Rational Bureau of Standard

Library, E-Ol Admin. Bidg.

JUL 4 19?0 NBS TECHNICAL NOTE 531

ARPA-NBS Program

of Research on High

Temperature

Materials and Laser

Materials

Reporting Period

July 1 to December 31, 1969
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NBS TECHNICAL NOTE 531

ISSUED JUNE 1970

Nat. Bur. Stand. (U.S.), Tech. Note 531,75 pages (June 1970)

CODEN: NBTNA

ARPA-NBS Program of Research

on High Temperature Materials

and Laser Materials

Reporting Period

July 1 to December 31, 1969

Edited by A. D. Franklin and H. S. Bennett

Inorganic Materials Division

Institute for Materials Research

National Bureau of Standards

Washington, D.C. 20234

Supported by the

Advanced Research Projects Agency

of the Department of Defense

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C, 20402.

(Order by SD Catalog No. C13.46:531). Price 70 cents.
TABLE OF CONTENTS

Page

1. Introduction 1

2. Objectives 1

3. High Temperature Materials Program 2

3.1 Objectives in High Temperature Materials. ... 2

3.2 Project Summaries in High Temperature

Materials 3

3.2.1. Diffusion in Oxides 3

3.2.1.1. Measurement of Diffusion

Coefficients in Oxides 3

A. L. Dragoo

3.2.1.2. Crystal Growth from Vapor. ... 4

H. S. Parker and C. A. Harding

3.2.2. Properties of Refractory Borides . ... 7

3.2.2.1. Electronic Structure of

Refractory Hard Metals 7

J. R. Cuthill, L. H. Bennett,

G. C. Carter, and A. J.

McAlister

3.2.2.2. Reactivity or Borides 11

J. J. Ritter and T. D. Coyle

3.2.3. High Temperature Metals 11

3.2.3.1. Optical Constants of Titanium. . 11

A. J. Melmed

3.2.3-2. High Temperature Creep

in Metals 12

A. A. 0. Rukwied, W. A.

Willard, and D. E. Harne

3.2.4. Polymers 15

3.2.4.1. The Volatilization and

Decomposition of Materials ... 15

L. A. Wall, S. Straus, and

G. Mattamal

4. Laser Materials Program 16

4.1. Introduction to Laser Materials 16

4.2. Objectives of Laser Materials 16

II
Table of Contents (continued)

Page

4.3. Overall Summary of Projects on Laser

Materials 18

4.3-1. Characterization of Laser Materials. . 18

4.3.2. Damage to Laser Materials 18

4.3.3. Degradation of Laser Materials .... 19

4.4. Individual Project Summaries 20

4.4.1. Characterization of Laser Materials. . 20

4.4.1.1. Physical and Chemical Properties of Laser Materials ... 20

G. W. Cleek and R. M. Waxier

4.4.1.2. Liquid-Liquid Phase Separation in a Laser Glass 31

J. H. Simmons and W. Haller

4.4.1.3. An X-ray Transmission

Method for Examining

Ruby Laser Rods 32

E. N. Farabaugh and

F. A. Mauer

4.4.2. Damage to Laser Materials 37

4.4.2.1. Laser-Induced Damage Studies . 37

N. N. Winogradoff, A. H.

Neill, Jr., and J. Mitchell

in collaboration with W.

Haller, G. Cleek and R. Waxier

4.4.2.2. Inclusions in Laser Materials . 45

Herbert S. Bennett

Appendix - Small Angle Scattering from Nd-doped Laser Glass . 53

4.4.3. Degradation of Laser Materials ... 61

4.4.3.1. Crystal Defect Studies on

Laser Materials 61

R. F. Blunt, T. Chang, M. I.

Cohen, and T. Tsang

III
ARPA-NBS PROGRAM OF RESEARCH ON

HIGH TEMPERATURE MATERIALS AND LASER MATERIALS

Work Performed at the National Bureau of Standards

Supported by the Advanced Research Projects Agency,

Department of Defense

Reporting Period 1 July to 31 Dec., 1969

High Temperature Materials Reports Edited by A. D. Franklin

Laser Materials Reports Edited by Herbert S. Bennett

Brief reviews are given of work performed

during the period July 1 to December 31 3 1969,

on a number of projects concerned with High

Temperature Materials and with Laser Materials.

Under the High Temperature Materials heading,

topics include diffusion of oxygen in oxides,

growth of AI2O3 crystals by chemical vapor deposition, the electronic structure of transition

metal borides and related compounds, the optical

constants of titanium, high temperature creep in

copper, and the mechanism of volatilization of

polymers and long-chain compounds . Work on Laser

Materials includes measurement of bulk optical

and elastic properties of laser materials, a

study of the "orange" degradation of ruby,

measurements of sub-crystal misalignment in ruby,

damage in glass induced by high-energy laser pulses,

chemical analyses for ruby and Nd-doped laser

glasses, and preliminary studies on detection of

submicroscopic inhomogeneities in glass.

Key words: Band structure, chemical analysis,

copper, creep, crystal defects, crystal growth,

diffusion, evaporation, glass, high temperature

materials, inhomogeneities in glass, laser

damage, laser glass, lasers, mass transport,

materials properties, metal properties, optical

properties, opto-elastic properties, oxides,

polymers, ruby, titanium and transition.

IV
1. INTRODUCTION

The National Bureau of Standards, with the support of

the Advanced Research Projects Agency (Office of Materials

Sciences) of the Department of Defense, is carrying out a program of research on High Temperature and Laser Materials.

This program includes projects on the preparation and characterization of research-worthy materials; on the development

of measurement techniques for and on the acquisition of critically needed data; and on the basic mechanisms controlling

properties contributing to or limiting the use of materials

at high temperatures. A summary of the results achieved in

the period July 1 to December 31 a 1969, is given here.

2. OBJECTIVES

The development of Defense technology often is limited

by the properties of the available materials. When such a limitation is met, It generates a search for ways to improve

the properties of existing materials or to find new and

better ones. Such a search is like a military campaign - objectives must be set and a strategy devised to reach the

objectives. Thus the devising of the strategy guiding the

search for a new or improved material is a key part of DoD

operations. If DoD is to continue to meet its commitments,

it cannot neglect the development now of adequate strategies

to meet future but foreseeable problems.

In order to devise a successful strategy, a great deal

of background information about the behavior of materials

in a given class may be needed, even though at times this

information is used in subtle ways. A case in point is the

development of missile-grade graphite* by DoD, 1957-1963-

As a result of previous basic studies of graphite, a

good deal was known about the fundamental properties of

this material, and this information acted as guidelines in

a concentrated, deliberate and successful attempt by DoD to

*See MAB-222-M, Report of the Ad-hoc Committee on

Principles of Research-Engineering Interaction,

July 1966 for details of this development.
find industrial processes whereby graphite could be produced

with optimum properties and high reproducibility for missile

use .

In this sense of providing support for the strategy for

the development of needed materials, the present program has

come to focus upon two problem areas, Diffusion in Oxides,

and Properties of Laser Materials. The ARPA support for the

other areas listed in the Table of Contents in this Report

is being phased out, and will for the most part cease with

the present reporting period, although the work on Properties

of Refractory Borides, which is included in a separate proposal to ARPA, may be continued for another six months.

3. HIGH TEMPERATURE MATERIALS PROGRAM

3.1. Objectives in High Temperature Materials

The operation of rocket and jet engines involves exposing

metals at high temperatures to oxidizing conditions, and

raises the problem of oxidation protection of high temperature refractory metal structural components. This same

problem, currently for superalloy turbine blades, is posed

again by jet engines. The oxidation protection of metals

requires some form of barrier layer to prevent diffusion.

This layer, either applied or developed by the early stages

of oxidation itself, will most likely be an oxide, and will

function to keep the metal and oxygen apart . It can work

only if the diffusion rates of oxygen and metal atoms through

the layer are small enough. Thus the strategy for the

development of oxidation protection of otherwise susceptible

metals at high temperatures will depend in part on being

able to control the rates of diffusion, and therefore, in

having data on the diffusion rates themselves.

Diffusion in oxides is important to other classes of

DoD problems. Thus improvements in the reliability and

efficiency of military communication, computer, and radar

circuitry could be made if ceramic magnetic and ferroelectric

components could be made more reproducible and reliable.

Because such important properties as initial susceptibility

and coercive force of ferrites, and dielectric and peizoelectric properties of ceramic ferroelectrics are very

sensitive to the microstructural features (porosity, grain

size) controlled by sintering, the strategy for improvement

here requires control over sintering in these ceramics. The

same is true of the ballistic response of ceramic armor.

The development of transparent armor requires new techniques

for the suppression of grain growth during otherwise complete

sintering, mainly of AlpO~.
Since sintering in ceramics is mainly brought about by

diffusion processes, the development of successful, longrange strategies needed to meet these DoD needs rests in

part on knowledge of the rates of diffusion of metal and

oxygen atoms in oxides.

Reliable techniques for measuring oxygen diffusion

rates are not yet available, and therefore reliable data for

oxygen diffusion does not exist for any save a few oxides.

Thus one objective of this program is to develop a reliable

technique for measuring the rate of diffusion of oxygen in

oxides

.

Further, diffusion rates are notoriously sensitive to

impurities, and strategies for control require knowledge of

the basic rate in the pure material and of the way various

classes of impurities influence it. This in turn requires

very pure crystals for study. To date, almost no oxide

crystals have been prepared pure enough to reveal the intrinsic diffusion rates. The second objective in this area is

to prepare intrinsically pure crystals of AlpO^, one of the

leading ceramic armor candidates.

3.2. Project Summaries in High Temperature Materials

3.2.1. Diffusion in Oxides

3.2.1.1. Measurement of Diffusion Coefficients in Oxides

A. L. Dragoo

Inorganic Materials Division

Institute for Materials Research

The objectives of this program are to develop a reliable

technique for the measurement of the rates of diffusion of

oxygen in single crystal oxides, and to measure and interpret

data on specific oxides. Experimentally these two objectives

consist of (1) extending the sensitivity of present techniques so that the 1°0 distribution ("concentration profile")

in a single crystal sample can be measured, (2) comparing

the results of these concentration profile measurements with

the measurements of the rate of exchange of 1°0 between the

gas phase and the oxide crystal, (3) determining the dependence of the diffusion rate on temperature, oxygen partial

pressure, and impurities in the solid, etc., and (4) obtaining reliable diffusion and exchange coefficients. The

experimental results will provide the basis for determining

the mechanisms for oxide ion diffusion in the oxide studied.

Currently, rutile (TiO

p

) is the oxide of interest. A mass

spectrometer is being used to determine isotope ratios.
Almost all work on the project during the past months

has been focused on the construction of the inlet system for

the isotope ratio mass spectrometer — consisting of roughing

and high vacuum manifolds, sample and reference transfer

lines, sample and reference storage, manometers and molecular

leak inlet. The system has the capacity for three oxygen

references and four carbon dioxide references of different

isotopic composition. Oxygen samples on the order of 0.3

standard cc can be transferred from the diffusion furnace,

stored and analyzed. It will be possible to convert the

oxygen to C0

? using a graphite filament before analysis with

the mass spectrometer or to analyze it directly.

3.2.1.2. Crystal Growth from Vapor

H. S. Parker and C. A. Harding

Inorganic Materials Division

Institute for Materials Research

The objectives of this program are, first, the growth

of aluminum oxide mono- and bicrystals of sufficient physical perfection and chemical purity for use as research

materials; second, the reduction of both cation and anion

impurities in vapor grown aluminum oxide crystals to

sufficiently low levels to permit meaningful property

measurements at the intrinsic level; and third, the extension of the technique to other materials of interest.

During this reporting period, work has continued on the

growth of bicrystals containing symmetrical tilt boundaries,

primarily devoted to an investigation of possible variations

in the growth technique designed to reduce or eliminate the

occasional veils which form in the crystal when the growth

cycle is interrupted. The use of a brief etching period of

30 to 45 minutes duration at the beginning of each growth

cycle, during which only hydrogen and chlorine are passed

over the crystal, appears to be sufficient. However,

attempts to utilize this etching on the original seed

crystals have shown that chemical polishing in phosphoric

acid is still required to completely remove mechanical

damage resulting from sawing and grinding the seed plates.

Additional bicrystal specimens have been supplied to

Dr. Heuer at Case Western Reserve University for use in the

ARPA program on Mass Transport in Oxides.

