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ABSTRACT

AN ANALYTICAL AND EXPERIMENTAL STUDY OF THE THERMAL
SPECTRAL PROPERTIES OF OXIDE-METAL COMPOSITE MEDIA

by Syed Abdullah Hassan

The purpose of this study was to determine the cor-
rosion rates of zinc and galvanized steel and to relate their
optical properties to the amount of corrosion in the radia-
tion spectrum of 0.35 to 2.75 micron wavelengths from a
10,0000R source (sun) and a 3000°R source (tungsten lamp).

Samples of zinc and galvanized steel were corroded
for several durations up to 3 months in outdoor atmosphere
and up to 4 weeks in a spray cabinet using a continuous spray
of water. The corrosion film thicknesses were measured by
the weight-change method (removal of the corrosion products
from the test surface), by the x-ray diffraction method and
by the metallographic method.

A Beckman DK-lA ratio recording Spectrophotometer
with a Beckman 24500 reflectance attachment was used to
measure the hemispherical reflectance at normal incidence
in the wavelength range 0.35 to 2.75 microns. The hemis-
pherical reflectance curves so obtained were normalized
with the energy distribution curves of the 10,ooo°R and
30000R sources to obtain the corresponding integrated

hemispherical reflectance curves. The average of these

Syed Abdullah Hassan

curves,called mean integrated hemispherical (MIH) reflectance.
were used as a criterion for the optical behavior of the
samples.

The corrosion films produced in the atmosphere were
smoother than those produced in the spray cabinet. The
film thicknesses varied from 1.2 to 12.6 microns. The rate
of corrosion was appreciable for the first 2 weeks in the
atmosphere and the first two days in the spray cabinet.

In the remaining period the rate was relatively small.

The MIH reflectance decreased with the growth of the
corrosion films. For the 10,0000R source nearly 75% of the
reduction occurred in films 3.0 microns thick, but for the
3000°R source the rate was relatively constant at all
thicknesses. The corresponding increase in MIH absorptance
was 76% for the 10,0000R source and 117% for the 3ooo°R
source.

The experimental values of MIH reflectance were
correlated with the theoretical predictions based on the
Maxwell's theory of wave propagation through stratified
media (assumed perfectly smooth) using a value of .0017
for the extinction coefficient of zinc oxide corrosion
film. The agreement was good at large film thicknesses but
was poor for films less than 4.0 microns thidkness. This
was attributed to the fact that the effect of surface
roughness, which was neglected in the theoretical analysis,

was in fact proportionately large at small film thicknesses.

Syed Abdullah Hassan

The MIH reflectance showed at least a qualitative
correlation with the surface roughness. The trends of the
curves were comparable with those reported in the literature.
The separate effects of the film thickness and the surface
roughness, however, could not be ascertained in this study

because of the simultaneous and uncontrolled variations of

these factors.

Approved 69V“)! H m

 

Major Professor

Approved W ”J M

Department Chairman

AN ANALYTICAL AND EXPERIMENTAL STUDY OF THE THERMAL

SPECTRAL PROPERTIES OF OXIDE-METAL COMPOSITE MEDIA

BY

Syed Abdullah Hassan

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Agricultural Engineering

1966

To

Mr. and Mrs. Mohsin Shah Bokhari

Syed Jafar Hassan

ii

ACKNOWLEDGEMENTS

I would like to extend my very sincere appreciation
to Dr. F. H. Buelow (Agricultural Engineering) for his
inspiring guidance during my graduate program.

I am especially thankful to Dr. A. M. Dhanak
(Mechanical Engineering) for hisvaluable suggestions and
active interest in my work. I benefited greatly from his
expert knowledge of the area of radiant heat transfer.

My sincere thanks are due to Dr. C. W. Hall
(Agricultural Engineering) and Dr. Herman Rubin (Statistics)
for serving on my guidance committee.

I am also indebted to Dr. D. E. Scherpereel (Metal-
lurgy, Mechanics and Materials Science) for help in the
x-ray and metallographic studies and Mr. Wayne Fredricks
(State Highway Laboratories) for use of the spectrophotometer.
Assistance of Mr. James Cawood and his staff in the
Agricultural Engineering Research Laboratory is thankfully

acknowledged.

iii

TABLE OF CONTENTS

INTRODUCTION 0 O 0 O O O O O O 0 O O O O O O O 0
Objectives
REVIEW OF LITERATURE . O O O O O O O O O O O O 0

Optical Properties

Surface Roughness

Corrosion of Zinc and Galvanized Steel
Preparation of Samples

Measurement of Film Thickness

THEORETICAL ANALYSIS . . . . . . . . . . . . . .
EXPERIMENTAL PROCEDURE AND EQUIPMENT . . . . . .

Total Reflectance Measurements

Exposure to Corroding Atmosphere
Atmospheric Test

Cabinet Tests

Measurement of Surface Roughness
Measurement of Corrosion Film Thickness

RESULTS AND DISCUSSION . . . . . . . . . . . . .

Measurement of Film Thickness

Rate of Growth of Corrosion Films

Surface Roughness Measurements

Hemispherical Reflectance Measurements

Mean Integrated Hemispherical Reflectance

Effect of Corrosion Film Thickness on the

Mean Integrated Hemispherical Reflectance

SUMMRY O O O O O O O O O O O O O 0 O O O O I I
CONCLUS IONS O O O O O O O O O O O 0 O O O O O 0
REFERENCES 0 O O O O O O O O O O O O O O O O O 0

APPENDIX 0 O O O O O O O O O O O 0 O O O O O O 0

iv

Page

12
15
16

21
36
38
41
41
42
45
45
51
53
57
59
6O
67
7O
81
83
86

95

LIST OF FIGURES
Figure Page

1. Beckman DK-lA spectrophotometer with
reflectance attachment . . . . . . . . . . 39

2. "Norelco" x-ray diffraction unit with
recorder . . . . . . . . . . . . . . . . . 39

3. Balphot Metallograph with camera attachment . 39
4. Light path in Beckman DK-lA spectrophotometer

for hemispherical reflectance measurements. 40
5. Spray cabinet . . . . . . . .'. . . . . . . . 43
6. Air atomizing spray nozzle assembly . . . . . 43
7. Corrosion films on some representative samples

of zinc and galvanized steel . . . . . . . 52

8. A close—up of the test samples imbedded in 1"
diameter plastic mold . . . . . . . . . . . 55

9. A micrograph of the surface corrosion film
(1000 magnification) . . . . . . . . . . . 55

10. Oxide layer development on zinc and galvanized
steel exposed to the atmosphere . . . . . . 58

ll. Oxide layer development on zinc and galvanized
steel exposed in the spray cabinet . . . . 58

12. Spectral hemispherical reflectance of clean
zinc and galvanized steel in the wavelength
range 0.40 to 2.75 microns . . . . . . . . 61

13. Spectral attenuations of hemispherical re-
flectance due to oxide layer on zinc
exposed to the atmosphere . . . . . . . . . 63

14. Spectral attenuations of hemispherical re-
flectance due to oxide layer on
galvanized steel exposed to the atmosphere . 64

Figure Page

15. Spectral attenuations of hemispherical
reflectance due to oxide layer on zinc
exposed in the spray cabinet . . . . . . . 65

16. Spectral attenuations of hemispherical re—
flectance due to oxide layer on galvanized
steel exposed in the spray cabinet . . . . 66

17. Change in the mean integrated hemispherical
reflectance of zinc and galvanized steel
versus time of exposure to the atmosphere . 69

18. Change in the mean integrated hemispherical re-
flectance of zinc and galvanized steel
versus time of exposure in the spray
cabinet . . . . . . . . . . . . . . . . . . 69

19. Mean integrated hemispherical reflectance
versus oxide film thickness . . . . . . . . 71

20. Extrapolation of refractive index (n) and
extinction coefficient (k) values of zinc . 73

21. Effect of the film extinction coefficient
(in the range 0 to 0.08) on the theoretical
MIH reflectance of the film-metal composite.
Source temperature: 10,0000R . . . . . . . 75

22. Effect of the film extinction coefficient (in
the range 0.1 to 0.857) on the theoretical
MIH reflectance of the film-metal compo—
site. Source temperature: 10,000°R . . . 76

23. Correlation of the MIH reflectance with the
surface roughness of the oxide films on
zinc samples . . . . . . . . . . . . . . . 79

24. Correlation of the MIH reflectance with the

surface roughness of the oxide films on
galvanized steel samples . . . . . . . . . 80

vi

LIST OF APPENDIX TABLES
Table Page

1. Thickness of oxide films on zinc and gal-
vanized steel samples measured by
(a) the weight change method and
(b) the metallographic method . . . . . . . 96

2. Measured r.m.s. surface roughness values (in
microns) of (a) clean surface, (b) oxidized
surface. and (c) metal surface after removal
of oxide . . . . . . . . . . . . . . . . . . 97

3. Experimental values of mean integrated hemis-
pherical reflectance . . . . . . . . . . . . 98

4. Spectral values of optical constants of zinc
and zinc oxide (International Critical
Tables, Vblume V, p. 250 and Vblume-VII.
p. 20) . . . . . . . . . . . . . . . . . . . 99

vii

INTRODUCTION

The present day reserves of fossil fuels are being
depleted very rapidly. To meet the ever increasing demands
for energy, need has grown to find new sources which can
provide energy at competitive cost and in large quantities.
Use of solar energy has been investigated very widely in
the last twenty years. Whereas some of the applications
like water heating, crop drying, and solar cooking are
already competitive and are in mass use, other applications
need further improvements in design and efficiency before
they can replace the conventional sources.

On a bright summer day (assuming 8 hours of sunshine)
a 100 square meter surface receives about 2.0 x 106 BTU's
per day of solar energy (Daniels, 1955), which is roughly
equivalent to 150 pounds of soft coal or 250 pounds of wood
per day.

Despite the great abundance, solar energy suffers
from a disappointingly low intensity level, which in most
-applications must be increased at the expense of efficiency.
Therefore best prospects for utilization of solar energy
lie in applications requiring low grade heat where the solar
energy can be used directly without concentration. Morse

and Dunkle (1962) estimated that by 1977 the per capita

energy demand will increase from 0.36 to 0.47 equivalent

metric tons of coal per annum, more than half of which will
be used as low grade heat. If solar energy were to supply
half of this, the fuel savings would amount to the equivalent
of one hundred million metric tons per annum.

The aforementioned water heating, drying of agricul—
tural products and space heating are some of the low grade
heat applications in point° Mass produced solar water heaters
are already in domestic use in Australia, Israel, and Japan
and provide hot water more economically than electric
heaters (Morse, 1962, Sabotka, 1961, Tanishita, 1961). Hay
and grain have been dried successfully using a solar heat
supplemented forced air drying system (Buelow, 1961, Davis
and Lipper, 1961). Air flow rates of ten to fifteen cubic
feet per minute per square foot of collector were used,
producing a temperature rise of ten to twenty degrees
Fahrenheit which reduced the drying time of the products to
less than half.

When utilized as a supplemental source, the solar
energy is used only as available, thereby eliminating the
need for a heat storage (Buelow, 1956, Sabotka, 1961). A
simple and inexpensive absorber design may be used to absorb
solar energy. A typical solar heater used for space heating
or crop drying consists of a metallic surface provided with
an air duct at the back. The air, heated by the metal sur-
face during its passage through the duct, is subsequently

used in the desired application.

