M

Km
NBS TECHNICAL NOTE 565

ARPA-NBS Program

of Research on High

Temperature Materials

and Laser Materials

Reporting Period

January 1 to June 30, 1970

UNITED STATES DEPARTMENT OF COMMERCE

Maurice H. Stans, Secretary

NATIONAL BUREAU OF STANDARDS • Lewis M. Branscomb, Director

NBS TECHNICAL NOTE 565

ISSUED JANUARY 1971

Nat. Bur. Stand. (U.S.), Tech. Note 565, 84 pages (Jan. 1971)

CODEN: NBTNA

ARPA-NBS Program of Research

on High Temperature Materials

and Laser Materials

Reporting Period

January 1 to June 30, 1970

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. C 13.46:565). Price 75 cents.

TABLE OF CONTENTS

Page

1. Introduction . 1

2. Objectives ...... 1

3. High Temperature Materials Program 2

3.1. Objectives and Summary of Program in High

Temperature Materials ... 2

3.1.1. Objectives 2

3.1.2. Summary of Progress to Date 3

3.2 Projects Summaries in High Temperature Materials . 5

3.2.1. Diffusion in Oxides 5

3.2.1.1. Crystal Growth from Vapor ... 5

H. S. Parker and C. A. Harding

3.2.1.2. Diffusion in Refractory Materials 9

A. L. Dragoo and F. P. Knudsen

3.2.2. Properties of Refractory Borides .... 11

3.2.2.1. Electronic Structure of

Refractory Hard Metals .... 11

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

G. C. Carter, and A. J. McAlister

3.2.3. High Temperature Metals 17

3.2.3.1. Optical Constants of Titanium . 17

A. J. Melmed and J. J. Carroll

4. Laser Materials Program ...... 26

4.1. Introduction to Laser Materials ... 26

4.2. Objectives and Summary of Program in Laser Materials 26

4.2.1. Objectives ...... 26

4.2.2. Summary of Progress to Date ....... 27

4.2.2.1. Characterization of Laser

Materials 27

4.2.2.2. Damage to Laser Materials ... 28

4.2.2.3. Degradation of Laser Materials . 29

III
Table of Contents (continued)

Page

4.3 Project Summaries in Laser Materials , 30

4.3.1. Characterization of Laser Materials .... 30

4.3.1.1. Physical and Chemical Properties

of Laser Materials ....... 30

G. W. Cleek and R. M. Waxier

4.3o2„ Damage to Laser Materials 41

4.3.2.1. Laser Induced Damage Studies . . 41

Albert Feldman, Roy Waxier, and

Deane Horowitz

4.3.2.2. Inclusions in Laser Materials . . 46

Herbert S. Bennett

4.3.3. Degradation of Laser Materials . . . . . . 54

4.3.3.1. EPR Measurements on Normal and

Orange Ruby .......... 54

R. F. Blunt, T. Chang, and

M. I. Cohen

4.3.3.2. Optical Absorption Determination

of Chromium in Ruby 65

R. F. Blunt

3+

4.3.3.3. Analysis of Cr in Orange Ruby

by Magnetic Susceptibility

Measurements 72

R. F. Blunt, G. A. Candela,

R. A. Forraan, and A. H. Kahn

IV
ARPA-NBS PROGRAM OF

RESEARCH ON HIGH TEMPERATURE AND LASER MATERIALS

Work Performed at the National Bureau of Standards

Supported by the Advanced Research Projects Agency

Department of Defense

(ARPA Order 373-62)

Reporting Period 1 January to 30 June, 1970

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 this reporting

period on several problems in the areas of High Temperature Materials

and Laser Materials. Under the High Temperature Materials extremely

pure Al crystals have been prepared and analysed chemically with the

aim of providing specimens for research on mass transport, electronic,

and similar properties. Oxygen diffusion data on Ti0«, obtained by the

gas uptake method, agree with literature values, and work is now proceeding on developing a sectioning technique for oxygen diffusion. The

optical constants of titanium have been determined over the visible portion

of the spectrum. Soft x-ray spectra, nmr data, Mossbauer spectra,

magnetic susceptibility, and other probes of the electronic density of

states have been determined for a group of diborides of the first-series

transition metals (Sc, Ti, V, Cr, and Mn) and interpreted in terms of the

d-electron contribution to the density of states near the Fermi level.

Both this project and the previous one on the optical properties of

titanium have been completed.^ Under Laser Materials, the measurement of

bulk optical properties and chemical analyses of ruby and Nd-glass are 3+ complete. Several techniques for determining the Cr content in laser

ruby have been developed and shown to agree; with these, it has been

3+

shown that very little loss of Cr occurs when ruby turns orange under

optical (x-ray or Y~ray) irradiation. A theory of laser pulse-induced

damage at foreign particles in Nd-glass has been worked out; it suggests

that detection before damage might be easiest with pulses of microsecond

or longer duration. A high -power Nd-glass laser, Q-switched, has been
purchased for damage studies. The beam characteristics, which must be

properly controlled for meaningful damage threshold measurements, are currently being studied.

Key words: Aluminum oxide, band structure, borides, bulk optical

properties, chemical analysis, chromium ions, corundum, crystal defects,

crystal growth, density of states, diffusion, glass, high temperature

materials, laser damage, laser degradation, laser glass, laser materials, mass transport, neodymium glass, optical properties, opto-elastic properties, oxides, ruby, rutile, titanium, titanium dioxide, transition metal.

VI
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. The overall objective of this program is to

provide some of the key elements needed by DoD in its pursuit of new

technology through research and development. These elements include:

i. The preparation and characterization of materials needed for

critical studies where exacting criteria of chemical purity,

crystalline perfection, etc. must be met if progress is to

be made,

ii. The development of new measurement techniques where these are required, and the acquisition of critically-needed data

on certain material properties, and:

iii. The elucidation of the basic mechanisms contributing to or limiting the use of materials under extreme conditions

(e.g. high temperatures, high intensity laser light, etc.).

A summary of the results achieved in the period January 1 to June 30,

1970, is given here.

2. OBJECTIVES

The development of new technology is often limited by the properties

of the available materials. New material development requires a great

deal in the way of background information about the behavior of the

materials of the given class, about data on their properties, about methods

of preparation of re search -worthy specimens, and about measurement techniques capable of operating in new realms of application.

In a program of this kind, economy demands that key areas where new

knowledge is needed be identified, and the work focussed upon these. We

have chosen to emphasize the key problems of matter transport, expecially
oxygen, in oxides, and the degradation of laser materials, especially but

not exclusively neodymium-doped glass, under high -energy laser pulsing.

The work on the Optical Constants of Titanium is completed, the study of

the Properties of Refractory Borides will be continued on another program.

APRA support for both is ended with this report.

The Report is divided into two parts, High Temperature Materials and

Laser Materials. Each part will open with a brief summary of objectives

and accomplishments, followed by detailed Project summaries.

3. HIGH TEMPERATURE MATERIALS PROGRAM

3.1. Objectives and Summary of Program in High Temperature Materials

3.1.1. Objectives

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 micros tructural features (porosity, grain size) controlled by

sintering, the strategy for improvement here requires control over sintering in these ceramics. The same is true of 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 A1_0 .

Since sintering in ceramics is mainly brought about by diffusion

processes, the development of successful, long-range strategies 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 those materials for which mass

transport data is sorely needed. The first candidate has been Al , an important constituent in many ceramics, in particular for ceramic

armor.

3.1.2. Summary of Progress to Date

The work on the preparation of very pure Al crystals has now

produced what appear to be the purest and, from a chemical viewpoint,

best characterized oxide crystals yet made. These crystals are clearly

3
pushing the capabilities of the most sensitive techniques for chemical

analysis. Specimens have been made available to Prof. Arthur Heuer of

Case Western Reserve University, who plans to study oxygen diffusion

in them with his newly -developed proton activation technique. Such a test may ultimately be the only way of determining whether these

crystals have reached the goal in this work, sufficient purity to

achieve intrinsic, as distinct from impurity -con trolled, mass transport. In the meantime, modifications have been made to the apparatus

and starting materials that should further lower the concentrations of

the remaining major impurities, especially silicon. It is planned to

offer a limited amount of these high purity crystals to other laboratories for use in critical studies.

In the work on the development of a technique for measurement of

Diffusion Coefficients in Oxides, the mass spectrometer for analysis of

the oxygen isotope ratio (our means for following the transport of the

oxygen tracer) has now been completed and put to use. With it, determination has been made of the oxygen diffusion coefficient in TiO_ at

several temperatures and a fixed oxygen partial pressure, by analysing

the exchange between gas and crystal. The agreement between these

results and recent values in the literature is good and gives confidence that the portions of the system so far in operation are performing satisfactorily. Still to be completed is the technique for moving

oxygen from ground-off sections of the crystal into the mass spectrometer, so that the oxygen tracer penetration profile may be determined.

The project under the Properties of Refractory Borides heading,

which now leaves this Program, has produced data on soft x-ray spectra,

low temperature electronic specific heat, boron nmr Knight shift,

electric quadrupole coupling, and x-ray lattice parameters for the

series of diborides ScB„, TiB , VB„, CrB„, and (except for the soft

x-ray spectra) MnB„. Having such a complete set of data across the

early part of the first transition series of metals has revealed

distinct trends that can be correlated with atomic and physical properties. These, together with band structure calculations now in

4
progress, should help in developing a fundamental understanding (bf the

properties of this class of compounds.

The determination of the Optical Constants of Titanium has been

completed. Our results are in good agreement with the best work in

progress elsewhere. From our results and those of other laboratories,

it is possible to understand the influence which oxidation of the surface has had on measured values in the past. With the current results,

the basis is available for work on such problems as the initial development of oxide films, in the early stages of oxidation of the metal

and its alloys. The very sensitive ellipsometric techniques are used

in these studies.

3.2. Project Summaries in High Temperature Materials

3.2.1. Diffusion in Oxides

3.2.1.1. Crystal Growth From Vapor

H. S. Parker and C. A. Harding

Inorganic Materials Division

Institute for Materials Research

The objectives of the 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 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, considerable effort has been devoted

to the further chemical characterization of our aluminum oxide vapor

grown crystals. Because neutron activation analysis cannot detect

some likely impurities in an A1„0 matrix, spark source mass spectrometric analysis was used as an alternative technique. The results,

together with the previously reported activation analysis results for

comparison, are given in Table 1.
Table 1 Chemical Analyses of NBS Vapor Grown Alo^i

Element level, parts per mil lion weight

Activation Analysis Mass Spectrometric

Cu 0.027 - 0.038 1

Ir 0.0005 - 0.002 n.d.

