GRADED INDEX ANTIREFLECTIVE COATINGS FOR GLASS
FINAL REPORT
by
John S. Haggerty
MIT Energy Laboratory Report No. MIT-EL 82-016
September 1978 - February 1982
DOE/ER/05003
MIT-EL82-016
FINAL REPORT
September. 1, 1978 - February 28, 1982
cd
. 0
GRADED INDEX ANTIREFLECTIVE COATINGS FOR GLASS
by
John S. Haggerty /
Massachusetts Institute of Technology
Cambridge, Massachusetts
02139
Prepared for
U. S. Department of Energy
Agreement No.
DE-ACO2-78ER05003
April 1982
NOTICE
This report was prepared as an account of work sponsored by the
United States Government. Neither the United States nor the
Department of Energy, nor any of their employees, nor any of their
contractors, subcontractors, or their employees makes any
warranty, express or implied, or assumes any legal liability or
responsibility for the accuracy, completeness, or usefulness of
any information, apparatus, product or process disclosed or
represents that its use would not infringe privately-owned
rights.
I~L~L_
_I
_
ABSTRACT
Glass compositions and process conditions by which broad band gradedindex antreflective films can be produced on glass surfaces have been
developed.
The end use for the treated glass sheet is as cover plates for
flat plate solar-thermal collectors; thus, cost issues dictated that the
process conditions fall within constraints imposed by the float glass
process.
To accomplish this objective, both the film formation process and the
characteristics of the graded-index films were investigated in detail.
A
model, borosilicate glass was used for initial work that served to verify
experimental procedures, to confirm essential features of the film forming
process and to determine whether the porous surface film and the phase
separated structure of the host glass had an adverse effect on mechanical
properties.
Glasses and film surfaces were characterized chemically (atomic
absorption, Auger and SIMS), microstructurally (SEM, TEM and replica
microscopy), by weight loss, by specific surface area (BET), by small angle
X-ray scattering (SAXS) and optically.
Based on the results with the borosilicate glass, a candidate soda-limesilica glass composition was defined that satisfied the phase separation and
float glass process criteria.
Heat treatments were defined for the glass
that produced appropriate microstructures and selective etchants were defined
that produced porous films by selective dissolution.
^
TABLE OF CONTENTS
Page
I.
INTRODUCTION
CHAPTER II - Surface Chemistry of Porous Anti-Reflective
Films on Borosilicate Glasses
I.
II.
III.
II-1
Introduction
Experimental Approach
II-1
II-2
Results and Discussion
11-8
IV. Summary
V.
VI.
I-I
Acknowledgements
References
II-21
11-22
11-23
CHAPTER III - Microstructural Characterization of GradedIndex Anti-Reflective Films
I.
II.
III.
IV.
V.
Introduction
Experimental
III-1
111-2
Results and Discussion
III-3
Conclusions
References
111-7
111-9
CHAPTER IV - Exact Computation of the Reflectance of a
Surface Layer of Arbitrary Refractive Index
Profile and an Approximate Solution of the
Inverse Problem
I.
II.
III.
IV.
V.
Introduction
Calculated Reflectance: Exact Theory
Calculated Profile: The Inverse Problem
Conclusions
References
CHAPTER V - Strength and Fatigue Behavior of a Borosilicate
Glass with an Anti-Reflective Surface
I.
II.
III.
IV.
III-1
IV-1
IV-1
IV-2
IV-7
IV-13
IV-14
V-1
Introduction
Experimental Apparatus and Procedure
V-1
V-2
Results and Discussions
V-3
References
V-14
TABLE OF CONTENTS (cont.)
Page
CHAPTER VI - Effect of Proof Testing Soda-Lime Glass in
a Heptane Environment
VI-1
CHAPTER VII - Development of Selectively Etched Films on
Phase-Separated Na 2 0/CaO/Si0 2 Glass
VII-1
I.
II.
III.
IV.
V.
VI.
VIII.
Introduction
Literature Review
Experimental Approach
Results
Discussion
Conclusion
SUMMARY
VII-1
VII-3
VII-1O
VII-26
VII-35
VII-39
VIII-1
_I^__X___I
_
I.
INTROD UC TIO N
A research program has been conducted leading to the definition of
glass compositions and process variables by which broad band anti-reflective
(AR) coatings can be formed on glass.
The glass compositions were selected
in terms of compatibility with the temperature limitations imposed by the
float glass process and durability to exposures anticipated for flat-plate
solar collectors.
The elimination of reflection losses from glass cover plates permits
the extractable heat from flat-plate solar collectors to be increased by
30-50% compared with their performance under equivalent solar flux, surface
temperature and ambient conditions without broad band AR coatings.
Conventional single layer or multilayer AR coatings do not reduce reflection
losses significantly over the entire solar spectrum even though they are
extremely effective in the narrower visible portion of the spectrum.
Thus,
they contribute very little added value to the solar collector and cause
significant incremental manufacturing and maintenance costs.
Graded index
surface films can virtually eliminate reflection losses if controlled
properly.
The economic value of this performance gain has been estimated.
It
appears that the manufacturing cost of glass sheet can be roughly doubled
and remain cost effective, if reflectance losses are completely eliminated.
1 2
We and others ' have demonstrated graded-index films on a borosilicate
glass (Corning Glass Works No. 7740, Pyrex
I-1
).
While glass treated this way
IIII_
exhibited adequate optical properties,
the glass itself,
cannot be
fabricated by the float glass process because of excessive working
temperatures, and consequently is too expensive for solar applications.
The
principal objective of our work was to define glass compositions and
processing steps which result in graded-index surface films exhibiting broad
band AR characteristics on glasses that can be fabricated by the float glass
We proceeded on the basis that the mechanistic processes leading
process.
to the surface films as well as the films themselves must be characterized
in detail.
Also, the absence of an adverse effect on long term strengths
must be verified.
The mechanism by which graded-index surface films are produced on glass
surfaces consists of preferentially dissolving one phase from a phase
separated glass.
The film which remains consists of a porous structure in
which the fraction of solid phase increases continuously from the free
surface toward the bulk glass.
Scattering effects are eliminated by
limiting the size of the pore structure to dimensions that are substantially
less than the wavelength of light.
refraction is
With this structure, the local index of
proportional to the fraction of solid phase which is
present.
The initial research was conducted using a borosilicate glass
(CGW
No.
7740) as a model composition because so much work has been done on
studying phase separation in
this glass and also it
is
available in
the
large, uniform quantities needed for the mechanical testing phase of the
program.
Because the scale of the observations required to characterize
these porous surface films generally approaches the effective resolution
limits it is extremely important to work with a glass host whose
1-2
microstructural and phase characteristics are known.
Once characterization
techniques were verified, it was possible to conduct compositional and
process research with confidence.
Our characterizations defined the microstructural and chemical nature
of the surface films throughout their thickness.
These parameters included
defining the characteristic dimensions, the morphologies, the volume
fractions and the chemistries of the phases (solid and pore) throughout the
thickness of the film.
This information permitted optical characteristics
to be calculated and compared with observed results.
Because it was not
feasible to characterize the surface films with adequate resolution to
permit optical properties to be calculated with diagnostic precision,
research was undertaken to find means of using the optical charactistics to
define the index gradients in the surface films.
The effect of the porous
surface films on the strength of phase separated glass was studied in a
manner that measured both the initial
populations
and the post-processing
flaw
and the static fatigue characteristics without ambiguities
caused by free edges.
were characterized.
Chemical polishing and selective dissolution kinetics
Characterizations were made on model and candidate
glass compositions as a function of prior processing history.
From this
basis, a specific glass composition, a time-temperature annealing cycle and
the composition of a
selective dissolution acid and etch time were defined
that should satisfy the objectives of the program.
The optical
characterizations of the candidate glasses had not been completed at the
time this report was submitted.
The majority of the research conducted in this program was carried out
at the Massachusetts Institute of Technology by students and research staff
I-3
under the direction of Dr. John S. Haggerty.
The mechanical property
characterization was carried out under subcontract at the-University of
Massachusetts under the direction of Professor J. E. Ritter.
The individual
contributions are reflected by the authorship of individual chapters.
This report is a compilation of documents that have been submitted
for publication.
The first chapter summarizes the characterization of film
properties and kinetics of film formation on the model borosilicate glass.
The second summarizes issues relating to microstructural characterization.
The third deals with the optical characterization of graded index films and
the deduction of the index gradient from reflectivity measurements.
The
fourth and fifth summarize results of mechanical property research.
The
sixth chapter summarizes the definition of a candidate glass based on
previously developed characterization techniques.
conclusions are given in
the Summary.
1-4
Principal results and
REFERENCES
la. M. J. Minot, "Single-Layer, Gradient Refractive Index Antireflection
Films Effective from 0.35 to 2.5 pm", J. Opt. Soc. Am., 66, 515
(1976).
lb. M. J. Minot, and U. Ortabasi, "Antireflective Layers on Phase Separated
Glass", U. S. Patent Number 4,086,074, April 25, 1978.
2. A. Iqbal, S. C. Danforth, and J. S. Haggerty, "Surface Chemistry of
Porous Anti-Reflective Films on Borosilicate Glasses". Submitted for
publication to the J. Am. Ceram. Soc., April, 1982.
I-5
CHAPTER II
Surface Chemistry of Porous Anti-Reflective
Films on Borosilicate Glasses
by
A. Iqbal,
S. C. Danforth,
J. S. Haggerty
Energy Laboratory and Department
of Materials Science
12-011
Massachusetts Institute of Technology
Cambridge, Massachusetts 02139
ABSTRACT
Gradient-index anti-reflective (GIAR) films are formed on Pyrex
a process employing phase separation and acid etching.
7 74 0
(TM ) by
Experiments were
conducted to characterize the development of the GIAR films by chemical
means.
Solution chemistry, SIMS, Auger, and weight loss analyses were used
to evaluate a proposed model for film formation.
The results suggest that
the acid etching/leaching process is more complicated than proposed:
the
completeness of phase separation and/or the co-continuity of the phases is
in doubt for a 600*C, 3 hour heat treatment; the chemical polishing
treatment removes both phases at equal rates; major compositional variations
exist on the as-received glass surfaces; and only after longer than optimum
heat treatment times was significant selectivity of the etching/leaching
solutions indicated chemically.
* Present Address: Fairchild Corp., Sunnyvale, CA
** MIT, Cambridge, MA 02139
94086
Submitted for Publication to the Journal of the American Ceramic Society
__I~~__
I.
I IIYIYIYIIIIYIIIil
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.,iUII .11111mbII
lIi
INTRODUCTION
It has been demonstrated 1 that gradient-index, anti-reflection films on
borosilicate glass reduce reflective losses from a typical value of 3-4% per
surface to between 0.05 and 0.45% per surface over the entire solar
spectrum.
These films are important for flat plate solar heating
applications because performance calculations show that their use gives a
30-45% increase in extractable heat over uncoated glass for typical
operating conditions.
Conventional single or multilayer AR coatings do not
achieve low reflectivities over a sufficiently large fraction of the solar
spectrum to have a significant effect on performance.
The weathering stability of GIAR films on borosilicate glass was
demonstrated in a recent study 2 in which the solar transmittance remained
virtually unchanged after 37 months of continuous atmospheric exposure.
A
study 3 associated with our own indicates that the strength of the treated
glass has a complex dependence on the processing steps and the specific
glass batch from which the test plates originated.
More importantly, it was
determined that the fatigue resistance was not influenced by any of the
processing steps used in film development.
1 4
The model '
used to describe the formation of the GIAR film relys on a
microstructural feature in a phase separated glass.
A co-continuous,
interconnected two phase microstructure is generated by an appropriate heat
treatment.
In this model,1 the GIAR films are formed by preferential
removal of the more soluble phase from the glass surface by an etch/leach
11-1
(T
operation, similar to the Vycor
)
process. 5 The resultant film is a three
dimensional interconnected network of pores and solid glass (high silica
phase), where the volume fraction porosity varies across the film thickness.
The porosity gradient, shown schematically in Figure 1, results from the
acid solution acting longer at the outer surface (z = 0) than at the film glass interface (z = d).
The acid solution presumably dissolves all of the
low silica phase and some of the high silica phase at z
-
0, with
progressively retarded dissolution of both phases with increasing depth into
the bulk glass.
This porosity gradient gives rise to a refractive index
gradient, n(z), shown schematically in Figure 1.
While the optical properties ' '
qualitatively with those predicted for
of treated borosilicate glasses agree
graded-index films, to date, there
has been no reported attempt to confirm the essential features presumed in
the film formation process or to establish a quantitative relationship
between the film'and optical characteristics.
This research reports
characterization of the films in terms of the film thickness, pore size,
total porosity and selectivity of the disolution process.
Ultimetely, this
information will be used to define glass compositions, heat treatments and
surface treatments by which broad band anti-refletive characteristics can be
7
produced on glasses that can be processed by the float glass process.
II.
EXPERIMENTAL APPROACH
The detailed characterization of the GIAR films was undertaken to
provide a basis for modeling the formation process.
These characterizations
included the distribution of elements within the surface film, the chemistry
of the bulk glass, weight loss, specific surface area and film thickness
measurements.
Chemical characteristics were analysed by Auger, secondary
ion mass spectrometry and atomic absorption techniques.
A.
Glass Selection and Film Development
An alkaliborosilicate glass, Pyrex(TM ) CGW No. 7740, was used as a
model composition because its phase separation characteristics had been
investigated, 8- 1 3 the procedures for developing GIAR films were
1 14
and the glass was available in adequate quantities for the
established, '
entire experimental program.
Pyrex(TM ) 7740 received from Corning Glass Works had two types of
surface finishes.
The four batches of glass used were designated:
A series glass = rolled; mechanically ground and polished.
B series glass = as rolled.
C series glass = as rolled.
E series glass
-
rolled; mechanically ground and polished.
The GIAR films were developed by the following procedures.
Samples
were cleaned and then heat treated (600*C for 3 hours) to induce phase
separation.
They were subsequently chemically polished (30 minutes in
10 wt.% NH 4 F*HF at R.T.) to remove surface inhomogeneities caused by the
heat treatment; followed by etching/leaching (20 min. in 0.1 wt.% NH4 F*HF
0.16N HN0 3 at 450C) to develop the anti-reflection film.
Variables
introduced into the film development process were; the heat treatment time,
the chemical polishing time and the preferential etching/leaching time.
11-3
For these experiments, the annealing time/temperature and film
formation solution temperatures were selected at values which differed from
those producing optimum optical properties.1
Lower annealing temperatures
were used to avoid viscous deformation of the glass plates and lower
solution temperatures were used to avoid instabilities in the bath
composition caused by volitilization.
The selected values were well within
the reported I range of process conditions causing broad-band anti-reflective
characteristics.
Our optical characterizations indicated reflectivities
that were intermediate between those reported in Figures 1 and 4 of
Reference 1.
Thus, while non optimal from optical performance criteria,
these process conditions produce representative film characteristics and
substantially facilitate the experimental procedures.
The code used to describe the glass samples and the various treatments
received is as follows;
W X - Y - Z,
(1)
where:
W = batch of glass used (A,B,C, and E series),
X = heat treatment time at 600*C, (hours),
Y = chemical polishing time at room temperature, (minutes),
Z = etching/leaching time at 45*C, (minutes).
B.
Chemical Characterization Techniques
The first group of characteristics were microscopic, direct observation
techniques consisting of Auger electron spectroscopy (AES), secondary ion
mass spectrometry (SIMS), and scanning electron microscopy (SEM).
11-4
The
._I__
_
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second group are macroscopic, averaging techniques consisting of anaylses of
acid solutions by atomic absorption spectroscopy, weight loss measurements,
and BET method for surface area determination.
B.1.
Auger Electron Spectroscopy (AES)
Auger analysis was used to give compositional depth profiles of the
GIAR films by Ar ion sputtering through the films and by tapered section
analysis (6* to give lOx apparent magnification).
In the latter analysis, a
nickel film was used as a fiducial for the true surface.
Two approaches 1 5 were used to control charging resulting from Ar+
sputtering used to perform depth profiling.
stopped while taking the spectra.
In some cases the Ar+ flux was
An AES sputter depth profile was also
done through a 30-40 am thick film of thermally evaporated gold on the glass
surface.
This enabled the Auger spectra to be recorded while sputtering
with minimum charging.
For reasons presented with the results, it was felt that AES could not
be used as a means of making quantitative concentration measurements;
however, it should have provided useful information about concentration
gradients and relative compositions of samples.
B.2.
Secondary Ion Mass Spectremetry (SIMS)
SIMS, using a primary ion beam of 0-, was also used to evaluate the
surface chemistries of the various glass surfaces.
Milling rates were
estimated from crater depths by optical interferometry.
Glass surfaces were
sputter coated with an " 35 nm layer of Au-Pd to provide a conductive path.
II-5
At present, SIMS can, at best, provide an order of magnitude estimate
of absolute concentration.
Like AES, it can be used to obtain useful data
on relative concentrations and concentration gradients.
B.3.
Scanning Electron Microscopy (SEM)
Scanning electron microscopy
microstructure of the GIAR films.
was used to investigate the
Samples for SEM were coated with w 2nm of
C and a 15nm of Au(60%) - Pd(40%) (thermally evaporated) to reduce charging.
12 13 16
indicate that
'
The results from this study combined with other work '
the normally heat treated glass exhibits a phase separated structure size of
7.5-10.0 nm and the AR films' surface exhibits a nodular structure
approximately 20 to 40 nm in size.
A coating having approximately the same
thickness as the dimensions of the microstructural features of interest
makes interpretation of the absolute microstructure unreliable, but the
decoration does render the AR film distinguishable from the bulk glass.
The SEM was used reliably to measure AR film thickness using both
fracture edges of etched glass and samples produced by diamond scribing the
film to reveal the AR film - glass interface along the scribe track.
B.4
Chemical Dissolution
Subsequent to phase separation, the glass is subjected to two chemical
treatments; a chemical polish, and an etch/leach.
Experiments were
undertaken to evaluate the rates at which the acid solutions dissolved the
glass by measuring weight loss as a function of exposure time and to
II-6
determine whether the acids were acting in a uniform or a selective manner
by analyzing the compositions of the liquors.
Weight loss measurements were performed by taking dry weights of the
7.62 x 7.62 x 0.318 cm glass slides before and after chemical dissolution.
The weight loss per unit area provides one measure of the thickness of the
layer effected by the acid solutions.
Combined with knowledge about the
selectivity of the acid and volume fractions of the phases in the glass, the
weight loss can also give an average measure of the thickness of the GIAR
film.
For analyses, the volume fractions of durable and soluble phases were
17
taken to be 0.55 and 0.45 respectively.
Atomic absorption spectroscopy (AAS) was used to evaluate the
chemistries of the acids used to process the glass surfaces.
For a
nonselective polish, this technique determines the glass composition at a
specific distance into the surface.
The technique also determines the
selectivity of the film forming acid solution.
The concentrations of Si, B, Na and Al expected in the acid solutions
can be estimated based on the total volume of solution, the compositions of
the glass phases,17 an assumed dissolution mechanism, and the weight loss.
The level of agreement between the predicted and observed concentration
serves to evaluate the accuracy of the model for producing AR films.
B.5. Surface Area Determination (BET)
Specific surface area measurements by BET method were made on crushed
and sized Pyrex( TM ) 7740 to evaluate the changes that occur with the GIAR
process.
Besides indicating the presence of a porous surface film presumed
11-7
to form by preferential dissolution, the characteristic dimension of the
pores in the film can be approximated using SEM determined film thicknesses.
The size of the pores generated during film formation on spherical powders
can be approximated by assuming that after acid treatment all the new
surface area is attributable to the surface treated layer.
This assumption
is largely justified if the surface area after film formation substantially
exceeds that of the untreated glass and if the GIAR film volume is much
smaller than the volume of the whole particle.
III. RESULTS AND DISCUSSION
A.
Auger Electron Spectroscopy
Because of difficulties associated with using AES on glass, one set of
samples was used which allowed comparisons of the maximum expected
compositional differences.
Fracture surfaces of as-received glass samples
(AO-O-O and BO-0-O) were compared with corresponding fully processed
surfaces (A3-30-20 and B3-30-20).
Because the Na signal was unstable, and
the Al was just slightly above the background, the ratio of B/Si was used in
the comparisons.
The proposed model indicates that etching/leaching preferentially
removes the alkaliborate phase from the glass surface.
This should result
In
in a decreased B/Si ratio in the glass surface after etching/leaching.
contrast, AES did not indicate a significant difference between the B/Si
ratio for the as received fracture surfaces (AO-O-O and BO-O-O and the fully
processed GIAR film surfaces (A3-30-20 and B3-30-20).
II11-8
AES performed by progressively milling through the AR film (B3-30-20)
using Ar+ sputtering, showed constant Si, 0, and B concentrations to a depth
of 0.35 pm, indicating an apparent absence of any elemental gradients (Si,
0, B) in the AR film.
Tapered section AES analysis revealed no
compositional gradients to a distance of 2 pm true depth into the glass
(B3-30-20).
The reasons for not observing chemical differences between treated and
untreated surfaces by AES are not known.
The B and Si levels are well above
detection limits and the presumed differences should have been detectable,
particularly in the as-received fracture surface vs.
surface comparison.
fully processed
The failure to resolve a gradient in the tapered
section is understandable in retrospect.
Even with the 10 fold
magnification resulting with a 6. taper, the variance in a 0.1 pm thick film
could not have been resolved with a 1.0 pm spacial resolution.
It was
originally believed that this film was approximately 1.0 pm thick until SEM
measurements were made after AES characterizations were completed.
The
sputter etching technique should have, but failed to, reveal a gradient on
the B/Si ratio.
Several factors may be responsible for not observing a chemical
gradient in the GIAR films.
The roughness and porosity associated with the
porous surface may have obscured the gradient by permitting AES signals to
be generated from a range of depths.
the problem.
Charging may also have contributed to
The mobility of Na under the e-beam and the rapid signal decay
hindered the acquisition of reliable data.
11-9
In addition, the Al
concentration was near the detection limit.
Whatever the cause, AES gave no
indication of chemical gradients in the GIAR films.
B.
Secondary Ion Mass Spectrometry
Secondary ion mass spectrometry was also used to evaluate the surface
chemistries and chemical gradients by monitoring the ratios of the elements
as a function of depth into the glass surfaces.
No concentration gradients (Si, 0, B, Na, Al) were detected for
sputtered depths of up to 0.2 pm for fully processed samples A3-30-20
B3-30-20.
and
In addition, B/Si, Na/Si and Al/Si ratios were determined for
samples E3-0-0, E25-0-0, E25-5-0, E25-15-0, and E25-30-0 to evaluate
variations in surface chemistry caused by heat treatment and chemical
polishing times (Table I).
A comparison of the data for these samples shows
that the Na/Si and Al/Si ratios are constant, and the B/Si ratio undergoes a
small, probably insignificant variation.
Finally, side by side comparisons
of an as-received sample AO-0-0, and a fully processed GIAR surface A3-30-20
revealed no differences.
Like the AES characterization of the GIAR films, the SIMS analysis
revealed neither a modification in surface composition nor a gradient in
composition.
These results are surprising since the signals were well above
detection limits and Na mobility was not a problem.
The problem of defining
the volume element from which the SIMS signal originates in a porous film
again hinders data interpretation.
II-10
C.
Anti-reflective Film Thickness
The thickness of the AR films is an important variable in relation to
the optical characteristics of the film and also for understanding the
mechanisms of film formation.
Film thicknesses were measured by SEM and
also calculated based on the weight loss per unit area measured during the
selective etching process.
A comparison of the film thicknesses determined
in these two ways reveals information about the mechanisms involved in the
etching process.
Samples B3-30-20 and E3-30-20 had measured thicknesses (SEM) of
~ 0.1 pm and calculated thicknesss (by weight loss) of 1.1 pm.
A3-30-20 had
measured and calculated thicknesses of ~ 0.2 pm and 1.1 gm respectively.
