 1800 A
in thickness prepared by the thermal oxidation of copper.
Such films would tend to have optical constants more
nearly like bulk CuO, whereas electrochemically prepared
thin films would tend to have gradients in the optical
constants. The optical constants of the film would be

93

o i

3 r-H

U CD

o

<\J

or
<

a:

Ih 0)
Cfl U

cu o

>> rt

rt -M

<D to

•H 3

S-i O

X oo ^

0 i-H U

o +->

sh x e

Cfl CL,i-H
O -H

•M 4-> 4H

U rt

<U O

^ u u
h rt

>

<^i o

•H O
■M O S

C« ni

O + ^H

^ &0

<u +-> o

rt CD

•p ^

£ u

rt o
Ch 6 u

o

94

more like those of copper at the copper/film interface,
and more like those of bulk CuO at the film/electrolyte
interface. As a result, calculated differential reflec-
tograms prepared from the optical constants of thermally
grown compounds should not be expected to exactly match
the differential ref lectograms of electrochemically pre-
pared compounds.

o

A CuO film 25 A thick may seem surprisingly thin, but
films near this thickness are necessary to give good
agreement between the experimentally observed and the
theoretically calculated differential ref lectograms . In
addition, Kruger observed CuO and Cu?0 film thicknesses

o

on the order of 100 A or less for films grown in air or
water. In addition, measurements were performed on
several films using an interf erometric microscope.*

o

Precise measurements of film thicknesses less than 100 A
are not possible with this instrument, so an exact mea-
surement of the film thickness was not obtained. How-
ever, the instrument did unambiguously indicate a film

o

thickness of less than 100 A for each film measured. In
order to be observed with the interferometric microscope

*Model M-lll Angstrommeter, Sloan Instrument Co., Santa
Clara, California

95

the film must be overcoated with a thin layer of eva-
porated aluminum or other metal. This involves placing
the sample in a vacuum which could conceivably have
altered the film, producing inaccurate measurements of the
thickness. For this reason measurements with an inter-
ferometric microscope are not entirely reliable for
corrosion applications.

Finally, a working ellipsometer has become available
recently at the University of Florida. Measurements of
a typical CuO film, prepared by potentiostating in a nil
chloride solution of pH 9.2 for eighteen hours at +100 mv

o

SCE, indicate a film thickness of about 45 A. All these
measurements point to film thicknesses for typical speci-

o

mens of well less than 200 A. In this thickness range,
the peak positions in the differential ref lectograms
remain essentially constant, and the peak intensities may
be used to calculate the film thicknesses to a high degree
of precision.

Non- in Situ Experiments
In this section the results of experiments which were
not performed in the in situ cell will be discussed.
Longer exposures to the electrolyte are possible using
this method than in true in situ studies because of the

96

tendency of the protective collodion film, used in
in situ experiments to cover the copper reference side of
the sample, to break down after a certain amount of time
in the electrolyte. The disadvantage is that changes in
some films are possible between the time of removal of
the sample from the electrolyte and the measurement of the
differential ref lectogram. Three types of film formation
were studied: films formed in air; films formed in dis-
tilled water; and, films formed in electrolyte solutions
during potentiostat ing .

Films formed during exposure to the atmosphere were
prepared by the simple technique of covering half the
sample with a protective layer of Miccroflex and per-
mitting the sample to remain exposed to the atmosphere.
An inverted beaker or glass plate was used to prevent
dust from settling on the specimen. Similar experiments
were performed with samples exposed to an atmosphere of
pure oxygen. In these cases the sample was placed in an
airtight dessicator which was repeatedly flushed with
oxygen .

The results of the experiments where the sample was
exposed to the uncontrolled atmosphere were seldom com-
pletely reproducible. Greater or lesser amounts of
various oxides could be formed depending on the initial

9 7

conditions, length of exposure time, and relative humidi-
ty. As a result, between ten and twenty runs were made
for each variation in the experiment, under conditions
which were kept as identical as possible, in order to
determine trends of film formation. Normally approximate-
ly 80% of the runs produced essentially identical results.