Mg a/ 1

Mn -0.0005 0.2

Cr n.d. (<1) 0.3

Sc -0.015 <5

Si b/ <1(&

B y <0.01

V b/ 0.1

CI n.d. (<0.1) <10

Analyses performed by Spectrochemical and Activation Analysis

Sections, NBS

a/ Interference, in A1„0 matrix

b/ Cannot detect in A1„0 matrix

c/ Possible interference

It should be emphasized that where a value is shown as "less

than," it represents an upper limit and should not be interpreted as

the actual level in the material. At the levels of purity indicated

in Table 1, determination of the absolute amounts present is a formidable problem. For example, compare the copper and manganese values

shown in the table as determined by the two techniques. Thus, although

magnesium, chromium, silicon and vanadium may be present as impurities,

the actual amounts present remain in doubt. It is possible, however,

to compare samples on a relative basis as shown in Table 2, where the

NBS alumina is compared with some of the best Czochralski grown ruby.

Barium and strontium, not detected in the NBS vapor grown Al tend to

vary over a considerable range in the Czochralski ruby. The section

of this report entitled "Physical and Chemical Properties of Laser

6
Materials" by Cleek and Waxier, from which the values quoted here for

ruby were taken, discusses this point further.

Table 2

Comparison of NBS Vapor Grown A1

2 with Czochralski Grown Al

Activation Analysis

ppm by weight

Element

Cu

Ir

Mn

Sc

Ga

Ba

Sr

Cu

Mg

Mn

V

Si

B

NBS Czochralski

Vapor Grown Grown

0.027 0.016

0.0005 0.041

-O.0005 0.0006

-0.015 n.d.

n.d. <0.006

n.d. 1.74

n.d. 0.085

Mass Spectrometric Analysis

ppm by weight

1 1

1 1 0.2 0.7

0.1 0.4

<kA7 <2C^

<0.01 <0.01

a/ Possible interference

As can be seen, the NBS vapor grown Al is of higher overall

purity. In spite of the discrepancies between the techniques and

possible interference (see silicon, Table 2), on a relative basis the

results should be valid.

In an attempt to place an upper limit on some classes of impurities, two other techniques have been utilized in cooperation with

Dr. R. A. Forman of NBS. The first is a measurement of the bulk

7
magnetic susceptibility and its temperature dependence from 300 K to

2 K. This measurement should lump together all paramagnetic impurities

in terms of a temperature dependent (Curie Law) paramagnetic contribution to the susceptibility. Previous measurements on commercial

sapphire by this means have detected a paramagnetic contribution. No

Curie Law dependent part of the susceptibility was found and the susceptibility of the sample remained virtually constant at a value of

-12 3

0.318 ± 0.002 x 10 m /g from 300 K to 2 K. The limits of precision

of the measurement allow us to set an upper bound of 3 ppm of S = 5,

g = 2 paramagnetic centers in the sample, which corresponds to the

maximum errors in the measurement. In the same units commercial

sapphire (not the Czochralski ruby discussed earlier) has been found to

contain approximately 125 ppm of paramagnetic centers.

The second technique utilized is optical absorption from the

vacuum ultraviolet to the near infrared. Polished specimens of

1 to 3 mm nominal thickness were used. The transmission was measured

over the wavelength range of about 140 to 7000 nm. Over this range, no

evidence of absorption bands were found. Calculations of the absorption

coefficient, uncorrected for the higher reflection losses in the ultraviolet as compared to the visible spectrum, show that the absorption

coefficient drops essentially to zero at a wavelength of 200 nm. This

optical measurement should be extremely sensitive to most of the transition metals, which would display strong charge transfer bands in the

ultraviolet region, and should be sensitive to many of the common anion impurities which might be expected such as OH . While these

measurements do not allow us to give a limit on the concentration of

impurities present, they indicate the extreme purity of the material.

Assembly of the new growth apparatus is currently in progress. It

is hoped that the use of higher purity aluminum (99.9999%) together

with the minimized contact of chlorine and aluminum chloride with exposed metal in the new apparatus will further reduce the impurity level in

the vapor grown aluminum oxide.
A paper entitled "Vapor Growth of Bicrystals of Aluminum Oxide"

has been accepted for publication in the Journal of the American

Ceramic Society.

For the next reporting period, continued emphasis will be placed

on reduction in impurity levels. Although it appears that it will be

necessary to evaluate chemical purity on a relative basis at this stage,

further investigation of possible methods of chemical characterization

will be continued. The completion of the second, improved growth

apparatus should make limited numbers of crystals of the high purity

aluminum oxide available to a greater number of investigators.

3.2.1.2. Diffusion in Refractory Materials

A. L. Dragoo and F. P. Knudsen

Inorganic Materials Division

Institute for Materials Research

The objectives of this program are to measure and to interpret

diffusion of oxygen in single crystal oxides. Experimentally these two

objectives consist of (1) extending the sensitivity of present tech18 niques so that the distribution in a single crystal sample can be

measured, (2) comparing the results of these concentration profile

18

measurements with measurements of the rate of exchange of between

the gas phase and the oxide crystal, (3) determining the dependence of

the diffusion rate on temperature, oxygen partial pressure, impurities

in the solid, etc., and (4) obtaining reliable diffusion and exchange

coefficients. In regard to interpretation, this objective translates

into determining the mechanisms for oxide ion diffusion in the oxide

studied. Currently, rutile (TiO ) is the oxide of interest.

Since the previous report, the inlet system for the isotope ratio

mass spectrometer has been completed. We have found it possible to

analyze quantities of oxygen as small as 0.02 standard cc. Oxygen

samples obtained from the diffusion furnace are on the order of 0.3

standard cc with a pressure in the furnace of about

9

4 2

3x10 N/m (1/3 atm). The mass spectrometer and inlet system
were used in conjunction with the diffusion furnace to measure the

diffusion coefficient reported below.

A diffusion anneal was carried out in a platinum tube diffusion

/ o chamber at 1275°C, at a pressure of 4.29x10 N/m (0.424 atm) and for a duration of approximately 124 hours. Fifteen 0~ samples were taken

from the diffusion chamber during this time and the decrease in

18

0-content of the gas (about 3% for the entire anneal) was analyzed to

determine the diffusion coefficient.

For diffusion parallel to the c-axis of a single crystal rutile

-12 2

disc we obtained D = 8.9x10 cm /s

This result agrees well with the result of Haul and Dumbgen as

(2) did our previous result at 1350°C. Recent measurements by Lees,

Calvert, and Derry, using a resonance capture of protons to study

oxygen diffusion in titanium dioxide, have yielded diffusion coefficients at 1000° and 1400°C which agree well with the results of Haul

and Dumbgen. The sample used in the current study had about 20% of its

surface covered with small platinum crystals by the time the anneal was

terminated. The previous sample was annealed in an alumina tube and

thus was not subjected to this interference. Haul and Dumbgen who

carried out their measurements on rutile powders in platinum tubes

(3) experienced no platinum deposition. We are currently investigating

ways of eliminating this problem.

References

1. R. Haul and G. Dumbgen, J. Phys . Chem. Solids 26, 1 (1965),

2. D. G. Lees, J. M. Calvert, and D. J. Derry, "A technique using

resonance capture of protons to study oxygen diffusion in

titanium dioxide," paper presented at the Thomas Graham Memorial

Symposium on Diffusion Processes, University of Strathglyde,

Glasgow, Scotland, 1969.

3. R. Haul, private communication.

10
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 soft x-ray spectroscopy, nuclear magnetic resonance, and

electronic structure calculation results obtained during this report

period are as follows.

A series of boron-K valence band x-ray spectra obtained from the

diborides in the first transition series, i.e. ScB„, TIB , VB

?

, and

CrB

9 as well as from pure single crystal boron reveals some pronounced

trends in the fine structure and shift in the maximum peak energy that

appear to correlate with d -electron concentration and with melting

point. The pure boron spectra peaks at about 185 eV. With increasing

d-electron concentration the peak shifts downward in energy to 183 eV

for the location of the boron-K peak in CrB_ (see Figure 1). The

trends in fine structure are also evident in Figure 1. The structure

on the high energy edge (at "A") becomes increasingly more pronounced

with increase in d-electron concentration, i.e. becoming most pronounced

11
in CrB~. Meanwhile, the structure on the low energy side at "B"

appears to show an intensity variation correlated with melting point

of the diboride. There has been evidence of this peak shift and the

fine structure on the high energy edge in boride spectra that have been

reported on previously in the literature but this is the first time

that data on the complete series has been obtained which, together with

the results of the APW calculation of the band structures for these

borides, should make the possibility of a fundamental interpretation of

these data much more promising.

Work on the augmented plane wave calculations of the transition

metal diboride band structures is continuing. A serious practical

limitation to the extent of these estimates is posed by the large

secular equations necessitated by the C32 cellular basis. In view of

this, we have been forced to limit the scope of the work to state

distribution calculations for CrB„, using a reasonable crystal potential,

with the aim of constructing a useful model of the electronic structure of the series via a semi-rigid band picture.

New data have been obtained for Knight shifts and electric quadrupole coupling constants. These, together with previous results, are

plotted in Figure 2. This now shows some general trends of the NMR

results, which fit in fairly well with data on electronic specific

heats (also shown in Fig. 2), and susceptibilities, both of which show

increased d-like contributions for the three compounds on the right

hand side of the plot (CrB„ becomes antiferromagnetic at T ~ 86°K,

and MnB„ becomes ferromagnetic at T ~ 143°K). Increased d-like

contributions are also suggested by Hall effect and resistivity data.

The increased d electron contribution is apparent in the Knight shift

11

data as well: K(Sc B ) = 0.00(1)% for the compound most to the left

of the plot, with a steady decrease towards MnB„ with K = -0.05(3)7o.

This latter value was obtained using a sample which was analyzed to

contain some 20% second phase. This second phase was apparent in the

quadrupole spectrum in that more than one set of satellites were

2

present, one of which gave a value of e q Q close to that reported in

12

h
the literature. A value for the B Knight shift in MnB„ has not been

previously reported. Our K value includes a contribution due to the

second phase. However, the shape of the central line is rather broad

(<~ 35 gauss) and fairly symmetric. The central line shows no structure

due to a second phase, but does have rather wide wings. We believe the

actual K value to lie within the indicated range. The results on the

ScB

? samples are being prepared in final draft for publication.

The general results thus indicate increased d-electron contributions at (or near) the Fermi surface as one goes across the series

ScB

2

, TiB„, VB

2

, CrB

2

, MnB_. For the Knight shift results this means

increased d-core polarization causing more negative Knight shifts.