The thickness determined by weight loss presumes complete dissolution of the
soluble phase, a stable co-continuous two phase structure and both constant
volume fractions and compositions of the two phases throughout the film.
These estimates of film thickness were based on a value of 45% for the
17
alkaliborate phase volume fraction at 600*C.
These results indicate that
the film thickness inferred by weight loss is 5-11 times greater than that
measured by SEM for this particular heat treatment.
Figure 2 presents the film thicknesses determined by both techniques
for samples annealed for various times at 600*C and then processed by the
standard chemical polishing and etching/leaching procedures.
Both
techniques indicate that the film thickness increases progressively with
longer annealing times until approximately 100 hours, remaining constant
thereafter.
II-11
The discrepencies between the results of the SEM and weight loss
determinations probably result from two issues.
The assumptions regarding
microstructural development and the selective nature of the acid treatment
become increasingly accurate with longer annealing times.
The discrepancy
between the long annealing time thickness estimates may result from an
incorrect value for the volume fractions of the two phases.
A value of 37%
for the volume fraction of the alkaliborate phase brings the long term
values into coincidence as shown by the open circles in Figure 2.
Given the
uncertainties about the accuracy of the volume fractions of the phases as
well as the variability in local chemistry that we revealed, it appears
appropriate to attribute the systematic differences to erronious volume
fractions.
It is clear though that the directly measured GIAR film
thickness is substantially less than that inferred by weight loss for the
shorter annealing times.
This result indicates that the initial film
forming dissolution process is not totally selective and it becomes
progressively more selective with longer annealing times.
There are several reasons why the apparent selectivity of the
etch/leach can change with annealing time.
The scale of the microstructural
features coarsen with time, the two phases may still be evolving
compositionally and proportionally in this time scale, and the morphology of
the two phases may be changing from discontinuous to co-continuous
structures.
If the dissolution process is not perfectly selective, the
apparent selectivity will decrease with decreasing scale of the phase
separated structure because an increasing fraction of the more durable phase
will be consumed with a constant linear dissolution rate and dissolution
time.
This effect can also cause the remaining more durable phase to become
mechanically unstable if it becomes overetched.
The effects of time variant
volume fractions and compositions of the two phases on the dissolution
characteristics are apparent, albeit complex.
Also, the true selectivity
would not be observed with a discontinuous microstructure once the
etching/leaching depth becomes greater than the size of the isolated phase.
The film thickness measurements indicate that the thicknesses of the
films are uniform for different glass batches and can be manipulated by
varying the heat treatment or etching/leaching times.
They have also shown
that the processes involved in the formation of the GIAR films change with
annealing time.
With conditions normally used to produce good optical
characteristics, the discrepancy between thicknesses measured by SEM and
inferred by weight loss indicates that the acid is not operating selectively
on one phase.
Although, the factors responsible for this behavior have not
been determined, the apparent non-selectivity is consistant with AES and
SIMS results.
D.
Weight Loss
Weight loss measurements were performed to evaluate any.differences
exhibited in chemical polishing between the rolled (B series) and the
mechanically ground and polished (E series) glasses.
In addition, the
influence of heat treatment time on chemical polishing was determined.
The rolled glass (B series) had a polishing rate of lx10
5
g/cm 2min
while the mechanically ground and polished glass (E series) had a polishing
2
rate of 1.3 x 10- 5 g/cm min after 5 minutes, in the un-heatreated states.
II-13
This difference was determined to be significant (90% probability) and the
E series glass exhibited the higher polishing rate to 30 minutes of chemical
polishing.
The higher rate probably results from residual surface damage
occuring in the mechanical grinding and polishing operation.
The polishing rates of all of the rolled glasses and of the heat
treated ground and polished glasses, BO-Y-0, E3-Y-0, B3-Y-0, E25-Y-0, and
B25-Y-0, were all very close to 1 x 10-
5
g/cm 2min.
Statistically, these
samples were found to be part of the same population so all of the results
were combined into the master curve in Figure 3 for weight loss in chemical
polishing as a function of chemical polishing time.
The best fit slope is
1.187 x 10-5g/cm 2 min and the best fit intercept is 0 g/min at zero polishing
The linearity of the curve and its passing through the origin are
time.
strong indications that the polishing process is both uniform and nonselective in nature.
It also indicates that the glass is uniform in terms
of criteria which control the polishing process to a depth of at least
2.5 pm.
In contrast, a similar analysis of dissolution rates of individual
glasses EO-30-Z, E3-0-Z, and E25-0-Z in the AR film forming solution did not
show consistant behavior or clearly demarked trends in dissolution rate
versus time.
The weight loss on etching/leaching for sample E3-0-20 was
much lower than that of E3-30-20, indicating the presence of a surface layer
which was inhomogenious in terms of the etching/leaching process.
This
result was not expected because compositional layers produced by selective
1 18
evaporation during manufacturing are usually approximately 1 pm thick. '
The grinding and polishing process removed much more glass than 1 pm based
11-14
on the roughness of the as-rolled surfaces, so that manufacturing gradients
should have been removed.
Either the manufacturing induced surface layer
extends much deeper than thought, or the phase separation heat treatment
induces an inhomogeneity.
Weight loss per unit area on etching/leaching for 20 minutes was
determined as a function of chemical polishing time for E series glass to
explore the existance of such an inhomogeneous layer.
The results in Figure
4 show that the dissolution rate increases linearly with polishing time.
It
was our expectation was that the etching/leaching rate might change during
an initial transient but would eventually reach a steady state value upon
removal of the surface affected layer.
The results indicate that the
surface layer is not fully removed after 60 minutes of chemical polishing
(2.5 pm removal).
Figure 5 shows the weight loss per unit area on etching/leaching
function of etching/leaching time for the E3 series glass.
as a
The linearity of
the curve indicates that the dissolution process is not rate controlled by
diffusion through the GIAR film.
We anticipate that a preferential
dissolution process should eventually exhibit such a rate controlling step
and the slope would decrease with increasing etch time.
It is possible that
the observed steady state behavior follows the development of such a rate
controlling step at very short times.
However, the intersection of the
curve with the origin indicates that the transient behavior during the
emergence of the rate controlling step was not very pronounced, if it
occured at all.
II-15
These weight loss experiments present anomalies.
Although the
polishing process suggests that the glass is uniform in composition, the
etching/leaching process indicates that a surface effected layer is present.
The etching/leaching rate increased progressively as material was removed by
chemical polishing.
In contrast, the etching/leaching rate remained
constant during the etching/leaching process at a value which depended on
the extent of prior chemical polishing although the penitration depths for
the two processes were comparable.
The etching/leaching process behaved as
if the rate were controlled by the composition of the surface at the
beginning of the etching/leaching process.
The etching/leaching process did
not exhibit the feature of being rate controlled by diffusion through the
porous GIAR film which we had anticipated for selective dissolution.
E.
Solution Analysis by Atomic Absorption Spectroscopy
Atomic absortion spectroscopy (AAS) was used to evaluate the
chemistries of the glass surfaces and bulk glasses used in this study.
indications were that the chemical polish is non-selective
dissolution characteristics.
All
in its
As a result, the chemistries of the bulk glass
were determined by fully dissolving crushed glass in the chemical polishing
solutions.
Analysis of an as received B series glass yielded a composition
of 80.7% Si0 2 , 13.3% B 20 3, 3.9% Na 2 0 , and 2.0% Al 2 0 3 .
This is almost
M
exactly the composition quoted in the literature 9 for Corning Pyrex(T ) 7740
of 81.0% Si0
2
, 13.0% B 20 3, 4.0% Na 20, and 2.0% A120 3 .
In a similar manner, the surface composition of as-received ground and
polished EO series glass was determined by AAS analysis of chemical
II-16
____
_
_I_
X
IILIIIYIII
polishing liquors after removal of 1.2 pm of glass.
^~ _I I
The composition so
determined was 89.5% Si0 2 , 5.6% B 20 3 , 3.1% Na20, and w 2% A120 3 . These
results indicate that the surface composition differs substantially from
that of the bulk, even after a layer of material had been removed by
grinding and polishing.
A progressive dissolution technique was used to evaluate the chemical
The
profiles of B series glass in the as-received, rolled condition.
results shown in Figure 6 show the following trends.
The SiO
2
content
gradually decreases from nearly 1.2 times the bulk composition at the
surface to that of the bulk after more than 100 pm.
Both the B 2 0 3 and Na 2 0
increase from 0.2 and 0.4 times the bulk composition respectively at the
surface to that of the bulk, beyond 100 pm.
that of the A1203.
The most striking behavior is
Starting from a value 1.05 times the bulk composition,
it decreases rapidly to 0.1 times the bulk value at between 20 and 100 pm
and then rises to the bulk at greater depths.
It is not surprising perhaps that the Na20 is low at the surface,
18 19
that boron oxides
because it is so volatile. It has also been reported '
can be carried with the Na 2 0, perhaps explaining the low B 20 3 content at the
surface.
Tomozowa
18
has reported a surface layer (1-2 pm thick) having an
A1203 concentration > 2 times the bulk level.
He reported no indication of
the surprising behavior we observed with the A1 2 0 3 concentration dropping
substantially below the bulk composition at intermediate distances.
These findings have a significant impact on both controlling and
understanding the process.
First, it is clear that the Pyrex (T M
)
7740
examined is not uniform in composition over a large fraction of its
thickness.
This result makes control over the phase separation and
etching/leaching process very difficult.
Second, knowledge of the chemical
gradients are required before the uniformity of the chemical polishing
solution and the selectivity of the etching/leaching solutions can be
evaluated.
Based on the information in Figure 6, atomic absorption analysis was
used to evaluate the selectivity of the film forming solutions on various
glass samples.
Table II presents the local glass compositions and the
etchant/leachant compositions for AR films on glasses E3-30-20 (1.5 pm
removed in chemical polish), B3-8600-60 (358 pm removed in chemical polish)
and B25-4000-60 (167 pm removed in chemical polish).
For sample E3-30-20,
it can be seen that the etch/leach composition is slightly lower in Si02,
and is higher in B 20 3 , Na 2 0, and A12 0 3 than the local glass composition.
These differences are in the anticipated direction, but are smaller than
expected for the proposed highly selective etch/leach solution.
For sample
B3-8600-60 the selectivity is in the anticipated direction again but is less
marked than for E3-30-20.
The indication then, for the 3 hour anneals, is
that the alkaliborate phase has not reached a composition, a scale, or
morphology where the etch/leach solution acts in a highly preferential
manner.
In contrast, etch/leach solution analysis by AAS of sample B25 4000-60
reveals quite significant changes in composition relative to the bulk glass
composition.
The SiO
2
content is down by 10%, while the B 20 3 , Na 2 0, and
A1203 contents have risen by 29%, 67%, and 95% respectively.
II-18
This indicates
that the etch/leach dissolves the two phases differentially after 25 hours
of annealing.
For annealing times producing nearly optimum optical properties (~ 3
hours), all chemical analyses indicate that the etchant/leachant removes
both phases at roughly equal rates.
Only with longer than optimum anneals
does the film formation solution exhibit significant selectivity.
F.
Specific Surface Area Determination
Based on the model presented for formation of GIAR films, it is
anticipated that the chemical polish should have little effect on specific
surface area, while the selective dissolution process should cause the
specific surface area to increase significantly by the removal of the
alkaliborate phase leaving a skeleton with interconnected pores having
characteristic dimensions on the order of 10 nm.
No significant change in surface area occured with polishing
(Table III), indicating that the chemical polishing process operates
uniformly on the glass surface.
Also, the equivalant spherical diameters of
the unpolished and polished powders agree within a factor of two with the
sieve sizes.
Table III also lists the specific surface areas, the calculated pore
sizes assuming both spherical and cylindrical pore geometries of the
etched/leached glasses and the characteristic dimensions of the phase
separated glasses measured by TEM and small angle X-ray scattering (SAXS)
techniques.
12
The characteristic pore sizes were calculated using GIAR film
thickness measured by SEM on bulk samples.
II-19
In contrast to the polishing process, the etch/leach process caused a
substantial increase in the specific surface area of the glass powders
demonstrating that the films are porous.
The variability in observed
specific surface areas is attributable in large part to the variable
thicknesses of the GIAR films which range from 0.1 pm to 1.6 pm.
Also, the
characteristic dimensions of the pores are the same order of magnitude as
those of the phase separated glasses.
The factor of 2-4 difference in
absolute values is easily attributable to uncertanties inherent to the
physical model used for the calculations.
In contrast to the chemical
analyses, this agreement shows that the porous surface film results from the
selective removal of the more soluble phase of a two phase bulk glass for
all annealing times.
By corroberating many of the features presumed for the formation of the
GIAR films, the BET results accentuate the failure of the chemical
characterization techniques to reveal the anticipated consequences of a
selective etch.
The problem may be attributable to the inherent resolution
limits of the various chemical techniques or to a departure from the
idealized process for film formation.
With short annealing times, film
thickness and weight loss measurements show that the etch/leach does not
operate selectively although it does produce a porous film having
approximately the anticipated pore dimensions as measured by BET analyses.
This result shows that outer layers of the GIAR film are eventually
dissolved by the film formation solution that does not operate in a
completely selective manner.
With longer annealing times the weight loss
and thickness measurements agree with one another, indicating the
11-20
selectivity shown by both BET and etch/leach solution analyses but not shown
by direct chemical analysis (SIMS and Auger).
The stability of the porous
film results from increased dimensional scale combined with possibly more
complete compositional and microstructional development of the phase
separated structure.
If dissolved alkaliborate salts reprecipitate in the
porous film, it would obscure the indication of selectivity by SIMS and
Auger analyses and cause the dimensions of the solid phase in the film to be
larger than the characteristic dimensions of the phase separated glass.
Both of these results were observed.
IV.
SUMMARY
(
The development of GIAR films on a borosilicate glass, Pyrex 7740
),
were examined in terms of several chemical and physical characteristics.
Chemical analysis by SIMS, Auger, and AAS as well as weight loss
experiments all indicate that the chemical polishing solution removes both
phases at equal rates.
This is further indicated by the smooth surfaces
seen in SEM and the low specific surface areas of polished samples.
Measured dissolution rates were high enough to have removed anticipated
surface effected layers in the polishing times employed.
Analysis of the
GIAR films by AAS, SIMS, and Auger gave no indication that the selective
etch/leach operated preferentially on one phase for annealing times around
3 hours.
For longer than optically optimum annealing times, some
selectivity was indicated.
The discrepency between film thicknesses
calculated by weight loss and those measured by SEM for annealing times less
than approximately 100 hours also reveals a lack of selectivity in the
11-21
etch/leach process.
Despite the weak selectivity of the film formation
solution, porous surface films were developed with thicknesses ranging from
0.1 to 1.6 pm (SEM) and calculated pore sizes of 11.6 to 74.8 nm (BET) for
anneals from 3 to 50
hours respectively.
The pore sizes were of the same order as the size of
the phase separated structure.
Major compositional variations existed to
distances greater than 100 pm from the free surfaces of the glass slides
complicating controlled formation of the GIAR films and interpretation of
chemical analyses.
These results corroberate the proposed model for the formation of the
GIAR film in general terms, yet it is clear that under process conditions
1
optimized for optical properties, the process is not simply one of
preferentially dissolving the sodium borate phase, leaving behind the high
SiO
2
skeletal film.
Film formation has a complex dependence on local glass
composition, and phase composition, morphology, and size.
V.
ACKNOWLEDGEMENTS
We would like to thank the Department of Energy for supporting this
work under contract number DE-AC02-78ER05003.
II-22
VI.
REFERENCES
1.
M. J. Minot, "Single-Layer, Gradient Refractive Index Antireflection
Films Effective from 0.35 to 2.5 pm", J. Opt. Soc. Am., 66, 515
(1976).
2.
J. M. Power, T. H. Elmer, "Weathering of Gradient-Index Antireflection
Am. Ceram. Soc. Bull., 59, 11, 1124
Films on a Borosilicate Glass",
(1980).
3.
J. E. Ritter, Jr., K. Jakus, K. Buchman, G. Young, and J. S. Haggerty,
"Strength and Fatigue Behavior of a Borosilicate Glass with an
Antireflective Surface", To be published in Glass Technology, April,
1982.
4.
B. Sheldon, J. S. Haggerty, A. G. Emslie, "Exact Computation of the
Reflectance of a Surface Layer of Arbitrary Refractive Index Profile
and an Approximate Solution of the Inverse Problem", To be submitted to
J. Opt. Soc. Am.
5.
W. D. Kingery, H. K. Bowen, D. R. Uhlmann, Introduction to Ceramics,
2nd Ed., 110, John Wiley and Sons, (1976).
6.
T. H. Elmer, F. W. Martin, "Antireflection Films on Alkali-Borosilicate
Prodiiced by Chemical Treatments", Am. Ceram. Soc. Bull., 58.
rleqqa
11, 1092 (1979).
7.
V. Tengzelius, "Development of Anti-Reflective Films on Na20/CaO/Si0 2
Glass", Masters Thesis, M.I.T., December, 1981.
8.
W. Haller, D. H. Blackburn, F. E. Wagstaff, R. J. Charles, "Metastable
Immiscibility Surface in the System Na 2 0-B 2 0 3-Si0 2 ", J. Am. Ceram.
Soc., 53, 1, 34 (1970).
9.
W. Haller, G. R. Srinivasan, I. Tweer, P. B. Macedo, A. Sarkar,
"Phase Separation in Si0 2 -B 20 3-Na 2 0 System", J. Non. Cryst. Sol., 6,
221 (1971).
10.
T. H. Elmer, M. E. Nordberg, G. B. Carrier, E. J. Korda, "Phase
Separation in Borosilicate Glasses as Seen by Electron Microscopy and
Scanning Electron Microscopy", J. Am. Ceram. Soc., 53, 171 (1970).
11.
M. Tomozawa, T. Takamori, "Viscosity and Microstructure of Phase
Separated Borosilicate Glass", J. Am. Ceram. Soc., 62, 7, 373 (1979).
12.
M. Tomozawa, Personal Communication.
11-23
13.
S. C. Danforth, J. S. Haggerty, D. Imeson, A. Iqbal, J. B. Vander
Sande, "Microstructural Analysis of Broad Band Anti-Reflective Films on
Glass", Am. Ceram. Soc. Annual Meeting and Exposition, Chicago,
Illinois, April 27-30, (1980).
14.
M. J. Minot, U Ortabasi, "Antireflective Layers on Phase Separated
Glass", U. S. Patent Number 4,086,074, April 25, 1978.
15.
C. G. Pantano, "Glass Surface Analyses by Auger Electron Spectroscopy",
J. Non. Cryst. Sol., 19, 41 (1975).
16.
S. C. Danforth, D. Imeson, A. Iqbal, J. S. Haggerty,
J. S. Vander Sande, "Formation and Microstructure of Graded-Index AntiReflective Films", To be published.
17.
J. H. Simmons, S. A. Mills, A. Napolitano, "Viscous Flow in Glass
During Phase Separation", J. Am. Ceram. Soc., 57, 3, 109 (1974).
18.
M. Tomozowa, T. Takamori, "Relation of Surface Structure of Glass to HF
Acid Attack and Stress State", J. Am. Ceram. Soc., 62, 7-8, 370-3
(1979).
19.
M. Shinbo, "Volatilization Loss of Sodium Borosilicate Ternary
Glasses", Yogyo Kyokai Shi, 74, 11 346 (1966).
11-24
I
I
I
I
Air
A.R.Layer
Z=d
Z=O
C
C
. 100
100.2
o E);E
0
(Jgb..
4-
E
Figure 1.
Bulk Glass
Schematic of index of refraction, n, and volume fraction
air/glass for a GIAR film. 1
II-25
O BY WEIGHT LOSS (0.37 VOLUME FRACTION)
0 BY WEIGHT LOSS (0.45 VOLUME FRACTION)
BY SEM
EA
3.0
0
(I)
o
c
2.0-
A
0.0
0.
0
20
40
60
80
100
500
HEAT TREATMENT TIME (HOURS) AT 600 OC
Figure 2.
GIAR film thickness (determined by weight loss and SEM) as a
function of annealing time at 600 0 C.
11-26
1000
E
60
-
I0
~ 0 0
z
3II-27
i
w
20
40
60
20
()
C)
0
-j
1
00
60
40
20
CHEMICAL POLISHING TiME (min)
Figure 3. Master curve of weight loss per unit area during chemical
polishing versus chemical polishing time for B and E series
glasses.
11-27
E
0
0
CD
z
12 k
U
w
z
w
8 1-
z
cc:
w
a..
()
03
0
CD
20
40
CHEMICAL POLISHING TIME (min)
Figure 4.
60
Weight loss per unit area during etching/leaching versus chemical
polishing time for E3-Y-20 glass.
II-28
()
_o
x
0
0d
8
CL
4
Cn)
-
2
0J
0
Figure 5.
10
20
30
40
ETCHING TIME (min)
Weight loss per unit area during etching/leaching versus
etching/leaching time for E3-30-Z glass.
11-29
1.2r-
1.01o
BULK
COMPOSITION
0.8-
SiO 2
0.6-
B2 03
z
0
No2 0
OAF
0
SA1 2 0 3
8.
8
0. 2 "
I
.I
0.o
Figure 6.
I.O
I
10.0
100.0
DEPTH (p.m)
Ratio of actual composition, to bulk compositio
function of depth into the as-received Pyrex
glass surface.
II-30
C/C asa
7740 B series
TABLE I
SIMS Elemental Ratios
for E Series Glass
Sample
B/Si
(xlO- 2 )
Na/Si
- )
(x10O
Al/Si
(x10 - 1 )
E3-0-0
4.9
3.0
1.0
E25-0-0
3.5
3.4
1.0
E25-5-0
10.1
3.1
1.0
E25-15-0
6.2
2.4
0.9
E25-30-0
5.7
2.5
0.9
11-31
TABLE II
Comparison of Local Glass Composition with that Inferred from the
Etchant/Leachant Composition Determied by Atomic Absorption Spectroscopy
(Wt. %)
Etchant
Comp.
Local
Glass
Comp.
89.5
88.0
5.7
B3-8600-60
80.7*
78.3
13.3*
B25-4000-60
80.7*
72.4
13.3*
Sample
Designation
Local
Glass
Comp.
E3-30-20
Al 2 0 3
Na20
B 20 3
SiO 2
(Wt. %)
(Wt.
(Wt. %)
)
Etchant
Comp.
Local
Glass
Comp.
Etchant
Comp.
Local
Glass
Comp.
Etchant
Comp.
6.5
3.9
5.5
0.9
2.1
13.5
3.9*
5.0
2.0*
3.1
17.2
3.9*
6.5
2.0*
3.9
* Taken as bulk value from crushed glass dissolved in polishing solution.
TABLE III
GIAR Film Thickness,
Specific Surface Area, Pore Size, and Phase Separated
Structure Sizes for Various Glasses Tested
Sample
GIAR Film
Thickness
(pm)
Specific Surface
Area
Pore Size
Spherical
Cylindrical
Assumption
Assumption
(cm 2/g)
Phase Separated
Structure Size
TEM
LAXS
(nm)
(nm)
BO-0-O
525
7.5 ± 2.5
B3-5-0
900
7.5 ± 2.5
B3-30-0
570
7.5 ± 2.5
A3-30-20
0.2
6,660
19.4
11.6
7.5 ± 2.5
B3-30-20
0.1
2,300
28.1
20.4
7.5 ± 2.5
E3-30-20
0.1
3,580
18.0
11.7
7.5 ± 2.5
C50-30-20
1.6
13,900
74.8
42.6
15.8 ± 3.5
CHAPTER III
Microstructural Characterization
of Graded-Index Anti-Reflective Films
by
S. C. Danforth and J. S. Haggerty
Energy Laboratory
and
Department of Materials Science
Massachusetts Institute of Technology
Cambridge, MA 02139
ABSTRACT
Microstructural characterization of graded-index anti-reflection films
has been performed using TEM, SAXS, replication and SEM.