Much of the effort has been devoted to the problem of

improving the chemical purity of the crystals by changes in

the technique and apparatus. Neutron activation analysis of

representative samples has been completed and are compared
with the previously reported spectrochemical analysis in

Table 1. Only four impurity elements were actually detected

Table 1

Chemical Analysis of NBS Vapor Grown A1

? 0_

Spectrochemical Neutron Activation

Element Analysis Analysis

Cu <10 ppm 0.027 - 0.038 ppm

a/ Fe questionable <4 ppm—

Ir not detected 0.0005 - 0.002 ppm

Mg <10 ppm b/

Mn <10 ppm ^0.0005 ppm

Sc not detected ^0.015 ppm

Si <10 ppm c/

CI c/ 0.1 ppm-7

"

a/ Detection limit, not observed in specimens

27 27 b/ Interference between Al and ! c/ Could not be detected if present

by activation analysis: copper, iridium, manganese and

scandium. The question of magnesium and silicon content

remains unresolved and an alternative analytical technique

will be required to determine the actual level of these

impurities

.

In Table 2, analyses of the aluminum metal used as a source material are given, both before and after use in the

chlorinator. Comparison of these analyses with those of the

crystals in Table 1 shows that considerable improvement in

purity is inherent in the growth process. The comparison

also suggests that, at the purity level under consideration,

the aluminum may well be the chief source of contamination

in the crystals. The marked reduction of silicon in the

aluminum after use and its subsequent detection in the

crystals indicates that this may be the most troublesome

impurity. Reaction between the chlorine and metallic parts

of the system is also evident from the new impurities found

in the aluminum after use. The disappearance of gallium

from the aluminum after use indicates that it also is being

transported. A particular search was made in the crystals

for gallium but if present, it is there at less than the

0.003 ppm level, the detection limit for activation analysis
Table 2

Spectrochemical Analysis of Aluminum Source Material

Element Material

Al Metal, Same, after

as received, use in

nominal 5N purity Chlorinator

Ag - <10 ppm

B <10 ppm <10 ppm

Ca questionable

Cr questionable questionable

Cu 10 - 100 ppm 10 - 100 ppm

Fe 10 - 100 ppm 10 - 100 ppm

Ga 100 - 1000 ppm

Mg 10 - 100 ppm 10 - 100 ppm

Mn - - Ni - 10 - 100 ppm

Pb - 100 - 1000 ppm

Si 10 - 100 ppm <10 ppm

A new furnace and chlorinator have been designed and

are currently under construction. In this apparatus, contact between chlorine gas, aluminum chloride and metal

parts will be minimized in order to reduce exposure to this

source of contamination.

Single crystals of high purity AlpO.-, have been provided

in a cooperative effort to the ARPA Laser Materials Program

at NBS for use in spin resonance studies where a chromiumfree specimen was essential.

Plans for the next reporting period include completion

of the new growth apparatus and continued emphasis on

improvement in purity levels. The use of 6N aluminum as

the source material will be tried. The possibility of

utilizing spark source mass spectrometry to determine the

silicon and magnesium levels will be investigated, as well

as the use of NMR to determine, at least qualitatively, the

hydrogen ion content of the crystals.
3.2.2. Properties of Refractory Borides

3.2.2.1. Electronic Structure of Refractory Hard Metals

J. R. Cuthill, L. H. Bennett, G. C. Carter

and A. J. McAlister

Metallurgy Division

Institute for Materials Research

The objective of this project is to study changes in

the density of states upon compound formation, especially

in high temperature borides. The information should contribute to the understanding of the basic principles leading to the design of high temperature alloys with prescribed

properties. The class of compounds being considered in this

study are those binary and pseudo-binary compounds characterized by one of the constituents having an incomplete d

or f shell and the other constituent having no d or f

electrons. The transition metal borides, aluminides, and

beryllides are examples.

Information is being obtained in the present study from

soft x-ray spectroscopy, nuclear magnetic resonance, Mossbauer spectroscopy, magnetic susceptibility, and other

probes of the electronic density of states.

The efforts again this report period will be summarized

: under the following three general headings for the purpose

of emphasizing their parallel importance: (1) Preparation

and Characterization of Transition Metal Borides, (2) Physical Property Measurements of Transition Metal Borides, and

jl (3) Electronic Structure Calculations.

1. Preparation and Characterization of Transition Metal

Borides

The wide range ± n most physical property values in

the literature to date, particularly on the transition

metal borides, has been repeatedly pointed out to be due to

the poor quality, inadequately characterized specimens from

which the data were obtained. Mono- and diborides of the

first, second, and third transition series metals made by

what is generally accepted to be the best hot pressing and

sintering technique, were found to be too high in carbon

(>100 ppm) . A modification of the method is now being

tried.

In addition to the simple borides we are experimenting

with mixed substitution type borides such as (Cr,_ V ) B~

where the V might be expected to substitute for the Cr in

all proportions and thereby provide an opportunity to study

the effect of intermediate electron/atom ratios without
changing the crystal structure. Rather than mutually diffusing the previously prepared pure Cr and V diborides,

which would require a very high temperature, a CrV alloy was

made and ground to - 325 mesh. The alloy powder was pressed

together with pure boron powder and sintered at 1500°C for

1 hour. Diffusion had progressed about 1/4 of the way into

the center of the alloy grains. Good diffusion results might

be obtained by this method but the development of extraneous

second phases is still possible.

NMR has again provided us with critical specimen

characterization information. The x-ray diffraction pattern

of one of our ScB„ specimens revealed the proper pattern of

lines for ScB„, plus a few additional weak unidentified

lines. When this specimen was put into the NMR spectrometer

the characteristic Knight shift for scandium metal was

observed in addition to the Knight shift corresponding to

ScB„, indicating that the ScB„ specimen was contaminated

witn excess scandium metal. After reheating the sample the

resonance corresponding to elemental scandium metal was

reduced. (Compare fig. la, showing both resonances before

reheating, with fig. lb, showing only the Sc in ScB„ resonance. Note that the quadrupole effect in the Sc in ScB„

resonance remains after the reheating.)

2 . Physical Property Measurements

Of the boride rod specimens that we have acquired thus

far the CrB and CrB„ specimens would appear from the metallography, x-ray diffraction and nuclear magnetic resonance,

to yield meaningful soft x-ray spectra. Some data on the

CrM spectrum and the 4th order ~B„ spectrum has been obtained

from the particular specimens which, as of this writing,

permit some general features to be compared. The B„ 4th

order spectra from both the CrB and CrB„ peak are at the same

energy and are of the same general width although it is

evident that there are differences in the detailed shape of

the bands. Neither does there seem to be any significant

difference in the CrM peak position between the two compounds. A definitive study of the M

?

_ soft x-ray spectrum

of pure chromium has been completed, 'corrections have been

made for background, and sub-band and satellite overlap.

The estimate of the pure CrM emission band thus obtained

was compared with recent photoemission data and good

correlation has been found.

We have obtained NMR Knight shift and quadrupole data

on ScBp, which is one of the few diborides upon which no

previous measurements of such properties have been reported

in the literature. This work has been completed between

room temperature and 4°K. Both the Knight shift and the

quadrupole coupling constant are the same at both temperatures. This, together with linewidth measurements, shows no

8
Sc

metal Sc in ScB

Figure 1.

Nuclear magnetic resonance spectrum of

scandium^5 at 16 MHz in a sample of

scandium diboride; (a) sample as originally received, exhibiting a resonance

characteristic of elemental scandium

metal, in addition to a resonance

corresponding to Sc in ScB2j and (b)

same sample after reheating and the

elemental scandium metal resonance no

longer discernible. The second order

quadrupole effect present in the Sc in

SCB2 resonance is seen to remain after

the reheating.

9
indications of magnetic behavior. The B resonance is

much as it is in the other diborides. The central line

shows a little structure in the middle which does not disappear at higher frequencies (21 MHz). Our past experience

tells us that much of this can be ascribed to noise arising

from boron in the glass tube and, more importantly, the

probe itself. With these, limitations we find the Knight

shift K = 0.00 (l)Jg*for B, with respect to triethylborate

.

The quadrupole satellites are low in intensity, compared

with, say CrB„ . This would suggest either a poor quality

sample with large distributions of quadrupole interactions

or the exciting possibility of an appreciable asymmetry

parameter. The latter could have important consequences

for understanding the crystallographic symmetries.

45 The Sc resonances shows strong second order quadrupole effects. The value for e^qQ/h, using second order

quadrupole theory, coincides with that observed from the

three pairs of satellites (I^-3 = 7/2), and has a value of

6.1(3) MHz. The linewidth of this resonance is proportional to 1/v so that the structure is due simply to second

order quadrupole effects, without complications due to K , which is also expected to be present for this hexagonal

structure. The position for v was deduced from the position of the central ^5Sc resonSnce line, giving K = +0.07(1)%

at both temperatures. This is in contrast to a negative

Knight shift as observed for 51y in VB ?

, which has important

implications regarding the electronic structure.

3. Electronic Structure Calculations

Generally the most solid progress is made when there

is a parallel experimental and theoretical effort. Thus far

the only work on borides has been experimental. There have

been no electronic structure calculations on the mono- or

diborides. Meanwhile, to explain experimental results

there has been much discussion in the literature as to

whether electrons are transferred from the metal to the

boron or vice versa, or to the conduction band, etc., without anything being resolved. Therefore to complement the

experimental program, computer routines are being prepared

for augmented plane wave calculation of the band structure

of the hexagonal diborides, XB

?

, where X is a transition

metal ion. It is these compounds which display metallic

properties and high melting points, and are thus possibly

of greatest technical interest. While these calculations

are simple in principle, certain practical problems are

encountered when studying compounds, and these are further

complicated by the presence of transition metal ions, and

the hexagonal lattice structure. The problem is one of

convergence in the reciprocal lattice expansion. The larger

the basis necessary, the lengthier and more expensive will

=f? In this expression, K=0.00(1)#, the number in parentheses

is the uncertainty in the measurement, and belongs in the last

decimal place given for the quoted value. This expression is

therefore equivalent to K=(0.'00+.01)#.

10
the calculations be. At the present stage, our investigation should be regarded as a feasibility study.

3.2.2.2. Reactivity of Borides

J. J. Ritter and T. D. Coyle

Inorganic Materials Division

Institute for Materials Research

This project was initiated in September, 1969 . The

principal objectives are to investigate the chemical reactivity of refractory borides and related materials toward

selected families of reagents. The reagents to be used

include interhalogen compounds (ClFo, BrFc, etc.) and noble

gas fluorides (XeF2), which, as powerful oxidizers, fluorinating agents, and non-aqueous solvents may afford extensive and structurally selective reactions. Initial emphasis

will be placed on development of degradation techniques

useful in chemical and isotopic analysis. Volatile intermediates produced in the reactions and related molecular

compounds will be investigated as possible precursors and

vapor transport reagents for synthesis of the refractory

materials

.

The initial work on this project has involved the

design of laboratory facilities required for safe and rigorously controlled handling of the reagents and for precise

and quantitative investigations of the reactions. The

design has been completed, and necessary procurements have

been initiated. Construction of apparatus will begin

shortly after 1 January 1970.

3.2.3. High Temperature Metals

3.2.3.1. Optical Constants of Titanium

A. J. Melmed

Metallurgy Division

Institute for Materials Research

The objective of this project is to determine the

optical constants (complex index of refraction) of titanium

by ellipsometry at room temperature in the visible region

of the light spectrum. It is recognized that titanium, at

room temperature, is optically anisotropic and chemically

reactive with the normal atmospheric environment. Therefore

measurements in different crystallographic directions, under

appropriate clean surface conditions are necessary for a proper determination of optical constants. In addition it

is recognized that considerably more polycrystalline

11
titanium than single-crystal titanium is used outside of

the laboratory, so that optical constants of poly-crystalline

specimens will also be determined.

The new experimental tube described in the last report

has been completed and tested. All aspects of the tube

are functioning properly. However, a problem of specimen

contamination with carbon was encountered. Efforts to

eliminate the problem were begun early in the present

report period, but were temporarily suspended due to scheduling difficulties. This project is being terminated, but

it is hoped to complete at least some of the measurements

in the future.

3.2.3.2. High Temperature Creep in Metals

A. A. 0. Rukwied, W. A. Willard and D. E. Harne

Metallurgy Division

Institute for Materials Research

The objectives of this investigation are to investigate the microscopic mechanisms that control high temperature creep, i.e., creep occurring at temperature T>T /2

,

where Tm is the melting point. More specifically it is

planned to study: (a) the effect of temperature on the

creep rate and compare this to the temperature dependence

of dislocation velocity, (b) the effect of stress and compare this to measurement of dislocation density carried out

by etch pit techniques, (c) study the effect of stacking

fault energy through its variation in an alloy series and

(d) study the effect of grain boundaries by comparison of

studies in single crystals and polycrystals . For these

studies copper and copper-alloys have been selected to

begin with especially since etch pit techniques for these

materials are already developed.