Since the performance of the system depends on the
ability of the metal surface to absorb incident solar radia-
tions which lie in the wavelength range of 0.3 to 2.5 microns,
efforts have been made to find new materials with good ab-
sorption in this range and to treat the existing materials
so as to improve their absorption characteristics (Duffie,
1961).

Coating the absorber surface with a non—selective
black (or dark) paint of high absorptivity is one of the
oldest and most widely used methods. More recently, how-
ever, selective surfaces have been used (Edwards, 1961,
Tabor, 1961, Trombe, 1961, Close, 1961) which exhibit high
absorptivity in the solar spectrum and low emissivity at
longer wavelengths (thus reducing loss with long wave-
length radiations emitted at the surface temperature).

The selective surfaces are formed by coating, folding,
grooving or etching (Duffie, 1961). Selective coating of
nickel black on galvanized steel (solar radiation absorp-
tivity 0.89 and emissivity 0.12 at temperatures less than
one hundred degrees Celcius) and Ebonol C on copper

(a = 0.91, 6 = 0.16) are already in commercial production
for use in solar water heating and optical applications
respectively (Tabor, 1961, Edwards, 1961).

The treated surfaces (selective and painted) suffer
from one or more of the following inherent disadvantages:

1. High cost of initial treatment.

2. Unattractive appearance.

3. Recurring expenses in maintenance.
4. Greater resistance to heat transfer through the
absorber surface owing to poor conducting coating

or paint layer-

5. Gradual deterioration of absorption properties of the
coated surface.

Untreated metal surfaces, on the other hand, improve
their initially low absorption properties with time. When
exposed to the atmosphere during use, a thin film of
corrosion products (oxide) is formed on the metal surface
which increases its absorption owing to multiple reflections
in the film (Born, 1964, Duffie, 1961). In addition, the
surface does not require extensive maintenance and is a good
conductor of heat.

Even though corrosion starts a destructive process
on the metal surface, metals most commonly used in solar
heaters (galvanized steel and zinc) form protective layers.
The layers formed first protect the underlying base metal
and consequently retard the further rate of corrosion.

It is therefore of interest to investigate the
behavior of untreated absorber surfaces in regard to both
their radiation properties and corrosion (oxide) layer

development.

Objectives
This study was undertaken with the following

objectives:

To determine the thickness of corrosion (oxide)
films of zinc and galvanized steel as a function
of time.

To determine the spectral radiation properties of
zinc and galvanized steel in the wavelength range

of 0.35 to 2.75 microns at various film thicknesses.

REVIEW OF LITERATURE

A review of the literature on the corrosion behavior
and the optical properties of zinc (and other metals)
reveals two facts:

1. Extensive work has been done by chemists on the
corrosion of zinc (and other metals), explaining

the mechanism of corrosion, the rate of layer build-

up and the influence of various factors.

2. Equally elaborate work is reported by physicists

on the optical properties of "thin films" of evapor-

ated metals and metal compounds and thermal oxides

(produced by heating in air).

Yet no effort has been made by either group to study
the growth of relatively "thidk" corrosion films on metals
and simultaneously investigate the associated changes in the
optical properties. Very recently, however, interest has
grown in this area because of the demands of aerospace
applications for information on thermal radiation properties
of coatings used as heat shields and selective coatings used
on satellites. The first reference cited below is a case
in point.

Francis and Love (1966) investigated the radiant
behavior of isothermal absorbing coatings on conductors by

solving the transport equations across the coating using

6

what they called the "attenuated intensity" and the ”at-
tenuated flux" approaches. They obtained plots of mono-
chromatic absorptivity and emittance of aluminum, copper,
nickel, gold and silver into absorbing coatings with a range
of refractive indices and several thicknesses (from 0.075

to 0.600 micron (u)). These curves show that as the optical
thickness (refractive index times the geometrical thickness)
of the absorbing coating was increased the emittance became
more nearly that of a dielectric. At small angles the
directional emittance into the coating was found to be
greater than into the air. The attenuated flux and the
attenuated intensity approaches yielded different results.
This was explained by the fact that the attenuated flux
approach could not "detect" the directional variations of
the intensity.

Hall and Ferguson (1955) measured reflectance and
transmittance of several evaporated ZnS films (on non-
absorbing glass and rock salt substrates) ranging in thick-
ness from 1 to 4 u in the spectral region of 0.6 to 14 u.
Substituting these values into the theoretical equations,
they calculated the absorption coefficient k and the Spectral
values of the refractive index n. The absorption coefficient
was found to be approximately 0.001 and the refractive index
ranged from 2.34 at 0.6 u to 2.15 at 14 u.

Hass and Salzburg (1954) prepared evaporated films
of pure SiO in thidknesses ranging from 0.033 to 1.950 u,

which were later oxidized to SiO2 by heating in air at 800

degrees Celsius. A comparison of the absorption curves of
pure SiO films and the oxidized (8102) films in the range
0.24 to 14 u showed that the ten micron absorption peak,
characteristic of SiO, shifted toward shorter wavelengths
and the total absorption was increased.

Sennett and Scott (1950) obtained reflectance curves
for evaporated films of eight different metals with thick-
nesses varying from 0.003 to 0.05 u. For a monochromatic
wave of 0.6 micron the absorptance of chromium, palladium,
nickel and antimony films increased from zero at zero film
thickness to between 0.40 and 0.55 for a 0.06 H thidk film.
The rate of film evaporation was observed to affect both
the film structure and the optical properties. Slow rates,
in general, produced a more aggregated structure and increas-
ed absorption.

Scott (1955) stated that the optical constants of
thin metal films may differ radically from those of the
bulk metals. Bock (1945) observed that the curves of the
electrical conductivity (which determines the reflection
behavior) of evaporated zinc films in the range 0.48 to 2.4
u were identical in shape with those reported for bulk zinc,

but the absolute values were only about half.

Surface Roughness

It is well known that the surface roughness influences
the reflection behavior of materials. A published account

of this fact can be traced back 50 years. H0wever, it was

not until a few years ago that a rigorous mathematical
analysis of this effect was presented.

Except for Agnew and McQuiston (1953) who worked
with powders, most of the studies are concerned with metallic
surfaces. A general concensus of the reported work indicates
that:

l. The influence of surface roughness O is more pro-
nounced in the short wavelength region (especially for large
values of O/A) than in the long wavelength region.

2. The influence is greater for small incidence angles
than for large incidence angles.

3. The surface roughness is much more critical in
specular reflectance studies than in total reflectance
studies.

In 1916 Gorton (1916) conducted experiments with
electroplated ground glass samples to investigate the effect
of surface roughness on the Specular reflectance at several
incidence angles in the spectral range 0.6 to 14.0 u.

His experiments showed that the specular reflectance was
independent of surface roughness at long wavelengths, parti-
cularly at large incidence angles. It was, however, strongly
influenced by the surface conditions at Short wavelengths

and small angles of incidence.

Three years later, based on the assumptions that the
distribution of surface irregularities follow the probability
law and that "the relative reflection of a rough surface

depends only on its topography and not upon the nature of

10

the material of which it is composed", Chinmayanandam (1919)
devised a mathematical equation describing the effect of
surface roughness, which was found to be in general agree-
ment with the experimental results of Gorton (1916) for
moderate angles. For large angles from perpendicular,
however, the agreement was poor. For these angles he sug-
gested an empirical equation with constants calculated from
Gorton's data.

More recently, Bennett and Porteus (1961) obtained
an expression for O<<A,-based on the diffraction theory and
Davies (1954) statistical approach relating the measured
reflectance R (which includes both specular and diffuse
reflectance) with surface roughness o and Slope m at normal
incidence and for instrument acceptance angle A9.

2 4

R=R e-(A) +R032—721-(%)(Ae)2
m

This expression suggested that the Specular reflec-
tance which is given by the first term was predominant in
the long wavelength region (or small O/h) whereas the diffuse
reflectance given by the second term was prevalent in the
Short wavelength region (or large U/A).

Aluminized samples of steel and ground glass were
used to measure reflectance as a function of surface rough-
ness (0.07, 0.2 and 0.81 u) in the wavelength range 2-22 0.
The results were found to be in excellent agreement with the

theoretical equation in the wavelength region 5—22 u. Below

11

5 u, however, large discrepancies existed which were explained
as due to the violation of the basic assumption that O<<A.

Porteus (1963) later extended the analysis to the
short wavelength region highlighting the restrictions on
application to surfaces with peculiarities. Bennett (1963)
tested the theory using aluminized ground glass samples.

He suggested that the theory could be used to determine
the height distribution of surface irregularities at suf-
ficiently short wavelengths.

Birkebak et a1 (1964) investigated the roughness
dependence of hemispherical and specular reflectance of
ground niCkel samples at several incidence angles using a
black body radiation source at different temperatures. They
found that the hemispherical reflectance was independent of
surface roughness beyond a certain roughness value (0.4-
0.8 u) but the Specular reflectance decreased steadily
with increasing roughness. The hemispherical reflectance
was also independent of incidence angles whereas the
specular reflectance increased with increasing angles.

Both hemispherical and specular reflectances decreased with
increasing source temperatures, the change being about 10%
for the range of temperatures considered (1700 - 660°F).
BirkebakanuiEckert (1965) later added aluminized ground
glass samples to these studies which were extended to
include biangular reflectance and hemispherical—angular

reflectance measurements.

12

Corrosion of Zinc and Galvanized Steel

Atmospheric corrosion of zinc and galvanized steel
depends primarily on the purity and surface condition of the
metal, the presence of moisture and the extent of contamina-
tion of the atmosphere with dust and corrosive gases.
Presence of moisture is by far the most important factor.
Vernon (1935) found that the corrosion rate of zinc remains
negligibly small below a critical humidity value of about
70%. Above this value, however, the rate increases with
increasing relative humidity.

Atmospheric dust containing suspended particles of
soils, salts, carbon and carbon compounds or metal oxides
is present to some extent in all atmospheres. Kutzelnigg
(Uhlig, 1963) reported that rural atmOSpheres contain, on
the average, about 2 mg/cm3 of dust whereas the industrial
atmospheres may contain as much as 1000 mg/cm3. When settled
on a metal surface, the dust combines with the moisture
present in the air and initiates corrosion by forming
galvanic or differential aeration cells. To show the
influence of atmospheric dust,Vernon (1935) compared the
corrosion of screened and unscreened samples exposed indoors
for several months. The screened samples were found free
of rust whereas the unscreened samples showed considerable
rust and weight gain.

Among the gases polluting the atmOSphere, sulphur
dioxide is most corrosive to zinc and galvanized steel.

It is produced mainly from the burning of coal, oil and

13

gasoline (Evans, 1961). Seasonal variations of fuel con-
sumption affect the content of sulphur dioxide and therefore
the corrosiveness of the atmosphere. This was confirmed
by Schikorr (Uhlig, l963),who exposed zinc samples to Berlin
and to Stuttgart atmOSpheres and found that the samples
corroded more rapidly in winter than in summer.