TEM and SAXS
results agree with one another for the entire coarsening history of the
phase separated Pyrex
glass.
The complexity of the replication process and
the metallization used for SEM caused the effective resolution limits for
GIAR films to be much larger than the inherent resolution limits for each
instrumentation.
Submitted for Publication to the Journal of the American Ceramic Society
I.
INTRODUCTION
1 2 34
This communication presents the results ' ' '
of microstructural
characterization of graded-index anti-reflective (GIAR) films on a phase
separated borosilicate glass (Corning Glass Works No.
7740, Pyrex ).
The
mechanism by which these GIAR films are produced has been discussed in
detail elsewhere.1-6
In developing a description of the surface films, we
have examined the microstructures of the as-phase separated glass as well as
the microstructure of the GIAR films.
For the as-phase separated glass the desired details were:
a
characteristic dimension of the phase separated structure; phase separated
morphology, i.e.
discrete or interconnected; volume fractions of each
phase; compositions of the two phases; and knowledge of how each of these
varied with annealing history.
The details pertaining specifically to the
GIAR film were: pore size, discrete or interconnected pore morphology,
volume fraction porosity as a function of depth into the GIAR film, and
thickness of the GIAR film.
Film characteristics were related to the as-
phase separated structure.
Complementary characterization methods were used to corroborate
observations because the scale of the microstructural features was near the
resolution limits of the techniques and were subject to many artifacts.
TEM
and small angle X-ray scattering (SAXS) yielded microstructural information
concerning the as-phase separated structure while replication and SEM were
used to evaluate details of the GIAR films.
III-1
II.
EXPERIMENTAL
The glass was supplied in sheet form with a ground and polished
surface.
Heat treatments were carried out on cleaned samples at 600*C in
airl for times up to 1000 hours.
Transmission electron microscopy (TEM) was performed on phase separated
glasses.
Efforts included use of finely crushed shards of glass 7 on carbon
grids, and carbon coated ion milled disks.
In both cases specimens were
featureless, indicating that if two phases did exist on the small scale
5 6
suggested by the model, ' they produced insufficient "mass thickness" or
"phase contrast" to be detected.
The most successful means of TEM sample
preparation was to lightly etch/leach the ion thinned samples on one side
with the GIAR film forming solution (2-5 min. at 20*C in 0.1 wt.%
NH 4 *HF+1.6 HNO 3) followed by rinsing, drying, and carbon coating.
A completely independent measure of the phase separation
characteristics of 7740 Pyrex
was obtained from small angle X-ray
scattering data provided by M. Tamazowa.8
Historically, the most commonly used means of investigating phase
separation in glasses has been the use of replication electron microscopy on
a selectively etched/leached surface.
Since the GIAR film is modelled as
being generated by such a selective dissolution mechanism, replication was
thoroughly examined as a means of characterizing the surface structure.
Replicas were formed by pressing acetylcellulose replicating tape, (softened
with methyl acetate) onto the GIAR film.
After drying, replicas were slowly
stripped, shadowed with metal, coated with ~ 50 nm of carbon, collected, and
111-2
-
examined.
-- W-WMM'fM14
The most reliable metallization was found to be 10 nm Cr at a 30"
angle of incidence.
Scanning electron microscopy (SEM) made possible a more direct
observation of the GIAR film surface than the replication technique.
Although in SEM it is necessary to coat the glass surface with a conductive
layer having a good secondary electron yield, it was felt to be less
susceptible to artifact introduction than the many steps inherent to the
potentially higher resolution replication process.
Experimentation with a
number of different coating techniques and materials was undertaken.
A two
part process involving thermal evaporation of - 2-4 nm of carbon followed by
-
10-15 nm of a 60% Pd 40% Au was found to be the most successful.
III.
RESULTS AND DISCUSSION
Transmission electron microscopy (TEM) of the etched/leached annealed
samples revealed 9 a structure related to the phase separated microstructure.
From Figure la and lb it can be seen that after three hours (la),
microstructural details are not clearly revealed, i.e. size,
interconnectivity, etc., while after 25 hours of annealing (Ib), the
structure is much more clearly'delineated (especially when viewed
stereoscopically).
At the longer time, it is clear that the structure is a
co-continuous ribbon type network with a characteristic dimension of (width of remaining glass phase).
15 nm
Figure 2 shows the characteristic
dimension as a function of annealing time at 600*C.
This data indicates
that the phase separated structure is a 7.5 nm in size at three hours
annealing time which is near the optically optimum process condition.
II-3
In
addition, for t > 100 hours the microstructure size increases in a manner
consistent with models
0
for coarsening,
i.e. ~ r c t1
/ 3
.
The nature of the sample preparation technique and the microstructure
itself make size determination and quantitative measurements of the phase
separated volume fractions difficult to do reliably.
The overlapping nature
of the three dimensional etched/leached structures seen in Figures la and
Ib, makes normal means of metallographically measuring either a
characteristic size or volume fraction inappropriate.
A possible solution
was to examine the structures only at the edge of a foil for size and volume
fraction determination.
These efforts revealed that the edge structures
were not the same as observed away from the foil edge.
This difference
resulted from the evaporated films warping when irradiated by the electron
beam.
3
With other glasses, we determined nominal volume fractions and
dimensions as a function of etch/leach time to permit estimations of true
values by extrapolation to zero etch/leach time.
It can be stated though,
that for this borosilicate glass, both phases are similar in volume fraction
in
agreement with published values of 45:55.
11
The ability of the TEM to discern the phase separated structure relys
on the chemical dissolution of the soluble phase by the film forming acid.
1
Results in this investigation and those published earlier indicate that the
selectivity of the acid to the glass phases increases with annealing time,
further complicating the exact quantitative interpretation of size and
volume fraction data.
8
The results of the small angle X-ray scattering are presented in
Figure 2.
Distinct evidence of phase separation was detected for anneals as
III-4
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IUIIUIEIIUIh,,YIY ,
1,h4
1 1 1 l,,1
l
lki
16
t l II
ll IIII
f0I
short as 1/2 hour although two hours was the shortest time for which a
specific size could be calculated.
The coarsening behavior measured by SAXS
is qualitatively similar to that determined by TEM.
There is however a
systematic difference between the two sets of data.
This may result from:
assumptions used in reduction of the X-ray scattering data; slight
differences in bulk glass composition between that examined by SAXS and that
examined by TEM; our choice of the ribbon width as the characteristic
dimension; or use of the acid to delineate the structure in TEM.
Despite
the differences, it appears that the data on the coarsening behavior of the
7740 Pyrex
determined by TEM and SAXS agree quite well.
The dimensional
range of interest substantially exceeds the effective resolution limits of
the TEM and SAXS techniques so they can be used reliably.
A representative replica
12
of the GIAR film surface (polished with
10 wt.% NH4*HF and etched/leached)
is
shown in
Figure Ic.
The surface is
quite rough in nature with nodular or hilly features; the smallest of which
is n 18 nm in size.
Figure 2 shows that the characteristic size of the
smallest features is constant for heat treatment times up to five hours and
is consistantly larger than both those indicated by the TEM or SAXS results
for the as-phase separated glass structure as well as the equivalent
spherical size determined from specific surface area measurements 1 (BET
technique) of the porous GIAR films.
With a 25 hour annealing time, the
size of the smallest features increased to 26 inm indicating a coarsened
structure similar to that observed by TEM, SAXS, and BET techniques.
These results show that the effective resolution limit for replica
microscopy of GIAR films is approximately 25-30 tim.
111-5
This substantially
IIII
I
,
exceeds the nominally 0.3 nm resolution limit of the TEM instrument and
10 nm features typically reported from replica observations.
It would
appear that the inherent nature of the porous GIAR film, or distortions
and/or dammage incurred during removal of the extremely adherent replica,
cause the increased resolution limit.
Replica microscopy evidently does not
provide a useful means of characterizing the detailed microstructural
features for near optimum GIAR films.
It was hoped that with an instrument resolution limit of 7
m, and a
more simplified sample preparation technique, SEM would enable us to
characterize the porous surfaces of the chemically polished and
etched/leached GIAR films accurately.
SEM micrographs of polished surfaces
with short annealing times are essentially featureless.
Figure ld is
representative of all SEM micrographs of the etched/leached GIAR film
surfaces annealed between 1 and 10 hours.
exhibits features - 30-40 nm in-size.
The rough surface clearly
As shown in Figure 2, SEM indicates
that there is no significant change in the size of the surface structure for
annealing times up to 25 hours.
After 500 and 1000 hours of annealing, the
observed feature size increased to m 65-70 tunmin approximate agreement with
TEM and SAXS techniques.
As with replication, the SEM images show a rough
surface whose structure size is independent of heat treatment for short
times, and which coarsens at long times similar to TEM and SAXS
observations.
It appears that SEM has an effective resolution limit of
30-40 nm for GIAR films.
The difference between characteristics of the chemically polished and
GIAR film surfaces indicates that the SEM technique can be used to reveal
III-6
___I__
_~~_ ___
__
1III,,11
the presence of the porous film.
M1
II
10I III+"
hl4Ii
Y,
u
lil
ililltllilhhlMI
ln
iid
For instance, SEM was used reliably to
measure the film thickness on fracture surfaces.
It appears that the
metallization obscures the details of the pore structure and thus limits the
spacial resolution to approximately 3 metallization film thicknesses.
The
metallization employed was selected after many experiments to maximize
resolution; thus, the thickness is not likely to be reduced significantly.
These results indicate that SEM cannot be employed to study detailed
microstructural features for near optimum GIAR films, although the
metallization does decorate the film providing a means of making macroscopic
observations.
SEM examination of 500 and 1000 hour annealed samples polished only
with 10 wt.% NH 4 *HF clearly revealed an interconnected ribbon type network
surface structure, quite similar in morphology, size, and time dependence,
to that observed in TEM micrographs.
The dimensions and morphology are both
different than revealed with the etch/leach acid on the same samples.
result shows that even with overaged samples,
topographical
features is
This
the precise nature of the
extremely sensitive to the means used to generate
them and are thus subject to erronious interpretation.
IV.
CONCLUSIONS
Quantitative microstructural characterization of GIAR films by TEM,
SAXS,
replication,
misinterpretation.
and SEM has proven to be difficult and subject to
TEM and SAXS agree quite well with each other and are
able to follow the coarsening behavior of phase separated Pyrex
times > 1.5 to 2 hours.
glass for
However, the complex nature of the phase separated
III-7
illinh
microstructure and the use of an acid treatment
that the TEM technique should be used cautiously,
to delineate it,
suggests
complicating quantitative
interpretation of data.
Replication and SEM techniques showed GIAR film microstructures and
coarsening behavior similar to one another.
Unlike TEM and SAXS,
both
indicated that the structure size was constant for short annealing times and
only with long annealing times was the coarsened structure qualitatively
similar to TEM and SAXS observations,
The complexity of replication and the
metallization processes appear to have set effective resolution limits, of
25-30 nm and 30-40 nm for replica and SEM techniques respectively.
III-8
I~
V.
__I
__
_ ___ 1_
_ ___Ili
REFERENCES
1.
A. Iqbal, S. C. Danforth, and J. S. Haggerty, "Surface Chemistry of
Submitted for
Porous Anti-Reflective Films on Borosilicate Glasses".
publication to the J. Am. Ceram. Soc., April, 1982.
2.
B. Sheldon, J. S. Haggerty, and A. G. Emslie, "Exact Computation of the
Reflectance on a Surface Layer of Arbitrary Refractive Index Profile
and Approximate Solution of the Inverse Problem". Submitted for
publication to the J. Opt. Soc. Am., April, 1982.
3.
V. Tengzelius, "Development of Anti-Refletive Films on Na 20/CaO/SiO 2
Glass", Masters Thesis, M.I.T., December, 1981.
4.
V. Tengzelius, S. C. Danforth, and J. S. Haggerty, "Development of
Gradient-Index Anti-Reflective Films on Na 20/CaO/Si0 2 Glass". To be
submitted for publication to the J. Am. Ceram. Soc.
5.
M. J. Minot, "Single-Layer, Gradient Refractive Index Antireflection
Films Effective from 0.35 to 2.5 pm", J. Opt. Soc. Am., 66, 515 (1976).
6.
M. J. Minot, and U. Ortabasi, "Antireflective Layers on Phase Separated
Glass", U. S. Patent Number 4,086,074, April 25, 1978.
7.
R. R. Shaw and D. R. Ulhman, "Subliquids Immiscibility in Binary
Alkilae Borates", J. Am. Ceram. Soc., 51 70, 377-82, (1968).
8. Private Communication M. Tomozowa.
9. D. Imeson, and J. B. VanderSande, "Direct Observation of the Phase
Separated Microstructure of a Sodium Borosilicate Glass and its
Development During Heat Treatment", Elec. Micro. Soc. of Am.,
39th Annual Meeting, 90-1, 1981.
10.
Moriya, Y., Warrington, D. H., and Douglas, R. W., "A Study of
Metastable Liquid-Liquid Immiscibility in Some Binary and Ternary
Alkali Silicate Glasses", Phys. Chem. Glasses, 8, 19 (1967).
11.
J. H. Simmons, S. A. Mills, and A. Napolitano, "Viscous Flow in Glass
During Phase Separation", J. Am. Ceram. Soc., 57, 3, 109 (1974).
12.
Danforth, S. C., Haggerty, J. S., Imeson, D., IqbaL, A., and
Vander Sande, J. B.,
"Microstructural Analysis of Broad Band Anti-
Reflective Films on Glass". Presented at the Am. Ceram. Soc., Annual
Meeting and Exposition, Chicago, Illinois, April 27-30 (1980).
111-9
(b)
(a)
Bar = 100
T
Bar = 100 nm
n
tC
(d)
(c)
Bar = 100 nI
Bar = 100 nm
Figure 1.
(a) TEM micrograph of CGW 7740 Pyrex after 3 hours at 600*C;
(b) T EM micrograph after 25 hours at 600*C; (c) Replica of GIAR
film surface after standard processing;1 (d) SEM of GIAR film
surface after standard processing. 1
III-10
111111
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103
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llv.1.
102
-
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2
_ 101
a
-15
-5-
5
f*
2-
SAXS
-TEM
o REPLICA
-
nSEM
-2
0
A SEM-polished only
01
IOo
,
2
5
10'
oI Il
102
I0
0
IO1
Annealing time (hrs) at 600C
Figure 2.
Influence of 600°C annealing time on size of characteristic
microstructural features by: TEM, SAXS, Replication, and SEM.
Time dependencies follow r = t1/ 3 0
III-11
IIIY
in~il IdYIYYI
IIIIIIhIAIIi
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II
I 11i
CHAPTER IV
Exact Computation of The Reflectance
of A Surface Layer of Arbitrary Refractive Index Profile
and An Approximate Solution of The Inverse Problem
by
B. Sheldon
J. S. Haggerty
Massachusetts Institute of Technology, Cambridge, Massachusetts
02139
A. G. Emslie
Consultant, Scituate, Massachusetts
02066
ABSTRACT
The angular reflectance of a graded-index layer, of arbitrary
refractive index profile, on the surface of a uniform substrate is
calculated exactly by direct numerical integration of the wave equation, for
both states of polarization of the incident light.
for a number of selected profiles shows:
A study of the results
(1) that oscillations in
reflectance versus wave number graphs have an almost constant period, (2)
the period, when plotted against angle of incidence, gives a curve that is
quite sensitive to the shape of the refractive index profile.
This
sensitivity is the basis of a simple graphical procedure by means of which
the inverse problem (i.e., deducing the index profile from reflectance
measurements) can be solved.
The procedure is applied to published
reflectance data to determine both the thickness of a graded-index surface
layer and the refractive index profile.
Present Address:
60540
Standard Oil Company (Indianna), Naperville, Illinois
I, I
1.
111JJ __ II IlIlll,IIdn
I,h
i,,I i lii,,ld
,1i , li l lHillI
lli lmmI
l lhilll
INTRODUCTION
Optical interference has been used to reduce undesirable reflections at
the surfaces of lenses in optical instruments.
The commonly used quarter-
wave film, however, gives zero reflection at only a single chosen
wavelength.
Multi-layer coatings can extend the cancellation over the
visible bandwidth.
The development of solar energy collectors poses the
problem of attaining very low reflection over the whole solar spectrum for a
collecting surface of a very large area.
Even the broadband multi-layer
coatings are not effective over this range of wavelengths and also would be
prohibitively costly for such a purpose.
The most promising solution to the large-area problem appears to be the
use of a surface
layer having a gradually changing refractive index in which
the index increases smoothly from a value as close as possible to the index
of free space (n=l) to a value that matches the index of the uniform
substrate.
If the graded-index layer is about one wavelength in thickness
at the longest wavelength of interest and contains no abrupt changes in
the
index or its first derivative, the reflection is expected to be very small
over the whole spectrum.
Investigators have tested the graded-index layer concept both
123
The layer is generally produced by
experimentally and theoretically. ' '
4 56
selectively leaching the surface of a phase separated glass substrate. '
Reflectance measurements are made as a function of wavelength, angle of
incidence,
and state of polarization of the incident beam.
IV-
,, 1
Two quite distinct theoretical
the reflectance.
approaches have been used to calculate
In the first approach the refractive index profile is
restricted to the few shapes for which a closed-form solution of the wave
1 2
equation is available. For example, an exponential profile ' yields a
solution in terms of Bessel functions of integral order, while a linear
profile2 gives Bessel functions of order 1/3.
The second theoretical approach, which can be applied to an index
profile of any shape, is to solve the wave equation numerically by computer.
Two equivalent ways of doing this are possible:
(1) by replacement of the
actual graded-index layer by a very large number of very thin uniform
235
layers, ' ' and determination of the reflectance by multiplication of the
characteristic matrices representing the individual thin layers; (2) by
direct numerical integration of the second order wave equation.
We prefer
the direct-integration method because of its relative simplicity and
computational speed.
We apply this method to study the reflectance for a
number of profiles in order to discover promising diagnostic features.
Based on this study, we then develop a simple approximate procedure for
solving the inverse problem, which is to determine the refractive index
profile from experimental reflectance data.
The procedure is used to obtain
5
the index profile corresponding to reflectance measurements of M. J. Minot.
II.
CALCULATED REFLECTANCE:
EXACT THEORY
layer of thickness d in which
I
the refractive index changes from the value n = n2 at z = 0 to n2 at z = d.
Figure 1 shows the case of a "bounded"
IV-2
The medium on the left of the layer has the uniform index n 1 = 1, while the
the medium on the right has the uniform index n 3 .
the layer is "unbounded".
n2 = n1,
If n
3
=
If n 3
=
n1 and n 2 4 nl, or if n
nj and n 2
3
* nf
-
nl,
and
Figure 2 shows the coordinate system
the layer is "semibounded".
used in the calculations.
For the case of a TE-wave (i.e., a wave with the E-field perpendicular
to the plane of incidence yz), arriving from the left of the xy-plane at an
angle of incidence
0, the
electric field E in the layer is given by the
x
equation 3
(1)
E = U(z) exp[i(k.sin0)y]
x
where U(z) is a solution of the second-order differential equation
dU
d
dz 2
dz
)
(log
dU
+ k.2 G
- sin2)
U=0.
(2)
dz
p.
Here k.=2x/X., X. is the free-space wavelength, the index n is a function of
z, and p/p. is the relative magnetic permeability of the layer.
For
simplicity, the time factor exp(-it) has been omitted from Eq. (1).
will be assumed that the layer is non-magnetic so that p/p.=1.
middle term in Eq. (2) is zero.
It
Then the
The boundary conditions at the interfaces
z=O and z=d are that E and dE /dz are continuous.
x
X
Therefore, from Eq. (1),
U and dU/dz are continuous across the interfaces.
In the case of a transverse magnetic (TM)
wave the corresponding
equations are
H = U(z) exp[i(k.sin¢)y]
X
IV-3
(3)
dU
dz
2
2
2
(log n ) dU + k. (n-sin
d
*)U=O.
(4)
dz
dz
In this case the boundary conditions are that H
continuous.
2
and (dH /dz)/n
2
are
2
From Eq. (3), this implies that U and (dU/dz)/n are
continuous.
In the region to the left of the graded-index layer (z < 0) the
solution of Eq. (2) or Eq. (4) is of the form
U
-
A exp(iklz)+ B exp(-iklz)
(5)
where
2 1/2
sin 4)
2
kl=ko(nland A, B are arbitrary constants.
(6)
Also, as mentioned earlier, nl 1 .
Therefore at the interface z=O,
(7)
U(0)=A+B
and
) =ikI(A-B).
(8)
The solution in the substrate to the right of the graded-index layer,
corresponding to an outgoing wave, is
U - C exp(ik3z.)
(9)
where
2
2
k 3 =k.(n3-sin2
and C is an arbitrary constant.
IV-4
)
1/2
(10)
Thus, immediately to the right of the interface z=d,
U(d + ) = C exp(ik3d)
d
(11)
(12)
= ik3C exp(ik3d)
The constant C is merely a scale factor that depends on the amplitude of the
incident wave and is set equal to unity.
Equations (11) and (12), along with the boundary condition stated above
for either a TE or a TM-wave, allow the values U and dU/dz to be determined
in the graded-index layer at z=d.
Numerical integration of either Eq. (2)
or Eq. (4), by means of the Runge-Kutta 7 method, can therefore be carried
out in the graded-index layer starting at z=d and proceeding to z=O.
The
boundary conditions at the z0O interface, given above, permit A and B to be
evaluated.
The reflectance is
then given by
2
R=
.
(13)
A
Figure 3 shows computed reflectance R (in %) versus d/X curves for a
TE-wave incident at 450 on a semi-bounded, graded-index layer for four
different refractive index profiles, all of which have an index
discontinuity from 1 to 1.1 at the free surface (z=0),
but no discontinuity
at the layer-substrate interface, where the index has the value nal.5.
From a diagnostic point of view, the most interesting effect to be seen
in the reflectance graphs is the presence of the interference oscillations.
For d/k greater than about 0.5, the period of the oscillations, A(1/X),
IV-5
is
almost constant.
This implies that the oscillations are produced by
interference of only two beams, reflected by fixed planes.
The outer
reflecting plane is clearly the surface of the graded-index layer where
there is a discontinuity in the refractive index.
For the index profiles in
Figures 3(a) and 3(b), which show strong oscillations, the inner reflecting
plane is almost certainly located at z=d where there is a large
discontinuity in the slope of the refractive index profile.
In Figures 3(c)
and 3(d), where there is no discontinuity in slope at x-d, the amplitude of
the reflectance oscillations is much smaller.
This indicates that the inner
reflecting plane gives only a weak reflection.
Figure 4 shows the calculated TM-wave reflectance curves for the same
set of refractive index profiles.
It is seen that both the reflectance
level and the amplitude of the oscillations are much less than for the
TE-wave.
Thus the TM-wave reflectance does not appear to provide useful
additional diagnostic information.
Figure 5 shows the effect of the angle of incidence
*
on the
reflectance oscillations of TE-waves for the case of the semi-bounded linear
profile as shown in Figure 3a.
Figure 6 shows corresponding theoretical
results for the case of a semi-bounded concave parabolic profile, as shown
in Figure 3b.
Of primary interest for diagnostic puroposes is the way in
which the period A(d/X), varies with *. Table 1 shows values of A(d/X),
determined from Figures 5 and 6, for the two refractive index profiles.
It
is seen that the A(d/A) dependence on 0 is quite sensitive to the shape of
the refractive index profile.
This sensitivity provides a way to solve the
IV-6
....-
inverse problem, i.e.,
..
m
II
IriiIih
to determine the index profile from measured values
of the reflectance at various angles of incidence.
CALCULATED INDEX PROFILE:
III.