In order to get a faster and more accurate evaluation

of the experimental creep data on high purity copper, digital computer data processing was employed. The second

stage true strain rates were determined using first and

second order least square fitting techniques. For the

derivation of the activation energies the slopes of the

Arrhenius plots of lne vs. 1/T (where e s is the second

stage creep rate and T the absolute temperature) also were

determined using linear least square fits.

The resulting value of the apparent activation energy

for second stage creep was Q = 39.5+1 kcal/mol

12
(165*4 kJ/mol) for stress levels of 1000 and 1500 psi

(6.89x106 and 10.34xl0 6 N/m2

, respectively), only slightly

less than the previously reported value of 42±1.5 kcal/mol

(176±6 kJ/mol). However it turned out that another test

series measured at a stress of 2250 psi (15.51x106 N/m2

), the minimum creep rates of which resulted in an apparent

activation energy of k2.k kcal/mol (177 kJ/mol), has to be

considered with great caution with regard to its value of

the apparent activation energy for steady state creep. It

could be shown from the residual curvature of the fitted

parabolic curves as well as from Andrade-type plotting of

the creep curves (e* vs. tl/3), that in these tests at the

onset of third stage (leading to fracture) steady state

was not quite reached yet.

The apparent activation energy for steady state creep,

Q c , is usually assumed to be identical with the thermodynamically defined enthalpy of activation, AH, which is

measured as the temperature sensitivity of the strain rate

at constant stress and structure, i.e.

q = AH = -R(3lne/3 1/T) , , (1)

c 'a, structure

Within this definition, correct values of AH are derived

from steady state creep rates only if the structure in

I second stage is a function of stress only and is independent

of temperature.

One can hope to get additional information with regard

to this point by employing the differential temperature test

method (AT-method), where the creep rates are measured

immediately before and after a small and rapid change in

test temperature, which does not allow the structure to

change significantly.

Three such AT-tests were carried out on high purity r copper at stresses of 1000, 1500, and 2250 psi (6.89 x 10

I 10.34 x 106, and 15-51 x 10 6 N/m2) and temperatures of 672°,

; 5^0°, and 485°C, respectively. The temperature was dropped

by about 20°C in each case and was measured by a thermocouple

attached to the specimen. The values obtained for AH were

71, 67.5, and 65 kcal/mol (297, 283, and 272 kJ/mol),

respectively. This clearly is at variance with the steady

1 state measurements in the high temperature regime up to

700°C, where 39-5 kcal/mol (165 kJ/mol) was found. It also

cannot be reconciled with the measurements of Barrett and

Sherby, who obtained from steady state creep rates values

of AH of 61 kcal/mol (255 kJ/mol) at temperatures T >600°C,

and of 29.5 kcal/mol (121 kJ/mol) at 400°C<T<600°C (both

13
values of AH are computed from their published steady state

strain rate data).

Moreover, in order to get further insight into the

influence on high temperature creep of the purity of the

test material, the grown-in substructure, and the pre-test

annealing treatment, a test series on OFHC copper (nominal

99 • 99% Cu) at a stress of 1500 psi (10. 3^ x 10° N/m2 ) was

started, and a few AT-tests on both types of materials are

being carried out presently. At this time these results

are still inconclusive.

If, however, we apply to our data obtained by the ATmethod the analysis of activation parameters as given by

Schoeck, then we obtain for the high purity copper a value

of the Gibbs free energy, AG, of ho kcal/mol (167 kJ/mol).

In computing AG, we have assumed that the rate controlling

process is diffusion, thus having an activation volume of

the order of one atomic volume. In this case in the

relation for AG as given by Schoeck the term involving the

activation volume can be neglected and the entropy contribution is wholly described by the temperature variation of

the elastic modulus,

AG = AH - TAS = — (2)

1 - (T/y)(dy/dT)

The temperature variation of the elastic modulus, y, has

been measured by Barrett and Sherby and by Koster.

The observed discrepancy of the activation enthalpies,

AH, as derived from the steady state tests (39.5 kcal/mol,

165 kJ/mol) and from AT-tests (»70 kcal/mol, 293 kJ/mol),

clearly indicates the need to check on the theory and/or

its assumptions.

According to the theory of thermally activated dislocation processes, the activation enthalpy for the rate

controlling process is determined by measuring creep rates

at different test temperatures under conditions of constant

structure. The term constant structure means that during

a small change In test temperature, or at different test

temperatures in the case of steady state testing, the number

of defect configurations at which under the action of a

given stress thermal activation of a dislocation segment can

occur does not change. The structure, thus comprising all

defect configurations in the body which determine its creep

behavior, gives rise to a long range internal stress in the

body. This internal stress depends on temperature through

14
the temperature variation of the elastic modulus. Therefore,

for steady state type creep testing over a wide range of

temperature, it seems doubtful that the assumption of

constant structure is realistic. Then the activation

enthalpy as determined from the slope of an Arrhenius plot

of lne vs. 1/T would be incorrect, since it would be based

on a set of different structures. On the other hand, a AT-test would more likely measure creep rates at constant

structure, assuming that the structure adjusts reasonably

slowly at the new test temperature.

The previously reported study attempting to better

characterize the nature of the cellular solidification substructure in the high purity material (99-999% Cu) was

continued. Ion probe microanalysis, carried out at CAMECA and

at Bel}, and Howell, could confirm the segregation of carbon

and silicon at the cellular structure. Moreover, the presence of

these elements in form of clusters or particles of about

j<10 nm (100 ft) size could be detected. Due to its high

chemical affinity to the other possible contaminants (i.e.,

C and 0) the silicon should be present in form of silicon

oxide or carbide. It is obvious that such particles cannot

be removed from solid copper by mechanical and/or thermal

treatment. This explains the stability of the grown-in

substructure, which in some way will interact with moving

dislocations

.

No time could be spent on the single crystal program.

3.2.4. Polymers

3.2.4.1. The Volatilization and Decomposition of Materials

L. A. Wall, S. Straus, and G. Mattamal

Polymers Division

Institute for Materials Research

No actually new compounds were studied in the past six

months. Previous work was repeated. The energy of vaporization for the Coi| n-alkane was checked by carrying out the

measurement of Izs rate of vaporization at four different

temperatures covering a larger temperature range than previously .

A final manuscript covering the alkanes, entitled

"Rates of Molecular Vaporization of Linear Alkanes" by

L. A. Wall, J. Plynn, and S. Straus has been submitted

15
to the Journal of Physical Chemistry for publication.

Another paper entitled "Vaporization of Organic

Plasticizers" by L. A. Wall, J. H. Flynn, and S. Straus

has now been published in Polymer Engineering and Science,

Volume 10, page 19, January, 1970.

Finally, we have been synthesizing and purifying

compounds for study. These include:

Series (1) Series (2)

Tributyrin . Di n-butyl sebacate

Tricaproin Di n-hexyl sebacate

Trictanoin Di n-octyl sebacate

Tridecanoin Di n-decyl sebacate

Trilaurin Di n-dodecyl sebacate

Trimyristin Di n-tetradecyl sebacate

Tripalmitin Di n-hexadecyl sebacate

Tristearin Di n-octadecyl sebacate

We have also obtained three dimethylsiloxane oligomers

from Dr. Walter Zisman for study. The study of the vaporization of these compounds should give some new insights into

our comprehension of vaporization phenomena.

4. LASER MATERIALS PROGRAM

4.1. Introduction to Laser Materials

The National Bureau of Standards, with support from

the Advanced Research Projects Agency of the Department of

Defense, is carrying out a program of research on laser

materials. This program includes studies to characterize

laser materials, to define and evaluate damage measurements

in laser materials, and to investigate the degradation of

laser performance. A summary of the results achieved during

the reporting period is given here.

4.2. Objectives of Laser Materials

One of the important factors which is limiting the

advance of ultra high power laser technology is the failure

or degradation of laser materials due to optically induced

damage. In the past, the empirical approach to laser

materials has been adequate. That is, the damage or degra16
dation to laser materials has been circumvented by equipment

design or by a cut-and-try improvement in the laser materials

This problem of optically induced damage now poses a serious

threat to the successful application of laser devices to an

important class of needs of the Department of Defense.

This fact has been recognized and the Advanced Research

Projects Agency supports research to improve the performance

of laser materials. The convening within the last nine

months of three committees to examine the optical damage to

laser materials illustrates the present concern and importance of solving this class of problems. These committees

are the Subcommittee II of ASTM Committee F-l, the Institute

for Defense Analysis study, and the National Materials

Advisory Board Committee on the Fundamentals of Damage in

Laser Glass.

The success of these efforts depends upon having the

knowledge and proper skills available when they are needed.

In the case of laser technology, they include the science

and techniques of laser materials preparation and characterization and of the measurement and evaluation of those

properties which are relevant to the damage and degradation

of lasers. It is the overall objective of the present NBS

program on laser materials to identify some of the more

important problems concerning damage and degradation of

lasers and to provide the necessary advances in those areas

for which NBS possesses the competence to do so. These

efforts will be directed mainly toward providing the techniques for the preparation and characterization of laser

materials to be used in tests for the measurement and

evaluation of material properties pertinent to the damage

and degradation of lasers, for the tabulation of key damage

data, and for the improvement in the knowledge and skills

necessary to advance the performance of lasers.

In pursuit of this program, a continuing attempt is

being made to analyze the technological problems associated

with high performance lasers and the materials from which

they are constructed, and to distill from this analysis

major scientific problems whose solutions would advance

laser technology. In addition, the problems chosen should

fall within areas in which NBS has available competence.

Also, the number of problems included in the program should

be kept small enough so that each one can be approached

in a reasonably comprehensive manner.

In accordance with these criteria, the present program

contains three subdivisions — Characterization of Laser

Materials, Damage to Laser Materials, and Degradation of

Laser Materials. Damage and Degradation as used here are

distinguished in that Damage is localized and occurs during

17
the course of a very few pulses whereas Degradation implies

the much more gradual and general deterioration of performance over many pulses. There may of course be some overlap .

4.3« Overall Summary of Projects on Laser Materials

4.3.1. Characterization of Laser Materials

There is a continuing need for the characterization

of laser materials. Suppliers frequently make changes in

composition and usually do. not provide adequate data on

those physical and chemical properties which influence

laser performance and the distortion of wave fronts propagating in laser materials. The index of refraction, thermal

change in the refractive index, elastic constants, photoelastic constants, thermal expansion, density, and

chemical composition have been measured for five commercial

Nd-doped laser glasses. The possibility of eliminating

electrostrictive effects by judiciously altering the glass

composition has been examined. A lithium-silicate laser

glass whose composition approximates that of some commercially available laser glasses was found to have a consolute

temperature between 440°C and 480°C. Since the consolute

temperature occurs near the transformation region, a large

degree of phase separation may occur during annealing.

Other compositions will be examined in the future. The

relation between phase separation and the performance of

a laser is not understood very well and could require

quantitative studies if one can show that phase separated

glasses have consistently lower or higher tolerances to

damage or degradation. X-ray diffraction techniques have

been employed to characterize ruby laser rods and a correlation between crystal perfection and its performance in a

laser has been considered.

4.3.2. Damage to Laser Materials

Inclusion damage (bulk) has been a serious source of

difficulty for the laser systems engineer concerned with

ultra-high power pulses. Although surface damage and

intrinsic damage (self-focusing or beam trapping) contribute

additional problems, these are at present apparently not as

great an obstacle to the advance of laser technology as the

inclusion damage is. A laser glass damage test facility is

being constructed at NBS to study the damage problem and to

attempt to bring some unity to the great proliferation of

18
damage data. This test facility will center around a one

gigawatt neodymium laser system. Preliminary experiments

on the damage of silica and glass samples by exposure to a Q-switched ruby laser pulse of 3 joules studied the variation

of damage threshold with water content. These experiments

also indicate that knowing the samples' total history is

essential for interpreting and understanding the results of

damage studies. The detection of incipient absorbing centers

before they initiate a damage site would be most helpful in

the chemical analysis of the site and its immediate neighborhood. Some ideas to detect incipient damage centers have

been screened in a search for useful analytic methods.

These include dielectric relaxation, nuclear magnetic resonance, azimuthal light scattering, forward light scattering,

and infra-red detection techniques. None appear sufficiently

promising to pursue at this time for the detection of

inclusions leading to damage. Methods which employ optical

interference or stress-birefringence principles have also

been suggested. A theoretical model of an absorbing center

in a laser glass host has been formulated. This model

enables one to compute the space and time dependence of

the temperature near the center, the thermal stress, and the

stress-birefringence as functions of the laser pulse width,

energy content of the laser pulse, and radius of the absorbing center. Preliminary computations indicate that such

optical methods are promising.