Samples exposed to a normal indoor atmosphere for a
moderate period of time (one to three days) yielded dif-
ferential ref lectograms essentially the same as Figure 13;
that is, indicative of cuprous oxide, Cu?0. Other samples
exposed to air for longer times (five to fourteen days)
tended to produce CuO patterns, as did all the samples
exposed to a pure oxygen atmosphere. Kruger has pointed
out that Cu?0 is the oxide produced upon initial exposure

of copper to an uncontrolled atmosphere. However, the

5 7
Cu-0 phase diagram predicts that CuO is the stable

species if copper is exposed to dry air below 375°C. This
apparent inconsistency can probably be explained by the
fact that the normal Florida atmosphere is not at all
dry. Water vapor probably induces the formation of Cu?0
rather than CuO. In addition, CuO tends to be reduced to
Cu90 in the presence of metallic copper, so it is likely
that there is at least a monolayer of Cu-0 at the inter-
face between Cu?0 and Cu. Hence copper exposed to the

98

atmosphere for a brief period of time may well show more
of a Cu?0 pattern than a CuO pattern. Presumably exposure
to the atmosphere for longer times or exposure to pure,
dry oxygen would favor the growth of the equilibrium
oxide, CuO, as was observed.

In order to study the films formed in distilled
water, samples were prepared in the usual manner, par-
tially covered with Miccroflex, and immersed in a beaker
containing approximately 500 ml of triply distilled water.
A magnetic stirrer was used to maintain circulation. In
some cases the water was simply exposed to the atmosphere;
in others oxygen was bubbled through the water at a rate
of about 10 cc/sec.

Samples placed in distilled water which was exposed
to the atmosphere usually produced differential reflecto-
grams indicative of mixed oxides (CuO and Cu?0) with the
Cu20 being predominant. In a few cases only Cu^O was
apparent. This is in agreement with the work of
Kruger, who also found Cu^O films. Kruger has also
noted that the Pourbaix diagram predicts the formation
of CuO, rather than Cu20, under these conditions.

One of the advantages of the differential reflecto-
meter is its ability to clearly demonstrate the presence
of mixed oxides, such as are found in the above experi-

99

merit. The results seem to show a simple addition of the
spectrum of one compound to the spectrum of the other.
In the case of samples placed in distilled water through
which oxygen was continuously bubbled, mixed oxides of
Cu20 and CuO were again produced. A typical result is
shown in Figure 24, where the structure at 310, 330, and
380 nm is characteristic of Cu~0 (see Figure 13), and the
rising tail visible below 300 nm is characteristic of CuO
(see Figure 14) . Although a quantitative analysis of
such mixed oxides is not possible at this time due to a
lack of information on the optical constants of the Cu?0
phase and to the increased mathematical complexities of
multilayer reflection, such analyses are certainly pos-
sible in principle.

The most extensive studies to date have been in boric
acid buffered electrolyte with samples potentiostated in
some particular region of the Pourbaix diagram. For the
most part these experiments agree well with the Pourbaix
diagram determined experimentally by electrochemical
techniques (Figure 12B). However, the differential
ref lectometer provides additional insight into the com-
position, thickness, and uniformity of the corrosion pro-
ducts.

An example of the additional information which may
be obtained using optical techniques is shown in Fig-

100

p

CD

p

nj

£ <D

re; •

13 PO

o

o

rH M

•h 3-d

ro

on in dist
bbled thro
of Cu?0 an

O

■H 3

o

C/) 43 CD
P T3

*-

d by imme
of oxygen
mixed oxi

o

CD

P 6 rt

o

£

Ph CD <4H

10

CD p O
P P

(_

ftui (J

' — •

•H
CD to P

s<

sampl
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teris

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arac

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o xi

o
o

o
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00

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cr

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ro

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03 CD CD

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101

ure 25, which shows a differential ref lectogram of a
sample potentiostated at -50 mv SCE and pH 9.2 for
eighteen hours. Three scans are shown, taken at three
different areas of the sample. Several points are
readily apparent.

1) The thin film corrosion product is primarily
Cu20, as indicated by the structure at 315, 330, and
380 nm.

2) The rising slope between 300 and 200 nm indi-
cates a small amount of CuO present in the sample.