THE INVERSE PROBLEM
In solving the inverse problem we find that, instead of using exact
numerical integration of the wave equation to determine the theoretical
A(d/X)
versus
*
curves, as in Figure 7, it is more convenient to use the
following approximate procedure.
The positions of the reflectance maxima
and minima on a graph of R versus d/X depend primarily on the phases of the
two interfering waves reflected by planes at z=0 and z=d rather than on the
amplitudes of the two waves.
Thus, to a good approximation, the inverse
problem requires only the phase factor of the solution of the wave equation
for U, Eq. 2.
2
According to the Wentzel, Kramers, and Brillouin (WKB) approximation
the phase factor is given by
U = exp[±ik.f (n2-sin
2
) 1 / 2 dz]
(14)
where the plus and minus signs refer to waves travelling to the right and
left,
respectively.
A wave of wavelength X, travelling from the outer to the inner
reflecting plane and back to the outer plane, therefore undergoes a phase
retardation Y, relative to a wave reflected at the outer plane, which is
given by the expression,
IV-7
llmIUihd Id
I111iaill10lAml
l w
d
V=
(n2-sin 2 t)1 /2dz
(15)
since k.=2,/k.
The two reflected waves will interfere constructively to give a maximum
in the reflectance versus wavelength graph if
V = 2mn
where m is an integer.
(16)
The next reflectance maximum occurs at a wavelength
' for which
Y'= 2(m+l)
(17)
where T' has the value,
T = -4.
f
d
(n 2 -sin 2 )1/ 2dz
(18)
0°
1
On subtracting (15) from (18) and using (16) and (17),
one finds for the
wavenumber separation between consecutive reflectance maxima
d
21
X
1
(n 2 -sin2 ) 1 / 2 dz
(19)
1
X'
(20)
where
A
(1)
X
1
X
Table 2 shows values of A(d/X) calculated by means of Eq. (19) for the
same two refractive index profiles used in the exact computer calculations
given in Table 1.
Comparison of Tables 1 and 2 confirms that the accuracy
IV-8
~~--~~
--
IIIIIIIIIIlr
--
of the WKB approximation used in the derivation of Eq.
(19)
is very
satisfactory.
The inverse problem involves deriving the refractive index profile n(z)
by means of Eq.
(19)
from a set of measured values of A(1/%) obtained at a
.
number of fixed angles of incidence
Since the thickness d of the graded-layer is unknown, the first step is
to separate d from the integration limits by the substitution
z = sd
(21)
where s is a dimensionless variable which covers the range 0 4 s < 1.
Eq. (19) then becomes,
a
(22)
1
(n 2 (s)-sin 2 4)1/ 2 ds
2d f
where the index profile is now regarded as a function of s.
One can obtain
a complete separation of d by taking the logarithm to the base 10 (Log) of
both sides of Eq. (22):
Log (A-)
X
-
Log
(
21
1
(n (s)-sin 2 o)
2
) - Log(d).
1
(23)
2
/ ds
Eq. (23) can be written in the form,
E(O) = T(O) - Log(d)
(24)
where E(W) is an experimentally determined function of 0 given by,
E(O)
-
Log (A-
).
The theoretically determined function T(O) is defined by the relation,
IV-9
(25)
T(W) = -Log
The inverse problem is
[2f (n 2 (s)-sin 2*)
1
/ 2 ds] .
(26)
therefore reduced to finding a profile n(s) for
which the shape of the theoretical curve T(W) matches the shape of the
experimental curve E( ) when the two curves are plotted on separate graphs
with the same horizontal and vertical scales.
Eq. (24) shows that the
vertical shift of the E($) graph relative to the T(O) graph required to
superimpose the two curves is equal to Log(d), from which d can immediately
be found.
In practice, it is most convenient to plot, on a single graph, a
family of T(M) curves corresponding to various values of an adjustable
parameter in a suitable algebraic expression for n(s).
The E(O) graph is
then slid vertically over the T(O) graph until a match in shape to one of
the E(O) curves is
found.
To illustrate the method we take the data of M. J. Minot 5 for TE-waves
(i.e. S-polarization) given in his Table 2, for Corning Glass Works Code
No. 7740 glass with a graded-index layer produced by a chemical "etch-leach"
process.
The data in Minot's Table have been corrected by him with respect
to the reference reflectance of an aluminum mirror.
Since the corrections
were performed point by point at 0.5 p~ wavelength intervals, the details of
the reflectance versus wavenumber behavior are not immediately available
from the data.
However, we have been able to reconstruct the oscillation
pattern fairly accurately for each angle of incidence by free-hand fitting
of an oscillating curve to the data points on the assumption that the
oscillation period is constant when R is plotted against l/%.
IV-10
These plots
are shown in
IlIb
-----
-
Figures 7-12 for angles of incidence
60', and 70", respectively.
shown on the graphs.
For each
*
= 20",
, the value of A(1/X)
30", 40",
50",
is determined as
The value of E(O) for each angle of incidence is then
calculated by Eq. (25) and is shown in Figure 13.
To calculate a family of T(O) curves for comparison with E()
we first
assume that n(s) is given by a parabola, similar to the semi-bounded
parabola shown in Figure 3b, represented by the formula:
2
n(s)
=
N. - (3N. - 4N1/ 2 + N1)s + (2N.
- 4N1/
2
+ 2N 1 )s
(27)
where N., N 1 /2 and N 1 are the values of n at s = 0, 1/2, and 1,
respectively.
The reason for the choice of a semi-bounded parabola is that
a leaching process, which involves liquid diffusion, would be unlikely to
produce a discontinuity in refractive index at the interface zud between the
For the front surface of the
graded-index layer and the glass substrate.
graded layer, Minot gives the value n = 1.118 and for the bulk glass
substrate the value n = 1.474.
N 1 = 1.474, leaving only N1/
2
We therefore assume that N. as an adjustable parameter.
1.118 and
Figure 14 shows a
family of plots of T(O) versus 0 calculated by numerical integration of
Eq. (26) for various equally-spaced values of N1/
2.
The experimental values
of E(O) from Figure 13 are also shown on Figure 14, adjusted vertically to
give the best fit to the set of T(O) curves.
Figure 13 relative to Figure 14 is 0.160.
which d -
The vertical shift of
Therefore Log(d) = 0.160, from
1.45 pm.
This value of d is considerably larger than the porous-layer thickness
in the range of 0.21 to 0.42 pn estimated by Minot in an earlier paper 6 from
IV-11
"over the edge" electron micrographs.
However, Minot remarks that, "We
recognize that the true thickness of the film can be considerably larger
than that indicated by the porous region, as for example by ion depletion".
Besides giving the graded-index layer thickness, the procedure also
determines the refractive index profile.
From Figure 14 it is seen that the
best fit of E( ) to the T( ) curves corresponds to N1/
along with the given values N. = 1.118 and N 1
=
2
This value,
= 1.15.
1.474, permits n(s) to be
calculated for all values of s by means of Eq. (27).
The refractive index
profile so obtained is shown in Figure 15.
It is seen from Figure 15 that the calculated index n(s) decreases at
first with increasing s, reaches a minimum, and then increases monotonically
to its final value of 1.474.
This behavior is an artifact imposed on the
profile by the choice of general parabolic function (Eq. 27).
Physically,
the leaching process would be expected to give a profile that increases
monotonically over the whole range of s from 0 to 1.
We therefore try the profile
n(s) = N. + (N1 - N.) sp
(28)
where N O and N 1 are the initial and final values of n(s), as before, and
p is an adjustable parameter.
N1 > N..
This profile is monotonic provided that
As before, we take N. -
1.118 and N 1 = 1.474.
Figure 16 shows the
family of T(W) curves for various values of p, along with the experimental
points E($) from Figure 13 adjusted vertically for the best fit.
vertical shift is again 0.16, and the value of d is 1.45
parabolic profiles.
IV-12
The
nm,as with the
~ImIii
-I,
The optimum value of p is seen to be 4, which, along with the fixed
values of N. and N 1 , yields the refractive index profile shown in Figure 17.
It is to be noted that n(s) departs markedly from a linear profile, which
=
corresponds to p
that Minot
5
1 in Figure 16.
indicates that,
In this connection it is interesting
based on his understanding of etching phenomena,
it is unlikely that the profile is linear.
IV.
CONCLUSIONS
The main conclusions to be drawn from this paper are as follows:
1.
The reflectance R of a graded-index layer on a uniform substrate
can be calculated rapidly for an arbitrary refractive index profile
by numerical integration of the second order wave-equation, for any
angle of incidence, wavelength, and state of polarization of the
incident beam.
2.
Calculations
for various profiles show that (a)
R versus 1/
plots
contain oscillations of almost constant period A(1/A), (b) the
period A(1/X) varies with angle of incidence 0 and (c) the A(1/A)
versus
3.
*
curve is quite sensitive to profile shape.
A simple graphical procedure, in which an experimental A(I/X)
versus
0 plot is compared with a family of theoretical A(1/X)
versus
*
curves, allows both the thickness of the graded-index
layer and the refractive index profile to be found.
IV-13
V.
REFERENCES
1.
S. F. Monaco, "Reflectance of an Inhomogeneous Thin Film", J. Opt. Soc.
Am., 51, (3), P. 280, (1961).
2.
Z. Knittl, Optics of Thin Films, John Wiley and Sons, London,
pp. 429-79, 1976.
3.
Born and Wolf, Principles of Optics, Pergamon Press, pp. 51-5, 1964.
4.
T. H. Elmer and F. W. Martin, "Antireflection Films on AlkaliBorosilicate Glasses Produced by Chemical Treatments", Am. Ceram. Bull.
58, (11), pp. 1092-7, 1979.
5.
M. J. Minot, "The Angular Reflectance of Single-Layer Gradient
Refractive Index Films", J. Opt. Soc. Am., 67, (8), p. 1046-50, (1977).
6.
M. J. Minot, "Single-Layer, Gradient Refractive Index Antireflection
Films Effective from 0.35 pm to 2.5 pm", J. Opt. Soc. Am., 66, (6),
p. 515, (1976).
7.
A. Ralston and H. S. Wilf, Mathematical Methods for Digital Computers,
Vol. I, John Wiley and Sons, Inc., pp. 110-20, 1967.
IV-14
~
1-
111111"~
11h
TABLE 1
A(d/l)
vs
*
for TE-Waves, from Computer Results
A(d/X)
(deg)
Semi-bounded
linear profile
Semi-bounded
concave parabolic profile
0
0.386
0.409
25
0.409
0.442
50
0.482
0.528
75
0.589
0.663
TABLE 2
A(d/X) vs 0 for TE-Waves from WEB Theory
S
Semi-bounded
(deg)
linear profile
Semi-bounded
concave parabolic profile
0
0.385
0.405
25
0.407
0.432
50
0.478
0.520
75
0.582
0.664
IV-15
Figure 1.
Figure 2.
Refractive Index Profile.
Coordinate System, in which the x-y plane is in the surface of
the graded-index layer and the y-z plane is the plane of
incidence.
The diagram shows a ray of a TE-wave at an angle of
incidence *.
The ray is in the y-z plane.
The E-field is
perpendicular to the y-z plane and to the ray.
For the case of a
TM-wave the E-field would be in the y-z plane and perpendicular
to the ray.
IV- 16
10.001
7.50-
I-.-
o
bJ
w
z
w
o
cc
W
n-
2.501-
0.00
0.00
d/X
Figure 3.
Reflectance of TE-Wave at 450 Angle of
Incidence for:
(a) Semi-Bounded Linear Profile.
(b) Semi-Bounded Concave-Parabolic Profile,
(c) Semi-Bounded Convex-Parabolic Profile,
(d) Semi-Bounded Cubic Profile.
S :0.50 - 1.00
___
_
I
1.50
I
2.00
I
2.50
d/X
Figure 4.
Reflectance of TM-Wave at 450 Angle
of Incidence for Semi-Bounded Linear,
Semi-Bounded Concave-Parabolic, SemiBounded Convex-Parabolic and SemiBounded Cubic Profiles. Differences
between individual lines are negligible.
I
3.00
40.00
= 750
a 75*
p
_0w
h=J
-J
U.
20.00
[I
w
z
I.-Z
w
CL
I0.00
0= 50
=
50*
25*
25*
= O*
2.00
1.00
0.00
0.50
TE-Wave Reflectance, SemiBounded Linear Profile for
Varying Angle of Incidence
(- = 0*, 250, 500, 750).
I.50
2.00
2.50
d/X
d/X
Figure 5.
1.00
Figure 6.
TE-Wave Reflectance, SemiBounded Concave-Parabolic
Profile for Varying Angle of
Incidence ( = 00, 250, 500, 750).
3.00
22
21
Ik
"40"
AM.
R(%)
1.6
i
((
I
,,
ii
Figure 9.
I CI
"
r:i3
Lt
- i Y.
I2I
-,t!{F 'i),;..$Y;I
S 2.2
X(r)
i
-1rL5
-
Experimental Reflectance Versus
Reciprocal Wavelength Plot, * - 40'
5
(From M. J. Minot Data ).
1
- 1.50
A(l/X) - (2.90 p- 1
pm-1)/4 cycles - 0.350 pm
1cipqq4l
(Ia)
A.
1Pt
a
( i1
-i!-1 )')3 c.ycles
67
, ..
t,8O
,
an, I
C
W
0.6
0.6
* 20*
* 0.309Lml
* 30*
0.314/±m'
,,
0.5
0.5
R(%)
0.4-
0.4
0.3
1.4
1.6
1.8
" (
Figure 7.
2.4
2.2
2.0
Fm) -
2.6
2.8
3.0
I.4
.6
1.4
1.6
I.8
2.0
2.2
2.4
2.6
2.8 I
1.8
2.0
2.2
2.4
2.6
2.8
I3.0I
(Fm)-'
I
Experimental Reflectance Versus
Reciprocal Wavelength Plot, # = 200
(From M. J. Minot Data 5 ).
A(1/X) = (2.86 pm - - 1.625
pm-1)/4 cycles - 0.309 pm-1
I
Figure 8.
Experimental Reflectance Versus
= 300
Reciprocal Wavelength Plot,
(From M. J. Minot Data 5 ).
A(1/X) = (3.00 pm- 1 - 1.43
pm-l)/5 cycles = 0.314 pm 1
*
3.0
*
Il
L
4.6
4.4
4.2
4.0
3.8
3.6
3.4
R(%)
R(%)
4
2.8-
60*
* 70*
A() * 0.417.Lm-'
A()" 0.485/.m-'
2.6 2.4
2.2
2.0
51 1
1.4
1.4
1 11
1.8
1.6
1
2.0
I
I
2.2
2.4
I
2.8
2.6
(1L,
4QX
F'ii
Figure 11. Experimental Reflectance Versus
Reciprocal Wavelength Plot, 0 - 600
(From M. J. Minot Data 5 ).
A(l/X) - 2.70 pm- 1 - 1.45
pm- 1 )/3 cycles 0.417 pm-1
Figure 12. Experimental Reflectance Versus
= 700
Reviprocal Wavelength Plot,
(From M. J. Minot Data 5 ).
A(1/k) = (2.62 p 1 - 1.65
pm- )/2 cycles - 0.485 pm-1
*
3.0
O
-0.1
-0.1I
-0. 2 1-
0.3
E (4)) -E(
T()
- 0.4 -
-0.5 h
0
-0.
0
I
10
I
20
I
30
I
40
I
50
I
60
I
70
I
80
I
90
Cf (deg.)
Figure 13. Experimental Function E(¢)
(Derived from M. J. Minot Data).
10
20
30
40 50
S(deg.)
60
70
80
90
Figure 14. Comparison of E( ) with Theoretical
Functions T( ) for Various
Parabolic Profiles.
0.4
0.6
0.8
Figure 15. Best Fit Parabolic Profile for n(s).
0.00
15.00
30.00
45.00
4 (deg.)
75.00
Figure 16. Comparison of E(O) with Theoretical
Functions T( ) for Various
Power-Law Profiles.
90.00
1.501
1.40
1.30
1.20 -
!.10-
1.00
0.0
0.2
0.6
0.4
0.8
S
Figure
17.
Best Fit Power-Law Profile (p= 4 )
IV-24
for n(s).
1.0
CHAPTER V
Strength and Fatigue Behavior of a Borosilicate Glass
With An Anti-Reflective Surface
J. E. Ritter, Jr., K. Jakus, K. Buckman, and G. Young
Mechanical Engineering Department
University of Massachusetts
Amherst, MA 01003
J.S. Haggerty
Energy Laboratory
Massachusetts Institute of Technology
Cambridge, MA 02139
ABSTRACT
The effect that an anti-reflective surface has on the strength and
fatigue resistance of a borosilicate glass was studied.
The fatigue
resistance, as measured by the stressing rate technique, was found to be
independent of the processing stages to produce an anti-reflective surface.
The critical stress intensity factor was found to decrease on the phase
separation heat treatment but then was relatively constant through the
additional processing stages involved in producing an anti-reflective
coating.
Strength was found to depend in a complex way on both processing
and the original place from which the samples came.
It is believed that
these results illustrate the complex nature of crack propagation in a glass
containing both a phase separated microstructure and a chemical composition
gradient from the surface to the interior.
Accepted for Publication in Glass Technology
ilM91
W,
I iII11
I.
INTRODUCTION
An anti-reflective surface can be produced on alkali-borosilicate glass
by heat treating to produce two co-continuous phases, and then selectively
etching one of the phases from the glass surface.
The resulting surface
exhibits very low reflective losses in the visible and near infrared
regions, even at-high angles of incidence.
It is believed that this low
reflectance is attributable to a surface layer composed of a spatially
varying concentration of interconnected micropores in a silica-rich matrix
that acts as a film of graded refractive index.1-3
The use of glass with an
anti-reflective surface is important for flat-plate solar collectors since
such glass could increase the extractable heat by as much as 30-40% under
most solar flux and ambient conditions.4
In assessing the overall viability of this technology, it is necessary
to determine both the long-term optical and mechanical strength
characteristics of glass with anti-reflective surfaces.
The excellent
durability of the anti-reflective surfaces on an alkali-borosilicate glass
was shown in a recent study
5
in which solar energy transmittance remained
virtually unchanged after 37 months of continuous exposure to weather.
The
purpose of the present study was to evaluate the effects that the formation
of an anti-reflective surface has on the strength and fatigue behavior of an
alkali-borosilicate glass. This study forms part of an overall research
6 7
program ' aimed at studying the microstructural and chemical characteristics
of anti-reflective surfaces on glasses and the process optimization for
achieving anti-reflective coatings on new glass compositions.
V-I
II.
EXPERIMENTAL APPARATUS AND PROCEDURE
A.
Sample Preparation
Square samples (7.62 x 7.62 cm) were cut from borosilicate plates
(30.5 x 30.5 x 0.318 cm) that had been rolled and then ground and
mechanically polished.
All samples were labeled to identify the plate from
which they came and randomized prior to processing.
An anti-reflective surface is produced by first heat treating the glass
to cause phase separation into a relatively durable silica-rich phase and a
soluble phase consisting primarily of B 20 3 and Na 2 0 8.
The soluble phase is
then preferentially etched, leaving a hydrated porous layer, largely silica,
at the glass surface.
To determine the effects that the various processing
steps involved in producing an anti-reflective surface have on strength and
fatigue behavior, five groups of samples were selected for testing, each
representing a given stage of processing.
The five groups were:
1.
As-received.
2.
Heat treated at 600*C for three hours to produce a phase-separated
glass with a microstructural size of approximately 0.01 pm.
3.
Chemically polished for 30 minutes at room temperature with 10 wt%
NH 4 F HF to remove a possibly inhomogeneous surface layer (I
pm)
caused by volatilization of compounds during heat treatment.
4.
Fully-treated by selectively etching the chemically polished glass
2 3
The
for 20 minutes at 45*C with 0.1 wt% NH 4 F + 0.16 N HNO 3 . '
anti-reflective surface so produced is 0.1 to 1.0 pm deep and has a
nodular surface structure of size 0.04 pm and a phase-separated
6 7
microstructure of approximately 0.0075 pm.
Code 7740, Corning Glass Works, Corning, NY
V-2
5.
Overaged,
fully-treated but with a heat treatment of 25 hours at
The resulting phase-separated structure
6 7
has a microstructural size of - 0.2 pm. '
600"C instead of 3 hours.
B.
Strength Testing
A biaxial strength test was used to determine the effect of surface
processing history on sample strength without spurious edge effects.
An
apparatus was constructed based on a model designed by Wachtman et al. 9 to
Interchangeable
be used in conjuction with a universal testing machine.
support fixtures and loading rods enabled either ring-on-ring or 3-ballIn the ring-on-ring test, the
piston strength tests to be conducted.
loading rod was fitted with a loading ring of radius 7.14 mm and the samples
were supported by a ring of radius 20.6 mm.
In the 3-ball-piston test, the
samples were loaded by a piston of radius 0.79 mm and supported by three
12.7 mm diameter steel balls spaced equidistantly on a circle of radius
14.3 mmn.
rigid elastic disks,
For thin,
the maximum stress in
test occurs inside the loading ring and is
a
max
3P
4%t 2
a
2(1+v)ln-
b
+
the ring-on-ring
given by:10
(1-v)(a
a2
2
-b
2
)
-
a2
R2
(1)
where P is the fracture load, t is the plate thickness, a is the radius of
the supporting ring, b is the radius of the loading ring, R is the radius of
the specimen, and v is Poisson's ratio.
Instron Corp., Canton, MA.
V-3
For square samples, the equivalent
radius R is taken to be one-half the average of the edge and diagonal
lengths.
Finite element analyses have shown that Eq. (1) represents the
maximum stress at the center of square samples with an accuracy of better
than 3%.11
For the 3-ball piston test, the maximum stress in the center of
the sample was determined by finite element analyses,11 since it was shown
11 12
'
inaccurate.
was
stress
maximum
this
for
that the analytical expression
For both tests the stress level decreases to near zero at the free edges of
the samples.
The fatigue resistance of the glass after each stage of processing was
determined by measuring strength in distilled water at two stressing rates
at least two orders of magnitude apart.
The fatigue resistance parameter,
N, was determined from:13
1
N+1
a
-
*
(2)
max 2
is the median fracture strength, a is the stressing rate, and
where a
max
subscripts indicate the values at the two different stressing rates.
values of N signify greater fatigue resistance.
Large
Values of N measured in the
presence of water generally range from about 13 to 17 for soda-lime
15 16
and from 32 to 38 for
'
glass,14-16 from 27 to 40 for borosilicate glass,
16 17
fused silica. '
Strength tests were also conducted with the samples wetted with mineral
oil to minimize fatigue effects.
In this way, it was hoped to determine the
effect on strength of the various processing stages in the absence of
complicating fatigue effects.
V-4
C.
Measurement of KIC
Fracture surface analysis
intensity factor, KIC,
processing.
18 19
'
was used to measure the critical stress
of the glass at each of the five stages of
It is believed by the present authors that KIC determined by
this analysis more accurately reflects possible effects of the interaction
between crack propagation and microstructure than KIC values determined by
fracture mechanics techniques that utilize specimens with large, preexisting cracks.
Fracture surface analysis relies on the empirically
observed relationships between fracture stress and characteristic fracture
18 19
Immediately surrounding the flaw is a smooth shiny
surface features. '
region commonly known as a mirror.
This mirror region is bounded by a
region of small, radial ridges, known as mist, which in turn is bounded by
macroscopic crack branching.
The distances from the fracture-initiating
flaw to any of these boundaries is inversely related to the fracture stress
18 19
by:
S
=
iAr
max
-1/2
(3)
where r is the distance to a particular boundary and A is the corresponding
"mirror constant".
The critical stress intensity factor has been shown to be related to
18 19
the mirror constant by:
'
1/2
IC
(4)
where c is the size of the initial flaw and
geometry of the flaw.
*
is a constant dependent on the
The initial flaw size to mirror radius has been shown
20
to be a constant for glasses and equal to 1/12.5 for borosilicate glass.