4.3.3. Degradation of Laser Materials

At present, the coloration of some ruby and YAG laser

rods after continued use is not well understood. The reasons

are in part a lack of sufficient data on the differences

among coloration by laser pump light, x-ray irradiation, and

Y-ray irradiation. The causes responsible for degradation

in performance of solid state lasers after continued use

have been studied by electron paramagnetic resonance and by

optical means. Good laser quality ruby and "orange" degraded

ruby samples were examined by both their absorption spectra

and their electron paramagnetic resonance. Also, particular

attention has been given to the valence states of the

chromium ion's, magnesium ions in doubly doped rubies, and

of impurity ions. Similar studies are planned for YAG

crystals

.

19
4.4. Individual Project Summaries

4.4.1. Characterization of Laser Materials

4.4.1.1. Physical and Chemical Properties of Laser Materials

G. W. Cleek and R. M. Waxier

Inorganic Materials Division

Institute for Materials Research

The objective of this project is to determine the physical properties of laser glasses and crystals and to relate

these properties to their chemical composition.

Accomplishments

Measurements on five commercially-made Nd-doped laser

glasses have been completed. Data were obtained on such

properties as refractive index, thermal change in refractive

index, elastic constants, photoelastic constants, thermal

expansion, density, and chemical composition. These data

are needed to calculate the corrections for the distortion

of the wavefront in light generated by the lasers. The

distortion is produced by thermal effects when the rods are

operated. The results have been presented earlier in NBS

Technical Note 514.

The photoelastic constants of single crystal ruby doped

with 0.05 wt % of Cr203 have been determined and the results

have been prepared for publication.

Chemical Analyses *

(1) Ruby Boules - Neutron activation analysis was used

for the determination of trace impurities in three different

ruby boules. The three boules were doped with Cr20o at

nominal levels of 0.03, 0.05 and 0.064 wt % s respectively.

For the 0.03% and the 0.064% boules, two adjacent samples

from the same boule were analyzed.

The crystals were cut to obtain samples of a uniform

thickness and similar cross-sectional area. Each sample

was sealed in polyethylene and irradiated for 60 minutes in

pneumatic tube RT-4 of the National Bureau of Standards

Reactor at a power level of 10MW (~lxl0l3 n-cm~ 2 sec""-*-).

This facility was chosen because of its higher ratio of

thermal to fast neutrons over the facility used for previous

analyses. The remainder of the procedure was identical to

that reported previously in NBS Technical Note 514.

*Neutron activation analyses by Barbara A. Thompson, Analytical Chemistry Division

20
Table 1

Results of Activation Analysis of Ruby Crystals, ppm

Crystal Designation

Element

Cr

(Wt#Cr ? Ba

"0.03?' n "0.05$"

0.0443

9.4

"0.064$"

#1 #2 #1 #2

0.0222

J 42.6

0.0215

0.24

0.0442

15.2

0.0463

1.26

Sr 1.55 <0.2 0.41' 0.49 0.066

Cu 0.075 0.062 0.070 0.026 0.060

Mn 0.0013 0.002 0.0012 - 0.0018

Ga 3.05 2.98 0.004 0.014 0.016

W 0.032 0.052 0.034 0.015 0.030

Ir 0.239 0.245 0.0255 0.0500 0.0539

Na <2 <2 <2 <2 <2

Au <0.0002 <0.0002 <0.0002 <0.0002 <0.0002

La <0.002 <0.002 <0.002 <0.002 <0.002

Co <0.02 <0.02 <0.02 <0.02 <0.02

21
The results obtained are shown in Table 1. All results

are in ppm of the element except the Cr results which are

reported as percent Cr 2 0o- The improved ratio of thermal

to fast neutrons in the new irradiation facility resulted

in a reduction of almost an order of magnitude in the 2^Na

production from the reaction 2 'Al(n,ot) IhNa. 7

The measurementnOf short-lived activities such as

D Cu, Ga, 5o Mn ^ and ' m

Sr was thus made much more reliable. An upper limit

for Na in the crystals is reported which takes into account

the Na produced from the Al 2 0o matrix. Because of interferences, the values for W in the table should probably be

regarded as upper limits rather than firm concentrations.

For the crystals containing nominally 0.03% and 0.06h%

C^Oo, two adjacent samples were cut from each boule and in

each case the sample designated #1 was from the wider end

of the crystal.

(2) Neodymium-doped Laser Glasses - Five commerciallymade specimens of neodymium-doped laser glasses were analyzed

by neutron activation methods, with particular care taken

to determine trace impurities.

These glasses are very complex mixtures, containing

in some cases as many as ten principal constituents. For

activation analysis the constituents representing the most

serious interferences to the measurement of other activities

are sodium, antimony (1% or more in 4 of the glasses), and

neodymium (3-5%). The neodymium is especially aggravating

since on irradiation it yields three radionuclides: 15lNd,

with a 12 minute half-life; li4 9Nd, with a 1.8 hour half-life;

and l2j ?Nd with an 11 day half-life. ^Nd and l^Nd also

decay to form radioisotopes of promethium with half-lives

of 28 hours and 53 hours.

To try to obtain the maximum amount of information with

a reasonable expenditure of effort three sets of irradiations

were carried out. For each of the glasses a small sample

(10-50 mg) was irradiated for 2 seconds and used to determine

Na, K, and Sb . A larger sample (100-200 mg) of each glass

was irradiated for 1 minute, and dissolved in HF-HC10j..

After fuming to eliminate HF, the residue was taken up in

9N HC1 and most of the antimony was removed by extraction

into isopropyl ether. Sodium was then removed by passing

the aqueous phase through a column of hydrated antimony

pentoxide. The effluent was examined for low-level constituents of intermediate half-life. Those observed included

La, Pr, Eu, and Sm. Common impurities such as copper and

gallium were not observed.

A third set of samples (100-200 mg) was irradiated for

15 minutes and set aside for two weeks to allow all shorter22
lived activities to decay away. After dissolution and

extraction of antimony as before the aqueous phase was

counted and Nd, Ce , and Ba were determined (Glass E did not

require these chemical separations since it had very low

concentrations of Na and Sb )

.

All the samples were irradiated in the NBS Reactor at

a flux of about 6 x 10^3 n/cm2 sec. The maximum irradiation

time-sample size combination was fixed by the 2 %a, 122sb -

l 2 ^Sb, and -1 'Nd activities produced. All the samples were

specially cut 1-mm thick slices. With samples this thin,

neutron self-shielding was not a problem even for Glass E

with lk% Li 2 0. For this latter glass irradiation time was

not limited by Na or Sb because these were quite low, but

by Nd and by heating of the sample during irradiation by

absorption of alpha particles from the reaction: °Li (n,a)

•^H. All the samples were rinsed in acetone and in dilute

HNOo after irradiation to remove surface contamination. In

most cases concentrations were determined by comparison to

standards irradiated under the same conditions.

Results: The results obtained are given in Table 2.

The relative standard deviation is estimated to be about

±5$ in most cases. For the lower reported values of Sm

there is severe interference from Nd and these values are

probably no better than ±20$. For the lower reported values

for Eu and Ce the signal-to-background ratio was poor and

these values also are probably no better than ±20$. All

results are reported as the oxide rather than the element to

facilitate comparison with results from other methods.

Glass Composition and the Possibility of Eliminating Electrostrictive Effects

Several mechanisms for the cause of damage in laser

materials have been considered during this period. In some

of these mechanisms the effect is greatly enhanced by the

presence of electrostrictive self-focusings , which lead to

the formation of filaments. Chiao, Townes and Stoicheff

[1] have pointed out that electrostrictive pressure is given

by

P

= (E

2

/4tt) n (p dn/dp), (1)

where E is the electric field, p the density of the material

and n the refractive index. In addition, Chiao, Garmire

and Townes [2] have shown that the refractive index changes

due to the change in density caused by electrostriction are

23
Table 2

Results of Activation Analysis of Neodymium-Doped Glasses (wt#

Glass A Glass B Glass C Glass D Glass E

Na

2 0, % 6.9 7.8 3.2 6.4 0.044

K

2 0, % 9-2 14. 17. 17. <0.04

Sb

2

, % 0.90 0.86 2.5 0.93 0.0015

Nd

2 3

, % 5.5 5.8 3.5 5.7 3.5

BaO, % 5.1 3.3 3.5 2.8 <0.3

Ce0 23 % <0.006 0.005 <0.006 <0.006 0.521

LapO^, ppm <0.9 10. 18. 7.8 <0.8

PrpO-,, ppm <3 <3 <3 8.4 <2

Eu

2 0^, ppm 30. 0.6 <0.1 1.1 <0.5

SmpO^j ppm 0.37 0.2 0.2 2.2 <0.03

24
given by

An = (E

2

/i4-rr) Bn (p dn/dp) 2

, (2)

where B is the compressibility. It is obvious from equations

(1) and (2) that the electrostrictive pressure will be zero

and the change In index will be zero if (p dn/dp) = 0. The

possibility of finding a material which will meet this condition has been studied, and the results are presented in

this section of the report.

Data on (p dn/dp) for various cubic crystals are available from studies conducted at NBS [3] and other laboratories

[4,5J and these data are presented In Table 3. It can be

seen that there is a considerable range in values of

(p dn/dp) from +1.31 for PbN0

3 to - 2.84 for GaAs . For the

group of alkali halides there is a decrease in magnitude of

(p dn/dp) with increasing strength of interatomic binding.

There are several crystals which have negative values of

(p dn/dp). With these crystals the refractive index becomes

less under hydrostatic pressure because the decrease in

polarizability of the constituent Ions outweighs the positive

contribution to index due to the increased number of scattering centers per unit volume [3,4].

In Table 3, it can be seen that YAG (Yttrium Aluminum

Garnet) has a slightly negative value and very nearly fulfills the condition that (p dn/dp) =0. A boule of undoped

YAG has been obtained from Union Carbide Corporation, and

it is planned to study the effect of high energy laser

pulses upon the material. If equations (1) and (2) are

correct, electrostrictive effects should be largely eliminated.

Although YAG is a promising material, the rod of a high

energy pulsed laser will almost certainly have to be a glass,

because the broad fluorescent line of a glassy host lends

itself to Q-switching. In Table 4 values of (p dn/dp) are

given for several glasses. The first group shows values

for 5 neodymium doped laser glasses which have been studied

recently at NBS. The values are clustered closely around

0.34, although the Owens-Illinois glass has a slightly

lower value, 0.30. The second group of 10 glasses were

selected as being representative of 154 Schott glasses

reported in a very thorough study by Schaeffer and Nassenstein [6]. The highest value is .77 for SFS1 and the lowest

value is .24 for SSK8. In the third group are shown the

results of experimental studies on simple glass compositions

conducted at NBS. AS2S0 has very high value of 2.34, and

25
Table 3

Values of (pdn/dp) for cubic crystals*

Crystal (pdn/dp)

KI .44

KBr .35

NaCl .28

LiF .13

NaF .11

CaF

2

.25

YIG .31

PbNO^ 1.31

MgO -.31

ZnS -.22

SrTiCs -.22

GaP -1.90

GaAs -2.84

YAG -.01

* In the instances where the original data were reported

in terms of Pockel's elasto-optic constants, p. ., (p dn/dp) was calculated according to the equation,

n

3

(p dn/dp) = ^— [p 11

+ 2p 12 J.

26
the calcium aluminate, F75, has a value of .19 which is

significantly lower than the rest. The low value of

(p dn/dp) for the calcium aluminate glass (which contained

41.5 weight^ Al 2 0o) is consistent with the fact that with

applied hydrostatic pressure, crystalline AlpCU (sapphire)

exhibits a decrease in refractive index for Both the

ordinary and extraordinary ray [2,7].

Considering the fact there is a consistent trend toward

negative values of (p dn/dp) with increasing strength of

interatomic binding for the group of alkali halides shown

in Table 3, it is reasonable to assume that a similar trend

holds for the series of alkaline earth oxides. It can be

seen in Table 3 that MgO has a negative value of (p dn/dp)

so that substituting MgO for CaO in the calcium aluminate

composition of F75 might be expected to reduce the value

of (p dn/dp) to one closer to zero. Moreover, according to

the physical theory of photoelasticity , certain ions such

as Be and F~ if substituted could be expected to make an

even stronger negative contribution to (p dn/dp) [4]. The

electronic polarizability and binding strengths of the

constituent ions are the Important factors, and it should

be possible to formulate some glass composition where

(p dn/dp) would equal zero.

In conclusion, it should be noted that the basic material parameters which describe the interaction between

optical radiation and acoustic waves are Pockels' elastooptic constants [4,8,9]. One of the mechanisms that have

been proposed as the cause for laser damage in solid,

transparent dielectrics is the generation of coherent

ultrasonic phonons by stimulated Brillouin processes [1,10].