3) Variations in intensity indicate differences in
film thickness, with the film thickness decreasing from
position C to position A.

Mixed oxide films such as those indicated by the
spectra of Figure 25 are not uncommon. This sample is
typical of those potentiostated near the Cu?0/CuO equili-
brium line (-50 mv SCE at pH 9.2 is essentially on the
equilibrium line) . It illustrates the fact that in such
regions of the Pourbaix diagram one corrosion product is
not much more stable than the other. Initial conditions,
such as the presence or absence of a spot of oxide, or a
local homogeneity in the copper or electrolyte, may in-
fluence which corrosion product may form in any specific
microscopic area. Samples potentiostated well into a

102

<D O
13 r^

rd X

u Ph

• H

,C 4->

3 rt

-w

CD u

i-H CO

a

e >

co 6

V)

o

0) LO

E i

rt v— (

CO

CD

a> C

rC -H

4-> rH

m 6

O 3

■H

I/) Sh

CO ^

CD -H

E

(h i-H

CO -H
3

c

<o cr

CD CD

(h

,C| O

«^

+-> 3

u

<+H v-s

o o

(NI

CO 3

6 U

CO

Jh CD

MX

O +->

+-)

U fH

CD cO

rH CD

m C

CD

fmj i/i

CD U

H(J 3

cO cO O

•H +J ,C

+-> CO

rt o c

CD -i-l CD

^ +J CD

CD id +J

<+H CD X

m +-> to

•H O -H

Q ftd)

103

specific region of the Pourbaix diagram consistently show
only the expected corrosion product, as in the case of the
differential ref lectograms shown in Figure 13 (-225 mv
SCE, pH 9.2), which is typical of a pure Cu~0 film, and
Figure 14 (+200 mv SCE, pH 9.2), which is typical of a
CuO film.

A large amount of data was collected with the aim of
defining more precisely the positions of the lines de-
lineating the areas of stability of the experimental
copper/nil chloride Pourbaix diagram. This is complicated
by the fact that these lines are coexistance lines, so
that both compounds are present near the boundaries, as
confirmed by the differential ref lectometer . Furthermore,
the boundaries can be slightly time-dependent. For
example, a sample potentiostated just into the CuO region
of the Pourbaix diagram, but near the Cu^O area, might
show Cu^O components in the structure of the differential
reflectogram if the exposure time was brief. In this case
the CuO which formed against the copper surface might be
reduced when the potential was removed. Alternately, as
was mentioned earlier, a thin layer of Cu20 might always
be present at the Cu/CuO interface, regardless of where in
the Pourbaix diagram the experiment takes place. In this
case, very thin (that is, short exposure time) CuO films

104

may show appreciable Cu?0 structure due to a monolayer of
Cu-,0 at the interface. In this regard, it should be re-
emphasized that even a monolayer can produce significant
changes in the differential reflectivity. In the case of
CuO (see Figure 22) , a change in thickness of a single

o

monolayer (about 5 A) can cause a change in the dif-
ferential reflectivity of several percent. Such a change
is very readily detected with the present instrument.

As a prelude to true in situ measurement of the dif-
ferential reflectivity, certain experiments were under-
taken to monitor changes in film properties with changing
experimental conditions. Figure 26A shows a differential
reflectogram of a copper sample potentiostated in a nil
chloride solution of pH 10 at +500 mv SCE for sixteen
hours. This potential is well into the CuO region of the
Pourbaix diagram. The resulting spectra is similar to
Figure 14, and is characteristic of CuO. After measure-
ment, half of the sample which serves as a pure copper
reference, was recoated with Miccroflex lacquer, and the
sample immersed in fresh electrolyte. This time, how-
ever, the sample was potentiostated in the Cu~,0 region of
the Pourbaix diagram, at -225 mv SCE. After twenty hours
the sample was removed and remeasured, producing the

105

106

spectra of Figure 26B. New structure, characteristic of
Cu?0, is evident at 320 and 380 nm, superimposed on the
strong CuO background. The clean copper side of the
sample was again recoated, and the sample again potentio-
stated at -225 mv for an additional sixty-eight hours.
When the sample was measured for the third time, the
curve of Figure 26C was produced, showing clear evidence
of extensive Cuo0 film formation. The peak positions and
even their relative intensities are characteristic of