V-5
The mist-hackle boundary was measured on samples tested wet with
mineral oil (total of 50 samples for each processing stage) so that subcritical crack growth would not complicate the results.
The corresponding
mirror constant (A) for each sample was calculated from Eq. (3) and KIC was
then calculated from Eq. (4).
III.
RESULTS AND DISCUSSIONS
Preliminary strength tests were conducted both to compare as-received
samples to those with an anti-reflective surface and to determine if the two
biaxial strength tests give similar measurements of the fatigue resistance.
The results for both test configurations
and surface conditions are
summarized in Figure 1, where 25 samples were tested at each condition.
is
It
evident from the ring-on-ring tests that the samples with an
anti-reflective surface are significantly stronger than those in the asreceived condition although it is not clear when this strengthening occurs
in the process.
The values of N measured in these tests are not thought to
be significantly different from each other, and are within the statistical
reproducibility of the experiment.21
Also, the fatigue resistance (n - 35)
measured in these tests agree well with previous results for.this same
15 16
Thus, although samples with an anti'
glass.
borosilicate
commercial
reflective surface are nearly twice as strong as the as-received
samples, the fatigue resistance is not changed significantly.
These
strength results also show that the fatigue resistance is independent of the
biaxial loading configuration; however, the strength measured in the 3-ball
piston test is greater than that determined by the ring-on-ring test because
of the much smaller area of the glass that is placed in maximum tension.11
V-6
To determine the effects on strength and fatigue of the various
processing steps involved in producing an anti-reflective surface on
borosilicate glass, *amore extensive series of tests was carried out in
which the strength and fatigue behavior of the glass was determined after
each of the five processing steps using the ring-on-ring test.
During
processing of this second series of samples, it was noted that about onehalf of the samples developed numerous pits on the surface during chemical
polishing, which gave these samples a cloudy, whitish appearance.
By
correlating the occurrence or absence of etch pits with the original plates
from which each sample was cut, it was possible to identify exactly which
plates were susceptible to pitting during chemical polishing and which were
not.
Thus, the strength results were analyzed by separating the specimens
depending on whether they came from "pitting" or "non-pitting" plates.
These strength results are summarized in
noted that in
Tables I and II.
It
should be
all stages of processing including the as-received condition,
the strength of the "non-pitting" samples was higher and exhibited greater
variability than the pitted group.
Table III.
The KIC results are summarized in
It is significant to note that KIC did not depend on whether the
samples were "pitting" or "non-pitting";
thus,
the KIC results for the
"pitting" and "non-pitting" samples for a given processing step were
combined.
For both "pitting" and "non-pitting" samples, strength as measured in
mineral oil increased significantly on heat treatment whereas KIC decreased
about 15%.
The KiC value of the as-received glass agrees very well with
that previously determined by both fracture surface analysis and fracture
V-7
mechanics techniques.
19 20
'
The significant decrease in KIC on heat
treatment is probably related to the phase separation that occurs during
heat treatment.
K IC in homogeneous glasses is a material constant that
depends primarily on the bond strength;19 however,
complicated in
phase separated glasses.
the situation is
For example,
in
more
an earlier study 2 2
phase separation was found to produce an increase in KIC; whereas, it
The reasons for such
resulted in a decrease in KIC in this study.
variability in KIC are difficult to determine because the current
understanding of the mechanism of the initiation of catastrophic crack
propagantion in heterogeneous materials is not complete.
Undoubtedly, the
microstructural size and the nature of the interface between the separated
phases are likely to play an important role in determining KIC in phase
separated glasses.
It is interesting to note that in this study the
separated phases after heat treatment have a microstructural size of about
0.01 pa and the strength controlling flaws are about 3 orders of magnitude
larger (10-20 pm).
Since the increase in strength with heat treating is contrary to the
expectation based on the observed decrease in KIC,
alternative possibilities
such as surface residual stress or crack blunting/healing must be
considered.
Residual stresses are possible because the chemical
compositions of the surface and bulk can be quite different from one another
depending on thermal histroy.
Table IV summarizes the results of the
chemical analyses 7 of the "non-pitting" glass used in this study where it
can be seen that the surface is high in Si0
2
and low in B 2 0 3 .
Tomozawa and
Takamori 2 3 have also found that heat treating a borosilicate glass causes
V-8
evaporation of water from the surface during heat treatment and that the
resulting compositional difference produces a residual stress in the
surface.
However, the magnitude of this compressive stress (~ 1 MPa) is
much smaller than the measured strength increases upon heat treatment shown
in Table I and II.
Thus, a residual stress effect of this size cannot
account for the strength increase observed on heat treatment.
It should be
noted that this small residual stress is consistent with the fact than no
direct evidence of residual stress was observed by birefringence
measurements in the center areas of the samples used in this study before or
after heat treatment.
Also, a plot of the fracture strength versus (mirror
radius) 1 / 2 for the samples in all stages of processing always extrapolated
to a zero stress intercept within experimental uncertainty, which strongly
implies no residual stess.18,19
Thus, it is believed that the most likely
explanation for the strength increase on heat treating is
or healing that can occur during heat treatment.24
crack tip blunting
Crack healing is a
plausible mechanism since the heat treating temperature is about 100"C
greater than the annealing temperature and sufficient viscous flow at the
crack tip could occur at these temperatures under the forces of surface
tension to cause crack blunting.
On chemically polishing the glass about 1 pm of the surface was
uniformly removed and it was expected that the strength would increase due
to the blunting of pre-existing flaws.25
Instead, Tables I and II show a
decline in strength for those samples which tended to pit and no significant
change for samples which did not pit.
strength decrease.
It is evident that pitting caused the
On the other hand, it is possible that the reason for
chemical polishing not being effective in increasing the strength of the
V-9
"non-pitting" samples is because crack blunting had already occurred during
heat treatment.
Thus, the additional chemical polish did not cause any
significant changes in crack shape, hence strength, with these "non-pitting"
samples.
This explanation is consistent with the fact that the depth of the
material removed during chemical polish was much less than the strength
controlling flaw size.
Also, this explanation could explain why selective
etching did not cause any significant change in strength of the "nonpitting" samples.
However, with the "pitting" samples it appears that
selective etching did reduce the severity of the pits.
After heat treating it
can be seen from Table III that the additional
processing steps of chemical polish and selective etch do not significantly
affect KIC.
This would be expected since these processes only affect the
glass surface and not its bulk.
Also, the average heat treatment that
increased the microstructural size of the separated phases from 0.0075 to
0.015
im had no effect on KIC.
The fatigue resistance (N) results, which are based on the strength
data of Tables I and II, are given in Table V for "pitting" samples.
It can
be seen that processing had little effect on the fatigue resistance of the
"pitting" glass samples, and that the fatigue resistance of the glass is
somewhat lower than that previously observed for a similar commercial
borosilicate glass.
This could be due to small differences in chemical
composition between the glass used in this study and that used in other
studies.
These fatigue resistance results are consistent with crack growth
experiments 2 6 performed on a similar borosilicate glass, where the slope of
the crack velocity versus stress intensity curve (which equals fatigue
resistance N) was not affected by an increase in the microstructural size of
V-10
the separated phases from 0.01 to 0.15 pm due to heat treating, although the
curves did shift to higher subcritical crack velocities as the
microstructural size increased.
Interestingly, these crack velocity curves
exhibited at least four separate regions of crack growth behavior, and the
slope in the lower two regions, which affect strength behavior most
strongly, corresponded to N values of 84 for Region IV and ~ 31 for
Region III. 2 6
Initially, the fatigue resistance for "non-pitting" samples showed
great variability with no logical trend evident.
Upon close optical
examination, it was found that about one-half of the as-received "nonpitting" samples were relatively free of visible surface damage, while
For
others exhibited a relatively high number of surface defects.
equivalent processing, samples which came from plates with little visible
damage were stronger than those from the highly damaged plates.
This
suggests that variations in surface condition between plates due to
individual manufacturing history was the cause of the large variability of
strength and fatigue for the "non-pitting" samples.
For this reason, a
plate by plate analysis of fatigue resistance was performed.
The mean
strengths in water at the fast and at the slow stressing rate was calculated
for any plate which provided at least three samples at each stressing rate.
Fatigue resistance for each such plate was calculated using Eq. (2) and
these results were then averaged.
Negative values of N were discarded,
since they are not physically meaningful and are undoubtedly due to
statistical anomalies associated with the small sample size.
summarizes these results.
Table VI
Although a large degree of variability still
exists in the fatigue resistance, these values of N are in general agreement
V-11
with those reported in Table V; however, these results must be viewed with
caution due to the small data base.
It has been noted that subcritical crack growth in borosilicate glasses
seems to be more complex than in more homogeneous glasses.27
Even with
simple glasses, crack growth, hence strength and fatigue resistance, can
depend in a complex way on environment, crack geometry, and glass
28 29
With phase-separated borosilicate glass, other
composition. '
complicating factors arise.
First, the initial microstructure of as-
received samples is in an unknown state due to phase separation that occurs
during manufacture.
Subsequent heat treatment leads to compositional and
microstructural changes of both phases as they approach equilibrium.
Second, as noted previously, crack growth behavior of phase-separated
borosilicate glass is complex and exhibits at lease four distinct regions;26
hence, it is uncertain which region of crack growth has the greatest
influence on strength results.
Finally, it is not known how the chemical
compositional difference between the surface and bulk affects crack
propagation.
In summary, the results of the strength and fatigue measurements
presented in this paper illustrate the complex nature of crack propagation
and ultimate failure in a glass containing both a phase-separated
microstructure and a porous surface film.
Additional research is needed to
understand crack growth and its relation to strength and fatigue of phaseseparated glasses from a mechanistic perspective.
Phenomenallogically, the
results do indicate that the set of processing steps used to produce the
anti-reflective surface do not adversely affect the short- or long-term
strength characteristics of the glass.
V-12
In fact, short-term strengths were
increased.
More importantly, the fatigue resistance (N) of the glass was
not degraded by the process.
In the long-term, the reduced KIC value may
cause a slight decrease in strength.
it is anticipated that these
conclusions may vary with different glass compositions that are subjected to
analogous phase separation and selective etching processing.
ACKNOWLEDGEMENTS
This work was supported under subcontract to the Energy Laboratory,
Massachusetts Institute of Technology from DOE Contract No. ER-78-8-02-5003.
The authors wish to acknowledge Dr. S.C. Danforth's contributions in the
areas of microscopy and sample preparation.
by Corning Glass Works.
The glass sheets were donated
All contributions are gratefully acknowledged.
V-13
IV.
REFERENCES
1.
T. H. Elmer and F. W. Martin, "Antireflection Films on AlkaliBorosilicate Glasses Produced by Chemical Treatments", Am. Ceram. Soc.
Bull., 58 (11), 1092-7 (1979).
2.
M. J. Minot et al., "Antireflective Layers on Phase Separated Glasses",
U. S. Patent 4,086, 074, April 25, 1978.
3.
M. J. Minot et al., "Durable Substrates Having Porous Antireflection
Coatings", U. S. Patent, 4,080,188, March 21, 1978.
4.
J. S. Haggerty, "Graded Index Antireflective Coatings for Glass",
Interim report to Department of Energy, Contract No. ER-78-8-02-5003,
May 1979.
5.
J. M. Power and T. H. Elmer, "Weathering of Graded-Index Antireflection
Films on a Borosilicate Glass", Am. Ceram. Soc. Bull., 59 (11), 1124-6
(1980).
6.
S. C. Danforth, J. S. Haggerty, D. Imeson, A. Iqbal, and
J. B. VanderSande, "Microstructural Analysis of Broad Band AntiReflective Films on Glass,", Presented at the 82nd Annual Meeting of
Am. Ceram. Soc., Abstract in Am. Ceram. Soc., 59 (3), 331 (1980).
7.
A. Iqbal, "Determination of Surface Chemistry of Graded-Index,
Antireflection Films on Glass", M.S. Thesis in Ceramics, Massachusetts
Instutute of Technology, February 1981.
8.
W. Haller, D. H. Blackburn, F. E. Wagstaff, and R. J. Charles,
"Metastable Immicibility Surface in the System Na20-B 2 0 3-Si0 2",
J. Am. Ceram. Soc., 53 (1), 34-9 (1970).
9.
J. B. Wachtman, Jr., W. Capps, and J. Mandel, "Biaxial Flexure Tests of
Ceramic Substrates", J. Mater., 7 (2), 188-94 (1972).
10.
F. F. Vitman and V. P. Pukh, "A Method for Determining the Strength of
Sheet Glass", Zavodskaya Laboratoriya, 29 (7), 863-7 (1963).
11.
J. E. Ritter, Jr., K. Jakus, A. Batakis, and N. Bandyopadhyay,
"Appraisal of Biaxial Strength Testing", J. Noncryst. Solids, 38 & 39,
419-24 (1980).
12.
D. Shetty et al., "Biaxial Flexure Tests for Ceramics", Am. Ceram. Soc.
Bull., 59 (12), 1193-7 (1980).
13.
S. M. Wiederhorn, "Subcritical Crack Growth in Ceramics", Fracture
Mechanics of Ceramics, Vol. 2, 613-46, ed. R. C. Bradt,
D. P H. Hasselman and F. F. Lange, Plenum Press, New York (1974).
V-14
14.
J. E. Ritter, Jr., "Dynamic Fatigue of Soda-Lime-Silica Glass",
J. Appl. Phys., 40 (1), 340-4 (1969).
15.
J. E. Ritter, Jr. and R. P. LaPorte, "Effect of Test Environment on
Stress-Corrosion Susceptibility of Glass", J. Am. Ceram. Soc., 58
(7-8), 265-7 (1975).
16.
J. E. Ritter, Jr. and C. L. Sherbourne, "Dynamic
Silicate Glasses", ibid., 54 (12) 601-5 (1971).
17.
B. A. Proctor, I. Whitney, and J. W. Johnson, "The Strength of Fused
Silica", Proc. R. Soc. London Ser. A., 297 (1451), 534-57 (1967).
18.
J. J. Mecholsky, S. W. Freiman, and R. W. Rice, "Fractographic Analysis
of Ceramics", Fractography in Failure Analysis, pp. 363-79, eds,
B. M. Strauss and W. H. Cullen, Jr., American Society for Testing
Materials, 1978.
19.
S. W. Freiman, "Fracture Mechanics of Glass", Glass in Science and
Technology, Vol. 5, Elasticity and Strength in Glasses, eds.
D. R. Uhlmann and N. J. Kreidl, Academic Press, New York (1980).
20.
J. J. Mecholsky, R. W. Rice, and S. W. Freiman, "Prediction of Fracture
Energy and Flaw Size in Glasses from Measurement of Mirror Size,
J. Am. Ceram. Soc., 57 (10), 440-3 (1974).
21.
J. E. Ritter, Jr., N. Bandyopadhyay and K. Jakus, "Statistical
Reproducibility of the Dynamic and Static Fatigue Experiments",
Am. Ceram. Soc. Bull., 60 (8), 798-806 (1981).
22.
C. J. Brinker, and J. J. Mecholsky, "Influence of Microstructure on
Fracture of Phase Separated Glasses", presented at 82nd Annual Meeting
of the Am. Ceram. Soc., Chicago, April, 1980. Abstract in
Am. Ceram. Soc. Bull., 59 (3) 352 (1980).
23.
M. Tomozawa and T. Takamori, "Relation of Surface Structure of Glass to
HF Acid Attack and Stress State", J. Am. Ceram. Soc., 62 (7-8), 370-3
(1979).
24.
S. M. Wiederhorn and P. R. Townsend, "Crack Healing in Glass",
J. Am. Ceram. Soc., 53 (9), 486-9 (1970).
25.
B. Proctor, "Effects of Hydrofluoric Acid Etching on the Strength of
Glasses", Phys. Chem. Glasses, 3 (1), 7-27 (1962).
26.
C. J. Simmons and S. W. Freiman, "Effects of Phase Separation on Crack
Growth in Borosilicate Glass", J. Noncryst. Solids, 38 & 39, 503-8
(1980).
V-15
and Static Fatigue of
27.
Y. Utsumi, S. Sakka, and M. Tashiro, "Experimental Study on the Bending
Strength of Glass in Relation to Liquid-Liquid Phase Separation", Glass
Technol., 11 (3), 80-5 (1970).
28.
S. W. Freiman, "Fracture Mechanics of Glass", Glass: Science and
Technology, Vol. 5, Elasticity and Strength in Glasses, pp. 21-78, ed.
D. R. Uhlmann and N. J. Dreidl, Academic Press, New York (1980).
29.
S. M. Wiederhorn and J. E. Ritter, Jr., "Application of Fracture
Mechanics Concepts to Structural Ceramics", Fracture Mechanics Applied
to Brittle Materials, ASTM STP 678, pp. 202-14, S. W. Freiman, ed.,
Am. Soc. for Testing and Materials (1979).
V-16
-
_____________________________________iuminflIIII
10011,14 ,I
TABLE I
Strength of Samples Which Tended to Pit During Chemical Polishing.
All Tests Were Conducted Using the Ring-On-Ring Configuration.
Stressing
Rate (MPa/s)
min. oil
water
water
16.75
15.00
0.0261
75.9
56.4
42.6
(11)*
(11)
25
24
22
min. oil
3.87
3.74
0.0323
109.1
72.0
61.2
(13)
(14)
(9)
26
27
25
min. oil
Fully treated
Overaged
No. of
Samples
As received
Heat treated
Chemically polished
water
water
(7)
water
3.11
2.76
0.0267
60.3 (13)
36.3 (7)
30.2 (4)
28
22
21
min. oil
water
water
3.29
3.35
0.292
94.6
71.1
58.9
(10)
(12)
(13)
22
21
23
min.oil
water
water
3.46
3.78
0.0316
108.9
103.1
87.1
(17)
(19)
(18)
water
Number in parentheses represent the standard deviation.
.
Median
Strength (MPa)
Environment
Processing Stage
A
V-17
11W
I61MINONN IN"
TABLE II
Strength of Samples Which Did Not Tend to Pit During Chemical Polishing.
All Tests Were Conducted Using the Ring-On-Ring Configuration.
Processing Stage
No. of
Samples
Environment
Stressing
Rate (MPa/s)
Median
Strength (MPa)
100.5 (54)*
76.3 (36)
55.4 (30)
As received
min. oil
water
water
17.64
17.09
0.0257
Heat treated
min. oil
water
water
4.05
147.5 (43)
3.79
83.1 (21)
0.0365
78.4 (16)
Chemically polished
min. oil
water
water
3.52
3.39
0.0307
154.9 (41)
86.9 (23)
84.1 (26)
Fully treated
min. oil
water
water
3.40
3.65
0.309
162.6 (45)
min.oil
water
water
3.57
3.69
0.0320
136.1 (24)
107.1 (24)
97.9 (21)
"
Overaged
Number in parentheses represent the standard
deviation.
V-18
104.2 (30)
72.9 (20)
TABLE III
Summary of the Fracture Toughness (KIC) Results for
Borosilicate Glass
3 / 2
Processing Stage
A (MP/am3 /2 )
As received
2.11
Beat treated
1.80 (0.20)
0.63 (0.07)
Chemically polished
1.85 (0.17)
0.65 (0.06)
Fully treated
1.68
(0.09)
0.59 (0.03)
Overaged
1.71 (0.24)
0.60 (0.08)
(0.19)*
Number in parentheses represent the standard
V-19
KIC(MPa/m
)
0.74 (0.07)
deviation.
TABLE IV
Chemical Composition of the Borosilicate Glasses.
Constituent (wt.%)
Glass
Si0 2
B2 0 3
Nominal, Code 7740
81.0
13.0
4.0
2.0
As received, bulk
75.5
19.2
4.0
2.0
As received, surface
90.5
9.5
3.0
0.6
Heat treated, surface
92.1
4.5
2.9
0.3
V-20
Na 2 0
A12 0 3
TABLE V
Fatigue Resistance (N) in Water for Borosilicate Samples
That Tended to Pit During Chemical Polishing
Processing Stage
"Pitting Samples"
As-received
22 (3)*
Heat treated
28 (7)
Chemically polished
25 (9)
Fully-treated
24 (4)
Overaged
27 (8)
N* hiber In parent eses reoresent the standard deviation of the estimated
statistical re orducibility of the stressing rate technique for
determining N.31
V-21
TABLE VI
Fatigue Resistance (N) in Water for Borosilicate Samples.
from Plates which Did Not Tend to Pit During Chemical Polishing
Processing Stage
No. of Plates
Mean N-Value
As-received
3
29 (11)**
Heat treated
5 [1]*
28 (10)
Chemically polished
4 [1]
64 (46)
Fully-treated
5
]
15 (6)
Overaged
6 [2]
30 (5)
Number in brackets represents the number of plates discarded due to
negative N-values.
** Number in parentheses represent the standard deviation. 1 8
V-22
120
100
N140
80 F
N-3S
60 F
TiMedia ±o90%
I
501
Confidence Limits
O Fully Treated,
Ring-on-Ring
N-32
0
40
As Received,
Ring-on-Ring
A As Received,
3-Ball-Piston
32
3
10-3
_
,
-2
10
.3
.
1.
.
101d
STRESSING RATE (MPa/s)
Figure 1.
Stressing Rate Technique for Determining the Fatigue
Resistance (N) of a Borosilicate Glass in Water.
V-23
__
-
~ ---- ---- ~_hi
CHAPTER VI
Effect of Proof Testing Soda-Lime Glass
in a Heptane Environment
J. E. Ritter
Jr., K. Jakus, G. M. Young and T. H. Service
Mechanical Engineering Department
University of Massachusetts
Amherst, MA 01003
ABSTRACT
Soda-lime glass was proof tested in a heptane environment using three
different unloading rates.
Observed after-proof strength distributions
shifted toward weaker values of strength as the rate of unloading decreased.
The theoretical implications of the results are discussed.
Submitted for Publication to the Journal of the American Ceramic Society
ini-h
IMIYYIIA WIIIMM1I="
---
-
0010I
I
1i
Previous research showed that under certain conditions strength
degradation occurring during proof testing can be interpreted as a
1 2
Unfortunately, there
consequence of multiregion crack growth behavior. '
was not good quantitative agreement between theory and some experiments and
it was suggested that our understanding of subcritical crack growth in
specimens containing small flaws (<10 pm) is not complete and requires
further research.
The purpose of this note is to present results on
assessing the validity of fracture of mechanics theory in predicting the
strength after proof testing in an heptane environment where the effects of
3 4
multiregion crack growth are pronounced (see Figure 1). '
Samples of soda-lime glass were prepared by cutting sheets of window
glass (0.225 cm thick) into squares 7.6 cm on a side.
The samples were
abraded in the center with a standard blast of No. 240 SiC grit and then
annealed.
To avoid the complications of edge failures, all proof and
strenght testing was done using a biaxial loading apparatus 5 with a ring-onin conjunction
ring configuration (1.4 cm inner and 4.1 cm outer diameter)
with an Instron testing machine.
environment.
All testing was done in an-heptane
In the proof test samples were loaded up to the proof stress
at a rate of 3.9 MPa/s and then unloaded at one of three rates (394, 3.9,
0.066 MPa/s).
The time at the proof stress was momentary and the proof
stresses were 79.9, 78.3, and 62.0 MPa, corresponding to the fast, medium,
and slow unloading rates.
Samples that survived the proof test were
immediately strength tested at a stressing rate of 3.9 MPa/s.
VI-1
ilill
ft
The after-proof strength data are compared to the initial strength
distributions in Figures 2, 3, and 4.
It can be seen that the after-proof
strength data exhibit a shift to lower strengths at low failure
probabilities as the rate of unloading from the proof stress is decreased.
Since the failure probability of the three proof tests are approximately the
same (about 15 to 20%), these results show that the strength degradation of
those samples just passing the proof test is greater as the unloading rate
From the viewpoint of our earlier work, it would be expected
decreases.
that this difference in strength degradation is related to subcritical crack
growth during unloading.