This is indeed observed (Fig. 2b). The Knight shift at the metal site

45

shows a similar trend: For Sc in the diboride K - + 0.07%. This is

a value reduced substantially from the metal value of 0.25%, but is

still positive. For V in VB„, K = -0.3%, and temperature independent.

Usually, when d-core polarization is involved a temperature dependence

is observed. No temperature dependence is reported for the VB 9 Knight

shift however, and the susceptibility is also reported to be nearly

11

temperature independent. The B K values for these compounds are also

all temperature independent, and a likely mechanism for producing the

negative K values is that of inter-atomic exchange polarization. For

the 2p incomplete valence shell p-core polarization is thought to be

positive and therefore not the cause of negative K( B) values.

The quadrupole coupling constants show a smooth trend (Fig. 2c)

but their interpretation is still rather ambiguous. There seems to be no direct correlation with relative cell dimensions (Fig. 2d). There

is a possibility that the boron atoms do not lie in flat hexagonal

"rings", but are rather in a pleated, or puckered configuration, with

every other boron atom above and below the plane of the "ring". If for

these compounds such configurations are true, the quadrupole coupling

constant would be affected, possibly causing this apparent lack of

2 correlation between the e qQ/h, and c/a values. Such a puckered con- figuration is not easily observed as x-rays look at the transition

13
metal atoms, rather than the light boron atoms. Quadrupole effects

in NMR also do not reveal an asymmetry parameter, as the three fold

symmetry at the boron site is not destroyed by puckering.

2

NMR K and , "" values have also been measured in YB„ for the first

11

h 2

time. Again B resonance has a near zero shift. The quadrupole

coupling constant is 0.34(1) MHz and the central linewidth 8 gauss at

16 MHz and 7 gauss at 8 MHz (the line being somewhat asymmetric).

These samples are maybe 15% of the YB ? phase with several unidentified

lines in the x-ray diffraction pattern. This explains the slight

field dependence of the central linewidth. The Y nucleus has I = -^ and therefore no satellites are observed. The central resonance in our samples was not simple, also indicating lack of single phase. The

total width of the line was such that a Knight shift of + 0.3(2)%

39 14

could be deduced, as measured using KCOOH and H N0„ as references,

39 89 14 8 ^ employing the values vjfc^/v^ = 0.95247 and *,„<, /v^ = 1.47462,

respectively. These results are quite similar to those of ScB~, which

is isoelectronic to YB«.

14
^^^^

Boron

165 171 177 183 189 eV

FIGURE 1. The boron-K emission spectrum from crystalline boron and from

ScB„, TiB„, VB„, and CrB„. Based on the respective excitation '2' TiB 2' current in each" case, the specimen temperatures are estimated

to be on the order 500°C ± 50 for the crystalline boron and

700°C ± 100 for the transition metal diborides.

15
16

/el,

mJ/K mole

fc(B), %

0.00 -

-0.05 -

e

2 qQ

F * MHz

0.8

0.4 -

c/a

FIGURE 2.

CrB2

Plots of (a) low temperature electronic specific heat, (b) Knight

shift of the B nuclear magnetic resonance, at room temperature,

(c) room temperature first order electric quadrupole coupling

constant, and (d) c/a lattice parameter ratio at room temperature

for the diborides of the first transition series metals and having

the C32 structure.

16
3.2.3. High Temperature Metals

3.2.3.1. Optical Constants of Titanium

A. J. Melmed and J. J. Carroll

Metallurgy Division

Institute for Materials Research

The objective of this project was 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 con- siderably more polycrystalline titanium than single -crystal titanium is

used outside the laboratory, so that optical constants of polycrystalline

specimens were also determined.

Optical constants have been measured at X = 546 1A from a titanium

specimen which was prepared in ultra-high vacuum by vapor deposition

onto a (Oil) -oriented tungsten single crystal substrate followed by a low temperature (~ 500 C) anneal.

The vacuum system used was identical to that which was previously

described (1) with the exception of a Ti vapor source located about 1.5

inches from the substrate. Ti vapor was obtained by heating a high

purity Ti wire by resistively heating an encircling coil of W wire.

-9

The base pressure during thesQ experiments was 1 x 10 torr as indicated by corrected cold cathode discharge gage readings, except during

part of each Ti evaporation when the pressure rose continuously to

-9

about 8 x 10 torr.

Prior to Ti specimen preparation the W substrate was characterized

as being free from an overlay of an ordered contaminated layer as judged by low -energy-electron diffraction (LEED). A heat treatment

17
greater than 2000 g. of the W substrate was necessary to generate LEED

diffraction pattern display which had no extra ordered diffraction

features. At this stage ellipsometry measurements were made in order

to furnish the complex index of refraction (n) of the clean W substrate, where "n = n (1-ik). Immediately following the above characterization Ti was evaporated in short (2 minutes) and separate doses,

each dose being periodic in terms of a constant time interval between

equal heat treatments of the Ti evaporator. The as -deposited Ti

caused changes in the optical constants n and k of the specimen (substrate and film) as shown in Figure 1.

Successive Ti doses caused n to decrease and k to increase from

their respective W substrate values. The LEED pattern generated during

Ti depositon showed that the diffraction spots had doubled with an

increase in background intensity. Subjecting the specimen to a short

low temperature anneal following the 21st dose resulted in little

change in the LEED pattern and an expected discontinuous change in n

and k. Assuming a film refractive index of that obtained after the

21st dose and anneal on a W substrate having the initially measured

optical constants, the Ti average film thickness is calculated as being 348A.

Evidence from parallel experiments using Fe vapor deposition on

a similar (Oil) -oriented W substrate demonstrated that optical constants measured for the annealed film/substrate composite approach

bulk Fe values at an Fe film thickness of about 400A (2), due to a lack of a significant contribution to the measured values from the

W substrate at or beyond this thickness. Our optical constants data

obtained from the above described Ti film experiment, together with the

data that Tennyson Smith (3) obtained from bulk (0001) -oriented Ti

single crystal cleaned in ultrahigh vacuum by a combination of heating

and argon ion bombardment, demonstrate that the same is true for Ti.

See Table 1.

18
Additional measurements of optical constants from bulk

(0001) -oriented Ti single crystals were made in air under various conditions using several wavelengths between 3800 and 6000A.

Figures 2 and 3 depict the wavelength dependence of the index of

refraction, n, and absorption coefficient, k, of a specimen which was mechanically polished, washed successively in acetone and distilled

water, and air dried. The n-spectrum from such a sample closely resembles that of Kirillova and Charikov (4) in both its shape and measured

n values. However, the k values obtained from this specimen are about

20% lower than those obtained by these workers - excepting the points

at X = 6000A. Their measurements were carried out in air on Ti specimens which were "polished to the 14th class of finish."

The above mechanically polished specimen was subjected to a chemical polishing treatment, washed in water and air dried. The

chemical polishing treatment, which is considered to remove mechanical

polishing inclusions and to further smooth the surface, had the effect

of increasing n and k values throughout the wavelength span but not

changing the shape of either the n or k spectra.

The wavelength dependence of n and k values, obtained by Hass and

Bradford (5) from Ti films evaporated at about 10 torr, is similar

in shape to the results obtained from the present work as shown in

Figures 2 and 3. However, and in interesting contrast to the data

comparison between this work and that of ref . (4), the n values obtained from this specimen are about 207o lower than those obtained by

Hass and Bradford (5).

In addition, the observation was made that upon continued exposure

to air, the measured values of n and k changed, n values decreased

while k values increased in time. It is known that similar changes of n and k take place when (011) W is exposed to either air or oxygen and

that these changes from their respective clean surface values occur without disturbing the shape of the n or k spectrum (6).

19
Although the work of Tennyson Smith (3) is confined to one wavelength, he exercised considerable diligence in determining that the

Ti specimen used in the optical constant measurement was free from

impurities detectable by Auger spectroscopy.

In view of Smith's work, of the excellent agreement in optical

constant determination, and of the effect of contamination upon the

apparent optical constants, the n and k spectra can be inferred for the

clean (0001) Ti surface condition by parallel vertical shifts of the

spectra in their appropriate directions until curve intersection occurs at the correct n and k values for K = 5461A. The result of such a procedure is shown in Figure 4.

Finally, we note the progression of n values and k values as specimen purity and surface cleanliness is improved, similar to the

changes already noted (7) for optical constants of Fe. The situation

can readily be seen by inspection of Table 1. In order of improving

specimen surface conditions we rank the results as follows : l)Kirilla

and Charikov (1963) and our measurement on mechanically polished

(0001) Ti in air; 2) our measurement on chemically polished (0001) Ti

in air; 3) Hass and Bradford (1957) on Ti film prepared in vacuum and

measured in air; 4) our ultrahigh vacuum Ti film measurement and

Tennyson Smith (in progress). As the specimen surface is improved the

measured value of n increases and k decreases.

This project has come to its end and this constitutes the final

report.

20
TABLE 1 Titanium Optical Constants

1. Ti film (this work)

2. Tennyson Smith (present)

3. Kirillova and Charikov

(Bulk Ti polished in air, 1963)

4. Bulk (0001) Ti

(mechanically polished in

air, this work)

5. Hass and Bradford

(Ti film exposed to air and

corrected for oxide, 1957)

6. Bulk (0001) Ti

(chemically poiished in air,

this work)

n k

1.237 5461

nk

3.000 3.711

3.04-K). 04 1.234 5461 3.751

1.85 1.70 5500 3.145

1.81 1.37 5500 2.480

2.53 1.32 5461 3.340

2.05 1.51 5461 3.096

REFERENCES

1. A. J. Melmed, H. P. Layer, and J. Kruger, Surface Science,

9, 476 (1968).

2. A. J. Melmed and J. J. Carroll, Surface Science, 19, 249 (1970).

3. Tennyson Smith, Science Center of North American Rockwell

Corporation, Thousand Oaks, California (Private Communication).

4. M. M. Kirillova and B. A. Charikov, Physics of Metals and

Metallography (USSR) 15_, 138 (1963).

5. Georg Hass and Alan P. Bradford, J. Opt. Soc. Am., 47, 125 (1957)

6. J. J. Carroll and A. J. Melmed, Surface Science, 16_, 251 (1969).

7. H. T. Yolken and J. Kruger, J. Opt. Soc. Am., 55, 842 (1965).

21
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25
4. IASER MATERIALS PROGRAM

4.1. Introduction to Laser Materials

The National Bureau of Standards, with support from the Advanced

Research Projects Agency (Office of Materials Sciences) 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 and Summary of Program in Laser Materials

4.2.1. Objectives

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 degradation 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 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 studies, 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

26
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 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.