Cu20

The differential ref lectometer yields other informa-
tion on the films formed in Figure 26 in addition to
their identity. The zero lines of Figure 26 have been
shifted for clarity, but a superposition of the three
curves indicates that the CuO pattern remains relatively
constant, while the Cu?0 pattern "grows" on top of it.
Since the intensity of the CuO structure is directly pro-
portional to the thickness of the film (see Figure 22) ,
it is reasonable to assume that the thickness of the CuO
film does not change substantially when the potential is
shifted to the Cu?0 area of the Pourbaix diagram. Hence,
the shift in potential induces growth of a Cu20 layer under
the existing CuO layer, rather than the dissolution of the
CuO layer. This is significant observation which could

107

not be readily obtained with strictly electrochemical
techniques .

In Situ Experiments
One of the major advantages of the differential re -
flectometer compared to other techniques is its ability to
perform in situ measurements. Theoretical considerations,
explained in the experimental procedures section, indi-
cate that an electrolyte surrounding the sample and the
presence of a window to the corrosion cell should not
introduce additional structure to the differential re-
flectogram. Figure 27 shows two differential reflecto-
grams of samples potentiostated in the Cu?0 region of the
Pourbaix diagram (-200 mv SCE , pH 9.2) for five and one-
half hours. One is the spectrum of a sample prepared in
the normal manner, where Miccroflex covered half the
specimen surface. The other represents a sample prepared
in collodion covering half the specimen surface and
analyzed in situ- The sensitivity, or amount of amplifi-
cation, for the two curves is identical. Three points
stand out.

1) The peak positions of each curve are at the
same wavelengths.

2) There is no additional structure introduced in
the in situ spectrum.

108

109

3) There is some loss of intensity or amplitude of
the in situ curve compared to the non-in situ curve, and
an associated increase in the noise level.

The first two points are most important because they
establish the fact that this technique of making
measurements gives results which are consistent with
simpler measurements not performed in situ. The third
point indicates that absorption of the light as it passes
through the window, electrolyte, and collodion, as well
as losses due to reflection at the air/window and window/
electrolyte interface and small amounts of turbulence in
the electrolyte, combine to produce a somewhat less
intense and more noisy signal. This effect is not un-
expected, nor is it troublesome as long as no additional
structure is introduced in the differential ref lectogram.

The spectra of Figure 27 were made after only five
and one-half hours in order to minimize the degradation
of the collodion coating on the in situ sample. In order
to investigate the effect of the collodion on the inten-
sity of the spectra, an additional experiment was per-
formed. First, a sample was prepared in the usual manner
in the Cu^O region of the Pourbaix diagram. The sample
was removed from the electrolyte, dried, and the Miccro-
flex stripped off. Figure 28A represents the differential

110

reflectogram made from this sample. The sample was placed
in the dry in situ corrosion cell and another reflectogram
made, Figure 28B. The lack of significant changes in the
spectrum shows that the effect of the presence of the
window is negligible. (The zero lines of Figures 28A and
28C have been shifted for clarity.) Next the in situ cell
was filled with electrolyte and a third differential re-
flectogram taken immediately, before the thin film cor-
rosion product could be altered to any great extent. This
spectrum is shown in Figure 28C, which shows how an
in situ differential reflectogram would appear if there
were no collodion present on the "pure" copper side of the
specimen. Compared to Figures 28A and 28B, there is a
general sharpening of the peaks and an increase in in-
tensity. These changes can be attributed to the coupling
effect of the electrolyte, which acts as a light pipe to
optically couple the window and sample more efficiently
than when the sample is surrounded by air. The index of
reflection of the corrosion product and the quartz window
is more nearly matched by the index of refraction of the
electrolyte than that of air, resulting in a more ef-
ficient optical coupling of the two surfaces. A similar
effect is used in oil immersion optics. Here it partly
compensates for the absorption of the light beam by the

Ill

c

60

c

<D

■H

X

i

+->

o

nC

c

'/)