It is also evident that only the fast unload proof
test resulted in effective truncation of the strength distribution curve.
These proof test results are quite similar to those obtained by Wiederhorn
et al. 3 who also studied the effect of proof testing in a heptane
environment.
Based on fracture mechanics principles, theoretical predictions can be
1 2
Assuming single
made of the strength distribution after proof testing. '
region crack growth, the strength loss during a proof test cycle can be
analytically calculated; however, for multiregion crack propagation,
1 2
By
numerical analysis must be used to describe the strength loss. '
expressing crack velocity as a power function of the stress intensity
factor, V
-
AK~, within each of the three regions of crack growth,
appropriate values of the constants A and n were determined from the data
shown in Figure 1 for crack growth of soda-lime glass in an heptane
environment, see Table I.
Figures 2, 3, and 4 show the theoretical
VI-2
predictions based on considering stength degradation due to single region
crack growth, i.e., only Region I growth, as well as multiregion crack
growth.
Table II gives the corresponding predicted failure probabilities
along with those observed.
From Table II it is seen that there is not good agreement between
actual failure probabilities observed in the proof test and those predicted
based on assuming either single region or multiregion crack growth.
However, it should be noted that relatively small changes in the initial
Weibull strength distribution parameters can cause large varations in the
predicted failure probabilities.
The after-proof strength predictions shown
in Figures 2, 3, and 4, based on assuming single region crack growth, do not
depend strongly on the proof test unloading rate.
This is because in these
predictions the unloading rate is used to only calculate the proof test
failure predictions. 2
Since the failure probabilities between the three
proof tests are all similar (see Table II), the after-proof strength
predictions are similar and, hence, these predictions do not predict the
observed shift to lower strengths at the low failure probabilities as the
rate of unloading decreases.
On the other hand, the predictions based on
multiregion crack growth are quite sensitive to the proof test conditions,
however, there is still not good agreement between theory and experiment.
Better quantitative agreement between experiment and multiregion preditions
can be obtained by adjusting the crack growth parameters so that the crack
growth curve is shifted downward and to the right of the actual curve (see
Figure 1).
In making these calculations, it was found that these after-
proof strength predictions based on multiregion crack growth were highly
VI-3
sensitive to the crack growth parameters especially those for Region II.
This emphasizes the importance of having reliable crack growth data in
making predictions on strength degradation due to subcritical crack growth.
It is important to note that the required adjustment of the crack growth
parameters to get better agreement between theory and experiment could be
related to differences in crack kinetics between micro- and macro-cracks.
In summary, these results give additional evidence that our
understanding of the relationship between subcritical crack growth and the
related strength degradation is not complete.
the position and slope of the V - K
Recent research 6 showed that
curve for a particular glass in a given
environment could be governed by a balance between the tendency of corrosion
processes to increase the crack tip radius and the stress corrosion process
that sharpens it.
The fracture mechanics model of strength degradation
considers that the crack tip radii is constant and strength loss is due to
crack lengthening.
This suggests that a better model for strength
degradation may be one that incorporates the effect of changes in the crack
tip radius.
This concept is in direct analog with the model of Charles and
Hillig 7 and Doremus.8
ACKNOWLEDGEMENTS
This research was supported under subcontract to the Energy Laboratory,
Massachusetts Institute of Technology from DOE Contract No. ER-78-8-02-5003.
VI-4
REFERENCES
1.
J. E. Ritter, Jr., P. B. Oates, E. R. Fuller, Jr., and
S. M. Wiederhorn, "Proof Testing of Ceramics, Part I: Experiment",
J. Mater. Sci., 15, 2275-81 (1980).
2.
E. R. Fuller, Jr., S. M. Wiederhorn, J. E. Ritter, Jr., and
P. B. Oates, "Proof Testing of Ceramics, Part II: Theory", J. Mater.
Sci., 15, 2282-95 (1980).
3.
S. M. Wiederhorn, S. W. Freiman, and E. R. Fuller, Jr., "Effect of
Multiregion Crack Growth on Proof Testing", "Paper presented at 82nd
Annual Meeting of American Ceramic Society, Chicago (1980).
4.
S. W. Freiman, "Effect of Straight-Chain Alkanes on Crack Propagation
in Glass", J. Am. Ceram. Soc., 58, 339-40 (1975).
5.
J. E. Ritter, Jr., K. Jakus, A. Batakis, and N. Bandyopadhyay,
"Appraisal of Biaxial Strength Testing", J. Noncryst. Solids, 38 & 39,
419-24 (1980).
6.
C. J. Simmons and S. W. Freiman, "Effect of Corrosion Processes on
Subcritical Crack Growth in Glass, "J. Am. Ceram. Soc., 64, 683-6
(1981).
7.
W. B. Hillig and R. J. Charles, "Surfaces, Stress-Dependent Surface
Reactions, and Strengths", High Strength Materials, pp. 682-705, ed.
V. F. Zackey, J. Wiley & Sons, Inc., N. Y. (1965).
8.
R. H. Doremus, "Importance of Crack-Tip Radii in Fracture and Fatigue
of Glass", J. Noncryst. Solids, 38 & 39, 493-6 (1980).
VI-5
TABLE I
Crack Parameters, Soda-Lime-Silicate Glass in Heptane
(from Reference 4)
KIC = 0.75
*
106 Pa
*
m- 3 /2
Region I
N = 14.1, In A
Region II
N
Region III
N = 65.4, In A = -889.9
=
3.41, In A
-
-199.6
=
- 58.7
TABLE II
Proof Test Predicted and Observed Failure Probabilities
Prediction
Proof Test
Single Region
Multiregion
Observed
Fast Unload
0.32
0.29
0.18
Medium Unload
0.41
0.31
0.20
Slow Unload
0.39
0.75
0.15
VI-6
~~__III
YYI
--
-
10-"
ii11
'
1 1 llll
il M
1 IIinI
I
I
iO-
E 10- 5
I.0
I
ISTable
0
o
10"
1UIr
I
5
T
-
*
• Data for4
Heptane
/
/
10-I
Regression Line
-
/
/
for Table I
S---
Shift required
for best
10-9
3.0
/
4.0
1agreement
6.0
5.0
K,(Nm-"
Figure 1.
2
7.0
8.0
9.0
X10)
Crack velocity of soda-lime glass in a heptane environment as
a function of stress intensity.
0
FAST UNLOAD
qor
MULTI
:t
SINGLE REGIOI
PROOF * AFTER-PROOF DATA
STRESS
- INITIAL DIST.
-- PREDICTED
AFTER-PROOF
'4.00
4.10
4.30
4.20
Ln(S)
Figure 2.
. 4.40
4.50
4.60
(MPo)
After-proof strength data compared to prediction for proof
testing in a heptane environment using a fast unload from
the proof stress.
VI-7
1141
O
0
IT
MED. UNLOAD
0
C!
MULTI REGION
o
o
PROOF
STRESS
0
0.
I
* AFTER-PROOF DATA
- INITIAL DIST.
-- PREDICTED
AFTER-PROOF
REGION
o81
II
1'41%
4.10
'4.00
LN (S)
Figure 3.
o0
4.40
4.30
4.20
4.50
4.60
(MPa)
After-proof strength data compared to prediction for proof
testing in a heptane environment using a medium unload from
the proof stress.
O
4-
SLOW UNLOAD
oO
oj
MULTI REGION
S
* AFTER-PROOF DATA
- INITIAL DIST.
-- PREDICTED
AFTER-PROOF
PROOF STRESS inff
II
'4.00
4JO0
LN (S)
Figure 4.
4AO
4.30
4.20
4.50
4.60
(MPo)
After-proof strength data compared to prediction for proof
testing in a heptane environment using a slow unload from
the proof stress.
VI-8
CHAPTER
VII
DEVELOPMENT OF SELECTIVELY ETCHED FILMS ON
PHASE-SEPARATED Na 20/CaO/SiO 2 GLASS
by
VIVIAN TENGZELIUS
Submitted to the Department of Materials Science and Engineering
on January 14, 1982 in partial fulfillment of the requirements
for the Degree of Master of Science in Materials Science.
ABSTRACT
The development of selectively etched films on phase separated
Na20/CaO/SiO2 glass was studied to evaluate the glass with regard to
parameters important for graded-index antireflective (AR) film
development by acid leaching of the surface. This study indicated that
the composition 80/10/10 is compatible with the AR film development
process.
Nine glass compositions were examined, and based on
microstructural and viscosity criteria, the composition 80/10/10 was
selected for further study. Films were developed on the glass by
generating a two-phase interconnected microstructure using an
appropriate heat treatment, followed by selective etching of the more
soluble phase from the glass surface. This leaves behind a porous,
skeletal network of glass, and produces a density gradient at the glass
surface.
The compatibility of 80/10/10 with AR film processing depends on
the volume fractions of separated phases, etched film depth, etch
selectivity, and the size of the features in the films. These were
characterized using the scanning electron microscope, weight loss
analysis, atomic absorption spectroscopy, and BET surface area
measurements. Heat treatment time and temperature, and etch time were
varied. The volume fraction of the acid resistant high silica phase,
as determined by counting measurements on SEM micrographs, was 30-35%.
Increasing depth and complexity of the etched film was observed as etch
time increased. Good mechanical stability was observed to > 1 pm
thickness. The 2% HF etch was highly selective. A finite dissolution
rate of the more resistant phase caused mechanical instability near the
surface of the etched layer. The size of the microstructural features
increases with annealing time.
Thesis 'Supervisor:
Title:
Dr. John S. Haggerty
Senior Research Scientist
Co-Thesis Supervisor:
Title:
Professor H. Kent Bowen
Professor of Ceramics
I. INTRODUCTION
A process by which graded-index antireflective (AR) films could be
developed on soda-lime-silica glass by acid leaching of the surface
would be useful for application to solar collector cover plates.
Such
a process would serve to reduce reflective losses and increase the
efficiency of solar collection without a dramatic increase in
manufacturing costs.
This research addresses the selection of a soda-
lime-silica glass which exhibits compatibility with graded-index AR
film development, the characterization of the phase separated
microstructure of the glass as a function of annealing time and
temperature, and the effect of the etch time and selectivity on etched
film development.
Borosilicate glass exhibits broad-band antireflective properties
upon appropriate processing.
The procedure, which was empirically
developed,1 includes phase separation heat treatment of the glass to
generate a two-phase interconnected microstructure followed by
selective etching of one of the phases.
Minot's modell of the
resulting surface film suggests that a porous skeletal network of the
insoluble phase exhibits a gradual increase in density, and associated
continuous increase in index of refraction from the surface to the
bulk.
It is anticipated that soda-lime-silica glass should be lower cost
than borosilicate glass because of the lower forming temperature and
lower cost of constituent materials.
solar energy applications.
Minimizing cost is essential for
The selection of a suitable glass
VII-1
composition is based on the compatibility of the calculated viscosity
of the glass with float glass processing requirements, and the ability
to generate an appropriate two-phase interconnected microstructure by
heat treatment of the glass.
Glasses were fabricated in the laboratory and phase separation
was induced and manipulated by annealing heat treatments.
The
characteristic volume fractions of the phases, etched film thickness,
etch selectivity, and size of the microstructural features were
determined.
Information about the volume fractions of the resistant
and leachable phases and the dependence of etched film thickness on
etching time is important for understanding both the mechanical
stability of the surface treated layers and the optical properties of
the final film.
Evaluation of etch selectivity will indicate the
consistency of etched film development with the model.
Measurement of
the size of the features as a function of annealing treatment will
facilitate the selection of an annealing treatment which will yield a
microstructure suitably sized for AR film development.
VII-2
II.
LITERATURE REVIEW
A process has been developed by which broad-band graded-index
antireflective (AR) films can be formed on glass by acid treatment of
the surface.1
Graded-index AR films are desirable because they
minimize the reflectivity over a wide range of wavelengths in contrast
to single layer homogeneous AR coatings which exhibit a minimum
reflectivity at a specific wavelength.
The glass is heat treated to
generate a two-phase interconnected microstructure with (100-400 A)
features much smaller than the wavelength of light so that the glass
behaves as if it is optically homogeneous (i.e. negligible scattering
by interparticle interference).
An acid etch that preferentially
dissolves the more soluble of the two phases is applied to the glass.
According to the model, acid leaching of one of the phases leaves
behind a porous skeletal network on the surface which gradually
increases in density as one moves from the surface to the bulk.
This
effect of increasing density results from a finite etching rate of the
preferential etch on the more resistant phase.
As one moves from air
through the film and into the bulk the average index of refraction (n)
increases with density in a continuous manner from approximately nair
at the surface to nbulk at the film - glass interface.
Graded-index antireflective films have been developed on
1 The process was optimized
borosilicate glass by such a process.
empirically with respect to optical properties.
VII-3
Recent research 2 has
focussed on a more rigorous chemical and microstructural
characterization of the films to test the validity of the model.
Iqbal 2 studied the surface chemistry of graded-index AR films on
borosilicate glass.
Microscopic direct observation techniques like
Auger Electron Spectroscopy (AES), Secondary Ion Mass Spectrometry
(SIMS), Scanning Electron Microscopy (SEM); and macroscopic averaging
techniques such as solution analysis by Atomic Absorption Spectroscopy
(AA), Weight Loss Analysis, and BET method for surface area
determination were used to characterize the surface chemistry of the AR
films.
The compositional gradients within the glass, etch selectivity,
and film thickness were among the parameters investigated.
The results
confirmed that heat treatment generates the two-phase interconnected
microstructure which is required for AR film development.
The extent
of selectivity of the etching process was shown by AA analysis of the
etching solutions, specific surface area measurements of glass powder
by BET and direct observations of AR films by SEM.
to measure film thickness.
SEM was also used
Weight loss measurements were used to
calculate the etch rate of the preferential etch.
The data from AES
and SIMS indicated that these techniques are not sensitive enough to
detect the compositional changes in the surface layer before and after
etching.
Direct observation of the phase separation morphology by SEM
is limited to features >400 A due to the decoration of the surface by
the conductive coating.
Phase separation in glasses has been the subject of much study.
3 4
A glass which
Extensive reviews are available in the literature. '
VII-4
~-'-~ ~
"~s -
-- ~~~~-~-I
~~- II---
'
W
1111111wu
IYN111
WINNIN
11M'IN1IIIYIY
exhibits a sub-liquidus immiscibility gap will phase separate when
slowly cooled through this region or when quenched and held at a
temperature within the immiscibility gap.
The mechanism of the initial
stage of phase separation has been the subject of much investigation.
Phase separation causes a decrease in the total free energy of the
system.
The microstructural development of phase separation has been
described by two distinct processes:
and spinodal decomposition.
classical nucleation and growth,
Cahn and Charles 5 proposed that the
controlling mechanism of initial stage phase separation in glasses is
determined by whether the separation occurs inside or outside the
spinodal region.
The spinodal for a bianry system is formed by the
locus of the points of inflection of the free energy versus composition
curves (2G/8c
c
=
2 =
composition).
0 where AG = free energy change and
Inside the spinodal region of the immiscibility gap,
2
2
the second derivative of the free energy is negative (8 AG/ac < 0) and
the system is unstable to infinitesimal changes in composition so the
phase separation is expected to occur by a spinodal decomposition
mechanism.
The composition of the separated phases will change
continuously until phase separation is completed.
Outside the spinodal
region of the immiscibility gap, the second derivative of the free
2
energy is positive (82AG/ac > 0) and the system is metastable to
infinitesimal compositional fluctuations.
In this region, phase
separation is expected to occur by nucleation and growth.
An interconnected structure may be formed by either of the two
mechanisms. 6
Regardless of the mechanisms involved, the result of the
phase separation process will be equilibrium phase compositions, the
volume fractions of which can be determined by the Lever Rule.
VII-5
The
IHIIUM_
scale of the resulting microstructure is usually sufficiently small
that there is a high driving force for coarsening.
The coarsening of a highly interconnected two-phase microstructure
was investigated by Haller. 7
Because of the complex geometry of the
interconnected network, characterization of specific lineal distances
is precluded.
Haller employed BET surface area determinations of the
bulk property of interfacial area per unit volume (Sv ) which
effectively averages the size contributions of the network features.
Later stage coarsening of phase separated glass appears to be rate
8 9
and is characterized by S = t- 1/ 3 .
controlled by volume diffusion '
v
The characteristics of a phase separated soda-lime-silica glass
have been well documented by Burnett and Douglas.
their work will be presented here.
10
A brief review of
Phase separation as a function of
annealing time and temperature, and glass composition was investigated
as well as the effect of etching with 2% HF.
Observations were made
using electron micrographs of replicas of the etched glass surfaces.
The observed morphology of phase separation as a function of
composition is summarized
in Figure 1 for various glass compositions.
Boundaries defining the regions of interconnected, discrete, and nonphase separated microstructure were constructed on the basis of the
experimental observations.
The boundaries of the immiscibility region
were determined by observing temperatures above which opalescent
VII-6
-.- -
----
- ------
samples "cleared".
IYYI
Ylli
Determinations of the miscibility temperature (T
a
were made for compositions in the range of 50-85 mol % silica.
This
data and other published data for the soda-silica and the lime-silica
binaries were used to construct the surface of the immiscibility dome
shown in Figure 2.
The isotherms join compositions of the same T (OC).
m
The form of the immiscibility dome in the high silica region has not
been rigorously verified.
Two compositions were selected for more detailed analysis.
These
were a 75% Si0 2 + 12.5% Nap2 + 12.5% CaO glass which was only observed
to phase separate with a discrete microstructure, and an
80% Si0 2 + 10% Na2o + 10% CaO glass which developed an interconnected
microstructure upon appropriate heat treatment.
The term
"interconnected" refers to a two-phase co-continuous structure
resembling a sponge, in contrast to "discrete" which refers to a twophase structure consisting of one phase distributed within a matrix of
the other.
For convenience, glass compositions will be designated by
three numbers in the format %Si0 2 /%Na 20/%CaO from now on.
Both of
the glasses selected fall on the 1Na 2 0-1CaO-SiO 2 cross section of the
immiscibility dome (see Figure 3) with the 80/10/10 composition
representing a glass well within the immiscibility dome.
The coarsening of the two glasses was studied as a function of
time.
For the 80/10/10 interconnected microstructure the data
indicates S
a t-
1/3
and for the 75/12.5/12.5 discrete microstructure,
the initial time dependence was r = t1/2 followed by a change to
r
t 11/ 3 .
The initial t 1 /2 dependence is attributable to observation
VII-7
of the early stage nucleation and growth process.
In the later stages,
the interconnected and discrete structures exhibited coarsening with
equivalent time dependencies.
The t1/ 3 dependence suggests a long
range volume diffusion controlled coarsening mechanism.
Burnett and Douglas 1 0 also observed that etching time had a
noticeable effect on the observed volume fraction (Vv ) of the features.
For an interconnected structure, the observed (or apparent) volume
fraction would increase almost linearly with etch time due to the
gradual buildup of the complex structure.
For a discrete structure,
the increase in volume fraction reached a plateau after the first layer
was penetrated corresponding to the establishment of equilibrium
between the emergence of new particles and the loss of particles
loosened from the surface.
In an attempt to virtually eliminate the
errors imposed by etching, the observed volume fractions were
extrapolated to zero etch times.
The resulting values agreed with
those predicted from the immiscibility dome.
For quantitative analysis
of electron micrographs, short time etches with 2% HF gave an adequate
approximation of a planar section through the glass.
Evaluation of
etch selectivity was not performed.
The results of Burnett and Douglas' work
0
indicate that
appropriate soda-lime-silica glass compositions exhibit microstructural
characteristics necessary for AR film development by acid leaching of
the phase separated glass surface.
Acid etching of heat treated
samples of these glasses revealed an interconnected microstructure in
which the size of features could be manipulated by variation of heat
VII-8
I inIn11In
iii~
JII dIIIIIuIIEIIiMIu.
IlkI
11111IIhmIhIIIIIII
_____________________________________________
treatment time and temperature.
The 2% HF etchant appeared to
selectively remove one of the phases, leaving the other in surface
relief.
HF acid vapor has been used in the past to develop low
reflection films on glass.
11
This process does not employ phase
separated glasses and was difficult to implement.
The development of a process by which a graded-index
antireflective film can be developed on soda-lime-silica by acid
leaching of the phase separated glass is desireable.
This type of
process would be easily incorporated as an additional step after
standard float glass processing of the glass.
The low cost of
processing and high optical efficiency expected from this type of film
would render it useful for application in cover plates for solar
collectors.
This research addresses the selection of a soda-lime-
silica glass composition which seems compatible with graded-index AR
film development by the process reviewed above, and further
characterization of the parameters which are important to the success
of the procedure.
VII-9
IIIIIIIN
INNO
III.
EXPERIMENTAL APPROACH
A. GENERAL APPROACH
The goal of the experimentation was to choose and characterize a
soda-lime-silica glass which exhibits the properties required to
develop a graded-index antireflective film using surface leaching
techniques.
This was attempted in two stages.
Initially, several
compositions of interest were made and evaluated on the basis of
observed microstructure and calculated viscosity.
Then a specific
glass composition was chosen for more detailed testing and
characterization.
Within the experimental section, the basic procedures employed
will first be described in detail.
Then, specific application of the
procedures to the problems of identifying an optimum glass composition
and characterizing the chosen glass will be amplified.
VII-10
B.
GLASS PROCESSING
A wide range of commercially unavailable glass compositions were
needed.
In order to provide sensitive control over glass composition
and to assure consistent processing conditions the glasses were
fabricated in the laboratory.
prototype.
Soda-lime-silica glass was chosen as a
The phase diagram is simple and well documented, and the
glasses are expected to be compatible with float glass processing.
The glasses were prepared from Fisher high purity reagent grade
anhydrous sodium carbonate, and low flouride calcium oxide; and Fisher
silicon dioxide powder (140 mesh.
The silica and sodium carbonate were
oven dried at 100 0 C overnight and the powders were weighed to ± 0.01
grams.
The powders were mixed in the desired ratios to yield 500 gram
batches, and homogenized in a V-blender for an hour.
The glass was melted in air at temperatures from 1450-15100C in a
platinum crucible and cast into a graphite mold heated to 4500C.
In
order to prevent premature setting of the molten glass, the crucible
was mounted in a high density alumina brick which provided insulation
from the ambient temperature giving adequate time to cast the glass.
The heated graphite mold served to prevent thermal shock and resulting
breakage of the casting.
To provide stress relief, the freshly cast
glass was transferred to an annealing oven where it was annealed at
450"C for two hours.
This temperature is not high enough not to induce
phase separation.
VII-11
C.
PHASE SEPARATION ANNEALING
Samples of glasses were subjected to a variety of heat treatments
in air to induce controlled phase separation.
temperature controlled to ± 3°C.
The furnace was
Various temperature-time cycles were
applied to the glasses in the range 600-650*C for 2-100 hours.
The annealed samples were fractured and characterized
microstructurally in regions well into the bulk glass to avoid the
surface "skin" of devitrified glass that was sometimes in evidence.
Some of the opalescent samples were X-rayed to confirm their amorphous
structure.
VII-12
__
- I --
iii
ilYIil iilh11
Iilh
D. SCANNING ELECTRON MICROSCOPY
In the scanning electron microscope, 1 2 the electron beam
originating from the filament is demagnified by the electromagnetic
lens system to produce a microscopic electron probe.
This probe is
rastered across the sample and the impinging electrons provide energy
for the production and emmission of many secondary electrons from the
surface.
The secondary electrons are collected, and the signal
produced is transferred to the position on the CRT screen which
corresponds to the spot on the sample from which the electrons
originated.
Since secondary electrons have a characteristically low
energy, the degree of deviation of the sample surface from the line of
sight of the detector causes a corresponding variation in intensity.
This is the image contrast mechanism which makes SEM useful for imaging
the topography of rough surfaces.
This feature, combined with the high
resolution of SEM make it suitable for examination of the phase
separated microstructure of glasses.