Data on atmospheric testing of zinc and galvanized
steel is available from a number of sources (Uhlig, 1948).
However, the most widely accepted values are based on the
10 and 20 year tests of A.S.T.M. (1955), 10 year tests of
the New Jersey Zinc Company (Uhlig, 1948) and 10 year tests
of B.I.S.R.A. (Uhlig, 1948). The average reported values

for different atmospheres are summarized below:
ATMOSPHERE

Industrial Marine Rural Desert
mils/year mils/year mils/year mils/year

Zinc 0.210 0.048 0.040 0.008

Galvanized steel 0.270 0.120 0.090 --

Tests indicate that zinc and galvanized steel corrode
slowly and uniformly without deep pitting at a rate governed
by the composition of the surrounding atmOSphere (Uhlig, 1948).

Zinc and galvanized steel form protective corrosion
films which retard the rate of corrosion. Ellis (1949)
found that the corrosion rate of zinc exposed for 28 days to
an industrial atmOSphere depended largely on humidity and
moisture conditions during the first five days of exposure

and less on conditions arising later.

14

AtmOSpheric tests closely approximating the service
conditions provide a reliable method of predicting the
behavior of metals in actual use. However, they require a
long period of time before useful conclusions can be drawn.
The need for an accelerated test which could produce com-
patible results in a short time is therefore apparent.
Methods investigated so far include immersion tests, acidic
tests, electrochemical tests, air conditioner tests and spray
tests (Evans, 1961).

The spray testing method has been investigated very
widely in the past 40 years both in Europe and in America
(Evans, 1961). Intermittent or continuous sprays of pure
water (B.I.S.R.A., 1948),5% and 20% NaCl solutions (A.S.T.M.,
l962),natural and artificial sea water, dilute sulfuric
acid (I.S.I., 1931),and salt solution acidified with acetic
acid (McMaster, 1956) have been tried to simulate accelerated
conditions for different atmospheres. An excellent review
of spray testing literature is presented by voigt (1948)
and in a critique by Evans (1961). Thus far this method
has failed to become reproducible partly because of lack of
thorough understanding of such influencing factors as the
size and shape of spray nozzles, air—solution ratios, size
and location of samples and the size of the spray box.

The American Society for Testing Materials has adopted
a spray testing method (A.S.T.M. Designation B117—62) with
the reservation that it "does not prescribe the type of

test specimens or exposure periods to be used for a specific

15
product, nor the interpretation to be given to the results."

Preparation of Samples

As pointed out by Evans (1961), Meyers (1948),
A.S.T.M. (1952), Jelinek (1959), Knapp (1948) and Gwyther
(1947) it is essential to remove surface grease, oil, oxides
and other contaminants from the test samples in order to
obtain reproducible corrosion test results.

Surface preparation generally consists of a degreas-
ing process followed by rust removal by abrasion, machining
or pickling in an acidic solution (Evans, 1961). Wesley
(1953) prepared alloy steel samples by removing 0.0003
inches off the surface by machining. Mulvaney (1962) used
a pickling solution of 15% (by weight) hydrochloric acid
with 0.4% (by volume) Rodine 213 inhibitor at 200°F.

McCollan and Warrick (1948) reported that wide variations

are possible in pickling solutions and temperatures depending
on the material of the samples, the character of the scales
and the surface desired after pickling. Although the pickl-
ing method is preferred by many researchers, Evans (1961)
pointed out that it may leave a hydrogen charge or an organic
film when an inhibited acid is used.

A detailed account of the degreasing methods is
given by Champion (1952) and Meyers (1948). Simple solvent
cleaning, emulsifiable solvent cleaning and vapor degreasing
are among the methods most commonly used. Different solvents

are preferred by different workers. A partial list of

16

solvents includes acetone, benzene, xylene and carbon
tetrachloride (Evans, 1961).

Weast and Shulman (1962) degreased the samples by
successive washings in acetone, ammonium chloride solution
and distilled water. Researchers at New Jersey Zinc Company
(Uhlig, 1948) washed their samples with ether and alcohol.
Mulvaney (1962) followed A.S.T.M.‘s (1958) recommended pro-
cedure. He used successive washings in carbon tetrachloride
solution, trichloroethylene vapor degreasing bath, alcohol,
distilled water and finally acetone. Gwyther (1947) recom-
mended the use of emulsifiable cleaners mixed with kerosine

and subsequent rinsing with water.

Measurement of Film Thickness

The methods of film thickness measurements can be
categorized as gravimetric, electrochemical and optical.

The choice of a particular method will of course depend on
the requirements of an individual situation.

Gravimetric methods of thickness measurements are
based on the change in weight of the Specimen on corrosion
and are by far the most widely used methods in corrosion
studies. The change in weight may be measured either with
the corrosion film in place or after complete removal of the
corrosion products from the sample surface. For zinc,
Anderson (1946) reported that the only acceptable weight
change data are those based on chemically cleaned samples.
Data from samples weighed with the corrosion products in place

are misleading.

17

According to Champion (1952) and Knapp (1948) the
corrosion products may be removed mechanically (by Scrubbing
with a brush, abrasive or detergent), electrochemically
(by making the specimen a cathode), or chemically (using
various chemical reagents). Whatever the method, it must
be capable of removing all the corrosion products without
loss of the base metal.

Stroud (1951) used cold chromic acid containing
silver and strontium chromate to remove corrosion products
from zinc samples. He also tried ammonium acetate but found
that it removes only thin layers. At New Jersey Zinc
Company (Uhlig, 1948) a 10-minute immersion in 10% ammonium
acetate at 880 : 1°C was used. Hudson (Evans, 1961) cleaned
zinc samples first by removing loose products with a wooden
scraper and then immersing in cold 10% acetic acid solution
for 1 minute.

The electrochemical method consists of removing
corrosion film by cathodic reduction at constant current.
The completion of the process is indicated by a sharp shift
in the E.M.F. Campbell and Thomas (1959) used this method
to measure 0.002 B to 0.1 u thiCk oxide and mixed oxide-
sulfide films on copper and silver. The method can be used
even for very thin films. Eurof Davies (1957) detected a
0.0005 u film on silver heated at 800°C. The method has
mainly been used for films on silver, copper, and iron

(Evans, 1961).

18

Optical methods include interferometric, polarimetric
and metallographic methods of measurements. The interfero-
metric methods are based on the observation of the inter-
ference colors or fringes which occur when the film thick—
ness is an odd multiple of quarterwavelength (of the incident
ray). Interference colors were used by Tamman,et a1 (Evans,
1961), Evans and Bannister (1929), Constable (1927) and
Vermilea (1953) to measure thin oxide films produced by
heating the metal in the air. The color scale must,however,
first be calibrated with some other known method. For
absorbing media a knowledge of the phase change at the
two interfaces is essential. This method is unsuitable for
aluminum and other metals of high reflectivity with films
of low refractive index (Kelly, 1958). Hass (1949),
Winterbottom (1946), Kelly (1958) and many others measured
film thickness from interference fringes, a technique intro-
duced and developed by Tolansky (1948). The method is both
simple and accurate but requires smooth surfaces and inter-
faces.

For the polarimetric method the changes in amplitude
and phase of a polarized light on reflection from a film-
covered surface are used to calculate thickness. These
calculations are however, laborious and demand a thorough
understanding of the underlying theoretical basis (Evans,
1961). Reference of complete details may be found in the
pioneering work of Tronstad (1932) at Trondheim Labs, later

continued and improved by Winterbottom (1946). William and

l9

Hayfield (1957), Leberknight and Lustman (1939) and others
have used this method to measure oxide films. Here again

as pointed out by Tronstad (1935) the method is limited to
films which are fairly uniform both in thickness and optical
density.

Microscopic and metallographic methods have been
used extensively for measuring thiCkness of protective
coatings on metals (Blum, 1948). The method involves
viewing a prepared cross—section of the sample under a
microscope or projecting it on the graduated screen of a
metallograph. Heussner (Blum, 1948) has outlined the pro-
cedure for preparing the samples andifluanecessary precautions
especially for soft metals like tin and zinc. The method
is accurate to about i 5% but requires lengthy preparation
of samples.

Howells (1954) and Blum (1948) have reviewed methods
which are used to measure thickness of protective metal-
coatings. Whereas most of the techniques used are empirical
(like Preece test, Spot test, jet test, etc.), the x-ray dif—
fraction method needs special mention. The intensity of an
x-ray beam diffracted from a film-free metal surface is
attenuated after deposition of the film. From the ratio
of the two intensities and the known values of the mass
absorption coefficients of both the film and the base metal,
the film thickness can be calculated. The method can be
used according to Friedman and Birks (Heavens, 1965) for

films of thickness 0.1 to 100 u. Behr (Howells, 1954)

20

used x-rays to measure tin plating thickness on sheet

steel.

THEORETICAL ANALYS IS

When a clean metal is exposed to corrosive media
a thin layer of corrosion products is formed on the surface.
The radiation properties of the composite surface thus
formed will differ from the original surface depending on
the following factors:

1. The composition and the optical properties of

the corrosion products.

2. The roughness of the corrosion film and the
underlying metal surface.
3. The thidkness of the corrosion film.

The composition of the corrosion products can be
determined from the knowledge of the corroding atmosphere.
Once the composition is known the optical properties can
be calculated from the appropriate values of optical constants.

The influence of the roughness at the two interfaces
(air-oxide, oxide—metal) and the multiple reflections within
the film layer combine to form a very complex optical
situation which is further complicated in corrosion process
where the geometrical shape and the distribution of the
roughness can neither be controlled nor easily determined.

In order to render this problem to mathematical
analysis it is assumed that all surfaces are perfectly

smooth (and therefore the effect of the surface roughness

21

22

is neglected). The simplified model so obtained can be
investigated using Maxwell's theory of propagation of
electromagnetic waves through stratified media (Born, 1964:
Harris, 1951; Heavens, 1965: and Hilsum, 1954). It is
further assumed that:

1. The interface boundaries are sharp.

 

2. The material media are homogeneous and isotropic. 51a
3. The magnetic permeability u is unity in the fre—

quency range considered.
4. The electromagnetic radiations are plane, time-

harmonic and linearly polarized with the electric .t_;

vector normal to the plane of incidence (called
transverse electric, "TE" wave).
5. There are no currents and charges present, i.e.,
——
j = o and p = o
In the analysis that follows equations are derived
for three mathematical models.
1. A dielectric film surrounded by two dielectric
media (air).
2. A dielectric film on absorbing substrate (in air).
3. An absorbing film on absorbing substrate (in air).
An electric charge in space creates a state of excit-
ation in its vicinity called the electromagnetic field which
is represented by an electric vector-E and a magnetic induction
_. a» a»
vector B. Vectors E and B and the associated quantities
(magnetic vector-H: electric displacement vector'D and

electric current density vector j) are related by Maxwell's

equations.

” il£" 'H‘?’ l
curIH-ED—E—‘J ()
curl E +'E B = o (2)
and
'-.
div D = 4wo (3)
9
div B = o (4)
where p = electric charge density = 0 (assumed).

And "material equations" are used to describe the

effect of these fields on material objects.

—b -—.

j = 0 E (5)

-> ~v

D = e E (6)
and

—b -1.

B = u H (7)
where

o = specific conductivity

e = dielectric constant
and

u = magnetic permeability

Substances for which 0:# o are called ”conductors“
and those for which 0 is negligibly small are called
"dielectrics” or ”insulators." Therefore the electric and
magnetic properties of dielectrics are completely defined
in terms of e and LL. The magnetic permeability is p. = l
for most materials especially in the optical frequency
range. Materials for which u.#=l are called magnetic.