4.2.2. Summary of Progress to Date

4.2.2.1. Characterization of Laser Materials

There is a continuing need for the characterization of laser materials. Suppliers frequently make changes in composition and usually

27
are not able to provide adequate data on those physical and chemical

properties which influence laser performance and the distortion of wave

fronts propagating in laser materials. Trace impurities in two rubylaser crystals, grown by a domestic company, have been determined by

neutron activation analysis. The elements Cr, Ga, and Ir are distributed in a fairly uniform manner throughout a crystal; Cu and Mn are distributed less uniformly; and the concentrations of Ba and Sir vary

greatly from one region to another in a crystal of laser ruby. These

crystals also have Ba-rich inclusions which are as large as 20|-im in

diameter.

The strain -induced birefringence and refractive index variations

have been determined for a YAG (yttrium aluminum garnet) rod. Calculations of the strain -induced birefringence in YAG have been made for

various crystallographic directions. Although large variations are not

found for different orientations, the magnitude of induced birefringence

can be reduced by 30 per cent, if YAG boules are grown along the [100]

direction. They usually are grown along the [111] direction. A

Twyaan -Green interferogram of a YAG boule has been made. It shows a pattern having three-fold symmetry due to the strain induced when the

crystal is cooled during its growth. The refractive index decreases

from the center to the edge of the boule and the maximum variation in

the refractive index is 2 x 10

4.2.2.2. 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

is the inclusion damage. 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 damage data. This test

facility will center around a one gigawatt neodymium glass laser system

28
a,md will be used to develop standards for performing

meaningful (reproducible) measurements on the damage mechanisms which

are produced by high energy laser pulses. The construction of this

facility includes detailed characterization of the laser beam. Near

field intensity profiles of this laser have been made and have been

compared with other neodymium lasers. These profiles will be used as a guide to make certain that the NBS laser has a reasonably homogeneous beam. The necessity for having a homogeneous beam in order to

obtain meaningful damage measurements has been stressed at several

conferences.

A theoretical model for studying the thermal stresses produced by

inclusions in laser materials has been developed. The thermal stress

which is thought to cause fracture in laser glasses is the tangential

tensile stress near heated inclusions. The model has been used to study

three questions. First, how the maximum tangential -tensile stress

varies as a function of the radius of the spherical inclusion for a fixed energy density and pulse width of the laser beam. Second, how

the maximum of the tangential -tensile stress varies as a function of

the thermal conductivity and the thermal expansion coefficient of the

host. And third, if the maximum temperature of the inclusion is

limited to a fixed value, how the parameters of a laser beam should be

varied to increase the probability of detecting by optical techniques

a small incipient absorbing center before it causes damage. Two

important conclusions predicted by this model are that submicron -sized

inclusions have the greatest probability to cause damage in laser

glass hosts and that the lens effect arising from heated inclusions

probably does not cause damage.

4.2.2.3. Degradation of Laser Materials

At present, the degradation 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 electron

29
paramagnetic resonance (the EPR, An = 2 transition) in yvay irradiated

60

( Co) ruby and the optical absorption of x-ray irradiated ruby have

been measured as a function of the Cr concentration. The respective

results have been compared with one another. The comparison does not

permit us to make at present definite-positive models of the observed

color centers. The Cr concentration dependences of the EPR spectra in

y-irradiated ruby and of the optical absorption in x-ray irradiated

ruby suggest that the respective centers may have a mechanism in common. The coloration of x-ray irradiated ruby is too intense to be

explained by valence changes of the Cr ions because the required

oscillator strength would be unreasonably large. Thus, the coloration

is thought to arise from another, as yet unspecified, color center.

The center produced by v-ray irradiation could be related to, but does

not arise necessarily from the same center.

Independent evidence suggests that the concentration of the

3+

Cr ion plays an important role in the coloration process. Thus,

3+ techniques for determining the Cr ion concentration in several ruby

samples have been considered. Activation analysis does not provide

information on the valence states of the ions. Three promising techniques, examined thus far, include measuring the intensities of EPR

3+

lines, the magnetic susceptibility due to Cr ions, and the absorp3+

tion coefficients at the band maxima for the Cr ions. Theories are 3+

used then to relate these measurements to the Cr concentrations.

4.3. Project Summaries in Laser Materials

4.3.1. Characterization of Laser Materials

4.3.1.1. Physical and Chemical Properties of Laser Materials

G. W. Cleek and R. M. Waxier

Inorganic Materials Division

Institute for Materials Research

This project was established to determine the physical properties

of laser glasses and crystals and to relate these properties to their

chemical composition.

30
Accomplishments

Measurements on five commercially -made Nd -doped laser glasses and

single crystal ruby have been completed. Data were obtained on refractive index, thermal change in refractive index, elastic constants,

photo-elastic constants, thermal expansion, density and chemical composition. These data are needed to calculate the corrections for the

thermal distortion of the wavefront in light generated by laser rods.

Results of the study on the photo-elastic properties of single

crystal ruby have been published(tD • Data on the refractive properties

of Nd -doped laser glasses are being prepared for publication.

During the current reporting period, neutron activation analyses

have been completed on ruby samples, examinations of a YAG boule were

made to determine its optical quality by shadowgraph and interferometric

methods, and theoretical calculations of the photo-elastic properties

of YAG have been made.

Chemical Analyses*

Ruby Specimens - Neutron activation analysis was used for the

determination of trace impurities in specimens from two ruby laser

crystals grown by a domestic company. The specimens as received

were cut from ruby boules and had circular cross sections about

2 mm thick. Each specimen was then cut into four quarters. Each

quarter weighed about one gram. Two pieces from each boule were

sealed in polyethylene and irradiated for 60 minutes in

pneumatic tube RT-4 of the National Bureau of Standards Reactor at a 13 -2 -1

power level of 10 MW (1x10 n.cm sec ) . A Cu flux monitor was taped

to the outside of the polyethylene to permit normalization of small

differences. After irradiation the samples were rinsed in acetone and

1 :1HN0 to remove surface contamination. Their gamma spectra were

* Neutron activation analyses were performed by Barbara A. Thompson,

Analytical Chemistry Division.

31
Figure 1. Twyman -Green interferogram of YAG boule

32
oil

J /o

z / /

//a

no

*zi

IIZ

Figure 2. Stereogram showing the symmetry elements of the (111) plane

in a YAG crystal

.

33
Figure 3. Birefringence pattern of the YAG boule place between circular

polarizers

34
measured with a 47 -cc Ge(Li) detector and a 2048 channel analyser.

Concentration levels were determined for the elements observed by

comparison to standards.

The results obtained are shown in Table I. All results are in

ppm of the element except for Cr, which is reported in per cent Cr„0 . As was found in previous analyses, Cr, Ga, and Ir appear to be fairly

uniformly distributed within a crystal; Cu and Mn are less uniform and

Ba and Sr fluctuate wildly. Further examination by the optical microscope revealed small particles, which were up to 20 M-m in diameter,

embedded in the crystal. Examination by the x-ray microprobe indicated

that these were rich in Ba. The origin of these Ba-rich inclusions in

ruby crystal is not known.

TABLE I

Results of Activation Analysis of Ruby Crystals, ppm

Crystal Designation, Boule No.

Element

Cr (%Cr

2 3

) Ir

Ga

Mn

Cu

Ba

Sr

Studies on YAG

YAG (yttrium aluminum garnet) has proved to be one of the most

versatile crystalline host materials for solid lasers. An undoped

boule of YAG, 12,6 cm x 2.0cm dia. was grown by a domestic company

and shipped to NBS for photoelastic studies. The growth direction

in this boule is colinear with [111] and its threefold symmetry is

expressed by six (211) facets., {This crystal was grown by

the Czochralski method, and the melt was established in an iridium

35

2 -387-4

A B

0.0373 0.0351

0.045 0.041

0.008 <0.006

0.0008 0.0006

0.024 0.016

0.28 1.74

<0.03 0.085

4 -546-2

A B

0.0389 0.0377

0.052 0.051

0.030 0.031

0.0009 0.0056

0.027 0.137

6.5 265.

0.54 8.3
crucible containing a stoichiometric batch of single crystal alumina

crackle and yttrium oxide powder.

It has been found that one of the problems encountered in firing

a YAG laser is the thermal distortion introduced into the laser cavity

by the deposition of heat from the flash lamps (2). Because a thermal

gradient is established from the center to the edge of the rod, there

is a distortion of the wavefront of the light generated which arises

from the temperature -induced changes in refractive index.

In addition, the temperature gradient creates internal stresses

which produce further changes in index induced by the stress -optic

effect. Since YAG is a cubic crystal and is optically isotropic, the

change in refractive index with temperature is independent of crystallographic direction. Internal stresses, however, cause the crystal to

become anisotropic, so that an optimum optical element could be one selected on the basis of the crystal photoelastic constants. Until

now, the direction [111] has been accepted as the standard YAG growth

and lasing direction without justification other than that crystals

with that orientation are available (2),

Dixon(3) has reported that the elasto-optic constants of YAG are

pn

= -0.029

P

2 = +.0091

P44

= -.0615*.

6 * From these data, using the relationship q.. = Y^ p s t--> the piezoij

i ik kj

optic constants were calculated to be

q n

= -.0121 x 10"12

m

2

/N

q19 - +.051 x 10" 12

m

2

/N

-12 2

q 44

= -.535 x 10 m /N

The s represent elastic compliances. Values have been reported by

Spencer, El.al. (4).

36
On the basis of these data, calculations have been made of the straininduced birefringence in YAG for various crystallographic directions.

The results are shown in Table II where it can be seen that growth

along [100] is the most favorable direction. Although large variations

are not found for the different orientations, if boules are grown

along [100] instead of [111] as they are at present, the magnitude of

induced birefringence can be reduced by about 30 per cent.

The equations and background for the calculations can be found in

a paper by Bhagavan tarn (J>) . Because YAG is a cubic crystal, the thermal

conductivity and thermal expansion are independent of crystallographic

direction. It follows then, that for a given temperature distribution

in a specimen of YAG, the magnitude of induced strain is independent of

direction while the magnitude of induced stress is not (6), Accordingly,

the calculations have been made on the basis of constant strain.

Apart from the induced birefringence, it is important to minimize

the absolute changes that are induced by strain. Dixon (3) has pointed

out that in YAG the elasto-optic constant, p. „, is anomalously small.

This is desirable for a laser host. The elasto-optic constant, p. -

,

is also small. The largest of the elasto-optic constants is V,,-

Calculations have not yet been made, but it is apparent that growth

along [100] is the best direction for minimizing absolute changes in

refractive index. Along [100] the large contribution of p., to refractive index is eliminated, and only the small contributions of p 1 1 and

p „ remain.