Chiao, Townes and Stoicheff [1] have pointed out that

either compressional or shear waves may be excited, but

for compression the coupling between acoustic and optical

waves is simplest and may be described as electrostriction.

In this case, equation (1) still holds. Chiao, Townes and

Stoicheff have shown that, when the radiation is contained

in a resonant cavity, the threshold condition for buildup

of the acoustic and scattered wave is

8tt 2(pdn/dp) 2

k L k ' L

(3)

s s -1-1

where L and L_]_ are the decay lengths of the sound and

light waves respectively, and k s and k_i are the respective

27
Table 4

Values of (pdn/dp) for glasses

Glass Type (pdn/dp)

Neodymium- doped

Laser Glasses Glass A

Glass D

Glass B

Glass C

Glass E

.34

.34

.34

.36

.30

Schott Glasses

Fluoro Crown FK1 .37

Boron Crown BK5 .33

Crown K4 .37

Barite Crown BaK5 .39

Crown Flint KF2 .34

Dense Crown SSK8 .24

Barite Flint BaF8 .46

Flint F9 .41

Short Flint KzF2 .43

Special Dense Flint SFS1 .77

NBS Experimental

Glasses

Extra Dense Flint

Fused ASpS^

Fused SiOp

Fused GeOp

Fused B

2 Borate

Phosphate

Calcium Aluminate

F920 .81

2.34

.32

.44

.39

E1583 .40

F1329 .33

F75 .19

* In the instances where the original data were reported

in terms of Neumann's strain-optical constants, p and q,

(pdn/dp) was calculated according to the equation,

n (pdn/dp) = — [q+2p]

28
propagation vectors of the sound and light waves. These

authors have shown also that for the travelling wave case

the threshold condition is

2

E

o > B (L

- 1 + L~ 1

) 2

. (4)

> ~ s -1

8ir 2(pdn/dp) 2

From equations (3) and (4) it can be seen that in a material

where (p dn/dp)=0, the possibility of damage by stimulated

Brillouin scattering is eliminated.

Refractive Index of Ruby

Three ruby boules, doped at nominal levels of 0.03,

0.05 and 0.064% of C^Oo, respectively, were furnished by a commercial supplier. The crystallographic directions in

the boules were determined by x-ray methods and prisms of

known orientation were prepared for the refractive index

measurements. The results are shown in Table 5.

Specimens cut from the same boules were analyzed by

neutron activation methods and the results are given in

Table 1. As may be seen from the table the boules containing nominal levels of 0.05% and 0.064% Cr„0o were found to

contain essentially the same amounts of 0^03 . The

refractive index values in Table 5 do not disagree with

the analyses. The variations in refractive index for all

three boules are only one or two in the fourth decimal.

When these measurements were planned it was expected

that data would be obtained to allow the calculation of

the change in refractive index produced by a change in the

Cr203 concentration. Since the observed changes are so

small no meaningful calculation can be made.

A comparison of these data with data reported in the

literature on sapphire [11] and on ruby [12] show variations

of two or less in the fourth decimal so that specimens

containing appreciably more C^O^ would be required to

determine the effect of C^Oo concentration on refractive

index.

References

[1] R. Y. Chiao, C. H. Townes and B. P. Stoicheff, Phys . Rev,

Letters 12 592 (1964)

.

29
Table 5

Refractive indices of ruby with different

concentrations of Cr

? 0^ at 19.5°C

Wavelength

(vim)

.03$

n * Cr

2 g

e*

.05$

n

* Cr 2°3

n

* e

.064$

n

* Cr20o

n * e

0.4047 1.7859 1.7774 1.7860 1.7776 1.7859 1.7775

0.4358 1.7813 1.7729 1.7814 1.7730 1.7813 1.7730

0.4678 1.7775 1.7692 1.7776 1.7693 1.7775 1.7693

0.4800 1.7762 1.7680 1.7764 1.7681 1.7763 1.7681

0.5086 1.7736 1.7654 1.7738 1.7656 1.7737 1.7655

0.5461 1.7708 1.7627 1.7710 1.7628 1.7709 1.7627

0.5876 1.7683 1.7602 1.7684 1.7603 1.7684 1.7603

0.6438 1.7655 1.7575 1.7657 1.7576 1.7656 1.7576

0.6678 1.7645 1.7565 1.7647 1.7566 1.7646 1.7566

0.7065 1.7631 1.7551 1.7632 1.7552 1.7633 1.7552

* n signifies ordinary, and n extraordinary, ray.

Preliminary data obtained by I. H. Malitson and M. J. Dodge

30
[2] R. Y. Chiao, E. Garmie, and C. H. Townes, Proc. of the

International School of Physics, Enrico Fermi Course

XXXI, Academic Press, New York (1964) p. 326, "Raman

and Phonon Masers".

[3] R. M. Waxier and C. E. Weir, J. Res. NBS 69A 325 (1965).

[4] R. S. Krishnan, Progress in Crystal Physics, Vol. 1,

Interscience Publishers, New York, London (1959).

[5] K. Vedam and E. D. D. Schmidt, Phys. Rev. l4_6 548 (1966).

[6] C. Schaefer and H. Nassenstein, Z. Naturforsch 8A 90

(1953).

[7] T. A. Davis and K. Vedam, J. Appl. Phys. 38_ 4555 (1967).

[8] R. W. Dixon, J. Appl. Phys. ^8 5149 (1967).

[9] W. T. Mahoney and H. R. Carleton, IEEE Transactions on

Sonics and Ultrasonics, SU 14 135 (1967).

[10] B. M. Ashkinadze et al . , Soviet Phys. -Doc. 11 703 (1967).

[11] I. H. Malitson, J. Opt. Soc. Amer. 52 1377 (1962).

[12] M. J. Dodge, I. H. Malitson and A. I. Mahan, Appl. Optics

8 1703 (1969).

4.4.1.2. Liquid-Liquid Phase Separation in a Laser Glass*

J. H. Simmons and W. Haller

Inorganic Materials Division

Institute for Materials Research

A study underway at the National Bureau of Standards

has involved measurements on various glass compositions to

detect the possible presence of liquid-liquid phase transitions. This information is desirable as part of a laser

damage study. It was found that a liquid-liquid phase transition occurs in a lithium-silicate glass, very similar to

one in use as a laser glass, of the composition:

* An associated project, supported by the National Bureau

of Standards.

31
Si0

2

66.1% weight

Li

2

15.5%

CaO 10.1%

ai

2

o

3

4.4%

Ce0

2

0.5%

Nd

2

3.2%

This glass composition has a consolute temperature between

44l°C and 448 C C, a temperature range close to its annealing

point (approx. 460°C). Such results imply that a degree of

microstructure will appear in the glass when it is heattreated at temperatures below and around 440°C. The degree

and size of the microstructure will then increase with the

length of heat treatment. Since the consolute temperature

occurs in the transformation region of this glass, a large

degree of phase separation may (is likely to) occur during

annealing.

4.4.1.3. An X-ray Transmission Method for

Examining Ruby Laser Rods

E. N. Parabaugh and F. A. Mauer

Inorganic Materials Division

Institute for Materials Research

Objective

This study was undertaken to determine whether x-ray

diffraction techniques may be used to characterize ruby

laser rods. A correlation between crystal perfection and

laser performance is being considered.

Approach and Results

Work has continued on the correlation of laser crystal

perfection, as determined by x-ray diffraction techniques,

and laser performance

.

Since the last reporting period another group of laser

rods has been examined using a modified high voltage transmission technique developed during this reporting period.

The general features are shown in Figure 1. A slit, 11mm

by 1mm has been placed a distance of 10cm from the x-ray

source and the film placed parallel to the x-ray beam.

32
Pictures are taken at several points along the length of

each rod. The beam samples a disc-shaped volume of the

rod and produces an array of diffraction spots each of

which is a crude x-ray topograph of the cross section (fig.

2).

The most recently examined group of three ruby laser

rods was again obtained from Dr. J. Hall (NBS, Boulder).

These rods all have better laser performance than the first

group. Rod D, .330 in. in diameter by 3.0 in. long with

rod axis parallel to <0110>, has residual strain and is

described as "definitely inferior to rods E and F" by Hall.

Rod E, 3/8 in. in diameter by 1 1/2 in. long with its axis

parallel to <0110>, was described by Hall as being the best

rod for laser performance that he has seen. Rod F, a 60°

rod .620 in. in diameter by 3 11/16 in. long, was described

as typical of the best available currently. This rod has

some tracking damage. All rods are' still capable of the

laser performance described above.

Figure 3 is a composite of corresponding spots from

five films taken along the length of rod D. These topographs show how the crystal perfection of the rod varies

along its length. The best volumes of the rod are represented by those images of the cross section which are free

of distortion and have a minimum of splitting. A wide

range of crystal perfection is indicated by these films.

Rod D was described by Hall as having some strain present

which affected its angular distribution pattern. The

topographic method used is not sensitive to strain and the

films do not indicate this characteristic of the rod.

Figure 4 is a composite of corresponding spots from

five films taken along the length of rod E, the "best"

laser rod. These films also indicate a range of crystal

perfection along the length of the rod. When this rod was

examined under crossed polarizers, it was observed that it

did not exhibit extinction uniformly across its cross

sectional area (Hall was aware of this before sending the

rod to us). The subgrains in the rod appear to run from

end to end and are fairly regular. Thus, it is evident

that a ruby rod can have very good laser performance and

still not be very good crystallographically . In comparing

the films of rods D and E it is seen that films are in

general very similar, however, the laser performance of

rod E is superior to that of rod D.

Films were also taken along rod F. None of these films

are pictured because the images formed were very weak. The

faintness of the diffraction images is due to the fact that

33
SPECIMEN

BEAM STOP

Fig 1. Modification of the Laue transmission technique to

give a topograph of the cross section of the rods.

34
Fig. 2. Diffraction pattern of a rubyrod in which each spot is a crude

topograph

.

3b
co

<u p

•H

e

•Hm

(L) •H

M-le

o

5-1 M-l

T3O

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36
in this rod we are approaching the limiting thickness of

ruby rod that we can get an x-ray beam through. Inspection

of these films showed spots which were well formed in

every film with a minimum of splitting and distortion.

Since all of the films were of the same quality we would

evaluate this rod as better crystallographically than rod E.

The laser performance is however, inferior to that of rod E.

Rod F was described as possessing some tracking damage.

Although our images are weak and not many spots appear,

there is no evidence for this damage observable in the

images

.

The rods studied in the previous reporting period

were re-examined using the new technique of topographing

whole cross sectional areas. The results were in good

agreement with the previous results and the performance

could be correlated with the crystal perfection.

A badly damaged rod with bubbles, visible to the eye,

was also examined with the modified transmission technique.

The images formed gave no obvious indication that the bubble

defects were present.

It has been demonstrated that the modified transmission

Laue technique can detect misorientations in large single

crystals. However, topographs of the cross section of the

rods do not seem to be sensitive to defects other than grain

, boundaries, which are easily demonstrated. The first set of

rods examined showed a correlation between the laser performance and crystal perfection. There was no similar correlation found with the second set of rods.

A possible different view of the problem which might be

more fruitful is not to determine how many imperfections are

shown in the topographs but to try to determine what are the

features in the topographs we obtain which are important in

the grading of the crystals for laser applications.

4.4.2. Damage to Laser Materials

4.4.2.1. Laser-Induced Damage Studies

N.N. Winogradoff, A. H. Neill, Jr., and J. Mitchell

in collaboration with:

W. Haller, G. Cleek and R. Waxier

Inorganic Materials Division

Institute for Materials Research

Objective

This was to set up a well defined laser glass damage

facility for evaluating the damage threshold for various

37
samples of glass and elucidating the mechanisms responsible

for the damage.

Approach

On establishing the facility, it will be used to,

(1) measure the damage thresholds for various samples of

glass, (2) catalog the different types of damage observed,

(3) correlate the nature of the damage with the conditions

under which the damage occurred and with the composition

and heat treatment, etc. of the glass sample, and, (4)

elucidate the mechanisms responsible for each type of

damage

.

Status

A "one gigawatt" neodymium laser system, capable of

producing 20 ns . Q-switched pulses with energies in

excess of 30 joules per pulse has been ordered and delivered.

The system consists of an oscillator, Q-switched by

means of a Pockel's cell, feeding into two successive

amplifier rods, and is currently undergoing acceptance

tests

.

Pending the operation of the above system, preliminary

experiments on the damage of silica and glass samples by

exposure to 3 joules, Q-switched, ruby laser pulses were

undertaken

.

Introduction

Bulk physical properties of glass samples indicated

that the threshold for mechanical fracture decreased substantially as the water content was increased. This

suggested that the threshold for damage by laser pulses

might also be a function of the water content of the glass.