■H

„

T3

s

rt

r— 1

rt

3

u

>

>.

o

+j

u

IH

aj

rH

rt

Q)

x ,c

r — N

•M U

0)

v '

r— 1

fi

ft

•H

0)

s

+->

rt

~

>-

t/i

, — >

rH

<

o

rt

> — '

u

e

C

rt

■H^

»H

+->

bflT3 -H

O

<D £

4->

H

u

3TJ

a;

to a)

i— i

rt i— i

m

<D rH

<D

S-H

c

CX

<D

6

,3

(h

a

+i

a;

W

•rJ

Mh

rn

<-h

Q)

• H

^

K

Q

4->

•^

112

collodion. Without this coupling effect, uniform
absorption of the light by the collodion would decrease
the intensity of in situ measurements relative to non-
in situ measurements more than is indicated by Figure 27.

Several experiments have been performed to monitor
the growth of corrosion films in situ. One example is
shown in Figures 29 and 30 which represent the evolution
with time of the differential ref lectograms of a sample
potentiostated in the Cu-O region of the Pourbaix diagram
at pH 9.2 and a potential of -200 mv SCE. These curves
are typical for samples potentiostated under these condi-
tions, although in this case the collodion covering the
"clean" copper resisted breakdown by the electrolyte for
an unusually long time. Immediately after immersion
(t = 0) , the differential ref lectogram shows a reasonably
flat spectrum, with no evidence of structure. The dis-
placement from the zero line actually decreases during
the first three hours after immersion, perhaps showing the
dissolution of a previously formed oxide. It is also
possible that the decrease in intensity is due to inter-
ference effects discussed in the theoretical section.
This was probably not the case, however, since no further
oscillations were observed. In addition, interference

o

oscillations would imply a film thickness of over 500 A,

113

ES

+-> 03

DO

(D -H

03
+-> X

(/) -H
O 03

•H ,n
+-> ^

G 3

CD O

■P Cl,
O
P-, CD

B o
03
<S) G

o

Sh -h

O, 0)
& Sh
O

U O

(N

o3 =3

U

O 0)

s

o3 £
U -H

C>0

O c/)

4-> -H

0) ,c;

o3 oj

•H .
+-> CTl

G

en ac

0)

m w

•H CJ

T3 CO

3 >

£ CXI

Si
00

114

O
1^-

-C

IT)

-C

<*-

<T>

CD

if)

<fr

^

03 0)

U p

CO -H

r— 1

p

•H O

O

h

O

CD CD
&0 M

CJ

p

03 CD
U -P

rP tfl

o

+-> CD

o

CD >H

ro

■P P
O

CD

•xi

CTi 4->

o

CXI

o

<D P

<fr

,__,

Sh -H

3 M

E

U) ^

•H -0

c

Uh

*

X

X

<P i-H

o

O JD

n3

lO

p u

CD <D

6 U

■H P,

Sh p.

CD 03

o

P,

X CD •

o

p -P

CD

3 Oj.H

+> ,P P

V U cU

W i— 1

P O

K O

V C Is

o

O
CD O 4H

o

X, T3

h-

P n3
00 CD

m 0) 4->

O > MH

Si >H

P P ,P

O U oo

•H

P CD P

o3 ,p 0)

P P CD

P &

■H CD

P U <D

P P >

O -H 03

UOOX

115

which is generally not observed for Cu?0 in aqueous solu-

20
tions. Finally, few in situ experiments have shown a

similar decrease in intensity. This implies that the

initial anomalous intensity decrease is caused by the

dissolution of a previously formed film, which may

occasionally be produced under conditions such as lengthy

exposure to the air, high humidity, and so on.

After about three hours, typical Cu?0 structure be-
gins to appear. The amplitudes of the peak increase with
time, and the curves more nearly approach those of
"standard" Cu90 patterns, which were not measured in situ.