Consider a plane polarized transverse electric wave
incident on a stratified media. If the direction of strati—

fication is along z,and yz the plane of incidence then

 

24

-iwt
Ey = E2 = o = H*. Assuming time dependence e , the
Maxwell's equations reduce to:
5H 5H
__E._ __X. ' SE = ' = !-1
5y dz + l c EX 0 1 (8a)
oHX 5H2
"5—2 _ TX = 0 (8b)
5H oHX
45X - T = 0 (8C)
and
' HE =
i c HX 0 (9a)
5E
x _ - w_I~L. = A
52— l c Hy 0 (9b)
5E
§—§-+ i‘EE H = 0 (9C)
y c z

The above equations relate the field vectors by
simultaneous differential equations. By the process of
elimination, differential equations can be obtained repre-

senting each vector separately. When there are no currents

 

 

-.
and no charges (i.e7j = o p = 0), we get
2 2
BE 5E 5E
x + x + n2k2E = dglogg) _ x . (10)
2 2 o x dz dz
5y dz

where n = refractive index =,‘eu

and k = wave number in vacuo or reduced wave number =

(mg
I
>1»
o =# o

W»! urn-r- '1

 

25

A solution of (10) in the form Ex(y,z) = Y(y)U(z)

yields
i(k ay-wt)

EX = U(z)e ° (11)

where U(z) is a function of z and may be complex. Similarly

we can obtain

ifk ay-wt)
H = V(z)e ° (12)
Y

i (k ay-wt)
Hz = W(z)e 0 (l3)

Eliminating w from equations (12), (13), (8a),

(9b) and (9c), we get

 

, _ dU(z) _ .
U — dz — i kOuV (14)
2 .
' — MEL —__- ' ‘_ 9..
V -— dz 1 ko(€ U»)U (15)
and separating V and U respectively from equations (14)
and (15)
2
__dU__$_£_J£H 1° .g—t—I +k2(n2-OL2)U=o (16)
d 2 dz 2 o
z
2
a
2 d [log (e- —)1
—d X - 4* -’ - 9‘1 + k2 (n2-a2)V = o (17)
dz dz 2 0

Similar relations may be obtained for a transmagnetic
("TM") wave using the substitution rule based on the symmetry
of the Maxwell's equations.

Since both U(z) and V(z) satisfy a second order
differential equation, each may be expressed as a linear

U and V , V .

combination of two particular solutions U1, 2 l 2

 

Ill!
3

26

Therefore from equations (14) and (15)

I __ ' I _ '
U1 — 1 k0 LL V1 U2 — 1 k0 H. V2
a2 d2
. — . - — | = . -
Vl — 1 kO (6 u )U1 and V2 1 ko(€ E—)U2

which give

C
II

I _ I I _ I =
V1U2 U1 2 o and U1V2 V1U2 0

Thus

d _
dz (U1V2 " U2V1) ‘ 0

which implies that the determinant~

U1 Vl
D = = constant (18)
U2 v2

Most convenient choice of particular solutions is

U1 = f(Z) U2 = F(Z)
(19)
Vl = 9(2) V2 = G(z)
such that f(o) = G(o)= o and F(o) = g(o) = 1 (20)
Then solutions U(o) = U0 and V(o) = Vb may be written as
U = FU + fV
o 0
V = GUO + ng
U F(z) f(z) U6
or = (21)
v G(z) g(z) Vb
or Q = N Q (22)

O

 

27

Square matrix N is a constant since the determinant

D in (18) is a constant. Actually "N" is unimodular as can

be seen immediately at z 0.

Let us define

QO = M Q (23)

which from equation (21) is

g(z) -f(z) mll KHZ

M = = (24)

-G(z) F(z) m m

21 22
M is a unimodular matrix and is called the
"characteristic matrix" of the stratified media. It relates
the x and y components of the electric (or magnetic in case
of a "TM" wave) vectors in the plane 2 = o to the components
in an arbitrary plane of constant 2. Knowledge of the
characteristic matrix for any stratified medium determines
the propagation of the electromagnetic wave through it.
Expressions for reflection and transmission co-
efficient can be derived in terms of the elements of the
characteristic matrix, using the boundary condition that

14> -.-
(when j = o and p = o) the tangential components of E

-.
and H are continuous across a surface of discontinuity.
For the "TE” wave incident at angle 91 and transmitted at

angle Ql' where subscript 1 refers to the first medium and

"L” to the last, we get reflection coefficient

_ (mll + m12 9L) p1 ' (”21 + m22 PI)
r — (m + m ) + (m + m ) (25)
11 12 PL p1 21 22 pl

 

and transmission coefficient

28

2 pl (26)
t =
(“11 + m12 pt) pl + (m21 + m22 pl)

] e~ .
where pi = 'E% cos 9% b = 1,2,
1.

For the "TMF'wave, the above expressions can be

 

used by replacing pi with qi where

cos 6= 1 = 1,2

5-0
p.
H

e- In? )
(a

Let us now investigate some particular cases.

1. A Hemogeneous Dielectric Film Surrounded by TWo Dielectric
Media.

If the normal to the incident wave makes an angle 0

with the direction of stratification, then

a = n cos 9
For an homogeneous medium

 

 

 

Q.
6 and u are constant (u=l) and n2=Jgé ' (2) h
1
so the refractive index n = Ju€= is
n =3?—
is also constant. Therefore, the l l q (1)

middle terms in equations (16) and

(17) drop out and we get

2
.g_g + (k2 n2 c0529) U = o (27)
0
dz
d2V 2 2 2
—2+(k n cos 9)V=o (28)
dz 0

which yield, subject to (14) and (15), the following solutions

29

U(z) = A cos (konz cos 9) + B sin (konz cos 9) (29)
) -'i -3 cos 6{:B cos (k nz cos 6) -
A sin (konz cos 9):] (30)

Using the boundary conditions given in equation (20), the

particular solutions become

f(h) 3: sin B

U = =

1 p2
U2 = F(h) = cos 8
Vi = g(h) = cos 8

V2 = G(h) = --1.p2 Sin 8
where
B = k n h cos 9 = 21, n h cos 6
2 2 A0 2 2
and 62
p2 — ‘E; COS 92

Therefore elements of the characteristic matrix are

m = cos B m ‘ = --i— sin 8
ll 12 P2
(31)

m21 = 1 p2 Sln 8 m22 cos 8

Therefore the overall reflection and transmission from
equations (25) and (26) are

. p193 . .
(pl cos B — 1 ———— Sin B)-(p cos B - i p Sin 8)

P2 3 2
r = (32)

p193
(pl cos 8 - i -———-
pz

 

sin B)+(p3 cos 8 - i p3 sin 8)

 

30

 

 

 

2pl
t — 33)
P P . . . (
(p1 cos 8 - 1 Sin 8)+(p cos 8 - 1 p3 Sln B)
2 3
The reflection and transmission coefficients for
the two interfaces 1,2 and 2,3 can be obtained from the
well known Fresnel's equation. For "TE" wave
r nl cos 91 - n2 cos 9 pl - p2 (34)
12 n1 cos 91 + n2 cos 92 pl + p2
Ei
since pi = ‘E: cos 9; = J2; cos 9; = ni cos 9; (for u = l)
and 2 n cos 9 2p
tl2 _ n coslG + n1 cos 6 _ + l (35)
1 1 2 2 p1 p2
Similarly
p2 ' 1;)3
r - (36)
23 p2 + p3
and 2p2
t =
23 p2 + p3

(37)
substituting from equations (34) to (37) in (32) and (33),
it can be shown that

and

(38)

(39)

 

31

Therefore

ll
H
M
II
H
N
N
w
H
N
N
A
.b
O
v

Reflectivity R

and transmissivity

 

 

2 2
T = FAHZ = r13 cos 93 t12 t23 (41)
p n cos 9 2 2
l 1 l 1 + r12 r23 + 2 r12 r23 cos 28
From equations (40) and (41) phase change, Sr,of
the wave may also be obtained.
2 .
r (l-r ) sin 28
tan 6r = tan (arg r) = 232 12 2 (42)
r12(l + r23)+r23(l + r12)cos 28

2. A Homogeneous Dielectric Film On An Absorbing Substrate
In Air.

Formulae developed above for stratified dielectric

(transparent) media can also be applied to the conducting
(absorbing) media provided K‘\\__/,__\\./’_,_L/““““
appropriate changes are

METAL 03
incorporated. n3

 

 

 

 

 

For absorbing media DIELECTRIC n2
(metals, semi-conductors) the
optical constants e and n are no AIR 9 nl
longer real but are complex
I I A A I
quantities e and n, given by
A .
e = e + 131:2 (43)
w
fix .
n = n (1 + l K) (44)

32

K is called "extinction coefficient".

Formulae for dielectric media that involve only
linear relation between the components of the field vectors
of a time-harmonic wave can be used for the absorbing media

A

A A
on replacing e, n, K etc. by e, n and K as defined above.

If U3 and V3 are real quantities, we may write

A e — ' 45)
n3 cos 3 — U3 + 1 V3 (

and from the law of refraction

h~ . .
n3 Sin 93 — n2 Sin 92 (46)

Then from (45), (46) and (44) equating real and imaginary

parts, we get

 

 

 

- 2
2_ 2 2.2 2 22.2] 42
2 U3 — n3(1 K3) - n2 s1n 62+Jn3(1-K3)-n251n 92 + 4 n3 K3
(47)
and
2__2 22.2]
2 V3 — [n3(1-K3)-n251n 92 +
l_ (48)
2
2 22.2] 42
[n3(l-K3)-n251n 62 + 4 n3K3
Fresnel's equation (34) for a "TE" wave may now
be written for absorbing media as
6 A) 9
r - é¢23 = n2 cos z-n3 cos 3 =
23 923 A
n2 cos 92+n3 cos 93
(49)

n2 cos 92-(U3 + 2 V3)
2 cos 92+(U3 + 1 V3)

 

n

33

where p23 is the amplitude ratio and $23 the phase change.

From (49) the following is obtained on separating real and
imaginary parts.