Since samples of silica with two distinctly different

water contents [as measured by infra-red absorption, Figures (1) and (2)] were available, the above investigation

was centered on these samples.

Experimental Procedure

The damage threshold of each sample was determined by

changing the radiant flux density photons per square centimete:

per second incident on it by moving a thin plate of the sample

along the axis of a convergent, pulsed, laser beam.

The latter was generated by placing a biconvex lens

with a focal length of 32 cms in close proximity to

38
WAVELENGTH IN fJ.m Figure 1. Infrared transmission of the two samples of high

water content silica. Note the severe extinction

at 2.7 ym indicating the presence of water.

(G. W. Cleek)

39
5

to

z.

<t

3 4 WAVELENGTH IN /xm

Figure 2. Infrared transmission of low water content silica

Note the absence of the water absorption band at

2.7 ym indicating that this sample had

a very low water content.

^0
the ruby laser. The radius of the beam emerging from the

lens was measured at several points along the beam axis

by its "printing" effect on black pvc adhesive tape. The

resulting beam profile was as shown in Figure (3).

While it was recognized that this way of defining the

beam profile was limited by the threshold for the printing

effect, it proved to be fast and reproducible so that the

data could easily be reduced to the low power peripheral

contours which would be observable with a suitable photodetector.

The total energy in a single pulse emerging from the

lens was measured with a calibrated solid state calorimeter

placed near the lens. The resulting measurement was

correlated with the signal generated by an ITT bi-planar

photo diode having an SI spectral response, reacting to

a fraction of the light beam reflected from a glass plate

aGting as a beam splitter as shown in Figure (4).

The correlation was carried out by using 10 successive

shots, and these measurements showed that an ITT photo

detector signal of 250 ±17 volts corresponded to pulsed

beam energies of 1.5 ±0.1 joules.

The ITT detector was therefore used as a sensitive

monitor for each flash of the laser used in our damage

studies

.

In measuring damage thresholds, the laser controls

were adjusted so as to keep the monitor signals to within

250 ±17 volts and results obtained with monitor signals

outside of that range were discarded.

Results

Neglecting refractive index and absorption effects, the

results of our measurements and the damage threshold for

silica samples with high and low water contents, together

with that for a sample of Calcium Aluminate F75 are summarized in Table 1 and showed that:

(1) All the damage observed was restricted to the

surface and was In the form of surface pitting.

(2) The onset of damage was accompanied by an

acoustical signal and a flash of "white" light.

(3) Different samples, cut from the same slug gave

damage thresholds which were reproducible to within 2.5

J/cm^/30 ns.

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Sample

Position at

which damage

could be detected

Monitor

Signal

(Volts)

Damage Threshold

30 ns . pulses j/cn

High Water Content , Silica

Sample Source (1)

High Water Content , Silica

Sample Source (2)

Low Water Content, Silica

Calcium Aluminate

57.9

63.5

55.5

61.3

208

198

205

210

11.3

25.3

8.5

17.5

i

v

(4) Silica samples with the higher water content

yielded a higher damage threshold than those having a lower

water content.

Discussion

Samples of high water content silica derived from

sources 1 and 2, of allegedly identical material showed very

different damage thresholds, i.e. 12.5 and 26.5 J/cm2 for 30 ns

pulses. These two sets of samples could have had different surface

polishing treatments and they were therefore both re-ground

and re-polished by identical processes to ensure identical

surface characteristics. However, the re-polished samples

still showed the above difference in damage threshold, the

cause of which is not understood.

Another factor of considerable interest was that, even

after re-grinding and re-polishing, the high water content

samples invariably damaged on the back surface where the

energy density would be expected to be larger, while the low

water content silica samples invariably damaged on the

upstream surface.

The reason for this difference is not understood, and

may be related to absorption effects in the samples.

kk
' Conclusions

Samples cut from one slug of silica containing a considerable amount of water (as indicated by Cleek's infrared

absorption data of figure 1) indicated that the sample with

the higher water content had a higher threshold for damage

for 30 ns . pulses, 25 J/cm 2 versus 8 J/cm2 respectively.

This conclusion is rendered less certain by the fact that

samples from the other slug of silica also known to contain

a similar amount of water, had a damage threshold of only

11.8 J/cm2 for the 30 ns . pulses.

It appears that factors other than water content play a major part in determining the damage threshold. Assuming

that the two compositions can be regarded as being the same,

it appears that the heating and cooling conditions used in

the fabrication may have been different and may have a strong effect on the damage threshold.

Definite knowledge of the sample's total history is

therefore essential for understanding the results of damage

experiments

.

4.4.2.2. Inclusions in Laser Materials*

Herbert S. Bennett

Inorganic Materials Division

Institute for Materials Research

Objective

One of the severe problems encountered in high power

laser systems is the internal damage of the laser and its

optical elements. One type of internal damage arises from

metallic or dielectric inclusions. The present study

examines the feasibility of using optical techniques to

detect such inclusions before they cause damage. Detecting

an inclusion before it causes damage eases the burden of

the chemical analysis near the incipient damage area. During this report period, attempts have been made (1) experimentally to detect incipient damage centers by light

scattering techniques, and (2) theoretically to evaluate

the prospects of detecting such centers by the thermal

disturbance created in the glass around them when subject to

a laser pulse having an energy below the damage threshold

energy

.

* An associated project, supported by the National Bureau

of Standards.

45
Light Scattering Experiments

Azimuthal and forward light scattering techniques have

been suggested as possible ways to detect such centers.

Two Nd-glass rods (Owens-Illinois ED-2, 2.5^ cm in diameter

by 5.08 cm In length) have been examined in such light

scattering experiments at NBS and at the Air Force Cambridge

Research Laboratories. The object is to see whether

differences between the two rods can be detected by

scattering methods which do not rely upon the human eye

and yet provide an examination of essentially the whole

rod. The search and seek ability of the human eye is very

advantageous when compared with the limitations of such

devices as photo multiplier tubes and photo-diodes. One

sample was rated excellent and the other sample was rated

as less than excellent but not poor either. The ratings

were given by H. A. Lee of Owens-Illinois.

The azimuthal light scattering measurements were

performed at NBS and were reported in NBS Technical Note

Number 514. These measurements indicated that the forward

scattering might be more fruitful. Dr. Martin Stickley

and Mr. Edmund Hoell agreed to perform small angle scattering measurements on the above two samples. Their results

were communicated to NBS in the form of a letter. A copy

of the letter and data is given with their permission in

the appendix to this project report. We thank them very

much for their cooperation and for their efforts in measuring the small angle scattering. Even though they can

distinguish rod A from rod B, the difference is marginal

for the detection of a small number of inclusions which

are less than tens of microns in size. The technique does

not seem feasible as a way to maintain quality control for

inclusions leading to damage. The technique does have

promise for detecting striae however.

Theoretical Treatment of Laser-Induced Thermal Disturbance

Near Inclusions

The heat diffusion equation with time dependent boundary

conditions is solved for the temperature as a function of

position and time. The optical path length change for a

light ray passing near the inclusion, the radial and

tangential components of the stress tensor, and the radial

and tangential changes of the local index of refraction due

to the thermal stress field are computed from a knowledge

of the space and time variations of the temperature.

h6
tf suits

The initial computations apply to two cases of prime

practical interest. These are platinum spheres in a laser

glass host.

Case 1. A 30 nsec. laser pulse with an energy density

of 30 (J/cm2) encounters a platinum sphere of

radius .01 cm. Case 2. A 30 nsec. laser pulse with an energy density

of 3 (J/cm^) encounters a platinum sphere of

radius .001 cm. Because the model assumes that strain is proportional to

stress the energy density of the laser pulse has been so

far limited to values such that the temperature of the

glass never exceeds the strain point of glass. Laser

glasses have strain points around 600°C. This is the

reason why the energy density is less for Case 2 than it is

for Case 1.

The theoretical model predicts for Case 1, that the

largest optical path length changes are about 5 x lO-^cm

and occur for a range of distances of closest approach to

the platinum sphere from .01 cm to .03 cm. The time interval during which the path length changes are large is from

.03 seconds to .3 seconds after the beginning of the 30

nanosecond pulse. The tangential and radial stress components have magnitudes which do not exceed lO-^ (dynes/cm2).

Maximum stress occurs at the end of the laser pulse and is

a factor of 10 less than the bulk moduli of the laser glass.

The magnitudes of the radial and tangential changes of the

index of refraction due to thermal stress birefringence

do not exceed 10~3. These values of the stress birefringence obtained for the same values of radial distance and

time as those for the optical path length changes. The

maximum temperature occurs at the end of the laser pulse

and is 6l8°C at the surface of the particle. The maximum

radial rate of expansion of the platinum sphere is 2 x 103

(cm/sec). This expansion occurs during the laser pulse

and its rate is about a factor of 100 less than the speed

of sound in laser glass.

The theoretical model predicts for Case 2, that the

largest optical path length changes are about 2 x 10~° cm

and occur for a range of distances of closest approach to

the platinum sphere from .001 cm to .01 cm. The time

interval during which the optical path length changes are

large is much smaller than that for Case 1. The maximum

path length changes occur at about .03 sec. At .003 sec, the path

length changes are less than 10 _ 1^ cm and at .3 sec. they

47
The magnitudes of the tangential^

>nts do not exceed 10-^ (dynes/cm ).

-25

are less than 10 cm,

and radial stress componei

The maximum stress occurs at the end of the laser pulse

and is a factor of 10 less than the bulk moduli of the laser

glass. The magnitudes of the radial and tangential changes

of the index of refraction due to thermal stress birefringence do not exceed 10~3. The latter values are greatest

for the same values- of radial distance and time as those

for the maximum optical path length change. The maximum

temperature at the interface between the platinum and the

glass is 6ll°C and occurs at the end of the laser pulse.

The maximum value of expansion of the platinum sphere occurs

during the laser pulse and is about a factor of 1,000 less

than the speed of sound in glass.

Conclusions

The above calculations suggest two possible methods by

which incipient absorbing centers might be detected. One

method would use the interference of two light rays which

experience different optical path length changes and the

other method would use thermal stress birefringence. Because

optical path length changes greater than one tenth the

wavelength of the probing light are required to produce

detectable fringe shifts, case 1 and case 2 indicate

marginal feasibility for either of the above methods. However, calculations such as case 1 and case 2 and preliminary

additional calculations, which apply to millisecond pulse

widths but are not reported here, suggest the direction in

which one should go to optimize the optical path length

changes without causing damage. Heating the inclusion

over a longer period of time to the same surface temperature of about 600°C gives greater spatial extents to the

changes in indices of refraction. Another approach is to

employ pulse widths and observation times which are less

than the relaxation times of the host. Relaxation times

for laser glasses between 800°C and 1100°C are approximately

between nanoseconds and microseconds. These are estimates

of the time during which stress is proportional to strain

in glasses which are not elastic for infinite time. Such

short time observations will permit one to raise the inclusion surface temperature substantially above the present

600°C reported here and still satisfy the assumptions of

the present model. The author plans to extend his calculations to longer pulse widths and to higher temperatures.

Most of the other optical methods that have been suggested are capable of examining only small volumes at

any one time and additional scanning methods are essential

if an entire sample is to be studied. For example, K. Vedam

48
et al., J. Appl. Phys. 37_ s 2551 (1966), report ultramicroscoplc techniques by which they illuminate a 20y thick

layer and by which they can detect 0.35y particles with a (1/32) sec exposure for the camera. They also have

estimated that 0.03y particles might be detected with one

hour exposure. The major disadvantage is that the layer

under observation must be less than about 2 cm from the

surface of the sample. Researchers should be able to

[examine much larger volumes of the sample by the techniques

considered in this report.

The above computations suggest that examining incipient

absorbing centers in laser glasses by methods which employ

thermal stress birefringence are more promising than methods

which use the interference of two light rays which experience different optical path length changes due to the local

variation of the index of refraction near the platinum

sphere. However, because the propagation of light in the

presence of a stress birefringence which has spherical

symmetry is complex, the interpretation of the birefringence data will be more tedious than the interpretation

of data from an interference method.

Additional computations suggest that the use of laser

pulses with pulse widths of the order of milliseconds may

be more promising for the detection of small incipient

absorbing centers. The longer pulses produce changes in

the index of refraction which extend over greater distances.

The present theoretical model can be applied to any

spherical inclusion which has a thermal conductivity greater

than that of the host. For example, antimony inclusions,

which have been detected in some laser glasses, can be

treated readily within the framework of the present model.