The intensity of the mean peak near 385 nm as a
function of time was fit to linear, power, logarithmic,
and exponential functions by the method of least squares.
The spectrum taken after three hours was used as a zero
line because of the presumed dissolution of a previously

formed film. The best fit was provided by a power curve

— 70

of the form AR/R[|] = .62t which had a correlation

?
coefficient of r = .99. If a theoretical curve of AR/R"

versus thickness were available for Cu?0 as in the case of

CuO (Figures 17 and 22) the kinetics of the growth of the

oxide could be readily determined.

Experiments to monitor the growth of CuO films were

not successful due to problems with breakdown of the

116

collodion protective layer after short exposure times.
The relatively high potentials applied to the sample when
it is potentiostated in the CuO region of the Pourbaix
diagram appear to accelerate the onset of crevice cor-
rosion under the film.

Further Discussion

When using the differential ref lectometer in cor-
rosion work, some way of matching the corrosion product
and a specific differential reflectogram must be pro-
vided. Perhaps the most elegant method is to calculate
the differential reflectogram from the optical constants
and thickness of the film. This method, described in
detail earlier in this section, works well when the opti-
cal constants of the film are known as a function of
wavelength. If these data are not available, as in the
case of Cu-,0, other methods must be employed to match the
compounds and the spectra.

One technique is to potentiostat a sample well into
a specific region of the Pourbaix diagram and assume that
the predicted species is the one which is observed. This
technique probably works well in most cases, but is rather
limited from a research point of view.

Another is to grow a thick layer of some corrosion
product, analyze it using X-ray diffraction techniques,

117

and correlate the results with a differential reflecto-
gram of the film. Thinner films, which would have the
same differential ref lectogram, could be identified even
though they themselves were too thin for X-ray analysis.

In order to test this idea, Cu70 and CuO films were
prepared by potentiostating copper in the normal manner
for periods as long as a week. X-ray analyses at the
University of Florida failed to detect any trace of the
corrosion product. The samples were sent to
Dr. B. Cavin at Oak Ridge National Laboratories where a
special X-ray apparatus employing monochromatic X-rays
and digital signal averaging techniques was used in an
attempt to detect the films. After runs as long as
seventy-two hours, the only X-ray lines which were ob-
served other than those belonging to copper were the
strongest line of Cu20 and the strongest line of CuO.
Both peaks were detected on both samples, and both peaks
were so weak as to be barely distinguishable from back-
ground. It is likely that the time lag between the forma-
tion of the films and their measurement enabled both
oxides to form on both samples. In any event, X-ray
analysis does not seem to be a promising technique for
confirming the identity of these films.

One final technique which may be used to confirm the
identity of a corrosion product is to match its band

118

structure or optical reflection spectrum with structure
evident in the differential ref lectogram. This technique
is useful in the case of Cu~0, because of the extensive
optical spectroscopy and band structure calculations

which have been performed on that particular

• , 20, 30-32,35-47
oxide. ' '

The band diagram of Cu~0 which is shown in Figure 5
reveals a band gap of 1.77 eV. According to these cal-
culations the smallest energy for optical interband
transitions should therefore be 1.77 eV. It is generally
realized that the accuracy of band calculations is between
0.5 and 1 eV and depends strongly on the method of calcu-
lation and the input data. The experimental value for the

20
band gap was found to be 2.2 eV, which, in the light of

the preceding statements, can be considered to be in fair
agreement with the calculations.

The differential reflectogram of Cu?0 shown in Fig-
ure 13 shows structure at 2.25 eV which, as stated above,
is identical to the energy associated with the band gap.
Therefore, the structure at 2.25 eV can be tentatively
attributed to the onset of interband transitions. From
the calculated band diagram (Figure 5) one may deduce that
the next set of interband transitions takes place approxi-
mately 1 eV above the threshold energy. This agrees with

119

our observations, where the second peak in the dif-
ferential reflectogram occurs at 3.26 eV (380 nm) .

Following this transition, the calculated band dia-
gram (Figure 5) predicts a multitude of possible closely
spaced transitions at higher energies. This is confirmed
by the differential reflectogram (Figure 13) which shows
complex and broad structure in the 3.4 to 5.4 eV energy
interval (365 nm to 2300 nm) .