2
(n2 cos 92 - U3) +

2
(n2 cos 62 + U3) +

2 _
p23 ‘ (50)

and

2 V n2 cos 9

tan ¢ = (51)
23 2 ‘3 2
U3 + 3 - n2 cos 62

MN

The overall reflection coefficient r can be derived

'¢
from equation (38) on replacing r23 by p23 6 23. Thus

i(¢ +28)
r + p e 23
r = 12 23 (52)

i(¢ +23)
1 + r12 p23 e 23

We observe that equation (52) is identical to (38)

with 923 replacing r and ($23 + 23) replacing'(28). kaing

23
this substitution in (40) and (42)'we obtain net reflecti-

vity and phase change. Thus

 

2 2
r12 + p23 + 2 r12 923 cos ($23 + 25)
R = 2 2 q) (53)
l + r12 p23 + 2 r12 923 cos ( 23 + 23)
and
p23 (1 - riz) sin (¢23 + 26)
tan5r = (54)

 

2 2
r12 (1 + 923) + p23 (1 + :12) CO3 ($23 + 25)

3. An Absorbing Film Over An Absorbing Substrate In Air.

In this case the Fresnel's coefficients for both

interfaces (1,2 and 2,3) involve complex quantities since

34

both the film and the substrate are absorbing. The equations

may be written in the form

 

 

A
nl cos 91 — n2 cos 92
r = - = g + i h (55)
12 n cse +9 cose l l
1 ° 1 2 2
9 ’\ 9
n cos - n cos _
r = 2 2 3 3:9 +ih (56)
23 A cose +’r\1 cose 2 2
n2 2 3 3

Equating real and imaginary parts in equation (44) and the

above, we get for Normal Incidence,

 

 

 

 

2 2 2
g = r11 - n2 - (n2K2) h _ 2 n1 n2 2
2 2 2 9 2 _ 2 2
(nl + n2) + (n2K2) (nl + n2) + (n2K2)
and
2 2 2 2
g _ n2 n3 + (nsz) -(n3K3) h _ 2 n2n3(K3 K2)
3 _ 2 2 7 3 _ 2 2
(n2 + n3) + (n2K2 + n3K3) (n2+n3) +(n2K2+n3K3)

Using boundary conditions at the discontinuities,
elements of the characteristic matrices expressed in terms
of the Fresnel's coefficients are obtained. Substituting
these in equations of the form (25) and after a lengthy
simplifying process, the net reflectivity R for Normal

Incidence is given by

(92+h2)e2K262 + (92+h2) e-ZKZaZ + A Cos 2 8 + A Sin 2 8
R_22 33 2 2

 

_ (57)
e2K252+(g§+h§)(g§ + h§)e-2K262 + c cos 2‘82 +‘D sin 2 82

where

A

D)
II

2 (9293 + h2h3) 2 (92h3 ’ 93h2)

c = 2 (gzg3 - h2h3) D = 2 (92h3 + g3h2)

35

and
2F n; h 2w ni h

Bi = _—_7—_— cos Bi = ———X—__ (for normal incidence)
The monochromatic reflectivity values for any of the
three models considered can be calculated by substituting
the monochromatic values of the optical constants n and
K (for each media) in the appropriate equations. The three
media used in this study were air, zinc oxide (corrosion

film) and zinc (substrates).

EXPERIMENTAL PROCEDURE AND EQUIPMENT

The main phases in the experimental procedure were:
1. Preparation of samples.
2. Reflection measurements, before and after exposure.
3. Exposure to corroding atmospheres.
4. Measurement of surface roughness and film thickness.

The materials used in this study were Specially
requested from the manufacturers. Commercial quality rolled
zinc (purity 99.6¥%) made according to A.S.T.M. specifi-
cations B 69 - 39, type I was received from Matthiessen and
Hegeler Zinc Company, LaSalle, Illinois and hot rolled
galvanized steel A.S.T.M. designation A - 526 - 64T
(0.0017 inch zinc coating) from Mfidwest Steel Division,
National Steel Corporation, Portage, Indiana. These were
wrapped in moisture proof packing immediately after manu-
facture to prevent weathering prior to tests.

1-1/2” x 2” size samples were cut from the zinc roll
and the galvanized steel sheets. Effort was made to obtain
the samples from as few sheets as possible so as to minimize
variations among samples due to the material.

Using a vibrating stylus, the samples were marked
at the top left hand and the bottom right hand corners for
identification. In all 26 samples each of zinc and galvanized

steel were used in the tests; eight with duplicates for the

36

37

atmOSpheric test and ten for the cabinet test. The scheme

of exposure is given below:
AtmOSpheric test: 3, 7, 14, 21, 28, 42, 56, and 84 days
Cabinet test: 1/4, 1/2, 1, 2, 3, 5, 9, 14, 21 and 28 days

The samples were degreased by brushing lightly in a
bath containing one part commercial emulsifier (Gunk) and
three parts kerosine oil (Gwyther, 1947). They were left
in the bath for about 5 minutes to allow penetration of
solvent into the soil. The samples were then washed under
running water, dipped in acetone to remove water from the
surface and dried in a desiccator. Samples thus cleaned
supported a continuous film when rinsed with cold water,
indicating complete removal of grease, oil and soils from
the surface (Gwyther, 1947).

Degreased samples are generally pickled to remove
surface scales. To study the effects of piCkling on zinc
and galvanized steel, duplicate samples were pickled in a
solution containing 2.0% HCl and 0.02% Rodine 213 (by
weight) for 2 minutes at a temperature of 1500F (Mulvaney,
1962). Based on the decrease in weight, average film removal
was less than 0.05 microns for both zinc and galvanized
steel. More significant, though, was the fact that pidkling
dulled the surface of the specimens thereby changing its
reflection characteristics. For this reason it was decided
not to pickle the samples.

The dried samples were weighed in a "Mettler" analy-
tical balance with an accuracy of.: 0.00005 grams. The

zero adjustment of the scale was checked before and during

38

each set of measurements. Specimen weight was indicated on

a vernier scale to 0.0001 grams.

Total Reflectance Measurements

Since a suitable instrument was not available on
the campus, facilities of the Michigan State Highway Labora-
tories in Lansing were used for reflectance measurements.

A Beckman DK - 1A ratio recording spectrophotometer
with Beckman 24500 reflectance attachment (Figure 1) was
used to obtain'total reflectance curves at normal incidence in
the wavelength range 0.35 to 2.75 microns for each sample
before and after exposure. Hemispherical reflectance (also
called total reflectance) includes both the specular and the
diffuse reflectance. Therefore an integrating sphere (in the
reflectance unit) is employed to direct all reflected beams
from the sample (and the reference) onto the detector. A
shift plate is used at the sample (and the reference) port
which positions the sample (and the reference) at an angle
of 50 to the incident beam, so that the specularly reflected
beam is also intercepted by the integrating sphere.

Ratio recording technique is based on the comparison
of the beam energy from the sample to the beam energy from
a standard reference. The method thus eliminates errors
due to source fluctuations, changes in amplifier gain,
variation in detector sensitivity or spectral response,
and presence of absorbing gases in the beam paths.

Figure 4 shows the optical diagram for reflectance

studies. A beam of light from a tungsten (3,0000R) source

 

39

 

Figure l. Beckman DK-lA spectrophotometer with reflectance
attachment.

 

Figure 2. "Norelco" x—ray diffraction unit with recorder.

III/ll
I

 

Figure 3. Balphot Metallograph with camera attachment.

40

 

.mucmEmHSmmmE
mucmuomammu amoeumsmmflEmn How umum50uonmouuommm «alxn cmexowm Ca numm uzmflq .v musmflm

peas mocmuomammm HoumEOHSUOCOE

 

 

 

 

 

 

 

 

 

 

 

     

 

 

 

 

 

AmHmEva
manom.An
uflxm
Amoamummmuv
mnmnmm Emflum uuumso
mcaumhmmucH Houomumm
I'll/Ill,mou50m unmflq

 

 

 

41

is resolved on passing through a high-dispersion quartz
prism. Using accurately adjustable slits, monochromatic
beams are obtained. Slit width is automatically adjusted
to maintain a relatively constant beam energy level. The
monochromatic beam is then chopped into alternate reference
beam and sample beam to provide a double beam system within
the sample compartment. Both sample and reference beams
are integrated, detected and amplified by the same components,
and the ratio recorded on the chart. A combination of any
one of the seven wavelength scanning rates and four separate
chart speeds can be used. Manufacturer's indicated accuracy
for reflectance measurements is i.2% depending upon the
accuracy of the reference standard.

A performance curve for barium sulphate, which was
used as a reference standard, was obtained and the reflec—

tance curves for the test specimens were corrected accordingly.

Exposure to Corroding Atmosphere

One set of eight samples, with duplicates, each of
zinc and galvanized steel was exposed outside to the atmosphere
and a second set of ten samples each was exposed to water
spray inside a cabinet. Each sample was exposed for a pre-
determined duration and, once removed from the test, was

not re-introduced.

AtmOSpheric Test

A wooden frame was built to hold the samples in four

rows for exposure to the atmosphere. The top ends of the

42

specimens were clamped between the wooden frame and a clear
plexiglass strip which was bolted down with winged nuts.

This arrangement not only permitted easy withdrawal of
samples but also provided an inert contact thereby preventing
localized corrosion.

The frame was placed at an angle of 450 to the hori-
zontal on the roof of a building south of the Agricultural
Engineering building on the Michigan State University
campus. In this position the samples were exposed unobstruct-
ed to the sun and the rain. The experiment was started on
September 1, 1965.

Following the exposure scheme, duplicate samples
were withdrawn from the frame, rinsed with water to wash
off dust particles, dried and weighed. Reflectance curves
were obtained and surface corrosion films measured by methods

detailed later in this Chapter.

Cabinet Tests

A 2' x 3' x 2' size Spray cabinet was built from
plywood according to A.S.T.M. designation B 117 - 61,
(Figure 5).Water spray in the form of fine mist was used
as the corroding medium. To prevent water from soaking into
the plywood, the inside of the cabinet was lined with heavy
aluminum foil and covered with a plastic sheet. For the same
reason, the Spray water was stored in a plexiglass trough
instead of directly in the cabinet as suggested in the

designation.

43

 

Figure 5. Spray cabinet.

 

Figure 6. Air atomizing spray nozzle assembly.

44

An air atomizing spray nozzle assembly, as shown in
Figure 6, was used to produce fine particle spray. The
assembly consisted of two plexiglass nozzles (tube diameter
3/8" and nozzle opening 0.02" and 0.03" for air and water
respectively) set at right angles to each other and mounted
on a frame which easily attached to the trough. When
mounted on the trough,the lower end of the vertical nozzle
dipped well below the water surface and the horizontal
nozzle was connected to an air supply regulated at 18 psi
through a pressure regulating valve. The nozzles could be
rotated in the vertical plane thus changing the angle of the
spray. The spray was directed at the wall to arrest large
size water droplets present in the spray.

The samples were held at the bottom between two
plexiglass strips bolted together with winged nuts. The
samples were so placed that they neither touched each other
nor the clamping bolts. Three rows of strips were placed
in the cabinet on supports 15" above the floor and 4" apart.
The first support was about 6" to the side of the water
trough. Thus the water dripping from the samples and the
strips fell on the sloping floor and was drained out.

Preliminary tests on the cabinet showed that the
specimens corroded differently on the two surfaces. In fact
the surfaces facing the spray (rebounding from the wall)
were corroded more vigorously and more evenly than the
others. Therefore in the final experiment the test surfaces

were placed facing the spray.

45

Water in the reservoir was replenished three to four
times a day. The Spray nozzles were cleaned periodically
to remove precipitated solid deposits. The relative humidity
inside the Spray cabinet remained above 98% during the test
and the temperature varied between 650 and 70°F.

Samples removed from the test were dried, weighed
and then subjected to the reflectance and the corrosion film

thickness measurements.

Measurement of Surface Roughness

Three measurements of surface roughness were made
on each sample as outlined below:
1. Before exposure (clean, degreased surface).
2. After exposure with the corrosion products in place.
3. After removal of corrosion products.
These measurements gave the roughnesses of the clean metal
surface, the oxide surface and the underlying corroded metal
surfaces respectively.

A Micrometrical Profilometer type ”0A" with
Skidmount type ”AA" was used to measure r.m.s. roughness
values at 1/2” tracer stroke. The radius of the Skidmount
was 0°000500".i 0.000150. Manufacturer's indicated accuracy

for the instrument was i 2%.

Measurement of Corrosion Film Thickness

Average film thicknesses were calculated from the
change in weight of the specimens on removal of the corrosion

products from the test surface. In addition,metallographic

46

and x-ray diffraction methods were tried to investigate the
feasibility of their application.

After getting the x-ray diffraction curves, the
corroded samples were cut in half. One half was used in
the metallographic method and the other in the weight-
reduction method.