Applying the present model to this and other cases is

planned. In addition, attempts will be made to remove

some assumptions contained in the present model in order

to make it applicable to a wider class of problems. Some

researchers suggest that metallic inclusions at very high

temperatures may have thermal conductivities comparable to

that of the host. For this reason, it would be most useful

to remove the restriction that the thermal conductivity

of the inclusion be greater than that of the host. Computationally feasible solutions do not exist at present for

this more general case; but additional efforts to this end

might prove successful. Also, the degree of thermal

contact between an inclusion and the host should be

examined during and after the laser pulse. It is certain

that the state of thermal contact at the initiation of the

laser pulse depends upon the past thermal history of the

49
host. Finally, any comprehensive study of inclusions in

laser materials should at least attempt to answer the

difficult question of how do the thermal properties and

elastic properties of the inclusion and host change during

and after the laser pulse. Workers in this area should be

aware of this last question, but rigorous answers are not

likely to be given in the immediate future. It is for this

reason that such theoretical models as the above can at

best serve only to guide the experimental researchers on

the damage problem.

Method

The author shall outline below the model upon which the

above calculations were based. He considers an absorbing

sphere of radius rQ imbedded in a host of infinite extent.

The thermal properties are the density p (gm/crrP), the

specific heat C (j/gm°C), and the thermal conductivity

K ( j/cm sec°C). The ^derived thermal quantities of

thermal diffusivity a = (K/pC) and the volume specific heat

h = pC also enter the calculations. The subscript c on any

of these thermal properties will refer to the absorbing

center and the subscript h will refer to the host.

The diffusion equation describes the time and space

dependence of the temperature T(r,t) for large distances

r and for large times t.

9T ^

at)

= a

2

V

2 T(r,t) (1)

dt ~

2 where V is the Laplacian operator. The diffusion equation

is valid only when local thermal dynamic equilibrium exists

It becomes suspect for distances comparable to atomic

dimensions and for times comparable to the phonon-phonon

collision time. A typical phonon-phonon collision time

at room temperature is lO -1 ! sec. Hence its validity for

nanosecond laser pulses is certainly more justified than

for picosecond laser pulses. The diffusion equation

requires a statement of initial conditions and boundary

conditions before a solution is uniquely defined. The

initial condition is that the

T(r t) = <f° t -° U (2) <£' tj (T(r,t) t>0 k ;

50
The boundary conditions are time dependent for any realistic

treatment of the problem. The temperature must be finite

everywhere, T(r=°°»t) = finite and T(r=0,t) = finite. The

continuity of the temperature across the center-host interface is

T (r=r r,t) = T,(r=r r,t)

c ~ o

} h ~ o'

The host is assumed to be very transparent to the laser

energy and absorbs only a negligible amount of energy from

the laser beam. The conservation of heat flow at the

interface gives

-K

h

VT

h (r=ro^,t).^= -K^Cr-iv^t ) •^+H(t)'zv.^ (3)

where £ is the unit radial vector and /£ is the unit vector

in the z direction. The heat flux H(t)

the heat absorbed by the sphere from the laser beam.

(Q ^:t^ t

H(t) = (4)

10 t>T and t<0

The radiation of heat by the interface and by the glass

close to the sphere is not included in this model. A

p black-body at 600°C produces a heat flux of .735 (J/sec cm ) The laser beam for Case 1 contains a heat flux of 1()9

(J/sec cm2

). The temperature gradients which occur from

the time of cessation of the laser pulse to the time of

maximum optical path length change are always sufficiently

large so that | K, VT, | is greater than the heat flux due to

the radiation. Of course, the heat flux -K, • VT, becomes

h h small for times greater than a second and the radiation

effects should be studied in both the diffusion equation

and in the boundary conditions. Because the temperature

is close to the ambient temperature whenever the time is

greater than a second the long time behavior is not in the

region of practical interest for detecting incipient centers

before they cause damage.

-2 -2 Because a c «.025 a^ and K

c«92 K^ the temperature

gradients in an absorbing center such as platinum would

51
be much less than those for the glass host. In the limit

of K c >> K

h

, Equation (3) simplifies to give a spherically

symmetric problem:

A

dTh (x=r/r,t) _ H(t) _ p^C^ dT c (r=rn r,t) ,-,. h dr H 3r dt

o

The solution for the temperature is obtained by taking

the Laplace transform of the diffusion equation, the initial

condition, and the time dependent boundary conditions. The

transformed equations become linear equations for the Laplace

transform U(r,S) of the temperature T(r,t). The analytic

properties of the Laplace transform U(r,S) for complex

values of S gives rise to three distinct types of behavior

for T(,£,t). The volume specific heat ratio (R = 4h c /3hh

) determines the three regions of behavior; namely R < 1,

R = 1, and R > 1. This ratio is about 2.97 for platinum

in laser glasses. For this case the function l/U(r,S) has

zeros at two complex values of /S=a±ib. The Bromwich

contour integral is evaluated to give the temperature

T(r,t) from a knowledge of U(r,S).

Having thus obtained the temperature T(r,t) one may

compute all the other quantities discussed above. The

optical path length change AL becomes

f AL = /L (dn/dT) T(r,t) dx, (5)

where the integration is along a ray that has a distance of

closest approach r-, to the absorbing center and the variation of the index of refraction with temperature is (dn/dT).

The calculation of the stress components require a few

more assumptions. The stress components satisfy second

order differential equations in position for a given time

and hence two coefficients must be determined. The

boundary condition that all stress components vanish at

distances infinitely far from the absorbing center determines

one of the two coefficients. There are three possible sets

of additional interface boundary conditions from which the

second coefficient may be evaluated. The author has chosen

to employ a slippery boundary at r = r

/ r\ A slippery

boundary obtains when the conditions listed below are valid:

52
a. The hydrostatic pressure in the absorbing center at

£ = r ^ equals the radial stress component in the host at

I = ?<&.

b. The tangential stress components are discontinuous

across the boundary at r = r

/r.

IGiven conditions a and b, one uses the poisson ratio

and the Young's modulus for the host and the isothermal

compressibility of the absorbing center to compute the

second coefficient. This second coefficient and the temperaiture T(r,,t) then yield the radial and tangential stress

components and the radial rates of expansion and contraction

of the absorbing center. From a knowledge of the stress

;components the stress birefringence may be computed. If

the rates of expansion and contraction of the absorbing

center approach the speed of sound in the host then the

above problem becomes a nonlinear one involving two coupled

differential equations. One equation treats heat diffusion

and the other treats energy transfer in the form of sound

or shock waves.

The author developed an extensive computer program to

evaluate all quantities given in Cases 1 and 2 for all

possible values of the ratio < R < M, where M may be

large but finite.

Appendix

Small Angle Scattering from Nd-doped Laser Glass

Appendix 1 contains the letter and data communicated to

NBS by Dr. Martin Stickley. This letter and data are

referred to in the Section 1 of the project report entitled

Inclusions in Laser Materials.

53
DEPARTMENT OF THE AIR FORCE

HEADQUARTERS AIR FORCE CAMBRIDGE RESEARCH LABORATORIES (OAR)

LAURENCE G. HANSCOM FIELD, BEDFORD, MASSACHUSETTS 01730

attn of: CROL./C M. Stickley / 2 6 94 23 December 1969

Dr. Herbert Bennett

National Bureau of Standards

Washington, D. C. 20234

Dear Herb,

Enclosed are graphs of the scatter loss vs. full angle for

Owens-Illinois Rods A and B. Also included is the data after

reduction by use of the formula found on the glossy figure

(AFCRL photo 109-344).

I think the system for measuring this scatter loss has been

working as well as it ever will be; to do better than we have done

would require a greater effort than I am willing to put into the

project. For full angles greater than 0. 35 milliradians the

standard deviation turned out to be about 0. 8% or less which

when converted into a loss coefficient gives a standard deviation

of about 0. 001cm" 1

.

As you can see from the graph of the average for 10 runs on Rod B, the loss is extremely low. I do not know how much of

this loss could be due to small angle surface scatter, thus it is included in these results. For the sake of computing a loss

coefficient I did not attempt to subtract out a representative

amount for it however. As you can see from the error bars,

the loss is about zero, however the averages for the 10 readings

were still on the positive side of zero for the largest angles

(1. 6 and 0. 8 mrad) where the data is usually the most reliable.

The uncertainty gets quite high at low angles (1. 6 x 10"^ radians)

probably because the intensity of the gas laser beam is highest

right in the center, and any error in replacing the aperture will

show up readily.

RESEARCH - The Key to Aerospace Superiority

54
A comparison of rods A and B shows that the average

transmission of Rod B is equal to or higher than that for

Rod A in every case even though the error bars overlap.

One factor that could cause this would be the optical quality

of the samples. We did position the beam so that it went

through the region of best quality of each rod, and to our

eye they looked the same, but whether this measurement

is more sensitive than our eye is unknown to me at the

present time. Thus, if this factor is negligible, I would say

Rod B is better than Rod A, but this difference is so slight

that it is unimportant in the operation of the material as a

laser. I am also enclosing photographs (positives and negatives)

of the intensity distribution in the far field for both rods and for

the case where no rod is present. The negatives can be used

for making more prints if you so desire. The far field distribution

is not what would be predicted theoretically since the illumination

of the 4. 2mm aperture was Gaussian-like.

I am going to send Haynes Lee a copy of this letter plus

attachments since I suspect he is interested in these results

too. We would also be interested in finding out which of these

rods is the better one. Ed Hoell, the person who made the

measurements, thinks Rod B is and the data supports his feeling.

Also, he is due credit for making these measurements. It is due

to his persistence and conscienciousness that they came out as well

as they did. I hope these results will be of use to you in your laser

glass program.

Sincerely,

C. MARTIN STICKLE

cc: Haynes Lee

Chief, Laser Physics Branch E. Hoell

Optical Physics Laboratory

55
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58
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60
4.4.3. Degradation of Laser Materials

4.4.3.1. Crystal Defect Studies on Laser Materials

R. F. Blunt, T. Chang, M. I. Cohen, and T. Tsang

Inorganic Materials Division

Institute for Materials Research

Objective

This investigation is a study of the causes responsible

for degradation of performance of solid state lasers. The

effort has been directed largely to a study of orange

degradation of laser ruby, by EPR and optical means. (See

NBS Technical Note 514 for previous report).

Technical Approach

Procedures followed are a continuation of those followed

previously with the incorporation of appropriate additions

and changes. Experimental measurements consist largely of

optical absorption spectra and electron paramagnetic resonance on a variety of specially prepared "ruby" samples:

1. Detailed spectra taken on undamaged ruby is

compared with corresponding spectra on "orange" degraded

samples. These include specially prepared "ruby" as well

as "laser quality" material.

2. Spectra will be examined for evidence of trace

impurities, and, in the case of "orange" ruby, typical EPR

crystal defect spectra that correlates with the orange

coloring bands. This is of particular interest in view

of the suggestion of Stickley, et al. [1] that discoloration may arise from color centers created by the pumping

light at defects initially present in the crystals.

3. Special attention will be given to the detection

of Cr4 + and/or Cr^ + ions that may exist in the orange

samples. This effort includes a study of the Am = 2 , EPR

transition reported by Hoskins and Soffer^ and by Mason

and Thorp. [3]

4. A number of doped sapphire crystals are grown and

studied. Included are: rubies covering a wide range of

Cr concentration; crystals containing other single metal

impurities; and several "double doped" with Cr and one

other metal.

5. Most crystals are colored by radiation with 50 KV

x-rays, but recently °0q o y-irradiation has been occasionally

employed.

61
6. Bleaching of the orange coloration by ultra-violet

t and by

is conducted.

light H„ plus heat in the case of the M doped rubies

» - j —j__j£- g

7. Coloration by laser pumping light and/or high power

mercury arc sources is under way.

Experimental Results

With very few exceptions measurements were made on

samples cut from Verneuil crystals grown in this laboratory.

Metallic dopant concentration quoted are the nominal "starting material" values or, in the case of Cr, usually the

value determined by the optical absorption method of Dodd,

Wood, and Barns. [4]

The previous report describes the -coloration produced

by x-ray irradiation produced in both "in house" rubies and

laser quality rubies. These several additional bands include, especially, a broad band centered near 0.47 um and

additional bands or long "tail" extending beyond 0.6 um.

Single doping of "pure" sapphire with various metals,

principally transition elements, yielded x-ray coloration

only in the ultra-violet.

Double doping with Cr and one additional metal, yielded,

in the case of Cr plus Mg, an orange coloration at the time

of growth. A careful choice of doping levels, viz. 0.025

mol$ MgO and 0.0034 mol# Cr 2 0o (i.e. 0.005 wt % Cr 2 3

) gave

an orange coloration, apparently identical to that produced

by x-rays. Further, it was shown that the coloration was

far greater than that of the normal Cr^+ absorption spectra.