Experimental reflectivity data, shown earlier in
Table 2, shows essentially the same picture. Table 5 is
a reproduction of Table 2 with the results of this study
added for comparison. The results evident from this
table, in addition to the prediction of the Pourbiax
diagram and the results of the X-ray analysis, seem to
establish beyond reasonable doubt that differential re-
flectograms typified by Figure 13 represent Cu-O-

Another complicating factor which can cause errors in
the analysis of thin film corrosion products when using
optical techniques is the effect of surface roughening.
The equations used in ellipsometry , or for that matter
differential ref lectometry , assume specular reflectance
from the metal substrate. Surface roughening causes
scattering of the light beam and can interfere with
ellipsometric measurements. Presumably the same sort of

120

o
(J

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>

3

■M

LO

r-l

LO

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t"s

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to

1— 1

Tt

to

LO

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u

X

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^ Pi

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O 0)

E

e o

CN

o +->

to

r< u

•+H CD

Tj

[^

vO

vO

to

LO

CT,

CD

c-^

OO

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LO

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to

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to

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to

r--

rH

oo

O

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rt

J3 -H

u

CNl

to

to

T*

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rt cd

Jh r<

o

+-> CD

<-> rx.

u m

0 m

0\ IO

\D vO

LO O

CNl vO CNl

to i—(

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lo r^

v£5 t~~

to Tt

t^~ r^ en

O CNl

CO Q

O^

'

"«

£*

CNl (X)

to to

Tfr T*

Tl" Tt Tt

LO LO

o o

r-i-M

3
CD

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00 LO

•H 03

M

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PL,

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PJ

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U)

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Ti-

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121

problems should exist with differential ref lectometry .
Surface roughening due to incomplete polishing causes no
problem in differential ref lectometry because both halves
of the sample undergo the same polishing procedure, so any
effect due to surface roughening should cancel out.
However, roughening caused by electrochemical means acts
only on the unprotected half of the specimen, and hence
should contribute to the differential ref lectogram. Since
no peak shifts or additional structure were observed when
samples were potentiostated for extended periods of
time, however, it may be reasonably concluded that any
surface roughening effects which did occur were insuf-
ficient to cause any significant changes in the dif-
ferential reflectivity.

Recently a certain problem has arisen with regard to
a few samples prepared potentiostatically when Miccroflex
is used to protect the reference half of the sample. The
differential ref lectograms which are taken from these
samples show Cu?0 structure, but with inverted polarity.
This implies that the "protected" side of the sample is
corroding preferentially and protecting the exposed side. The
Cu^O spectra are observed regardless of whether the sample
is potentiostated in the Cu?0 or CuO area of the Pourbaix
diagram. The reason appears to be a lack of adherence to

122

the copper by the Miccroflex, resulting in a concentration
cell in the gap between the Miccroflex and copper. This
increases the acidity of the electrolyte trapped under the
Miccroflex and drives the covered area anodic with respect
to the rest of the sample. Both effects tend to move the
area covered with Miccroflex into the Cu?0 area of the
Pourbaix diagram. This results in a film of Cu20 being
formed on the supposedly "clean" half of the sample,
while the exposed half of the sample is relatively pro-
tected. The solution to the problem is simply to obtain
fresh lacquer.

Finally, it was mentioned in Section II that elec-
troref lectance effects can complicate thin film corrosion
studies which employ modulation spectroscopy. Effects
due to modulation of the electrode potential, such as are
observed in electrochemical modulation spectroscopy
(EMS), are of no concern here since the sample potential
is not modulated. Effects due to the electric field

emanating from a sample which has a DC charge on it have

22 ? 7
also been observed. ' This field alters the optical

constants of the electrolyte near the sample surface, and

could affect measurements made in situ. However, the

electric field surrounding the samples used in these

experiments must be fairly uniform, particularly near the

123

center of the flat face which is being observed. Here
again the differential nature of the technique would tend
to cancel out any modifications to the index of refrac-
tion of the electrolyte, which must be small in any
event. The fact that there is no additional structure in
Figure 27B (measured in situ) compared to Figure 2 7A
(not measured in situ) seems to confirm this reasoning.