1. Weight-reduction method: A 10% acetic acid solution WEI
was used to remove the corrosion products (ZnO) from both I
zinc and galvanized steel samples (Evans, 1961). Since
the corrosion products were to be removed from the test

surface only, it was necessary to mask the back side. Pre— -

 

liminary tests with epoxy glue produced satisfactory results.
Duplicate Specimens of zinc and galvanized steel were coated
on both sides and edges with epoxy glue and allowed to dry
for a period of 12 hours. The samples were then weighed

and dipped in 10% acetic acid solution for 2 minutes (twice
the duration the test samples would be dipped for rust
removal). They were then rinsed with water, dried in a
desiccator for 6 hours and weighed. The average weight
change in the Specimens was observed to be less than 0.0003
grams. This would cause an error of less than 1% in the film
thidkness measurements.

The test samples were coated with epoxy glue on the
back and the edges, dried for 12 hours and weighed. The
samples were then dipped in a 10% acetic acid solution for
1 minute, scrubbing the surface with a nylon sponge. They

were then rinsed with water, swabbed to remove excess water

47

from the surface and dried in a desiccator for 4 hours.
Once again they were weighed and the reduction in weight
was obtained by subtracting this weight from the first.

Average film thiCkness h in microns was calculated from the

formula
_ 1L 4
h — AD x 10
where W = weight reduction in grams r—m
A = surface area of the specimen in cm2 5
3
D = density of the corrosion products in grams/cm3 {

Since the samples were exposed to water spray inside a
the cabinet and a relatively pure atmOSphere outside, it was
assumed that the corrosion is primarily due to oxygen and

that the surface rust is mainly ZnO. Therefore

___E___ 4_ _w_ .
h - 5.606A x 10 — 1783.803 ( A ) microns.

2. Metallographic method: It involves projecting a
polished cross-section of the sample onto a pre-calibrated
graduated screen of the metallograph and reading the layer
thiCkness directly from the screen. The method is laborious
in that it requires a long and careful preparation of the
samples.

The test samples were inbedded in cold plastic molds,
commonly used in metallurgical studies, to prevent damage
to the surface scale. Fine powder plastic was dissolved
in a solvent to form a thin paste and was poured into a
cylindrical ring placed over a flat aluminum plate. The

plate surface as well as the interior of the ring was coated

48

with a thin layer of petroleum jelly to keep the plastic
from sticking to these surfaces. A sample was then placed
vertically in the middle of the ring and held in place until
the plastic hardened (30 minutes). Four hours later it was
removed from the form and wiped clear of excess grease.

The sample cross-section was then polished, first
over three successive grades of emery cloth, and then three
grades of polishing wheels. The sample was rotated through
900 after each step to get better results. At the final
polishing operation which used an abrasive of 1 micron 1

particle size, the sample was polished across the width to

 

enhance the demarkation of the boundaries.
A Balphot Metallograph (catalog No. 42 - 31 — 22)

was used for thickness measurements,(Figure 3). Using a
20 x objective and a 10 x eyepiece, the image was projected
on a ground glass plate at a bellow distance of 20". The
plate can be replaced by a photographic film for taking
pictures. The length of the cross-section was scanned in
successive steps. An average film thickness was determined
for each step. From these step-measurements, average film
thickness was computed for the entire length of the cross-
section.

3. X—ray diffraction method: A beam of x-rays refracted

through a stratified media is attenuated according to the

following law:

E
I = IO e (- p) px

49

where IO = intensity of the incident beam
I = intensity of the refracted beam
(%) = mass absorption coefficient
x = thickness of the medium

Thickness of oxide film in an oxide-metal composite
medium can be calculated from the above equation by redefin-

ing the quantities as follows

 

IO = intensity of beam refracted through "clean"
metal
I = intensity of beam refracted through corroded
metal (oxide + metal)
(%) = mass absorption coefficient of ZnO
xf = oxide film thiCkness
x - Xf
_ c088.
l .

METAL

)
xf \ OXIDE

1.

 

 

 

 

 

 

91

For better accuracy the measurements should be made
at several "peak" values.

A "Nbrelco" x-ray diffraction unit type 12215/0
(Philips Electronic Instruments) shown in Figure 2 was used
and experiments were conducted with x-rays produced at 10

milliamperes and 20 kilovolts.

 

50

X-ray diffraction curves were obtained at two
"peaks" for each sample, before and after exposure. For
zinc samples peaks chosen were at 82.050 and 116.350;
however, for galvanized steel peaks had to be located for
each sample by scanning through the entire range of angles.
Mounting position was marked on each sample to eliminate
errors in the post-exposure measurements due to sample lo-
cation on the sample holder. Using an angle scanning speed
of 0.250 per minute, a plot containing the peak was obtained

on a pre-calibrated chart of a millivolt recorder.

 

 

RESULTS AND DISCUSSION

A visual examination of the corrosion films formed
on the samples showed that the films produced from exposure
to the atmosphere were uniformly spread over the entire sur-
face area, greyish in color and free of localized pitting.
There was a marked change in the appearance of the shiny
surface of clean samples even after a three-day exposure.
The films produced in the Spray cabinet, on the other hand,
were whitish-grey in appearance, spongy in texture and less
uniform (Figure 7). Films on samples exposed for a short
duration (up to one day) were discontinuous. In fact they
consisted of very small dots scattered uniformly over the
surface. This observation is not unexpected in View of the
manner in which corrosion of samples takes place in the
spray cabinet. Fine drops of spray (water) settle on the
test surface and react with the adjacent metal in the
presence of the oxygen in the air. Therefore at the
initial stages the corrosion pattern is drop-wise. As
time passes the number of drop-wise corrosion cells increases
until 100% of the surface is covered and results in a con-
tinuous film. Samples exposed in the Spray cabinet for one
day or more had continuous films.

Metallographic examination of the corroded samples

in general agreed with visual observations. However, at

51

 

Zinc.

Figure 7.

 

52

 

Galvanized steel.
Atmospheric test.
9

Galvanized steel.
Cabinet test.
4d

16 106

      

Atmospheric test.

Zinc.

Cabinet test.

Corrosion films on some representative samples
of zinc and galvanized steel.

See Table l for
exposure times for sample numbers marked.

53

high magnification (400 x) shiny metal background was seen
in spots for all but the 3-week and 4-week exposure samples

from the cabinet test.

Measurement of Film Thickness

The x—ray diffraction method failed to measure the
thickness of the corrosion films both on zinc and galvanized em.
steel samples. According to the equation I = IO e(- %0 p x
the diffraction peak values of corroded samples were ex-

pected to be smaller than the values for the corresponding

clean samples as outlined in the previous chapter. However,

1"“:5-33.‘ 552-1 i-'71:.-m-.€r erf "r- ‘-

the measured peak values for corroded samples were inconsis-
tent and in some cases were even higher than the clean
samples. Whereas the inconsistent behavior could be
explained as due to the uncontrolled variations in the
structure (grain size, orientation, etc.) and irregularities
of the corroded surface, the higher peak values after corro-
sion could be possible only if the values measured on clean
surfaces were erroneously too low. To investigate the
variations in repeated measurements of peak values of
diffraction from a clean surface, a new set of samples con-
sisting of four zinc and four galvanized steel samples was
prepared. Each sample was mounted on the sample post of the
x-ray machine at a fixed (peak) angle determined previously.
The diffraction peak values were measured (on both the re-
corder chart and the counter) three times without changing

the sample position or the x-ray settings. The variations

54

among the repeated measurements ranged from a minimum of
20% to a maximum of 45%. Such large variations (which evi-
dently caused the error in the data) in measurements from
the same sample without any change, deliberate or other—
wise in any of the influencing factors could not be ex-
plained. Under these circumstances the feasibility of this
method for corrosion film measurements was not pursued any '7‘-
further.

Film thickness values obtained by metallographic

method and by weight-change method (on removal of corrosion

 

products) are tabulated in Table l.

A comparison of the values measured by the two
methods showed that the values given by the metallographic
method were in general smaller than those given by the
weight-change method. The difference was more pronounced
for cabinet test samples where the metallographic values were
lower by a maximum amount of 18%. For the atmospheric test
samples the difference was small and the metallographic
values were lower by a maximum of about 8%.

The difference in film thickness values obtained
by the two methods can be explained from the consideration
of the following:

1. The weight-change method gives an average value for
the film on the entire surface of the test sample.

But the metallographic method measures the average

film thickness only at the cross-section viewed in

the metallograph (Figure 9). These values will

55

 

Figure 8. A close-up of the test samples imbedded in 1"
diameter plastic mold.

 

Figure 9. A micrograph of the surface corrosion film
(1000 magnification). The dark area is the
plastic, the intermediate band is the cor—
rosion film and the light area is the zinc
substrate.

56
therefore vary with the choice of the surface viewed.
For relatively uniform films the effect due to the
choice of location will be small and hence the
metallographic measurements will differ only
slightly from the average values measured by the
weight—change method. However, for relatively rough
films like those on the cabinet-test samples, the {*7
choice of the location becomes more important and i
large variations among the two methods can be

expected.

 

2. In the metallographic method some of the film material .
may be lost during the polishing operations resulting
in measured film values smaller than the actual.

The amount of the loss will depend, among other

things, on the nature and the characteristics of

the film. A rough and less adherent film, as on

cabinet-test samples, is more susceptible to

mechanical damage than the relatively smooth and
adherent films produced on the atmospheric-test
samples.

Therefore it can be concluded that the metallographic
method of film measurements in the form investigated in this
study is applicable to adherent films of uniform thickness.
For adherent films of non—uniform thickness the values ob-
tained by this method must be interpreted as the "local"

rather than the_“average" film thicknesses.

57

For non-adherent (loose) films special preparations
are required to prevent mechanical damage to the film during
polishing. In this investigation cold plastic mold was
used (Figure 8) for this purpose which did not prove
completely satisfactory. Electroplating the film before
imbedding the sample in the plastic mold could perhaps be

tried to advantage.

Rate of Growth of Corrosion Films

Thickness of corrosion films produced on zinc and
galvanized steel samples exposed for different durations to
the spray cabinet and the outside atmosphere are shown in
Table 1. Also the graphs of film thickness build-up with
time are plotted in Figure 11 for the spray cabinet and
in Figure 10 for the external atmosphere.

Figure 10 shows that for zinc the rate of film
growth is large during the first 2 weeks and then tapers
off to a slow rate. The decrease in the growth is more
gradual for galvanized steel samples which also Show large
rates at the beginning. Therefore at the end of the 12—
week exposure period (in the atmosphere) zinc samples had
already formed protective layers on the surface; however,
the galvanized steel samples were still undergoing corrosion
at a sizeable rate.

In the cabinet test, on the other hand, both the
zinc and the galvanized steel samples corroded at the same

rate as shown in Figure 11. Once again the film growth

58

 

 

 

 

Film thickness - microns

 

5.0—
~ Galvanized steel
1.0 L I l l I l L l l I l J
0 1 2 3 4- 5 6 7 8 9 10 ll 12

Exposure time - weeks

Figure 10. Oxide layer development on zinc and galvanized steel
exposed to the atmOSphere.

H
U1

0
1'

Galvanized steel ;

be H
h:
(3
l

— .A

U'IO\\J(D\OO

Film thickness - microns
.b

 

 

1' I) 1 1 1
10 .15 20 25 3o

EXposure time --days

 

1111
0 1 2 3 4 5

Figure 11. Oxide layer development on zinc and galvanized steel
exposed in the spray cabinet.