When high energy electrons impinge on an insulating material such
as glass, the absorbed electrons accumulate on the surface since there
is no conductive path to ground.
The resulting surface space charge
region interacts with the electron probe and interferes with secondary
electron emission leading to distortions in the image.
To avoid this
problem, a conductive coating was applied to the glass samples.
About
20 A of carbon was thermally evaporated onto the glass surface followed
by 150 A of Au(60%)- Pd(40%).
The conductive coating obscures features
smaller than 400 A, so the samples were heat treated long enough to
generate adequately large features. The minimum size of the features
VII-13
necessary for SEM observation is larger than is appropriate for good AR
film characteristics.
Observations of the coarsening of the large
scale features as a function of annealing time and temperature were
used to
predict annealing treatments which would generate the
appropriate small scale interconnected microstructure.
In the selection of a glass with which to carry on further
experimentation, the morphology of phase separation was a key issue.
The microscopy provided a rapid means of determining whether the
glasses of interest were phase separated in a discrete or
interconnected manner, or not at all.
Once the glass was chosen,
microscopy aided in the evaluation of effects of various processing
parameters such as annealing time and temperature, and etch time.
Heat treated and fractured glass samples were etched to bring the
surface into relief.
To measure the etch depth, samples were scribed
using a diamond pencil and the resulting fracture surfaces provided a
profile of the interface between the etched surface and the bulk.
Extracting quantitative information from SEM micrographs is
complicated by the geometry of image formation, instrumental image
distortion, 1 3 and the three-dimensional geometry of the
microstructure.
The SEM image is formed by the projection of the
specimen surface onto a plane.
If the specimen is tilted or the
surface is non-planar, there will be a variation of magnification
across the image.
This effect decreases at high magnifications as the
variation of height within the region of interest becomes negligible.
In addition to the image distortion due to tilting, there is an
inherent difference of magnification in the x and y directions of a few
VII-14
percent, and there is some instrumental distortion at the edge of the
The
SEM image due primarily to non-linearity in the CRT display.
geometry of projection of three dimensional regions onto a twodimensional image is mathematically complex. 14
The depth and true
shape of a feature is ambiguous, and some features can be masked by
For geometrically complicated three dimensional structures,
others.
characterization of features in terms of specific lineal distances such
as particle size, or distance between features is impractical.
With appropriately prepared samples, quantitative measurements of
bulk properties are possible.
The volume fraction of each phase (V
)
and the boundary area per unit volume of the sample (S ) are obtainable
from simple counting measurements:15
V
S
where P
P
P
p
v
.
= 2PL
is the point count obtained by superimposing a test line on
the sample, counting the number of points that lie on the remaining
phase, and dividing by the total number of points in the line and;
PL
is the number of intersections per unit length (corrected for
magnification) of test line with the interface between phases.
The S /Vv ratio for a system of discrete particles of a in a
matrix is described by:
(S )
(V ) a
VII-15
where a is the particle or phase of interest.
If these particles are
assumed to be spherical, the equivalent radius can be calculated:
3v
r a M-3S
The parameter P
]
v
a
is independent of magnification and hence
unaffected by image distortion, and the parameter PL can be accurately
determined using the average magnification across a micrograph.
To
accurately determine these quantities, one would like to approximate a
This two-dimensional section
random planar section through the sample.
would eliminate the problems of viewing a three-dimensional surface
with a two-dimensional image.
Glass samples were etched in 2% HF for times ranging from 5 to 600
seconds and prepared for SEM.
and a 450 tilt.
The images were compared at a 00 tilt
Metallographic counting measurements to determine Vv
and Sv were applied to 00 tilt micrographs.
The variation of apparent
volume fraction of remaining phase as a function of etch time was
determined for two glasses exhibiting an interconnected microstructure.
Using this information, an etch time was chosen which would approximate
a planar section through the sample by penetrating to a depth equal to
the characteristic size of the narrow dimension of the structural
features.
Interface area per unit volume (Sv ) was then determined for
the interconnected structure as a function of annealing time.
VII-16
- --
A
------- "------'--N
E.
I1II6110hlftY
MACROSCOPIC CHARACTERIZATION TECHNIQUES
In this section, techniques which employ measurement of average
macroscopic properties will be discussed.
First, sample preparation,
which is uniform for all the macroscopic averaging techniques will be
described, followed by descriptions of weight loss analysis, atomic
abosrption spectroscopy, and the BET method for surface area
determination.
1. SAMPLE PREPARATION
Glass samples which had been annealed to produce an
interconnected, phase separated microstructure were crushed using a
hammer, ground in a mortar and pestle, and the resulting powder was
sieved through two screens with a 150 pm opening and a 125 pm opening
successively.
The powders used in the experiments were approximated to
be spherical with dimensions > 125 pm and < 150pm.
2.
WEIGHT LOSS ANALYSIS
Weight loss measurements were done by determining dry weights
before and after etching of the powders.
with precision of ± 0.0001 grams was used.
solution of 2% HF by volume.
polyethylene beaker.
A Mettler analytical balance
Etching was done using a
The glass powder was placed in a
Etchant was added and the mixture vigorously
VII-17
stirred for the appointed time.
The etchant was decanted off and saved
for atomic absorption analysis, and the glass was rinsed in distilled
water several times and the mixture filtered through Teflon (TM) mesh.
The glass was dried in a vacuum oven for 8-10 hours both before and
after etching, and weighed immediately upon removal from the oven.
If the etchant preferentially removes the low silica phase, the
weight loss measurement combined with a knowledge of the volume
fractions of the two phases present and the density of the soluble
phase can be used to estimate the thickness of the etched film and the
associated etch rate (A/sec).
For a completely selective etch, the
thickness of the surface treated layer is given by:
PiAX
and the corresponding etch rate by:
t
where
Aw= weight loss upon etching
p-= density of soluble phase
A
=
calculated surface area of the sample
X = volume fraction of the soluble phase
1 = thickness of the layer removed
S= etch rate
t
=
etch time
VII-18
3.
ATOMIC ABSORPTION SPECTROSCOPY
Atomic absorption spectroscopy employs radiation directed through
the solution of interest, which causes energy transitions
characteristic of each type of molecule.
If the radiation leaving the
solution of interest is compared with that leaving the pure solvent one
can qualitatively determine the species present.
A quantitative
concentration of an element of interest can be made by comparing the
unknown solution with a standard solution made up of a known
concentration of that element in the same solvent as the unknown
solution.
Quantitative elemental analyses were done on the etchants used in
weight loss experiments.
These results permit a comparison of measured
weight loss with a weight loss calculated from atomic absorption data.
The concentrations of silica, sodium and calcium in the etchants were
determined.
The relative concentrations of these elements should give
an indication of the selectivity of the etch, and the composition of
the leachable phase.
The solutions were analyzed at the M.I.T.
Analytical Laboratory using a Perkin Elmer Atomic Absorption Unit Model
703.
4. BET METHOD FOR SURFACE AREA DETERMINATION
The BET techniques measures the surface area of a sample by
monitoring the change in thermal conductivity between the incoming and
VII-19
outgoing gas streams during adsorption and desorption cycles and
relating the change to the surface area of the sample.
The specific
surface area is obtained by dividing the BET surface area by the mass
of the sample.
The instrument used was a Quantasorb single point BET
manufactured by Quantachrome.
Krypton gas was used since the samples
have low specific surface areas.
BET surface area determinations were done on the etched powders
produced during weight loss measurements. The specific surface area
cm2
) of the powder coupled with the knowledge of etch depth (from SEM)
(c
gm
permits calculation of the equivalent spherical radius of the remaining
surface structure with the following parameters:
SBET
specific surface area of etched powder
m
= mass of a glass particle = 4/3 AR3 p
Sf
f
= surface area of film on a glass particle = mS
p BET
R
- average radius of unetched glass particle
p
- density of glass particle
t
= thickness of the etched film (by SEM)
p
Vf
ra
volume of film per etched particle - 4AR 2 t
= equivalent spherical radius of remaining phase.
This computational model assumes that all of the new surface area is
produced within an annular shell on the etched surface of the particle.
VII-20
The surface to volume ratio for the etched region defines the
equivalent spherical radius of the remaining phase (r ) as:
3Vf
S
f
-
r.
This calculated radius can be compared with the equivalent spherical
radius determined from SEM micrographs.
VII-21
F.
OPTIMUM GLASS COMPOSITION
The glass composition which was studied in detail was chosen on
the basis of viscosity and microstructure.
It was anticipated that the
most desireable compositions to work with would be those near window
glass composition because window glass materials are cost effective and
the production technology by float glass processing is well established
and would only require slight modifications to include AR film
development by a phase separation and acid leaching process.
Nine
compositions were selected in the soda-lime-silica system (see Table
I).
Each of these was made and evaluated on the basis of observed
microstructure and calculated viscosity.
1.
VISCOSITY
The viscosity of the glass should be compatible with standard
float glass processing (see Figure 4).
There have been many empirical studies of glass viscosity as a
function of composition.
Viscosities were calculated using an
empirically derived relationship:17
logl 0 T = bl + b
2
* %Na20 + b
+ b 4 * %CaO + b 5 *
+ b 7 " Na 2K 2 0
+ b9
3
* %K2 0
MgO + b 6
%ZA12 0
3
+ b 8 * %Na 2 0 * %CaO
2
* %Na 2 0 * %MgO + bl
0
* %K2 0 * %CaO
+ b 1 l * %K20 * %MgO + b 1 2 * %CaO * %MgO
+ b 1 3 * (%CaO)
2
VII-22
+ b 14 . (MgO)
2
_ _
--
-
I
NI,
which simplifies to:
log
10
TI
bl + b 2 * %Na20
+ b4
+ b 13
ZCaO + b 8 * %Na 2 0 * %CaO
*
*
(%CaO)
2
where the values of the temperature dependent constants are given in
Table II.
The viscosities were computed as a function of temperature for
each of the compositions of interest and compared with the viscosity
requirements for the float glass process.
2.
MICROSTRUCTURE
The microstructures of the appropriate glass should be phase
separated in an interconnected morphology.
Each of the compositions of
interest was subjected to phase separation heat treatment and examined
by SEM to determine the morphology of phase separation.
VII-23
G.
SUMMARY OF EXPERIMENTAL PROCEDURES
The glass compositions were mixed, cast, and then subjected to
specific temperature-time anneals in the range 600-700C for 15 minutes
Selected samples of phase
- 200 hours to induce phase separation.
separated glass were examined by SEM to verify that the behavior of the
microstructure as a function of annealing time and temperature agreed
The samples were prepared with a
qualitatively with expected behavior.
uniform etching and coating procedure.
Cast pieces of glass, large enough for several SEM samples, which
had been phase separation annealed for specific times and temperatures
were fractured into smaller pieces.
These were etched for various
lengths of time in 2% HF, diamond scribed on the fracture surface, and
prepared for SEM.
observed.
The variation of etch depth with etching time was
This provided information about the etch rate and
selectivity.
To learn more about the etch rate, etch selectivity, and the
chemistry of the phases, a few of the glasses were prepared for
macroscopic characterization techniques.
Weight loss measurements were
performed on the powders followed by atomic absorption analysis of the
etchants.
These provided information about the expected etch depth,
the selectivity of the etch and the chemistry of the phases.
The etch
depth calculated from weight loss measurements was compared with that
observed by SEM.
Finally BET surface area determinations were done on
VII-24
the powders to provide some information about the structural size of
An equivalent spherical radius calculated from BET
the features.
measurements was compared with the same parameter calculated from SEM
data.
The volume fractions of phases (V ) and surface area per unit
volume of the sample (S ) were determined by counting measurements on
SEM micrographs for selected samples.
The apparent volume fraction was
determined as a function of etch time for an interconnected
microstructure to provide an accurate determination of the volume
fractions of the phases.
The surface area per unit volume was
determined as a function of annealing time for an interconnected
microstructure.
This information was used to define a characteristic
size of the features in the porous films and to provide a basis for
extrapolating to an annealing time which yields a microstructure
suitable for AR film development.
VII-25
IV.
RESULTS
A.
IDENTIFICATION OF OPTIMUM GLASS COMPOSITION
The glass compositions summarized in Table I were heat treated for
temperature time cycles ranging from 600-6500C for 2-100 hours.
Glasses which did not seem to evidence phase separation were annealed
for long times at high temperatures to eliminate possible low
temperature diffusion limitations; and for long times at low
temperatures to indicate whether the composition lies near the boundary
of the immiscibility dome.
Glasses which evidenced discrete phase
separation at high temperatures were annealed for short times at low
temperatures to check whether this would push them into an
interconnected regime.
A lower limit of 600*C was placed on the
annealing temperature because at temperatures below this limit the
kinetics were too slow for observation of phase separation.
An upper
limit of 650 *C was set because the glasses which exhibit phase
separation are low silica, high sodium glasses with low set points.
the temperature is increased, these glasses begin to undergo serious
deformation.
An opalescent coloring generated by Rayleigh scattering from the
phases was taken as initial evidence of phase separation.
The
microstructural characterization was performed using SEM and the
results are summarized in Table III.
To assure that the compositions of glass castings matched the
starting powders, glass castings of several compositions of interest
VII-26
As
were compared to the starting powders by quantitative atomic absorption
of solutions of each one.
The powders matched the castings within
experimental error.
As can be seen in Figure 5, the experimentally determined
microstructures agree well with the boundaries between discrete and
interconnected structures proposed by Burnett & Douglas.10
The plot in
Figure 5 corresponds to an isothermal section through the soda-limesilica ternary at a temperature where the immiscibility dome is
intersected.
No visible changes in the phase separation morphology of
the glasses were observed to occur in the range 600-650*C, which
indicates that the shift of the proposed boundaries in this temperature
range is negligible.
The kinetics of phase separation, as expected,
change with composition and temperature so the annealing times required
to induce phase separation varied.
The majority of the glasses were eliminated from further
consideration on the basis of their discrete microstructures.
The
75/5/20 composition is anomalous.
Even when rapidly quenched from the
melt, the glass was opaque white.
An X-ray pattern of the glass powder
revealed that it had devitrified.
On that basis the glass was rejected
from further consideration.
The findings indicate that 80/10/10
exhibits the required interconnected phase separation morphology.
The viscosity of 80/10/10 was calculated as a function of
temperature and compared with the viscosity - temperature regime for
float glass processing as an evaluation of its compatibility with float
glass processing.
The results shown in Figure 6 indicate reasonable
compatibility.
VII-27
B.
CHARACTERISTICS OF 80/10/10 GLASS
In the following section, the results of the characterization
experiments performed on 80/10/10 are presented.
The experiments were
designed to explore the parameters which are considered important in
the development of AR films on phase separated glass.
1.
Volume fractions of separated phases
2.
Etched film depth
3.
Etch selectivity
4.
Size of microstructural features
Evaluations of:
are included herein.
1.
VOLUME FRACTIONS OF SEPARATED PHASES
Information about the volume fractions of the resistant and
leachable phases is important for evaluating the compositions of these
phases based on the tie lines, for understanding the mechanical
stability of the surface treated layers, and for interpreting the
optical characteristics of the final film.
From comparisons of micrographs taken at a 45* tilt with those
taken at a 0
tilt, Figures 7-10, it can be seen that the 00 tilt
combined with a short etch time minimizes the projection of the
protruding three-dimensional features onto the background.
Volume
fractions are measured from micrographs taken at a 00 tilt.
The
apparent volume fraction of the remaining phase is expected to increase
as a function of etch time.
This effect is due to overlap of the
features as the three-dimensional interconnected structure develops and
the result is shown quantitatively in Figures 11 and 12.
VII-28
Apparent volume fractions were corrected for the conductive
coating in the following manner (refer to Tables IV and V).
The
equivalent spherical radius was calculated from the bulk properties of
S
(as determined by SEM; see Chapter III.D.).
and V
V
The SV value was
V
determined from lightly etched samples observed at a 9* altitude.
Based on the observation of how many layers deep the film is, where one
layer is equal to the characteristic size of the narrow dimension of
the structural features, the volume fraction contribution from the
layer nearest the surface was calculated by dividing the observed
volume fraction by the number of layers which are contributing to this
value (V /# layers).
The resulting value for the volume fraction of
the top layer was corrected downward by the percentage of the material
attributable to the coating, i.e.
(300 A/ra).
Since the layers
beneath are observed through the top layer, features of the lower
layers which might otherwise contribute to the volume fraction are
masked by the coating on the first layer.
This effect is considered
approximately equal to any enhancement of the volume fraction by the
coating on lower layers.
The apparent volume fraction as a function of etch time (corrected
for coating) is plotted in Figures 11 and 12 for 650*C- 24 hours and
650*C - 60 hour anneals respectively.
At long etch times, the apparent
volume fraction levels off as the apparent volume occupied approaches
100%.
When the apparent volume fraction as a function of etch time is
extrapolated to zero etch time using the shorter etch time data where
the functional dependence is approximately linear, the volume fraction
of insoluble phase appears to be between 30 and 40%.
VII-29
2.
ETCHED FILM THICKNESS
The film thickness is an important parameter for optimizing the
optical properties of the AR film.
An understanding of the process of
film development as the characteristic size of the microstructure and
the length of etching time vary will be particularly useful when films
are developed on the smaller scale, phase separated glasses necessary
for AR film development.
The depth of the etched film was measured by SEM for a series of
etches on the 650C - 24 hour and 650C - 60 hour annealed glasses.
The micrographs in Figures 13-16 illustrate the increase of film
thickness with etch time anticipated when the etchant selectively
removes one of the phases.
From a plot of film thickness as a function
of etch time for the two glasses (Figure 17), it can be seen that the
etch depth has approximately the same functional dependance on etch
time for both of the glasses.
The depth of the etched film seems to
level off at long etch times.
The film thickness on the 24 hour anneal
appears to be slightly less than the film thickness on the 60 hour
anneal under the same etch conditions.
The porous structure was
observed to penetrate up to 10 layers into the surface indicating a
high degree of mechanical stability of the surface treated film on this
particular glass (the 650C - 60 hour anneal).
To further explore the issue of etched film thickness, weight loss
measurements were made on the 650C - 24 hour glass for a 15 second
etch and a 90 second etch.
The expected film thickness and the
expected etch rate were calculated from the weight loss data and a
VII-30
presumed volume fraction of 70% and density of 2.5 gns/cm 3 for the
soluble phase.
The film depth calculated by weight loss and the
associated etch rate are compared with the film depth observed by SEM
in Table VI.
The weight loss measurements indicate that the etch rate
remains constant with etch time predicting a linear increase of film
thickness with etch time.
The SEM results indicate that the initial
film development behaves linearly with etch time, as seen from the
agreement between SEM and weight loss for a 15 second etch.
As the
etch time increases, however, the actual rate of film development falls
off.
At 90 seconds, the weight loss measurement predicts a film twice
as deep as the observed film.
The results indicate that the film development initially follows
the model of an etch dissolving one phase of a phase separated glass.
With longer times, the discrepancy between predicted (wt loss) and
observed film thickness indicates that the outer film boundary does not
coincide with the original glass surface.
The 2% HF etch is probably
not completely selective and the outer layers of the film are not
observed because they either dissolved completely or become
mechanically unstable with etching.
VII-31
3.
ETCH SELECTIVITY
Evaluation of the etch selectivity is important because the
quantitative interpretation of the micrographs requires specific
After
assumptions regarding the selectivity of the etching process.
etching, the more resistant phase of a two-phase interconnected
microstructure remains.
The etchant used on the glass powders for weight loss measurements
of the 650 - 24 hour anneal was analyzed quantitatively by atomic
absorption spectroscopy for silicon, sodium and calcium.
Calcium
determinations were subject to inconsistancies attributable to the
aging process of the solutions.
The soda (Na0 2 ) to silica (Si0 2) ratio was calculated for an
80/10/10 composition and for a 75/12.5/12.5 composition.
The
75/12.5/12.5 glass was chosen for comparison based on the position of
the tie line endpoint on the cross section of the immiscibility dome in
the region lNa 20-lCa0-SiO (see Figure 3) which indicates that the
expected composition of the low silica phase at 650*C is 75/12.5/12.5.
This interpolation of the low silica phase composition is based on the
assumption that the high silica phase is almost pure silica.
From the data in Table VII, it is apparent that the soda (Na2 0) to
silica (Si0 2 ) ratio in the soluble phase of the glass under
consideration agrees quite well with that expected in a 75/12.5/12.5
composition.
The decrease in the soda to silica ratio with etch time
reflects an increasing silica contribution from the more resistant
phase.
VII-32
4.
SIZE OF MICROSTRUCTURAL FEATURES
The size of the features in the phase separated interconnected
structure is important to facilitate the selection of an annealing
treatment which will yield a glass microstructure well suited for AR
film development.
The equivalent radius (ra ) calculated from the
specific surface area (Sv) of the remaining phase was chosen as a
guage, since this quantity is easily derived from SEM and BET data.
The surface area per unit volume (Sv) was determined for samples
which had undergone 650*C - 24 hour, 48 hour, and 60 hour anneals.
volume fraction for zero etch time was used in the calculation.
The
The
S determinations were all performed on samples etched for 10 seconds.
v
Variation of feature size will affect the morphology of the layer
penetrated by a 10 second etch.
Ideally, when comparing S
values of a
variety of samples, one would want an etch time for each sample which
exposed exactly one layer of the structure.
However, this is
experimentally complicated at the relatively short etch times involved.
The technique employed here using a constant etch time limits rigorous
determination of the functional dependence of the size of features on
annealing time.
The calculated equivalent spherical radii were each
adjusted down by 300 A to account for the conductive coating.
results are tabulated in Table VIII.
versus log tann is shown in Figure 18.
The
A plot of log ra (corrected)
The slope of about 1/2 is close
to the value of 1/3 reported in the literature and the difference does
VII-33
not justify proposing a kinetic mechanism different from those
presented in the literature.
Such a plot is useful for predicting
annealing times which will yield a microstructure appropriate for AR
film development.
To develop a microstructure with an equivalent
spherical diameter from 200 to 400 A (corrected for coating), these
results suggest annealing times between 1 minute and 30 minutes at
650°C.
Equivalent spherical radii were calculated from the BET specific
surface area data for the 6500C - 25 hour anneal using the SEM measured
film thicknesses.
The results are tabulated in Table IX.
The
equivalent spherical radius is constant with etch time, indicating that
the average size of the structure does not change appreciably within
the layer.
This result indicates that the 2% HF etch does not have a
major effect on the principal dimensions of the acid resistant phase.
The equivalent spherical radius determined by BET agrees quite well
with that determined by SEM corrected for the conductive coating
thickness.
VII-34
V.
DISCUSSION
A soda-lime-silica glass composition with properties amenable to
AR film development by acid leaching of the surface was sought.
Heat
treatment of the desired glass should yield a two phase interconnected
microstructure.
An understanding of the coarsening of the features as
a function of annealing time and temperature is important for the
selection of an annealing treatment which will generate a two phase
interconnected microstructure with average feature size between 100400 A.
Another requirement is that of an etchant which will
preferentially dissolve one of the phases, leaving behind the porous
skeletal network characteristic of an AR film.
The characteristic
volume fraction of the phases and the etched film depth of the surface
treated layer are also parameters important to AR film development.
The compositon 80/10/10 was identified as suitable.
That this
glass exhibits the required two phase interconnected microstructure was
confirmed by direct observation by SEM.
The phase separated structure
was observed to coarsen with annealing time as expected.
The required
100-400 A microstructural diameter should be achieved with 650*C
anneals ranging from 1 minute to 30 minutes.
SEM observations of the
increasing depth and complexity of the surface treated film as a
function of etch time, and the mechanical stability of the skeletal
surface film for film thicknesses in excess of 1 pm confirmed the
interconnectivity of the structure.
A preliminary calculation of the
viscosity of the 80/10/10 glass from an empirically determined
relationship
17
indicated compatibility with float glass processing.