SECTION V
CONCLUSIONS AND SUGGESTIONS FOR FURTHER WORK

It is hoped that this work shows that the application
of differential ref lectometry to the study of corrosion
phemonema, even at its present early stage of development,
can serve as a valuable supplement to the more established
techniques of corrosion science. It has been shown that
differential ref lectometry can verify the existence and
identity of thin film corrosion products on metal sub-
strates. Different corrosion products have been shown to
produce unique differential ref lectograms , which can be
qualitatively predicted from reflectivity data and band
diagrams, or quantitatively predicted from the optical
constants of the film. As in the case of ellipsometry ,
the thickness of the film may be determined if the optical
constants are known. The technique is most useful in the

o

film thickness range 0 to 200 A, which covers the range
of most passive and semipassive films. This range is
often too thick for most surface analysis techniques which
do not require a vacuum, and too thin for X-ray analysis.
Finally, it has been shown that differential reflec-
tometry is capable of in situ measurements of thin film

124

125

corrosion products. More importantly, the electrolyte does
not add additional structure to complicate the analysis,
so measurements in optically dense electrolytes are pos-
sible.

There are many interesting possibilities for future
research. For example, the well-established techniques
of compositional modulation " can be used to investi-
gate dealloying, especially the dezincif ication of brass.
Small compositional changes, which are difficult to mea-
sure using conventional techniques, could be easily
monitored in real time while the sample was still in the
electrolyte. In order to facilitate such in situ studies,
additional work needs to be performed on the development
of transparent, protective coatings for the reference
half of the sample. They must be able to be applied
thinly and evenly, and must have uniformly low absorption
throughout the range of the instrument as well as being
immune to attack by the electrolyte.

More calibration curves of film thickness versus
differential reflectivity need to be calculated. The
curves for CuO shown in Figures 17 and 22 were calculated
for a wavelength of 600 nm, but any wavelength within the
range of the instrument could be used. In retrospect a
wavelength of approximately 400 nm would be better for

126

the case of CuO, since the differential reflectivity is
higher at that wavelength than at 600 nm for all thick-
nesses in the range of interest. As a consequence,
greater precision could be obtained in the determination
of the thickness of a film. Similarly, the calibration
curve should be made near the strong peak at 385 nm in
the case of Cu20, when the optical constants of that com-
pound are determined. Wavelengths shorter than approxi-
mately 300 nm should be avoided, since the output of the
Xenon light source is not strong in that area.

Additional metal/electrolyte systems could be
investigated using differential ref lectometry , with the
aim of developing experimental Pourbaix diagrams for
commercial alloys whose theoretical Pourbaix diagrams are
not easily calculated. Here the technique can be a
valuable supplement to electrochemical techniques,
especially when the corrosion product cannot be exposed to
vacuum.

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BIOGRAPHICAL SKETCH

Charles William Shanley was born March 20, 1949, in
Chicago, Illinois. He attended Loyola Academy in
Wilmette, Illinois, where he graduated in 1967. Beginning
in 1967, the author studied physics at the University of
Dayton, Dayton, Ohio, where he graduated with a Bachelor
of Science degree in 1971. He entered the graduate school
at the University of Dayton in the field of materials
science in 1971, and graduated in 1973 with a Master of
Engineering degree. The author entered graduate school
at the University of Florida in June, 1973, in the field
of materials science and engineering. He received the
degree of Master of Science in March, 1975, and has
pursued the degree of Doctor of Philosophy since that
date .

The author is a member of the American Institute of
Mining, Metallurgical, and Petroleum Engineers, the
American Society for Metals, and Alpha Sigma Mu.

131

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.

Hummel , Chairman
Professor of Materials
Science and Engineering

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.

3?>k

J. J. Hrdn
Professor of Materials
Science and Engineering

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.

E. D. Verink, Jr.
Professor of Materials
Science and Engineering

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.

:pinKKy
Professor of R

This dissertation was submitted to the Graduate Faculty of
the College of Engineering and to the Graduate Council,
and was accepted as partial fulfillment of the require-
ments for the degree of Doctor of Philosophy.

December 1977

Dean , College of Engineering

Dean , Graduate School

UNIVERSITY OF FLORIDA

3 1262 08553 1126