59

rate was very large in the first 2 days, then sharply dropped
off to a moderate rate for the rest of the exposure time.

In both the atmospheric test and the cabinet test
the corrosion films on zinc and galvanized steel samples
were of the same order of magnitude. The galvanized steel
films were large in absolute value for all but the short
duration samples of the atmospheric test as seen in Figures
10 and 11.

For reasons discussed in Chapter 3, no attempt was
made to correlate the results of the cabinet test with those

of the atmosPheric test.

Surface Roughness Measurements

,The root mean square (r.m.s.) roughness values of
clean metal surfaces, corroded (oxidized) surfaces and the
metal surfaces after removal of the oxides as measured by a
Micrometrical Profilometer (type "QA") are presented in
Table 2. The values shown are the average values for the
respective surfaces.

As seen from this table, the variations in the sur-
face roughness of the clean samples of zinc and galvanized
steel were small and the absolute values ranged between
0.12 and 0.15 microns for zinc and between 0.25 and 0.30
microns for galvanized steel. waever, for corroded surfaces
the variations were large,especially on cabinet-test
samples. The values ranged between 0.20 — 0.56 microns

for zinc and 0.36 - 0.89 microns for galvanized steel in

60

the atmospheric test and between 0.41 - 2.54 microns for
zinc and 0.58 — 4.45 microns for galvanized steel in the
cabinet test. The corresponding values after removal of the
corrosion products from the sample surfaces were small.

This should be expected from the fact that the densities of
zinc and zinc oxide differ roughly by a factor of 1-1/2 : 1.
Therefore for the same surface area a unit volume of zinc
will produce, on corrosion, about 1-1/2 units of zinc oxide

which will cause larger irregularities on the surface.

Hemispherical Reflectance Measurements

The hemispherical reflectance, by definition, is
the ratio of the total amount of energy reflected in all
directions in space to the energy incident from a specified
direction (normal in this case) The spectral hemispheri-
cal reflectance then refers to the hemispherical reflectance
when a monochromatic wave is used.

The graphs of hemispherical reflectance for clean
samples of zinc and galvanized steel in the wavelength range
0.35 to 2.75 microns are presented in Figure 12. The values
used in these graphs were averaged over all the samples.

An infrared absorption peak is observed at 1.0 micron which
agrees with the observations of Bor et a1 (1939) and
Coblentz (1920).

The curves for zinc and galvanized steel are almost

identical, the galvanized steel curves being lower by an

amount 0.08 — 0.10 throughout.

61

m.m

.msouods mh.m ou ov.o mmcmn numcwamgmz 93 CH Hmmum

 

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meHoHE I numcmam>mz
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62

The hemispherical reflectance curves for corroded
samples of zinc and galvanized steel were obtained in the
same manner as for the clean samples (using Beckman DK-lA
Spectrophotometer). The characteristic absorption peak at
1.0 micron was observed in every case. The shape of these
curves was essentially similar to that of the clean samples.
Since the change in reflectance due to corrosion rather
than actual reflectance was of interest in this study, the
reflectance curves of corroded samples are not shown here.
Instead, the change in reflectance computed from measurements
on clean and corroded surfaces (of the same sample) at 0.1
micron intervals in the wavelength range 0.35 - 2.75 microns
are presented in Figures 13, 14, 15 and 16 for some repre-
sentative samples. The corrosion-film thickness and the
surface roughness values for the samples are marked on each
figure.

From Figures 13 and 14 it is seen that for atmospheric
test samples (of both zinc and galvanized steel) the decrease
in reflectance was large at short wavelengths then declined
gradually with increasing wavelengths. For zinc samples
the decrease in the hemispherical reflectance was between
0.28 and 0.37 at 0.35 microns and between 0.0 and 0.04 at
2.75 microns, whereas for galvanized steel samples the values
ranged between 0.12 and 0.26 at 0.35 microns and between
0.0 and 0.06 at 2.75 microns wavelength.

For cabinet—test samples, however, the decrease in

reflectance was seen to be more constant throughout the range

63

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67

of wavelengths for all but the short exposure samples. For
samples exposed for 1 day or more the absolute decrease in
reflectance varied between 0.10 and 0.30 in the wavelength
range considered except the two extremes where the variations

were large.

Mean Integrated Hemispherical Reflectance

The hemispherical reflectance curves discussed thus
far were obtained using monochromatic waves of constant in-
tensity. However, the intensities of radiations for the
real sources are not uniform but exhibit a definite distri-
bution over the range of wavelengths. Therefore to investi-
gate the optical behavior of a surface exposed to a real
source, the hemiSpherical reflectance curves should be
normalized with the energy distribution curves of the
source. The average value of the resulting curve (which is
used as a criterion of the optical behavior) is called
the mean integrated hemiSpherical reflectance. Mathemati-
cally it can be expressed (assuming the source to be a black
body or a grey body) as:

JR“ ebl dA
19b). d”

where the emissive power ebk is obtained from Planck's

 

Mean integrated hemispherical (MIH) reflectance =

expression

68

 

2Wc

e - Wi - l
A (e -1)

8 4 2 . .
cl = 0.18892 x 10 BTU u /hr ft (Planck s constant)
c2 = 25,896IfR (Stefan-Boltzman constant)
T = source temperature, OR
A = wavelength of radiation, microns
R1 = spectral hemispherical reflectance

The mean integrated hemispherical (MIH) reflectance
values for the samples were calculated (by computer) using
d3 intervals of 0.05 microns for a 10,0000R source (sun)
and a 3000°R source (tungsten lamp). These values are given
in Table 3 andlareplotted against exposure time of the samples
in Figures 17 and 18.

The graphs of zinc and galvanized steel are seen to
be almost identical,particularly after long exposures.
These graphs clearly Show that the major portion of the
change in the optical properties of the corroding samples of
zinc and galvanized steel took place in the first three
days of exposure in the cabinet and in the first two weeks
when exposed to the outside atmOSphere. -The changes at
subsequent times were small. For a 10,0000R source (sun)
the integrated total reflectance values for zinc decreased
from 0.64 (for clean samples) to 0.35 in the cabinet and
to 0.37 in the external atmosphere, and from 0.55 to 0.33
and 0.35 reSpectively for galvanized steel samples. Similarly,

for the 3000°R sourCe the values decreased from 0.80 to 0.55

69

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0
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—43

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O
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O
u
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O
u)
I

Atmospheric test

I I I I I 3 I I I I
3 4 5 6 7 8 9 10 ll 12
_EXposure time - weeks

 

Mean integrated hemispherical reflectance
0
L.

Q
(.4
N

Figure 17. 'Change in the mean integrated hemispherical reflectance
of zinc and galvanized steel versus time of exPosure to

the atmosphere.

 

o.
o.
3 000°R
0.6 -______ _ _£-.
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0
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h:
I

Cabinet test
, I I 'I
0 l 2 3 4 5 6 7 ' I 14 . 21 .28
ExPosure time - days ~ .

 

Mean integrated hemispherical reflectance
0
0

Figure 18. Change in the mean integrated hemispherical reflectance
of zinc and galvanized steel versus time of exposure in

the spray cabinet.

 

70

and 0.65 for zinc and from 0.73 to 0.54 and 0.64 respectively
for galvanized steel.

Therefore the increase in the total integrated
absorptance (complement of reflectance) due to corrosion
was 75-80% for zinc and 45-50%.for galvanized steel for
radiations from a 10,0000R source. For 3,0000R source, on
the other hand, the increase was 75 to 125% for zinc and 33
to 70% for galvanized steel.

Effect of Corrosion Film Thickness on
the Mean Integrated Hemispherical Reflectance

Experimental results: The experimental values of the
MIH reflectance of clean and corroded samples (from Table 3)
are presented graphically in Figure 19 as a function of the
corrosion film thickness of zinc and galvanized steel samples
(combined). Figure 19 shows that for the 10,0000R source
nearly 75% of the total decrease in the MIH reflectance
occurred in films 3.0 microns thidk. HOwever, for the
3000°R source the decrease in MIH reflectance was almost
constant throughout. The mean integrated hemiSpherical
absorptance increased by 76% for 10,0000R source and by 117%
for 30000R source.

Theoretical results: In Chapter 3,theoretical equa-
tions were derived based on the Maxwell's theory of ane
propagation through stratified media to predict the behavior

of hemiSpherical reflectance from smooth surfaces as a

 

function of the film thickness. These equations consider

the changes due only to multiple reflections within the film

 

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72

which is assumed to have smooth surfaces. Therefore the
effect of the surface roughness is ignored.

In order to obtain the behavior curves from these
equations it is necessary to know the spectral values of
the optical constants n (refractive index) and K (the
extinction coefficient) of the film material and the sub-
strate metal. A search through the literature revealed
that such information is not available for bulk materials
except in the visible range. The Spectral values of optical
constants of thin evaporated films measured by polarimetric
methods have been reported. H0wever, these values may differ
greatly from those of the bulk material (Scott, 1955) and
hence are not reliable. Therefore it was decided to extra—
polate the known bulk values to the long wavelength region
using valid approximations.

The reported values (International Critical Tables,
1929) of the refractive index and the extinction coefficient
of zinc and the refractive index of ZnO are shown in Table 4.
The refractive index values of ZnO become very nearly
constant beyond 0.7 microns. Therefore a constant value of
1.96 was used for longer wavelengths. The n and K values
of zinc are plotted in Figure 20. The refractive index
curve was extrapolated to follow the Hagen-Rubens approxi-
mation which is valid strictly in the long wavelength region
(Born, 1964, p. 622). The extrapolation of the extinction
coefficient curve was based on the assumption that when n

is large (n >> 1) then K approaches 1 (Born, 1964, p. 615).

 

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74

Such approximations are bound to introduce errors in the
analysis but more exact data are not available.

Equations (40), (53) and (57) in Chapter 3 give the
reflectance behavior of a dielectric film in the air, a
dielectric film over a metallic substrate (in air) and an
absorbing film over a metallic substrate (in air) respectively.
By substituting the spectral values of n and k in these equations
the reflectance curves for the range of film thicknesses
can be obtained. The corresponding integrated reflectance
curves can then be computed by the process outlined earlier
in this Chapter.

The zinc oxide-zinc composite media formed by the
corrosion of zinc will fit in one of the last two models above
depending on whether the extinction coefficient K2 of the
ZnO film is equal to zero or has finite value greater than
zero.

In Figures 21 and 22 the mean integrated hemispheri—
cal reflectance curves for this composite media (calculated
from equations 53 and 57) are presented for K2 values rang-
ing from 0.0 - 0.857. It is interesting to observe that
the mean integrated reflectance values at first decreased
with increase of K2 values from 0.0 - 0.10 and then in-
creased as K2 increased from 0.1 — 0.857. This may be ex-
plained as follows:

When K2 = 0.0, 100% of the refracted wave traveling
through the film reaches the metal which, being a good re-
flector, reflects most of it back. Hence the reflectance

is high. As K2 increases, more and more of the refracted

75

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77

wave is attenuated during its passage through the film and
therefore less of it strikes and is reflected back from
the metal surface. Therefore the reflectance decreases.
Eventually a value of K2 is reached when all of the re-
fracted wave is absorbed in the film and none reaches the
back metal. The contribution of the metal (substrate)
becomes zero. The film then acts as a thidk absorbing
film in the air and the reflection behavior is determined
entirely by the properties of the film. Since the multiple
reflections within the film are then nonexistent, the
effect of the film thidkness,too,becomes negligible. As
K2 increases further, the reflectance increases since the
wave which is absorbed in a thin layer of the film next
to the interface is bounced badk (W01f, 1964, p. 615).