The ends of the YAG boule were ground and polished so that they

were flat and parallel. The He-Ne laser radiation of 632.8 nm was used to produce a Twyman -Green interferogram of the boule. The picture

is shown in Figure 1. This test affords a measure of the variations in

optical thickness; in the pattern shown, the fringes are lines of isooptical thickness spaced at one half wavelength. Calculations showed

that the maximum variation in refractive index was 2x10 . The refractive index decreases from the center to the edge of the boule. The

37
poor resolution of the fringes in the center of the picture is due to an optical inhomogeneity, known as the core, which runs the length of

the boule. The core is a problem peculiar to Czochralski growth. It

measures in this boule about 2 mm in diameter. Laser rods are cut from

regions which exclude the core.

In Czochralski-grown crystals, variations in refractive index are

caused primarily by strain and variations in impurity level. From the

symmetry of the pattern, it may be inferred that strain has been introduced during the cooling of the crystal. This is similar to the strain

patterns which exist in glass that has not been well annealed.

It is possible to account qualitatively for the three-fold pattern

of Figure 1 by using general symmetry principles. YAG is a cubic

crystal belonging to the 0, class. A stereogram showing the symmetry

elements of the (111) plane is shown in Figure 2. The open triangle

represents a 3 axis, the diad symbols represents 2-fold axis, and the

heavy lines indicate mirror planes. When the YAG boule became strained

during cooling, the strain pattern was independent of crystallographic

direction because the thermal conductivity and thermal expansion are

isotropic. The strains, therefore, will be essentially radial and

tangential(6) . The magnitude of the induced stresses will vary from

point to point. Furthermore, these stresses will, in general, make

the refractive index ellipsoid become triaxial, and the principal axes

of the stress ellipsoid and the refractive index ellipsoid will not

coincide in the general case. However a uniaxial stress which exists

along certain preferred directions of symmetry, i.e. parallel or perpendicular to one of the three mirror planes will constrain two of the

principal refractive indices to lie in the mirror plane. Therefore,

maxima or minima of the refractive index ellipsoid can be expected to

lie along or perpendicular to the trace of a mirror plane.

Laue back-reflection x-ray techniques make it possible to associate

directions in the strain pattern of Figure 1 with crystallographic

directions shown in Figure 2. The small circles shown in the margin

38
of Figure 1 correspond to the directions [211], [112] and [121].

A pattern of birefringence was obtained by placing the boule

between circular polarizers. This technique makes it possible to

ascertain the magnitude of the birefringence regardless of the

orientation. Using the sensitive red tint plate and color chart

indicates that the optical path difference excluding the core was

250 nm. A photograph of the pattern is shown in Figure 3. This figure

also exhibits a three -fold symmetry. The crystallographic directions

[211], [112] and [121] are indicated by the small circles in the margin,

REFERENCES

1. R. M. Waxier and E. N. Farabaugh, J. Res. NBS 74A,[2] 215 (1970).

2. D. E. Witter, Union Carbide Corporation, private communication.

3. R. W. Dixon, J. Appl. Phys. 38 5149 (1967).

4. E. G. Spencer, et.al., J. Appl. Phys. 34 3059 (1963).

5. S. Bhagavantam, Proc. Indian Acad. Sci. A3

585 (1953).

6. L. H. Adams and R. M. Waxier, Temperature -Induced Stresses in

Solids of Elementary Shape, NBS Monograph 2 (1960).

39
TABLE II

Calculations of the Birefringence

Induced in YAG by Strain*

Direction of

S tra in

[001]

[001]

[100]

[100]

[010]

[010]

[001]

[001]

[110]

[110]

[110]

[110]

[111]

[111]

[211]

[211]

[Oil]

[011]

irection of

Observation

Birefringence

nanometers per cm

[100] 7.1

[010] 7.1

[001] 7.1

[010] 7.1

[100] 7.1

[001] 7.1

[110] 7.1

[110] 7.1

[001] 11.5

[110] 9.3

[001] 11.5

[110] 9.3

[211] 11.4

[011] 11.4

[111] 10.0

[011] 10.9

[211] 10.7

[111] 10.0

* All calculations have been based on the strain, di/l - 62.0x10

This strain is calculated to produce a birefringence of 10 nanometers/

centimeter when the strain is along [211] and observation is along

[111]. This latter figure has been selected as a basis for comparing

the magnitudes of birefringence according to the various directions of

strain and observation.

40
4.3.2. Damage to Laser Materials

4.3.2.1. Laser -Induced Damage Studies

Albert Feldman, Roy Waxier and Deane Horowitz

Inorganic Materials Division

Institute for Materials Research

Objective

The objective of this work is the development of a laser test

facility to determine damage threshold parameters of laser glasses

used in pulsed -high energy laser systems and to establish the diagnostic procedures for identifying the dominant mechanisms of damage. To

achieve this objective, methods first must be developed for measuring

the laser beam characteristics.

Although damage test facilities exist at industrial laboratories,

it is desirable for the Federal Government to have its own laser test

facilities in which impartial tests can be performed. Present

planning indicates that the National Bureau of Standards will have

the only Government laser test facility available for laser glass

tasting on a full-time basis (1).

Technical Approach

There are three types of damage caused by high energy pulses in

laser glass; intrinsic bulk damage, surface damage, and bulk damage due

to inclusions. At the present time, the damage threshold data has a large scatter. From the literature one cannot determine whether the

scatter is due to sample variation or to variation of the test laser

beam parameters. Hence, in order to obtain reproducible and meaningful

damage threshold data, it is necessary to have a laser beam with well

defined beam characteristics (2) . These beam characteristics are listed

below

:

1. Total energy contained in the laser beam.

41
2. Cross -sectional energy distribution in the beam for the near

and far fields (beam profile).

3. Total power contained in the laser beam.

4. Time evolution of the beam intensity.

5. Frequency spectrum of the laser beam.

6. Time evolution of the frequency spectrum of the laser beam.

7. Reproducibility of the above beam characteristics.

The capability for measuring all these beam characteristics on

our laser system must be developed first. The laser system then must

be modified to produce a laser beam with the optimum beam characteristics for reproducible and meaningful measurements. At present, it

appears most important to have a beam with a uniform cross -sectional

energy distribution. Thus, the emphasis in this report is on measurement of beam profile.

Laser System

During this report period acceptance tests were being performed

on a commercial neodymium -doped glass laser system. The laser

system is depicted schematically in Figure 1 with nominal parameters

listed. It consists of an oscillator and two amplifiers, and is

Q-switched by means of a Pockels cell. The oscillator rod is 1/2 inch

(1.27 cm) in diameter by 6 inches (15.2 cm) long with flat ends. It is

apertured down to 1/4 inch (0.635 cm) diameter. A three-power beam

expander stands between the oscillator and the amplifier rods. The

first amplifier rod is 3/4 inch (1.91 cm) in diameter by 11 inches

(27.9 cm) long. The entrance face is flat and the exit face has a Brewster window. Both ends of the second amplifier are cut at the

Brewster angle. The output from the laser has been measured at 32.8 J

with a pulse vldth of 18 ns. .

42
Consultations

Consultations were held with John McMahon of the Naval Research

Laboratory, Henry Dardy of Catholic University, Harold Boyne, Donald

Jennings and Richard Smith of NBS (Boulder) and Merritt Birky of NBS

(Washington, D„C). Methods for measuring laser beam characteristics

were discussed. These conversations corroborated our own conclusion

that a well defined uniform beam is of prime importance for obtaining

reproducible damage threshold data. This conclusion was further con- firmed by discussions at the American Society for Testing Materials

(ASTM) Symposium on Laser -Induced Damage held in Boulder, Colorado,

June 23 to 25, 1970.

The ASTM is currently writing proposals to standardize measurements

of beam profile.

Beam Uniformity

Two basic methods, which we will attempt to use, were proposed

by the ASTM.

The first method developed by Merritt Birky(3) involves photographing the multiple images of a laser beam as it undergoes successive

reflection in a tilted glass plate. The beam becomes progressively

attenuated at each reflection. The photographic plate thus simultaneously records the beam at different intensity levels.

The second method involves photographing the diffuse image of the

laser beam that impinges on a MgO diffuser. The image is photographed

with a multiple lens camera. Behind each lens is a different neutral

density filter. Thus, the multiple images on the photographic plate

record different levels of intensity. A camera to do this is available commercially.

A major difficulty when using these methods with the 1.06 mm

radiation of a neodymium glass laser system is the photographic plates.

43
At present the only emulsion available is a Kodak Type IZ (4) i This film

is difficult to handle in that it must be hypersensitized in most

uses, and it must be stored in a freezer (4)

A difficulty with the second method occurs because the MgO diffuser,

which is made from compressed MgO powder, can disintegrate when hit by

a laser pulse.

Estimates of beam uniformity can also be obtained from burn

patterns. One method involves subjecting exposed polaroid film to a laser pulse. John McMahon has obtained beam profile measurements on

his laser by taking far field burn patterns on a calibrated French

photocopy paper while successively interposing different neutral

density filters. This method can be used only if the laser beam characteristics are reproducible from pulse to pulse. Nicholas N.

Winogradoff in our laboratory has developed a method for obtaining

high contrast burn patterns. This method involves exposing SchottNGl

glass neutral density filters to the laser beam.

Future Activities

Our present concern is to measure the laser beam characteristics.

We shall attempt to obtain single transverse mode lasing action. This

will yield a Gaussian beam profile. We shall accomplish this by

decreasing the aperture on the oscillator rod. Although the resulting

energy output will be much less than 30 J, we expect no difficulty in

producing glass damage because we intend to use a focused beam configu'

ration. With this system we intend to establish test procedures for

measuring thresholds of bulk damage in laser glasses.

REFERENCES

1. The Naval Research Laboratory has a glass damage testing program

but its laser is available for such purposes only on a part-time

basis. We refer the reader to the National Materials Advisory

Board Report on the Fundamentals of Damage in Laser Glass,

44
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45
Publication NMAB - 271 (July 1970), National Academy of Science

National Academy of Engineering, Chapter XI.

2. H. G. Heard, Laser Parameter Measurements Handbook, (John Wiley

and Sons, Inc., New York, 1968).

3. Merritt M. Birky, Applied Optics 8, 2249 (1969).

4. Kodak Plates and Films for Science and Industry, Kodak Publication

No. P-9, p. 20, 25.