The simple chemical picture of Mg converting even all of

the Cr3+ into Cr^ + would require very excessive oscillator

strength for Cr^ + . Thus we concluded that the x^-ray

coloration is probably not directly caused by Cr^ and is

quite likely derived from some other mechanism, perhaps

due to a trapped hole or electron model, i.e. a color

center. The possibility of the oxidation of Cr3 + to Cr 4+

still exists, and, of course, the presence of chromium is

essential to the coloration.

Several experiments reported earlier have been repeated

and extended. The possibility of defects being produced in

sapphire by Cr plus Ti doping and by doping with Mg alone

have been repeated using 50 KV x-ray irradiation. The

original results were obtained, viz. Mg doping gives susceptability to coloration in the ultra-violet only. The

Cr plus Ti doping results in coloration similar to that of

Cr alone.

62
We have attempted the bleaching of x-ray colored rubles

and find that the ultra-violet radiation from a 150 watt

Hg arc very effectively and quickly bleaches out the orange

color. The color is easily restored with x-rays. Semiquantitative tests with appropriate filters to remove only

the shorter wavelengths indicate that the bleaching is done

principally by wavelengths shorter than 0.3 urn.

It is also found that x-ray induced color is easily

and reversibly removed by heating in air. Various workers

report various temperatures as effective. We arbitrarily

chose l400°C as certainly higher than necessary but still

very low with respect to the 2050°C melting point. Thermal

bleaching of a number of samples was done with the expected

easy re-coloration.

Since the incorporation of Mg results in coloration

by what would seem by elementary chemical arguments to be

a simple oxidation of the Cr3 + to Cr^ + , the possibility of

reduction and hence bleaching by heating in a hydrogen

atmosphere must be considered. It was found that a 24 hour

heating cycle in hydrogen at l400°C results in bleaching,

of the orange color of a Mg plus Cr doped sample, back to

the normal Cr3 + pink color.

Heating in air restored the orange color. This apparent

! oxidation and reduction in the bulk sapphire at such a low

temperature is not understood at this time and warrants

further study.

As mentioned in the NBS Technical Note Number 5l4

(Progress Report for Project 300.0400 1 January to 30 June,

1969)5 we find that the x-ray coloration saturates with

i irradiation dosage, and reaches a saturation value for doses

near 5 x 10° R/cm2. In these discussions we consider only

the prominent 0.47 um band which we consider as typical.

This is very typical of the often used "growth" curves

employed in classical color center studies, and certainly

suggests a model involving either crystal defects initially

present or as we would prefer, mechanisms (defects or otherwise) definitely associated with the chromium ions in some,

as yet unknown, manner. Further, detailed study of the

saturation values at 0.47 um for a number of Cr concentrations has been made and is plotted in figure 1. Absorbtivity

at 0.47 um is plotted vs. mol$ Cr for a number of crystals.

The ordinate is in arbitrary units, normalized only for

sample thickness. This shows that the absorption coefficient reaches a broad maximum value at about 0.09 mol#.

Novotny and Spurny [5] report similar results. It is to

be noted that the "standard" pink laser ruby (0.05 wt %

63
1

Cr 2 0o) lies well down the curve at 0.03*1 % Cr. while the

"red" ruby that oscillates above 0.7 urn (on the N lines

rather than the R lines) lies well out in the tail near

0.34%. This marked reduction in susceptibility to damage

with increasing chromium might suggest Cr pairing as being

involved. The N lines, of course, are from Cr pairs;

various authors have studied pairs, including for example

Powell [6] and Gill [7].

The work of Stickley [1] indicates certain differences

in detail between discoloration produced by laser pumping

light and by ionizing radiation (i.e. x-rays). His work

indicates that the longest wavelength band in pumped laser

rods is near 0.4 urn and has a definite long wavelength tail

extending out to at least 0.7 um. He offers evidence that

"his" bands are in fact the same bands produced in "pure"

sapphire by ionizing radiation as described by Levy [8].

We have initiated experiments to produce and study

these pumped (i.e. ultra-violet light produced) effects.

Samples included "in house" crystals, and crystals from

two different commercial sources, both being reputed to be

particularly susceptible to pump discoloration. These were

mounted in an uncooled ruby laser head, with no UV filter

provided. The "head" was flashed at 2 minute intervals

and samples measured for discoloration. To date, after

some 300 flashes only slight coloration has been observed,

but this is insufficient to be clearly outside the limit

of experimental detectibility . Future work along these

lines should be done, perhaps with cooling, with a stronger

source, or perhaps with a strong CW mercury arc.

Electron paramagnetic resonance measurements have been

made on a number of these samples. As indicated, special

attention was given to a search for trace impurities of

paramagnetic ions or other paramagnetic defects in general

(i.e. color centers). Changes in the normal Cr3+ spectra

were searched for with the intentions of correlation with

the observed optical data. A very special effort was

directed at finding the EPR band studied by Hoskins and

Soffer [2] and by Mason and Thorp [3].

Included initially was a "pure" "in house" sapphire

that showed a clear Cr3 + EPR spectra and no change on x-ray

irradiation. A vapor phase grown sapphire, grown by anothe:

group at NBS, gave no Cr3 + EPR signal, attesting to its

unusual purity in this respect. A number of rubies yielded

the normal Cr3+ EPR spectra and no change after x-ray

coloring.

64
Subsequent to the above, the Hoskins and Soffer line

"2,3], which they attribute to Cr^+, has been observed in

his laboratory. Two laser quality samples of 0.05 and

).01 wt % CrpOo were obtained from the Naval Research

abpratory (NRL). These had been colored by 10^ R/ cm2 sec.

|f Co irradiation and carefully protected from all light

except dim incandescent bulbs.

The prior difficulty in observing this line is not

completely understood. It is possible that it is very

easily bleached optically, and hence is not caused by the

same mechanism responsible for the optical color. They

are related of course since they have been shown to be

generated both chemically (2), and by irradiation. The

difficulty is believed, very definitely, to be related

:o lack of proper sample preparation in the earlier experiments. It is found necessary to operate at low temperature,

I.2K.

Figure 2 is the EPR line obtained on a 0.005 wt % sample

rown here and irradiated by 2.6 x lo" (R/cm sec.) of ' Co. The

magnetic field increases to the right, the "zero" signal

level is indicated, and the position of the zero crossing

(indicated) is chosen as the center of this unsymmetrical

line. Nearby structure as well as the asymmetry indicate

a line of some complexity. The center field of 0.176 Tesla

and the frequency of 9-^671 GHz indicate a geff of 1.92,

assuming a Am = 2 transition. The power level into the

cavity was 355 y watts.

Figure 3 is that of the 0.05 wt % NRL sample showing

'the "line" at two power levels. The solid curve was taken

at 355 M watts, the dashed curve at 2.51 n watts. Thus the

'extreme sensitivity of the sidebands of this line to power

level is well illustrated. To study completely this line

land its side bands, it is evident that the power levels

required cover an extremely broad range. The lower end

of this range can only be observed by an excellent superheterodyne detector such as is available in this laboratory.

The apparent lack of the appropriate structure would

seem to rule out the existence of the normal hyperfine

structure anticipated for Cr^ , thus we currently find the

identification with Crij+ to be unsatisfactory. On the

i,other hand the geometry of the cavity, viz. the

iB d

// B

r f// p-aotis together with the rhombohedral field of

the corundum lattice, would make the identification of the

line with a Am = 2 transition extremely likely. Finally,

on cooling from 4.2K down to 1.7K the signal strength is

reduced by a factor consistent with an activation energy

of about 7 cm-1. Thus we envision a spin 1 model in which

65
the ground state is spin lying perhaps 7 cm below the

±1 states. The latter can be observed as a Am = 2 transition under proper conditions. Of course, this is the

model expected for Cr^+ but we currently rule this out for

other reasons.

O n C r\ We have also given 2.6 x 10 R/cm of Co irradiation

to several other samples of "in house" crystals, and as

before, protected them from strong light. A "pure" sapphire

crystal was found to contain Cr3+ } a trace of iron, and a weak An. = 2 line, although the sample geometry was probably

unfavorable in this case.

Also during this period both optical and EPR measurements were made on certain specially prepared samples of

Nd glass to test these methods as means of detecting Pt

inclusions. However, both the optical and EPR bands are

too broad to permit reasonable sensitivity, and these

methods do not seem very promising.

Future Plans

Experiments planned for the immediate future, some in

fact under way, are outlined in the following list:

1. Work is to commence immediately on YAG. The

obvious importance of rare earth doped YAG, together with

the report of discoloration/degradation of YAG during laser

operation, would seem to make such work significant. Damage

will be produced by both optical pumping and ionizing

radiation. Optical studies and EPR measurements will be

made in order to get some understanding of the nature of

this trouble. Greater emphasis will be placed on the

infra-red than has been done in ruby. YAG (pure, Nd doped,

and possibly double doped with Nd and Cr) will be included.

Some appropriate material is in hand and more is expected

shortly

.

2. The EPR facilities to be employed are expected to

include K - band capabilities soon. One bridge and a low

temperature cavity set-up is nearly in operation. A

K - band optical/EPR cavity has been designed that, hopefully, will soon be constructed. The use of optical/EPR

cavities allows optical bleaching or excitation in the

cavity. A true double resonance experiment has obvious

application in the study of the E excited state in ruby

and it may prove useful in YAG. Lastly, double resonance

of the excited state may be a means for meaningful EPR

study of laser glass. It is possible that the excited

state EPR bands may be narrow as contrasted with the broad

ground state lines usually encountered. Successful work on

66
these latter problems will probably depend upon Improvement In direct optical resolution, which is currently

being planned, and upon use of K-band frequencies; the

higher magnetic field will increase the optical splitting

and also help in this respect.

3. Some work will continue on ruby, with special

emphasis on the correlation between optical and EPR spectra,

now that the Am = 2 line seems to be readily available.

The hydrogen bleaching of the orange coloration in Mgdoped ruby is most puzzling, and could well be explored

further, such as by additional multiple doping experiments.

The possibility of the easy optical bleaching of the Am = 2

EPR line has not been examined as yet and will be shortly.

4. One interesting optical/EPR correlation experiment

suggests itself, and will be attempted soon. The pronounced

maximum in coloration with Cr concentration (fig. 1) could

oe correlated with the Am =2 line. These samples are still

available and can readily be prepared for EPR work. In

addition, the possibility of Cr pairing being involved can

be explored by examining the EPR pair spectra discussed by

Gill [7]. He found r,hese lines at concentrations as low

as 0.03 molft and the signal increased quadratically with

ccncentration

.

5. Further efforts at coloration of various ruby

samples with pumping light must be made and will involve

a 1 KW mercury arc.

6. Two other experiments are contemplated. One

involves a search for the expected 7 cm"-'- band In the

ground state of Cr^ + in colored ruby and the attendant

Zeeman splitting of that low lying excited state. This

must be done in the far infra-red. If it is done, it will

be done at NRL and positive results would be most interesting. This work would follow similar work on other ions

as reported by Joyce and Richards [91-

The second experiment will be a precision magnetic

susceptibility measurement of the paramagnetic spins in

ruby. This work would be done by G. A. Candela in this

laboratory, using existing equipment [10]. The sensitivity

available is believed to be more than adequate for precision measurements of the paramagnetic spin concentrations

involved. The identification of any particular ion, which

is absolutely essential for this method to be of any

interest, would be done as follows. The susceptibility

measurements are made on the sample while mounted in a special low temperature microwave cavity. Any ion, for

example Cr3 +

} that can be "saturated" at resonance, will

67
have its spin "removed" from the overall susceptibility.

The net loss in susceptibility can then be used to calculate

the Cr J+ concentration.

References

[1] C. M. Stickley, H. Miller, E. E. Hoell, C. C. Gallagher

and R. A. Bradbury, J. Appl. Phys. 40, 1792 (1969).

[2] R. H. Hoskins and B. H. Soffer, Phys. Rev. 133, A490

(1964).

[3] D. R. Mason and J. S. Thorp, Proc. Phys. Soc. (G.B.)

87, 49 (1966).

[4] D. M. Dodd, D. L. Wood, and R. L. Barns, J. Appl. Phys.-

35, 1183 (1964).

[5] J- Novotny and Zd. Spurny, Czechoslovak Jour, of Phys.

16B, 119 (1966).

[6] Richard C. Powell, B. DiBartolo, B. Birang, and C. S.

Naiman, Phys. Rev. 155., 296 (1967).

[7] J. C. Gill, Proc. Phys. Soc. (G.B.) 79, (Pt. 1), 58

(1962).

[8] Paul W. Levy, Phys. Rev. 123., 1226 (1961).

[9] R. R. Joyce and P. L. Richards, Phys. Rev. 379 , 375

(1969).

[10] G. A. Candela and R. E. Mundy , Rev. Sci. Instr. 36.,

338 (1965).

USCOMM-NBS-DC

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71

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