The integrated total reflectance curves calculated
with K2 = 0.0017 showed closest agreement with the experi—
mental data. Figure 19 shows that whereas the agreement was
good for thick films, large discrepancies existed for films
of small thicknesses. This can be explained from the fact
that for thick films the effect of multiple reflections within
the film is predominant and the error from neglecting sur—
face roughness is small. For relatively thin films, however,
the effect of surface roughness is large and therefore large
errors result if this effect is not accounted for in the
analysis.

To investigate the influence of surface roughness

on the integrated hemispherical reflectance of zinc and

78

galvanized steel samples, the reflectance data was plotted
against the r.m.s° roughness values of the corrosion film.
As seen from Figures 23 and 24, the data showed a tendency
toward a smooth curve for both 3000°R and 10,0000R sources.
This suggested, at least qualitatively, that correlation
did exist between the two factors. The trends of these
curves were in general agreement with those reported by
Birkebak et a1 (1964) even though the two situations were
quite different as discussed in the Review of Literature.
Since the variations of the surface roughness of
the corrosion film as well as the underlying metal were
uncontrolled and the geometrical shape of the irregularities
was not known, no attempt was made to draw any quantitative
conclusions. It is left to the future researchers working
with controlled films of known surface conditions to
study (quantitatively) the relative effects of the surface
films due to the multiple reflections, and from the surface
roughness due to systematic scattering depending on the

shape of the irregularities.

79

 

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S UMMARY

The purpose of this study was to determine the cor-
rosion rates of zinc and galvanized steel and to relate
their optical properties to the amount of corrosion in the r
radiation spectrum of 0.35 to 2.75 micron wavelengths from
a 10,ooo°R source (sun) and a 3ooo°R source (tungsten lamp).

Samples of zinc and galvanized steel were corroded

for several durations up to 3 months in outdoor atmosphere

 

and up to 4 weeks in a spray cabinet using a continuous

spray of water. The corrosion film thidknesses were measured
by the weight-change method (removal of the corrosion products
from the test surface), by the x-ray diffraction method and

by the metallographic method.

A Beckman DK—lA ratio recording spectrophotometer
with a Beckman 24500 reflectance attachment was used to
measure the hemispherical reflectance at normal incidence
in the wavelength range 0.35 to 2.75 microns. The hemis-
pherical reflectance curves so obtained were normalized
with the energy distribution curves of the 10,0000R and the
30000R sources to obtain the corresponding integrated hemis-
pherical reflectance curves. The average of these curves.
called mean integrated hemispherical (MIH) reflectance,were
used as a criterion for the optical behavior of the samples.

The corrosion films produced in the atmosphere were

smoother than those produced in the spray cabinet. The
81

82

film thicknesses varied from 1.2 to 12.6 microns. The
rate of corrosion was appreciable for the first 2 weeks in
the atmOSphere and the first two days in the spray cabinet.
In the remaining period the rate was relatively small.

The MIH reflectance decreased with the growth of
the corrosion films. For the 10,0000R source nearly 75%
of the reduction occurred in films 3.0 microns thick, but
for BOOOOR source the rate was relatively constant at all
thicknesses. The corresponding increase in MIH absorptance

was 76% for the 10,0000R source and 117% for the 3ooo°R

 

source.

The experimental values of MIH reflectance were
correlated with the theoretical predictions based on the
Maxwell's theory of wave propagation through stratified
media (assumed perfectly smooth) using a value of 0.0017
for the extinction coefficient of zinc oxide corrosion film.
The agreement was good at large film thicknesses but was poor
for films less than 4.0 microns thickness. This was attri-
buted to the fact that the effect of surface roughness, which
was neglected in the theoretical analysis, was in fact
proportionately large at small film thicknesses.

The MIH reflectance showed at least a qualitative
correlation with the surface roughness° The trends of the
curves were comparable with those reported in the literature.
The separate effects of the film thickness and the surface
roughness, however, could not be ascertained in this study
because of the simultaneous and uncontrolled variations of

these factors.

83

CONCLUSIONS

The corrosion films produced in the atmosphere for
exposures up to 12 weeks were relatively smooth and
were found to vary from 1.2 to 3.5 microns for

zinc and from 1.4 to 4.1 microns for galvanized
steel. The spray cabinet films ranged from 1.5 to
8.8 microns for zinc and from 4.0 to 12.6 microns
for galvanized steel for exposures up to 4 weeks.
The rate of corrosion of both zinc and galvanized
steel was substantial in the first 2 weeks (of
exposure) in the atmosphere and the first 2 days in
the spray cabinet. The rate then stabilized to a
constant low value.

The spectral attenuations in the hemispherical
reflectance due to corrosion were seen to vary,
depending upon the film thickness, from 0.27 to 0.37
at 0.35 microns and from O to 0.04 at 2.75 microns
for atmospheric test samples. For cabinet samples,
however, the variations were nearly constant through—
out the range of wavelengths considered except at
the two extremes. This indicated that relatively
high absorption took place in the short wavelength
region for the samples oxidized in the atmosphere.
The absorption increased at all wavelengths for

samples corroded in the cabinet.

84

The mean integrated hemiSpherical (MIH) reflectance
decreased with the growth of the corrosion film
thickness. For a 30000R source the reduction

in the MIH reflectance was nearly linear but for the
10,0000R source almost 75% of the change occurred

in films 3.0 microns thick.

The mean integrated hemispherical absorptance (comple-
ment of reflectance) of zinc and galvanized steel
samples increased by 76% for solar radiations(lO,OOOOR
source). For 3OOOOR source, on the other hand, the
increase was about 117%.

The theoretical predictions of MIH reflectance

based on the Maxwell's theory of wave propagation
through stratified media showed best fit with the
experimental data using a value of 0.0017 for the
extinction coefficient of the zinc oxide corrosion
film. The agreement was good for thick films but
large discrepancies existed for films below 4.0
microns. This was probably due to the failure of
the theoretical analysis to account for the effect
of surface roughness which is large for thin films.
The MIH reflectance data showed a qualitative cor-
relation with the measured surface roughness values
of corrosion films. The trends were comparable

with those reported by Birkebak et a1 (1964).
However, no quantitative conclusions were drawn

because of the uncontrolled variations of surface

85

roughness with film growth and unknown geometrical

shape of the irregularities.

REFERENCES

 

It'

AGNEW, J.
1953

ANDERSON,
1946

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BENNETT:
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BIRKEBAKI
J. W.
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APPENDIX

96

Table 1. Thickness of oxide films on zinc and galvanized
steel samples measured by (a) the weight change
method and (b) the metallographic method

 

 

Oxide Film Thickness, Microns

 

 

 

 

Exposure Zinc Galvanized Steel
Sample No. Duration (a) (b) (a) (b)
Atmospheric Test
9 3 days 1.2 1.1 1.4 1.4
10 1 week 1.9 1.8 1.7 1.6
11 2 weeks 2.7 2.5 1.9 1.8
12 3 " 3.2 3.0 2.4 2.2
1d 4 " 3.2 3.1 2.8 2.6
2d 6 " 3.2 3.0 2.9 2.8
3d 8 " 3.3 3.2 3.4 3.2
4d 12 " 3.5 3.3 4.1 3.8
Cabinet Test
16 % day 1.5 1.3 4.3 3.8
15 % day 2.4 2.2 4.0 3.7
14 1 " 5.5 4.8 6.0 5.5
13 2 days 6.6 6.0 10.8 9.3
5d 3 " 6.0 5.1 11.4 9.8
6d 5 " 6.6 5.9 9.4 8.4
7d 9 " 7.1 7.0 10.9 10.3
8d 14 " 7.9 6.8 7.1 6.7
9d 21 " 8.7 7.4 10.0 8.5

10d 28 " 8.8 7.3 12.6 10.4

 

97

 

 

 

 

 

 

Table 2. Measured r.m.s. surface roughness values (in mi-
crons) of (a) clean surface, (b) oxidized surface,
and (c) metal surface after removal of oxide

Zinc Galvanized Steel

Sample No. (a) (b) (C) (a) (b) (C)

Atmospheric Test

9 .13 .20 .18 .28 .36 .33
10 .12 .38 .28 .25 .61 .51
11 .14 .56 .31 .22 .56 .53
12 .10 .43 .31 .28 .71 .56
1d .10 .46 .33 .26 .89 .66
2d .12 .38 .31 .26 .84 .64
3d .11 .33 .31 .22 .89 .64
4d .13 .38 .33 .25 .89 .58
Cabinet Test

16 .14 .41 .31 .26 .64 .38
15 .10 .76 .46 .26 .58 .33
14 .13 1.40 .46 .28 .58 .33
13 .11 1.52 .71 .30 2.79 .89
5d .11 1.27 .46 .20 .89 .66
6d .12 1.52 .64 .25 1.78 .76
7d .14 1.40 .51 .28 3.30 .86
8d .12 1.91 .56 .30 2.29 1.02
9d .13 1.91 .76 .27 3.05 1.02
10d .10 2.54 .76 .29 4.45 1.14

 

98

Table 3. Experimental values of mean integrated hemispheri-
cal reflectance

 

 

 

 

 

 

Zinc Galvanized Steel
3ooo°R 10,0000R 3ooo°R 10.00003
Sample No. Source Source Source Source
Atmospheric Test
9 .781 .534 .699 .470
10 .723 .440 .694 .429
11 .679 .395 .672 .391
12 .689 .383 .658 .359
1d .711 .420 .693 .394
2d .714 .417 .696 .394
3d .666 .393 .676 .389
4d .651 .373 .645 .350
Cabinet Test
16 .687 .514 .705 .472
15 .643 .448 .645 .391
14 .626 .423 .594 .373
13 .610 .408 .504 .361
5d .524 .317 .509 .301
6d .558 .332 .564 .320
7d .578 .351 .523 .313
8d .574 .353 .648 .380
9d .566 .353 .593 .354
10d .551 .349 .496 .335

 

99

Table 4. Spectral values of optical constants of zinc and zinc
oxide (International Critical Tables, Volume V, p.
250 and Volume VII, p. 20)

 

 

 

 

 

Zinc Zinc Oxide
Wavelength Refractive Extinction Wavelength Refractive
Index Coefficient Index
Microns n k Microns n
0.257 0.55 1.10 0.434 2.1395
0.275 0.46 2.56 0.436 2.1358
0.298 0.47 3.41 0.447 2.1143
0.326 0.60 3.72 0.471 2.0806
0.361 0.72 3.63 0.486 2.0649
0.398 0.85 3.45 0.492 2.0593
0.441 0.93 3.40 0.502 2.0515
0.468 1.05 3.32 0.546 2.0228
0.508 1.41 2.92 0.589 2.0041
0.598 1.93 2.41 0.656 1.9843
0.598 2.21 2.61 0.668 1.9817
0.630 2.36 2.34 0.706 1.9740
0.668 2.62 1.94 0.768 1.9648

 

M'11171111111111!EIIHJEIIIWIIIIES

22