4.3.2.2. Inclusions in Laser Materials

Herbert S. Bennett

Inorganic Materials Division

Institute for Materials Research

Objective

One of the severe problems encountered in high -power -sol id -state

laser systems is the thermal damage to laser rods and optical elements.

One such type of damage is thought to arise from metallic or dielectric

inclusions. Such inclusions may absorb an appreciable amount of

incident laser radiation and thereby may undergo thermal expansion.

This produces major stresses within the host material. The objective

for this report period was to solve the heat diffusion equation and

the thermal stress equations in order to estimate such thermal properties of the absorbing center-host system.

Summary

The optical path length change for a probing light ray passing near the absorbing center, the radial and tangential stress components,

and the changes of the refractive index for radially polarized and

tangentially polarized light due to the thermal stress field were

computed. The dependence of the maximum value of the tensile stress

* An associated project, supported by the National Bureau of

Standards.

46
upon the size of the inclusion and upon the physical properties of the

of the host was examined. The feasibility of using optical techniques

to detect metallic and dielectric inclusions in laser materials before

they cause damage also was studied. These computations suggest that

the use of laser pulse widths of the order of microseconds or longer

may be more promising for the detection of small incipient absorbing

centers than the use of nanosecond pulse widths. In addition, the lens

effect was estimated.

Approach

The results to be summarized in this report are based upon a linear theory and upon a model whose elastic, thermal, and optical

properties are constants. The values for these properties are valid

for temperatures near 300 K and for small strains. This treatment is

not expected to be correct near the onset of damage. The problem is

certainly a nonlinear one near the region of catastrophic damage.

Whenever any of the assumptions become invalid, then the results

should be viewed as suggesting trends in the behavior of the system.

The inclusions which occur in laser glasses are most likely not the

spheres for which the model has been formulated. They could be irregularly shaped globules. Some platinum inclusions occur as hexagonal

platelets. Even though the model does not take into account such

geometrical aspects, one hopes that it does give a reasonable description of the actual system. One also hopes that the manner in which it

suggests one should proceed to increase the damage threshold, though

probably not quantitatively correct, is qualitatively correct.

A model to represent the behavior of absorbing centers in laser

materials is developed. Before the thermal properties of the absorbing center-host system can be discussed quantitatively, it is first

necessary to solve the time -dependent heat diffusion equation for the

temperature and the thermal stress equations with appropriate boundary

conditions for the stress components. This is discussed in detail in

Ref. 1 and Ref. 2. Reference 1 is given in the appendix to this report,

47
The model contains many physical assumptions which are necessary

to render the problem solvable. The major assumptions are summarized

here and also are discussed in greater detail in Ref . 1 and Ref. 2.

a) The inclusion is a sphere of radius r and is always in good thermal

contact with the host. The effects of shape and orientation to the

incident radiation are thus neglected.

b) The host material is isotropic, continuous and of infinite extent.

It also is initially at an ambient temperature T and free from all

stresses and strains. Because the energy content of the incident

radiation is finite, the latter statement requires the temperature

to be T at infinity and all stresses and strains to vanish at

o infinity. The distribution and nature of microcracks and optical

imperfections are not treated in the model.

c) The linear-thermal-elastic equations are assumed to give a reasonable description of the processes which ultimately may lead to

catastrophic damage. These equations are coupled equations relating the temperature and the displacement vector from which the

stresses and strains are computed. They are valid only when a local temperature exists and when distances are larger than atomic

-8

dimensions (~10 cm). A relaxation time t for the definition of

r

a local temperature T is approximately the reciprocal of a characteristic vibration frequency of the material. These relaxation

times t for Pt, Sb, A1„0~, and the laser glasses are about

-13 r -12

10 s to 10 ' s . Hence, the equations are physically meaningful

-12

when times t are much larger than 10 s

.

d) It is assumed that the radiation of heat by the center-host interface and by the heated glass close to the absorbing center may be

neglected in the thermal -elastic equations. The laser beams

4 studied in Ref. 1 and Ref. 2 contain energy fluxes at least 10

times greater than the energy flux produced by a black body at

600°C. The calculations of Ref. 1 also show that the energy flux

due to thermal conduction greatly exceeds the energy flux due to

radiation for times less than one second. Because the temperature

is close to the ambient temperature whenever the pulse width of the

48
laser beam is greater than a second, the long time behavior is not

in the region of practical interest for detecting incipient

damage centers before they cause damage. Hence, it is assumed

that all times are less than a second.

e) The linear -thermal -elastic equations contain a coupling term and an inertia term. These two terms may be neglected whenever the

three characteristic times which occur in the absorbing centerhost system satisfy a set of inequalities. These times are the

following. The pulse width T of the incident radiation determines

in part the rapidity of heat generation. The characteristic

relaxation time for temperature equilibration (thermal diffusion)

2 2

is t ~ (r /a ), where r is the radial distance from the center of

2

the inclusion and a is the thermal diffusivity. The characteristic mechanical time required for the production of stress waves is

t_ ~ (r/v), where v is the speed of propagation of elastic waves. Boley and Wiener have demonstrated that when T > > L. and

t > > tL A

, then the coupling and inertia terms are small compared

to the other terms in the equations(3) . The above inequalities are reduced to inequalities containing the pulse width t and the

radial distance r (l)j namely:

— ft —7

T > > 2.8x10 (s/om) y and r > > 6.7x10 cm. It is assumed that these inequalities are satisfied and thereby

that the coupling and inertia terms may be neglected.

In summary, the following inequalities describe the regions for

which the model is physically meaningful:

-3 -12 -12

10 s > t > 10 a, Is > t > 10 a, -7 —fi r > 6.7x10 cm, and T > 2.8x10 (s/cm) r.

Results :

The numerical results which the model developed in Ref . 1 predicts

are summarized here. Among the many input parameters, the absorptance

A(\,T) of the center-host interface is perhaps most sensitive to the

initial thermal contact and surface conditions of the inclusion and

49
host. The wavelength is X. The numerical results are given for the case in which A(\,T) = 1. This presents no additional problem because

the temperature T, (r,t), the optical path length change AL for a probing light ray passing near the inclusion, the stress components a and cr. = a for the spherical coordinates r, 9, and cp, and the

99 cpcp changes in the refractive index due to the thermal stress field for

radially polarized light An and for tangentially polarized light AnQ r y are all directly proportional to the absorptance.

The model has been used to study three questions. First, how the

maximum tangential -tensile stress varies as a function of the radius of

the spherical inclusion for a fixed energy density E and pulse width

Li of the laser beam t. Second, how the maximum of the tangential -tensile

stress varies as a function of the thermal conductivity and the thermal

expansion coefficient of the host. And third, if the maximum temperature of the inclusion is limited to a fixed value,7 T, (r ,t) = 600°C, h o' ' how the parameters of the incident laser beam should be varied to in- crease the probability of detecting by optical techniques a small incipient absorbing center before it causes damage. Optical techniques to

detect small inclusions become more promising, the greater AL, An , and

An

fi are.

The bulk thermal, elastic, and optical properties for the laser

material used in these calculations are representative of two Nd -doped

laser glasses manufactured domestically. The inclusions are Pt, Sb,

and polycrystallina Al^ ^ absorbin8 spheres.

The variation of the maximum tensile stress a (max-tensile) as a

cpcp function of r for a laser beam having an energy density

E = 20 (J/cm ) and a pulse width T = 30ns is studied. When 10" cm >

r > 5x10 cm, the maximum tensile stress exceeds by as much as a factor

°

9 2 of two the theoretical strength of the glass (6x10 N/m ). The calculations show that Sb and highly absorbing A1J) inclusions are more

50
likely to cause damage than Pt. The maximum tensile stresses for Sb

and A1„0 inclusions are about 20% larger than those for Pt. It is

interesting to note that one domestic manufacturer no longer uses

Sb as a fining agent.

These results demonstrate that submicron -sized inclusions have the

greatest probability to cause damage in laser glass hosts. Experimental

measurements performed by industrial researchers have verified

-4

tentatively this theoretical result. Very large (r > 10 cm)

and very small (r < 5x10 cm) inclusions are not likely to produce

damage

The maximum tensile stress as a function of the thermal conductivity IC and the- thermal expansion coefficient CX is also studied for

r = 5xl0

_5

cm, T = 30 , and E_ = 20 (J/cm ) o ' us' L

It is found that increasing K from 0.008 (W/cm°C) to 0.04 (W/cm°C)

with all remaining properties kept constant decreases the maximum

9 2 9 2

tensile stress from about 9x10 (N/m ) to 4x10 (N/m ). Again, all

the other properties of the host are kept the same except for the

thermal expansion coefficient. The maximum tensile stress is studied

then as a function of OL . The maximum tensile stresses are found to

have minimum values for

lOxlO"6

°c"

1 > C^ > 8xl0"

6

°C"

1

Values of a. outside this range yield larger stresses. They also are slowly varying functions of the thermal expansion coefficient.

Increasing Ct by a factor of three produces only a 107o variation in

the maximum tensile stress. Hence, the thermal conductivity influences

greatly the behavior near the region of maximum tensile stress and the

thermal expansion coefficient plays only a minor role in the value of

the maximum tensile stress. Among the many possible glass laser hosts,

the expansion coefficients vary by about an order of magnitude from

—(\ i —f\ —

10 a c~ to about 10x10 °C and all the remaining bulk elastic

and thermal properties vary by only small amounts. The latter variations usually do not exceed a factor of two. Hence, extensive research

51
on altering substantially the composition of present laser glasses to

increase the damage threshold due to inclusions is not warranted by the

predictions of this model. It suggests that probably at the best, a factor of two increase in the damage threshold could be achieved. This

suggestion agrees with one of the conclusions of the National Materials

Advisory Board Committee on the Fundamentsls of Damage in Laser Glass.

The model also shows that the maximum value for the tensile stress

does not depend upon the Young's modulus E in a straightforward manner

as some reseachers have suggested. The Lame constants are the independent elasticity variables and changes should be discussed in terms of

them. If it were possible to alter only the Young's modulus, then the

stresses would increase in a monotonic fashion with increasing values

of E. But such changes are not possible in practice. The model predicts

that glasses with higher E values are not necessarily more resistant to

damage

.

The optimum parameters of the incident laser beam to be used for

detecting incipient damage centers before they cause damage are examined

for the case in which the maximum temperature is 600°C at the cessation

of the laser pulse. The computations indicate that pulse widths of the

order of microseconds or longer heat the center more slowly and thereby

produce larger optical path length changes for a probing light ray pass-

-4

ing near the inclusion. For example, a Pt sphere with radius r =10 cm

-8

produces a path length change of about 2x10 cm for t = 0.1|J.s and of

—ft about 10 cm for t = lOOus. Researchers (American Optical Company)

-3 using microsecond pulses and holography have detected 5x10 cm inclusions without causing damage. It is not known yet whether this method

-4 can be improved sufficiently to detect 10 cm inclusions.