VII-35
The characteristics of the selectivily etched film which were
studied are the volume fraction of the remaining phase, etched film
thickness, etch selectivity, and size of microstructural features.
The volume fraction of the remaining phase was found by varying
the etch time and determining the apparent volume fraction of the
remaining phase at each etch time from counting measurements on SEM
micrographs.
As expected, the apparent volume fraction remaining
increases with etch time because of the projection of the threedimensional features onto a two-dimensional image.
The apparent volume
fraction as a function of etch time was extrapolated to zero etch time
for 650*C - 24 hour and 650*C - 60 hour anneals.
(Figures 11 and 12.)
The resulting volume fraction determinations of 30-35% high silica
minor phase are greater by 10-15% than those derived from the reported
phase diagram.10
The discrepancy may be due to a non-linear dependance
of apparent volume fraction on etch time, rendering the linear
approximation inexact.
An alternative possibility is that the tie line
lies slightly askew of the estimated high silicon (>98%) minor phase
endpoint.
As discussed in Chapter II (see Figures 2 and 3) the form of
the immiscibility dome in the high silica region is uncertain.
If
skewed toward either a higher soda or a higher lime composition in the
minor phase (e.g. 95% Si0 2 ), the tie lines superimposed on the
miscibility dome of Figure 2 predict an increase in the volume fraction
of the minor phase.
The position of the tie line and the true volume
fractions of the two phases, are issues that should be investigated in
future research efforts.
VII-36
The etched film thickness was observed to increase with etching
time.
Long etching times produced film depths up to 1 pa.
This
implies a high degree of mechanical stability of the skeletal
structure.
For short (650*C - 24 hour) and long (650*C - 60 hour)
annealing times, the film thickness as a function of etch time curves
are nearly identical.
The film thickness appears slightly deeper for
the 650*C - 60 hour anneal.
This may be attributed to th
lower
surface area of the larger features in this sample, which leads to a
lower dissolution rate of the more resistant phase.
Weight loss measurements predict a larger film thickness than that
observed by SEM with the discrepancy increasing with etch time.
Perhaps both phases are being dissolved, with the dissolution rate of
the major phase much more rapid than that of the minor phase.
It is
also possible that some of the skeletal structure may be breaking away
from the top layers of the surface.
These two effects may combine.
If
there is a finite dissolution rate of the more resistant phase, then
the features on the surface of the film which are exposed longer to the
etchant, would be mechanically weakened by the corrosive effect of the
etchant.
As films with smaller features are investigated, this effect
would be more pronounced.
Atomic absorption analysis indicates a high degree of etch
selectivity based on the assumption that one end of the tie line
extends to an almost pure silica composition.
The NaO/SiO 2 ratio
decreases slightly with etch time indicating a finite etching rate of
VII-37
the more resistant high silica phase.
As the etched film deepens, the
exposed surface area of this phase increases so the percentage of
excess silicon is higher as etch time is prolonged.
The dissolution of
the high silica phase appears small (by AA) so the discrepancy between
the film depth measured by SEM and that calculated from weight loss
measurements can be attributed to the longer exposure of the outer
layers of the surface to the etchant and consequential mechanical
weakening which causes some of the surface treated film to break off.
The higher than expected volume fraction of the minor phase (by SEM)
indicates the possibility of the tie line extending to a higher sodium
content major phase than suggested in the literature.
If this is the
case the Na20/SiO 2 ratio is lower than expected and the etch less
selective than it appears.
The relative size of the features in the films was determined from
calculations using SEM and BET data.
Good agreement between these
analyses indicates their validity for use as a gauge of relative
feature sizes.
important.
The size of the features in an optimized AR film is
Techniques that may be implemented in future research for
characterization of these small scale features include the BET
technique, high resolution microscopy using the transmission electron
microscope, and small angle X-ray scattering.
VII-38
VI.
CONCLUSION
A soda-lime silica glass composition, heat treatments, and etching
procedure were identified which are compatible with AR film development
by acid leaching of the phase separated glass.
The calculated
viscosity temperature characteristics of the glass meet the
requirements for float glass processing.
An 80/10/10 glass phase-separates to a two-phase interconnected
structure upon heat treatment at 650*C.
Observation of the coarsening
of the microstructural features with time indicates that an annealing
time between 1 minute and 30 minutes will yield the desired 100-400 A
diameter structure.
The volume fraction of the acid resistant, high
silica phase was found to be 35% at this annealing temperature.
A 2% HF etchant exhibited a high degree of selectivity based on
chemical analyses and microstructural observations.
The resulting
porous films were mechanically stable to thicknesses > 1 pm and the
principal dimensions of the resistant phase were not affected
significantly by this etch.
The etchant does attack the high silica
phase to a minor extent, and a higher degree of selectivity may be
needed for an optimized process.
VII-39
Acknowledgements
Many thanks to Dr. John S. Haggerty and Dr. Stephen C. Danforth
for their guidance in planning the experiments, and encouragement
through the slow times and the fast times.
I am thankful to Colin Kerwin and Dorshka Wylie for their help
with glass processing.
The support of the U. S. Department of Energy for funding this
work under Contract Number ER-78-8-02-5003 is gratefully acknowledged.
Above all, I am grateful to the Lord and His people for their love
and support during this time.
VII-40
Bibliography
1.
Minot, M. J., "Single Layer, Gradient Refractive Index
Antireflection Films Effective from 0.35 to 2.5 p", J. Opt. Soc.
Am., 66, 515 (1976).
2.
Iqbal, A., "Determination of Surface Chemistry of Graded-Index
Antireflection Films on Glass", S. M. Thesis, Massachusetts
Institute of Technology (1981).
3.
Uhlmann, D. R., and Kolbeck, A. G., "Phase Separation and the
Revolution in Concepts of Glass Structure", Phys. Chem. Glasses,
17, 146 (1976).
4.
James, P. F., "Review Liquid-Phase Separation in Glass-Forming
Systems", J. Mater. Sci., 10, 1802 (1975).
5.
Cahn, J. W., and Charles, R. J.,
"The Initial Stages of Phase
separation in glasses, "Phys. Chem. Glasses, 6, 181 (1965).
6. Srinivasan, G. R., Tweer, I., Macedo, P. B., Sarkar, A., and
Haller, W., "Phase Separation in Si0 2 -B20 3-Na20 System", J. NonCryst. Solids, 6, 221 (1971).
7.
Haller, W., "Rearrangement Kinetics of the Liquid-Liquid
Microphases in Alkali Borosilicate Melts", J. Chem. Phys., 42,
686 (1965).
8.
Moriya, Y., Warrington, D. H., and Douglas, R. W., "A Study of
Metastable Liquid-Liquid Immiscibility in Some Binary and Ternary
Alkali Silicate Glasses", Phys. Chem. Glasses, 8, 19 (1967).
9.
Zarzycki, J., and Naudin, F., "Spinodal Decomposition in the
B 20 3-PbO-A1 20 3 System", J. Non-Cryst. Solids, 1, 215 (1969).
10.
Burnett, D. G., and Douglas, R. W., "Liquid-Liquid Phase
Separation in the Soda-Line-Silica System", Phys. Chem. Glasses,
11, 125 (1970).
11.
Nicoll, F. H., and Williams, F. E., "Properties of Low Reflection
Films Produced by the Action of Hydroflouric Acid Vapor",
J. Opt. Soc. Am., 6, 434 (1942).
12.
Goldstein, J. I. and Yakowitz, H., et al, Proctical Scanning
Electron Microscopy, Plenum Press, New York, 1975.
13.
Hilliard, J. E., "Quantitative Analysis of Scanning Electron
Micrographs", J. Microscopy, 95, 45 (1972).
VII-41
Bibliography
14.
Underwood, E. E., "The Stereology of Projected Images",
J. Microscopy, 95, 25 (1972).
15.
Underwood, E. E., "Applications of Quantitative Metallography", in
Metals Handbook Vol. 8 Metallography, Structures, and Phase
Diagrams, 8th ed., American Society for Metals, 8, 37 (1973).
16.
Narayanswamy, 0. S., "A One-Dimensional Model of Stretching Float
Glass", J. Am. Ceram. Soc., 60, 1 (1977).
17.
Lyon, K. C., "Prediction of the Viscosities of Soda-Lime-Silica
Glasses", J. Res. Nat. Bur. Stand. A, 78A 497 (1974).
NO.SiO,
Figure 1.
\coo.asio
Morphology of phase separation in the soda-lime-silica
10
system. After Burnett and Douglas.
VII-43
CaO S1O.
S/
Na,O-SIO, 40
Figure 2.
30
20
line
10
S10,
Immiscibility in the soda-lime-silica system.lu
IAa
1200
1000
TmOC
800.
600
-a
|
SlO2
Figure 3.
90
Mol olo SO10
Cross section of the immiscibility dome through the psuedowhere o = experimental
binary section (lNa20-lCaO-SiOz),
values of Tm, x = values deduced by interpolation,
A = annealing temperature.10
ryVT
V
.
12T
11
10
9
8
0 7
O
3
SIII
7.0
Figure 4.
9.0
8.0
1/T x 10'"
10.0
(OK)
11.0
versus I/T for the float glass process.o
Plot of log on
0
VII-45
12.0
Si
sk
S
.3' *,8
14
Ne1CO.SsO, /
.\o.Sio,
Figure 5. Observed morphology of phase separation in the soda-lime silica
system.
VII-46
12j
/
10+
st
8t
/
06
7+
0
St
St
4+
x = 80/10/10
o * float glass
3t
7.0
Figure 6.
8.0
1/T
x
10.0
g90
10** (OK)
11.0
12.0
Comparison between the calculated viscosity of 80/10/10
glass and the standard viscosity of the float glass process.
VII-47
Figure 7. Micrograph of 80/10/10 - 650'C - 60 hour
anneal, etched 10 seconds; taken at a 45' tilt.
Magnification: x 51,000.
Figure 9. Micrograph of 80/10/10 - 650"C - 60 hour
anneal, etched 30 seconds; taken at a 45' tilt.
Magni fication: x 50,000.
Figure 8. Micrograph of 80/10/10 - 650C - 60 hour
anneal, etched 10 seconds; taken at a 0' tilt.
Magnification: x 50,000.
Micrologaph of 80/10/10 - 650*C - 60) h ,si
Figuie 10.
;t.noeal, ecched 30 s,conds; tkn at a 0' tilt.
x 50.000.
Magn f icat ion:
90
80
s
a
IC
C
C
S60
0-
250
c40
20-
10
Figure
11.
20
30
40
Etch Time (sec.)
50
60
Apparent volume fraction as a function of etch time for
an 80/10/10 glass annealed at 650C for 24 hours.
VII-49
90
0
80
S60E
*
C
E
50
L7
S50
E
o
20
a
a30
10
20
30
40
.50
60
70
10
20
30
4'0
.5
6'0
70
20
0
Etch Time (sec.)
Figure 12.
Apparent volume fraction as a function of etch time for
an 80/10/10 glass annealed at 650°C for 60 hours.
VII-50
Figure 13.
Figure 15.
SEM micrograph showing film thickness.
Sample annealed at 650C for 60 hours,
etched 5 seconds.
Magnification: x 25,000.
SEM micrograph showing film thickness.
Sample annealed at 650'C fur 60 hours,
etched 15 seconds.
Magnification: x 20,000.
Figure 14.
SEM micrograph showing film thickness.
Sample annealed at 650*C for 60 hours,
etched 10 seconds.
Magnification: x 25,000.
Figute 16.
SEM micrograph showing film thickness.
Sample annealed at 650"C for 60 houts,
etched 60 seconds.
x 20,000.
Magnification:
90
80
S
0
C
E 60
50
oa
0
CL
c 40
_e
30
20-
10
Figure 11.
20
30
40
Etch Time (sec.)
50
60
Apparent volume fraction as a function of etch time for
an 80/10/10 glass annealed at 650'C for 24 hours.
VII-52
.. --:"F~'.-~'I
__
3.34
3.32
3.30
3.28
3.26
C)
3.24
3.22
3.20
3.18-
3.16-
1.28
1.38
1.48
1.58
log t
1.68
1.78
1.88
8 nn
Figure 18. -Characteristic microstrucutural dimension (equivalent
radius from SEM) of 80/10/10 glass annealed at 650C
for various times.
VII-53
TABLE I
Soda-Lime-Silica Glass
Compositions of Interest (wt%)
Composition #
% Si0z
% NaO
1
80
10
10
2
78
11
11
3
75
12.5
12.5
4
70
15
15
5
80
12
8
6
80
15
5
7
75
20
5
8
75
5
20
9
70
10
20
VII-54
% CaO
TaBLE I I
Empirical constant.; used to calculate the
viscosity (log 10 n) of silca
glasses between 600-1300'C.
tn
nb
Symbol
Component
600"
bl
intercept
11.7404
b2
Na2 0
-1.4149
4
3.4391
CaO
700'
8.9040
L00'O
7.2752
900"
1000'
1100'
1200'
1300'
6.1155
5.2559
4.5912
4.0693
3.6486
-0.9424 -0.8101 -0.7182 -0.6535 -0.6051 -0.5700 -0.5436
2.0773
1.4369
1.0329
0.7104
0.5395
0.3738
0.2385
b8
Na 2 0 * CaO
-1.1861 -0.9619 -0.7368 -0.5912 -0.4816 -0.4076 -0.3447 -0.2936
b13
(CaO)
2
-0.2576 -0.1791 -0.2320 -0.2400 -0.2013 -0.2164 -0.1995 -0.1817
TABLE III
Summary of phase separated morphologies
observed for compositions of interest.
Composition #
Composition
Morphology
1
80/10/10
interconnected
2
78/11/11
discrete
3
75/12.5/12.5
discrete
4
70/15/15
discrete
5
80/12/8
discrete
6
80/15/5
discrete
7
75/20/5
discrete
8
75/5/20
inconclusive
9
70/10/20
inconclusive
VII-56
TABLE IV
Apparent volume fraction of acid resistant phase (V v ) and film
thickness for 80/10/10 glass samples annealed at 650°C for 24 hours.
Etch Time
Vv
Including
Coating
(seconds)
(X)
Vv
Corrected for Coating
Film
Number of
Thickness
Layers
(M)
(A)
1-1/2
10
900
20
1300
2
30
1600
2-1/2
45
2000
3
TABLE V
Apparent volume fraction of acid resistant phase (V v ) and film
thickness for 80/10/10 glass samples annealed at 650*C for 60 hours.
Etch Time
(seconds)
Vv
Including
Vv
Corrected for Coating
Coating
(X)
(%)
Film
Thickness
Number of
Layers
(A)
1/2
5
600
10
1000
1
15
1500
1-1/2
30
2000
2
60
3000
3
600
10000
10
VII-57
TABLE VI
Comparison of measured film thickness (SEM) with calculated
film thickness (wt. loss) for 80/10/10 glass samples
annealed at 650*C for 24 hours.
Etch Rate
Calculated Film
Thickness
(seconds)
Measured Film
Thickness
SEM (A)
15
1000
1340
89
90
3000
7660
85
Etch Time
(wt. loss) (A)
VII-58
(wt. loss)
A/sec
TABLE VII
Soda (Na2 0) to Silica (Si0 2 ) ratio in the acid soluble phase.
Method
Na2 0/Si02
calculated for pure
80/10/10 composition
0.125
calculated for pure
75/12.5/12.5 composition
0.167
AA determination
15 sec etch of
650°C-24 hour anneal
0.165
AA determination
90 sec etch of
650"C-24 hour anneal
0.154
VII-59
TABLE VIII
Surface area per unit volume of sample (S
)
and equivalent spherical radius (by SEM) in phase
separated 80/10/10 glass as a function of annealing time at 650*C.
ann
(including coating) (corrected for coating)
(hours)
(cm- 1)
(A)
(A)
6.06 x 104
1734
1434
4.49 x 104
2340
2040
4.10 x 104
2560
2260
VII-60
TABLE IX
BET surface areas and calculated equivalent spherical radii
for 80/10/10 glass annealed at 650*C for 24 hours;
etching time variable.
Etch Time
Measured Film
SBET
Thickness (SEM)
(sec)
I
(A)
(m2 /gm)
(A)
15
1000
0.0585
1220
90
3000
0.130
1230
*
VII-61
VIII.
SUMMARY
This research program had the objective of defining glass compositions
and process conditions by which broad band graded-index anti-reflective
films could be developed on glass surfaces within the restraints imposed by
the float glass process.
To accomplish this, we have conducted research on
the microstructure and phase chemistry of the phase separated glasses from
which the porous films are formed and related this information with process
kinetics to the characteristics of the films.
New optical diagnostic
procedures were developed that permit index gradients to be defined from
reflectivity measurements.
The mechanical properties of processed glasses
were investigated to determine whether the porous surface films on phase
separated glasses would have any adverse effect on long term strengths and
failure probabilities.
Based on a mechanistic understanding of the
processes involved, glass compositions and processing conditions were
defined that are compatible with the float glass process.
The research
program successfully accomplished all technical objectives and provides a
sound basis for development of a commercial process.
Our investigation of the mechanisms and kinetics of graded-index film
formation processes supported many of the basic features included in
published descriptions; but,
it was also shown that the process is more
complex than presumed under nearly optimum process conditions.
A
complicating feature was an unanticipated, major compositional gradient that
extended at least 100 pn into the glass.
VIII-1
This necessitated precise
definition of positions for corroborative chemical, microstructural,
specific surface area, optical and weight loss analyses.
The film formation process was demonstrated to depend on the existance
of a phase separated microstructure.
Optically optimum films were formed on
glasses having characteristic microstructural dimensions ranging from 75 to
100 A.
The selective removal of one phase from the surface of the phase
separated glass was demonstrated chemically with substantially longer than
optimum phase separation annealing times.
With near optimum annealing
schedules, no selectivity was demonstrated by the etch/leach acid treatment
either by analysis of the acid solutions or by direct analysis of the
surface films by secondary ion mass spectrometry (SIMS) or by Auger
techniques.
These observations combined with weight loss and film thickness
measurements showed that the etch/leach solution dissolved both phases such
that the microstructural scale, the etch/leach selectivity and the
dissolution rate must be matched to produce a mechanically stable surface
film.
The absense of apparent selectivity by SIMS and Auger analyses may
result from reprecipitation of the dissolved salts in the porous surface
film or from the detected signal originating from an unusually large volume
within the porous films.
Although preferential dissolution of one phase was
not demonstrated chemically for optimum annealing times, it is strongly
inferred by microstructural and specific surface area analyses.
The
characteristic dimensions and volume fractions of the films' microstructures
essentially match those of the phase separated glasses.
Chemical polishing and etch/leaching dissolution kinetics were
measured.
The distance from the original surface was an important,
VIII-2
It was
unanticipated factor that was attributed to chemical gradients.
anticipated that diffusion into and out of the porous film would ultimately
emerge as the rate controlling step in the etch/leach process.
This never
occurred; the weight loss rate remained constant for all time scales.
Curiously,
the actual etch/leach rate depended on the depth to which the
chemical polish had penitrated.
The etch/leach process behaved as if the
initial surface composition defined the rate.
Although the kinetics were
not fully understood mechanistically, they were defined, were reproducible
and were controllable.
The microstructural features were characterized by four techniques
since the microstructural scale approached the resolution limits of the
instrumentation and was clearly in a range that is subject to erronious
interpretation because of artifacts.
Direct observations were made by
transmission electron microscopy (TEM) and scanning electron microscopy
(SEM) of unetched and etched/leached samples.
Indirect characterizations
were made by TEM examination of surface replicas and by small angle X-ray
scattering (SAXS).
The microstructural characteristics indicated by all
four techniques agreed with one another for long annealing schedules.
With
nearly optimumn heat treatments, there was reasonable agreement only between
SAXS and TEM of etched/leached
thinned foils.
The SEM and replica TEM
microscopy results showed that even with highly optimized coating
procedures, the techniques were only reliable for microstructural scales
above 250 and 300 A respectively.
TEM characterization of unetched foils is
considered most reliable but the small differences in molecular weights gave
no phase contrast.
TEM of etched/leached foils should be considered suspect
VIII-3
because the contrast results from topographical features that penitrate to
uncontrolled, varying extents into the foils.
It was concluded that SAXS
provided the most general survey technique for monitoring the phase
separation process and that SEM microscopy of etched/leached surfaces was
suitable for studying over-aged structures and for measuring the film
thicknesses.
Near optimum microstructural dimensions were inferred by
extrapolations from over-aged samples.
The dimensional information about
porous AR films provided by BET specific surface area measurements combined
with SEM thickness measurements is probably adequate for monitoring
processing.
None of these characterization techniques individually or in
combination yielded sufficient information to permit the index (porosity)
gradient through the films' thickness to be described.
Also, there were no
general procedures for calculating reflectivities for arbitrarily shaped
index profiles.
Mathematical procedures were developed that permitted
reflectivities to be calculated for TE and TM waves as a functon of
wavelength and angle of incidence for any presumed index gradient.
Also,
for the first time, procedures were developed by which the index gradient
could be defined approximately from reflectivity measurements.
Using
published reflectivity data, we calculated an AR film thickness of 1.045
for optimized films on Pyrex .
.m
This compares with 0.21 to 0.42 pm reported
from measurements made by replica microscopy.
Both limits are within the
range of thickness observed in this program.
Interestingly the optically
determined thickness agrees with the thickness determined by weight loss
better than that determined by SEM.
This may be another indication that the
VIII-4
direct observation techniques employing a coating step are not reliable for
The reflectivity
characterizing the smaller scale microstructural features.
data used in these calculations was not reported in
calculation procedures particularly reliable;
thus,
resolve this issue without further experimentation.
a manner that made the
not possible to
it is
We believe that this
analysis will emerge as an important diagnostic procedure.
Biaxial strength measurements were made to subject the samples to a
stress field that decayed to nearly zero at all free edges.
This was done
to avoid spurious effects and provide a clear measure of the effect the AR
films and process steps have on sample strength.
Dry strength and wet
strength as a function of strain rate were used to measure the flaw size and
static fatigue resistance (N).
Fracture toughness (KIC) was also measured.
Samples were evaluated at all steps in
the optimum processing history as
well as with non optimum process conditions.
*
Heat treatment and chemical polishing caused the strengths of the
samples to increase, apparently because subcritical flaws were blunted.
This effect is expected to be lost with normal handling and exposures.
Otherwise, the strength characteristics were not markedly effected by the AR
film forming process.
We feared that the combination of the. phase separated
structure containing a relatively soluble phase and the porous surface film
would cause the static fatigue characteristics to be degraded.
observed.
The KIC value was slightly reduced by the process.
This was not
This may have
a slight adverse effect but it should not be significant.
The combined results of the studies with the model glass (Pyrex
) were
used to define a composition and process conditions by which graded-index AR
.
V
VIII-5
films could be produced on glass that can be formed by the float glass
process.
The phase separation region in the Na 2 0/CaO/Si0
2
system was
investigated in detail because these are the lowest cost constituents and
they are the major components in typical window glass.
consisting of 10 wt.% Na20, 10 wt.% CaO and 80 wt.% Si0
having suitable characteristics.
A composition
2
was identified as
Its viscosity - temperature relationship
coincides almost exactly with present commercial practice.
Interconnected
phase separated structures having correct dimensions can be generated with
heat treatment times (4 to 7 minutes) and temperatures (- 650C) that are
easily integrated into the glass manufacturing process.
For instance this
annealing cycle will relieve stress but will not cause samples to deform
viscously under their own weight.
Selective dissolution of one phase was
demonstrated with HF acid; it appears appropriate as an initial candidate
for the etch/leach process.
The research program accomplished all of its major technical
objectives, defined practical limits for various characterization techniques
that had caused spurious results in the reported literature and developed
new analytical techniques.
All of the essential issues have been resolved
for demonstrating process feasibility.
We did not complete the iterative
optimization of optical characteristics
and process variables but this
research is straight forward and the results have a high probability of
yielding a commercially viabile process.
VIII-6