Finally, the lens effect due to heated regions of the host is

estimated. Whenever the refractive index increases with temperature,

(dn / dT ) > 0, aiul even though the inclusion does not produce damage

at its site, the heated region of the host surrounding the inclusion

might focus the same laser pulse or a succeeding laser pulse which

52
occurs after sufficiently short times and before the heated region

cools. The lens effect is estimated by considering the focal length

f of a spherical lens having a radius r and mean refractive index n . The refractive index of the host is n, and because

h

(dn,/dT. ) > 0, n n > n, . Some numerical examples for platinum incluh h 1 h , ry sions are cited. When r = 10 cm, ET = 20 (j/cm ), and t = 30ns,

o ' L

' ' then an effective focal length due to the lens effect occurs at

T ~ 3|J.s and is about f ~ 14 cm. But the tensile stress at t = t = 30ns

exceeds the theoretical strength of the host before the lens effect

becomes most important. Consider now another example for Pt in which

the maximum tensile stress is less than the theoretical breaking

strength of the glass host. When r =10 cm, E

T = 0.33 (J/cm ).

T = 30ns, and T (r , t) = 600°C, the effective focal length attains a

" 4

° value of about 10 cm for times t ~ 3M-s . This latter focal length is

very long.

Hence, the model predicts that the lens effect arising from heated

inclusions probably does not cause damage. Those cases for which the

maximum tensile stress is less than the theoretical tensile strength of

the glass have minimum effective focal lengths which are much greater

than the dimensions of Nd -doped glass elements used in present laser

systems. In those cases for which the minimum effective focal length

is comparable to the size the host, the tensile stress exceeds the

theoretical strength of the glass and probably causes damage before the

lens effect becomes large enough to heat another inclusion or to

initiate an intrinsic damage mechanism such as self -focussing.

In conclusion, the model enables one to answer qualitatively many

questions concerning laser damage due to absorbing centers and concerning the detection of such centers before they cause damage.

53
REFERENCES

1. H. S. Bennett, "Inclusions in Laser Materials," to be published.

2. H. S. Bennett, "Heat Diffusion near Absorbing Centers in Laser

Materials," to be published.

3. B. Boley and J. Weiner, Theory of Thermal Stresses (John Wiley

and Sons, Inc., New York, 1960)

4.3 .3 Degradation of Laser Materials

Crystal Defect Studies on Laser Materials

4.3.3.1. EPR Measurements on Normal and Orange Ruby

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

Inorganic Materials Division

Institute for Materials Research

Objective

This investigation is a study of the causes responsible for degration 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 531 for previous report).

Technical Approach

In the work described here, the emphasis has been shifted away

from optical measurements to some extent, with greater effort expended

on the EPR and with the addition of magnetic susceptibility measurements. (The latter is described in a separate section of this report).

The activities include :

fin 1. The study of the £m = 2 EPR transition in Co irradiated

ruby has been extended to include a measure of the line inr

tensity as a function of the Cr concentration. The results are compared with fhe previously reported "orange" coloration

dependence.

54
3+

2. The Cr EPR line intensity of the -3/2 -» -1/2 transition was measured carefully under controlled conditions on various Cr

concentrations. This procedure is a potential analytical tool

3+

for Cr concentration determination and as such is a means of

3+

study of loss of normal Cr in "orange" degraded ruby (e.g.

_ 2+ , _ 44% conversion to Cr and Cr /.

The following experiment is supported in part by ARPA and logically

belongs to this list.

3. Magnetic susceptibility experiments were made on rubies of

several concentrations as a means of direct measurement of the

3+

Cr concentration. Measurements were made with and without

3+

microwave (EPR) saturation of the Cr ground state levels to

take into account the contributions to the paramagnetic sus- 3+ ceptibility which arise from species other than Cr . Finally,

60

measurements were made after Co irradiation to check on the

3+ reduction of Cr concentration in the damaged samples. (These

results are discussed in a separate section of this report).

Experimental Results

In a recent report (see NBS Technical Note 531) we described the

orange coloration of X -irradiation damaged ruby as studied by optical

absorption. The absorption coefficient of one prominent band, with a maximum at about 0.47 um, was shown in crystals colored to saturation

to depend on the Cr concentration, with maximum damage at about

0.1 mol7o Cr in Al 0„. The total added coloration at about 0.47 Mm

decreases at both higher and lower concentrations.

One effort at identifying the centers responsible for this coloration was reported. It involved the study of a Zki = 2 EPR transition in

"orange" ruby. These measurements have been continued.

55
A. The Study of the Am = 2 Transition

One type of paramagnetic center induced by high energy ionizing

3-

radiation is one that yields the Am = 2 transition observed in N

compensated ruby by Hoskins and Soffer(l) and in X -irradiated ruby by

4+

Mason and Thorp(2). They attributed the EPR absorption to Cr in A1~0_. 4+2 J The electronic configuration of Cr is 3d , hence the electronic spin

is one. The axial component of the crystalline field splits the

m = ± 1 and m = levels by about 7 cm . The m = ± 1 level will be

s s s split in a magnetic field and the transition between the components

(i.e. Am = 2) is normally forbidden. However, the axial crystalline

field mixes the m = ± 1 levels, and the transition can be observed in

s the experimental configuration with the dc and rf magnetic fields both

parallel to the c-axis of the sample. The line shape is observed to be

asymmetrical and g = 1.90.

A set of samples containing 0.35, 0.18, 0.088, 0.035, and 0.007 mol%

Cr were prepared. (0.05 wt % Cr„0- is approximately equal to 0.035 mol%

Cr). These samples were oriented by X-ray diffraction and irradiated to

fin o o o o saturation by Co. The flux 2.6 x 10 J/cm (« 2.6 x 10 R/cm ) used

was deemed more than sufficient from previous optical measurements.

Samples were irradiated at room temperature, stored at room temperature,

and kept in the dark except for brief exposure to dim incandescent lights

In addition, all measurements were completed within a few days after

irradiation. These precautions were felt necessary to prevent or at

least greatly reduce u.v. and thermal bleaching of the centers formed.

The spectrometer was operated at about 9.5 GHz and at liquid helium

temperature. The power input to the sample cavity was kept constant for

each measurement. The coaxial cable coupling scheme of the cavity

assembly (3) enables the coupling to be adjusted just slightly under

critical coupling, and the rectangular cavity was operated in a TE, n9

mode. Each sample wa6 cemented at the center of the bottom of the

cavity such that the c-axis was along the direction of the magnetic

vector of the microwave field, Rotation of the magnet about the fixed

56
cavity permitted the alignment of B parallel to the c-axis.

A typical first derivative curve is shown in Fig. 1 (a) and the

absorption line obtained after integration is shown in Fig. 1 (b). On

the high field side of the zero-crossing point (or the peak of the integrated curve), the absorption line is well defined and extends about

3 millitesla. The shape is distinct and almost the same for all

samples, but on the low field side, a long tail is observed. For the

0.007% sample, this tail extends more than 8 millitesla. For more

concentrated samples, the tail becomes long and flat. In the 0.088%

sample, the tail in the derivative curve (i.e. the signal in the detection method employed in our spectrometer) was not measurable beyond

about 3 millitesla. The integrated intensity does not fall very much

below the peak value in this case, thus it is apparent that the low

field tail extends much further than is observable and that the apparent

areas of the absorption lines are too small for the higher concentrations .

It is also found that the signal is weaker for the heavier doped

samples. The gain of the lock-in amplifier had to be set a factor of

10 higher for the 0.18% sample than for the 0.007% sample in order to

obtain a measurable signal. For the 0.35% sample, it was just barely

possible to determine the position of the absorption line only. Further

difficulty was encountered as numerous other lines appeared with

samples of 0.088% doping or greater. They increased rapidly both in

number and intensity with concentration. The An = 2 signal was located

on the wing of an intense line in the case of the 0.357o sample, for

example

.

3+

Extraneous lines (aside from the Cr ) appeared in all samples.

In the most favorable conditions for the An = 2 line, these extra

lines were not detectable in the two dilute samples. At proper power

level and temperature, the other lines could be much stronger than the

An = 2 line. The origin of these other lines was not investigated. It

3+

is quite possible that some of these are Cr pair lines, and that some

57
may be from other paramagnetic species such as color centers.

The absorption lines obtained by single integration (see Fig. 1

(a) and (b))were integrated a second time to get the area or total line

intensity. The areas were then normalized for amplifier gain and

sample volume. These final numbers are presumed to be a relative

measure of the Zkn = 2 transition. The results are listed in Table I,

and are also plotted as the four points on Fig. 2. The solid curve in

Fig. 2 is the added optical density at 0.47 M-m as presented in the last

report (NBS Technical Note 531), plotted as a function of mol% Cr.

The EPR measurements suggest that the centers responsible for the

Zm = 2 transition follow generally the same type of concentration dependence of the orange coloration. The maximum EPR intensity would

appear to occur at lower Cr concentration than that observed in the

optical data. From the discussion in the next experiment, the error

in the An = 2 measurement of intensity may be 20%. Also from the above

discussion of line shape, the true area of the line probably is larger

than indicated, in the more heavily doped samples. Moreover, the

optical measurements were performed at room temperature rather than at

4 K as were the EPR, which may cause some discrepancy.

The similarity in shape between the plots in Fig. 2 of the

Zkn = 2 EPR transition line intensity and the added optical density as

a function of the Cr concentration certainly suggest that they may have

a mechanism in common. It is not possible to suggest a definite model

at this time for this nor is it possible to offer models for the EPR

line and the orange coloration. We can only repeat earlier statements

that the coloration is too intense to be explained by Cr valence

changes, i.e. the required oscillator- strength would be unreasonable. Thus the color could most easily be explained as due to

unspecified color centers. The EPR line is related but not necessarily

due to the same center.

3+

B. Cr EPR Measurements

58
In this experiment, an attempt has been made to verify the validity

of the quantitative analytical application of the EPR technique as 3+

described in the previous experiment. The Cr EPR lines were measured

3+

in the same way with appropriate modifications in procedure. The Cr

EPR spectra has been studied extensively by various investigators at

various temperatures. E. 0. Schulz-du Boise (4) has given a theoretical

calculation and experimental verification of all the EPR levels and

transitions, and angular dependencies. R. P. Bashuk, et.al (5) attempted

to correlate the results of the determination of Cr concentrations in

ruby by several methods. The EPR measurement seemed in good agreement

with other measurements.

The samples were cemented on the side wall of the cavity with the

c-axis horizontal. This permitted the c-axis to take all possible

orientations with respect to B. and also made B, ^ B ... All measuredc dc rf

ments were made at liquid nitrogen temperature.

The first of two sets of samples measured were the £m = 2 set

3+

described earlier. For each sample, several Cr lines were measured,

integrated, and normalized for sample volume. The line "intensities"

so obtained failed to fit the presumed linear dependence on concentration and the errors seemed to be about 207o . It was subsequently

decided that the size and shape of the samples varied too much to ensure

equal coupling into all samples. This was indicated by changes in

cavity resonant frequency from sample to sample that seemed excessive.

In addition, difficulties prevented precise reproducible location of

samples in the cavity, and the Cr concentrations were not well known.

The second set of samples were then prepared from the optical

samples used for the solid curve in Fig. 2. The concentrations had

been measured by optical absorption. All samples were cut to the same

size, shape, and crystallographic orientation. In each case the sample

was placed in the cavity with some care. The -3/2 -» -1/2 transition

with B, -L c-axis was chosen as particularly favorable for a number of reasons. The results are given in Table II and the integrated

59
intensities plotted in Fig. 3. The resonant frequency of the cavity is seen to change little from sample to sample.

The concentration in sample X, (0.007%), is known to be in doubt

owing to the inconveniently low optical density of the original optical

sample from which it was prepared. For sample A, (0.34%), the determination was also in error, from some unknown cause. The remaining points

follow a straight line through the origin as expected, but with the

points for higher concentrations falling below the straight line as indicated by the dotted line. It is likely that the upper points do

not obey a linear law but too few points are available to determine

other than the departure from the lower solid line.

3+

It is known that Cr pairs start to become appreciable above

3+ about 0.1 mol% Cr(6). Thus, the normal Cr line intensities would be

reduced from the expected values at higher concentrations. Two other

interesting possibilities exist. The microwave power and the modulation field were both maintained the same for all measurements. The

power and the per cent of modulation may be too low for the more con- centrated samples because it was observed that the lines were broader.

Thus, the ions in the outer wings of the line may not have been integrated due to background (noise, nearby lines, and drift). Somewhat

opposite reasoning may be applied to the 0.007% sample in which case

the power may have been too high causing experimental line broadening

and a high area to concentration ratio.

The results presented here would indicate that for concentrations

below about 0.14 mol? it is possible, by this method, to obtain relative

concentrations to within 2%. It should further be pointed out that the

cavity was assembled and disassembled for each sample mounting and that

unlike other similar measurements (5) reference samples (e.g. DPPH)

permanently attached to the cavity were not necessary. We feel that

the reliability, reproducibility, and potential accuracy (with proper

calibration) is well demonstrated. Further, the extension of this

method to considerably smaller concentrations and even to other

60
paramagnetic species is quite feasible.

Table I

60

The comparison of EPR Absorption of the Zki = 2 Transition in Co

irradiated ruby with the Cr concentration.

Sample Concentration Normalized Integrated Area

mol7o Cr (arbitrary units)

0.35

0.175 45

0.088 410

0.035 1500

0.007 690

Table II

The measurement of the integrated area of the EPR absorption line

3+

of the m = -3/2 to -1/2 transition of Cr in ruby,

s imple Concentration

(mol % Cr)

Microwave

Frequency

Area of

EPR Line

Area

cone, x 100

(GHz)

" (arbitary units)

X 0.007 9.5384 66 94

L 0.04 9.5384 230 58

E 0.076 9.5380 436 58

B 0.075 9.5386 447 60

W 0.11 9.5337 655 60

Y 0.14 9.5342 820 59

H 0.20 9.5336 960 48

D 0.38 9.5381 1500 40

A 0.34 9.5398 3260 96

61
(a)

FIRST DERIVATIVE CURVE

.176 T

(b)

ABSORPTION LINE

Fig. 1. The Am = 2 EPR transition in y~ i rrad iated ruby,

ordinate in arbitrary units vs. magnetic induction

(a) experimental derivative curve; (b) absorption

line obtained by integration. Induction, T,

in Tesla.

62
30Nvayosav ivoiido aaznvwaoN

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to

OJ

c

o --» — E

o. >£ a) O -4" Kt/> • -Q O

ro —" •

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4-> —

CM TO O • leu) no +-» _ • ro E o </i "a

<] o >

C£

"O "O T3 a.

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ro +J "U +-» O fO T3 +J CO kTCM l m ox CT) — +* O CD CD Q.

<£

4-> C -M c —• >* c

_l .— -o _Q a) c 3 «n o <U O s- <D s _C Q. J- M trt T3 Q.

cd a) a; 4- S_ -M l_ O J- fO o — •» c o -o o

O 05 tn a> s- •» •~ _c u <n

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63
3

-

Z

ID>

cc<l

QC

CD

DC<

UJ 2 -

+

to

UJz

o

u.o

>

toz

UJ I

Q

Ul

!5

DCUJ

Fig. 3

0.1 0.2 0.3

CHROMIUM CONCENTRATION (mol %)

Integrated intensity of the -J>/2 -* -1/2 Cr3+ EPR

line in ruby vs. mol% Cr. Measurements made at

liquid N2 temperature, X-band frequencies, and

wi th Bxc.

64
REFERENCES

1. R. H. Hoskins and B. H. Soffer, Phys . Rev. 133, A490 (1964).

2. D. R. Mason and J. S. Thorp, Proc. Phys. Soc. (London) 8_7_, 49 (1966).

3. E. 0. Schulz-du Bois, Bell System Tech. Jour. 38_, 271 (1959).

4. T. C. Ensign and T. Chang, Rev. Sci. Instr. 40, 268 (1969).

5. R. P. Bashuk, et al., Zhurnal Prikladnoi Spektroskopii 5_, 172 (1966).

6. H. Statz, L. Ramai, M. J. Weber, G. A. Demars, Jour. Applied Phys.

32. 2185 (1961) and J. C. Gill, Proc. Phys. Soc. (London) 79,

58 (1962).

4.3.3.2. Optical Absorption Determination

of Chromium in Ruby

R. F. Blunt

Inorganic Materials Division

Institute for Materials Research

Objectives

The objectives of this investigation were:

3+

1. The Cr concentration determination in several laser quality

ruby crystals following the optical method of Dodd, Wood, and

Barns (1)

,

2. The correlation of the above results with analyses made by

other methods, both previously reported and current.

3+

3. A new determination of the Cr optical absorption coefficents

in ruby.

65
Experimental Results

The method used consists of measuring the absorption coefficient

at maximum absorption for the two major bands near 0.40 and 0.56 p,m. Measurements must be made for Exc, E||c, or both, and are made at

room temperature for convenience. As a further convenience most

measurements are made for E±c only, since this direction is always

available in samples having arbitrary orientation of the c-axis. Beer's

Law is presumed to be valid, that is, the absorbance, A, is expressed

by: A = log n (Io/I) = 0.434 p, C d, after appropriate corrections to

the experimental A are made for sample surface losses. It is customary

to give the sample thickness, d, in cm, and the Cr concentration, C,

in wt . % Cr 9, thus \i can be described as the absorption coefficient

(cm

-1

) for 100 wt. % Cr

2

.

The absorption is presumed to be due entirely to the well-studied

3+

Cr ions, and it is assumed that the wavelength regions around 0.32

and 0.68 |i,m have no bulk absorption. In this method, a smooth curve connecting these two regions is used as a surface loss baseline from

3+ which the Cr band maxima near 0.40 and 0.56 p,m can be determined.

It can be shown, that for materials with refractive indices less than

2, this method of surface correction is very good, providing, of course,

that the smooth curve is a reasonable approximation for the bulk material without the absorption bands

.

We find that for ruby with well polished surfaces, a straight line

of absorbance vs. wavelength joining, say, 0.32 and 0.68 p,m is usually

adequate. This straight line is approximately tangent to the presumed

baseline at both points. In those cases where the surfaces are not good,

and large surface losses result, the slope at 0.32 u.m is definitely

greater than at 0.68 p,m and a more complicated baseline is needed. The one chosen is made by estimating the slope and absorbance values at 0.32

and 0.68 p.m and joining the two points with the relation:

A

x = A

32

- m

32

(X - 0.32) + b (X - 0.32)

n

, where m „^ is the slope at .32 \xm. The constants b s and n > 1 are calculated to yield the "correct" slope and absorbance at 0.68 u.m.

66
Both baseline methods were employed at various times in the course

of these measurements and the results of the less simple curve are believed to be more realistic and reliable in those cases where the

need for a change of slope is clearly indicated. For even poorly polished samples the variable slope formulas resulted in at most a 3% in- crease in corrected absorbance, A, over that provided by the linear

baseline. In all cases the samples measured were restricted to those

having bands of corrected optical density of at least 0.3, preferably

more than 0.5, or in one case slightly over 1.0. Very well-polished

samples really required only the linear correction. On several occasions, samples were measured that had not been polished at all, merely

ground to size. The results appeared unreliable, and subsequent

measurements on the samples after polishing yielded values differing

by 10 to 15% from the earlier ones. Thus the desirability of polished

surfaces is quite evident, yet cases where a rough check of chromium

concentration is needed would indicate the convenience of the linear

baseline method on unpolished samples.

3+

Measurements of chromium concentration, presumably as Cr , on a number of samples are given in Table I. The absorption coefficients

used are the ones in the reference(l) u, , =u = 47.1 cm ; the

other values |i . u = 89.0 cm , and u. _, i> = 15.8 cm . The quoted

.4,|| •-> °jn

values for the R lines were not used or considered in these measurements

_Land //designate E perpendicular or parallel to the c-axis respectively.

We measured both bands and took the average. (The two values agreed

within 27 at worst). Since many of these samples came from boules

previously reported on, we repeat the earlier results for comparison

and use the same sample identification. We also include measurements

obtained by a magnetic susceptibility method discussed elsewhere in

this report, and three new activation analyses.

Concentrations are given as wt% Cr_0 . The C refer to the

2. j n neutron activation analyses (NA), the C and C to the current optical

and susceptibility measurements respectively. The C * values are very

recent determinations.

67
The samples designated "05" were cut from the nominal 0.05% boule

(Section 4.4.1.1. of NBS Tech. Note 531) a boule about 1" in diameter.

The position of the NA sample relative to the optical sample is unknown.

The 050, and 100 boules were nominally 0.05, 0.075, and 0.100% rods

about 1/2" in diameter. These were discussed in Section 3.6.5. of NBS

Tech. Note 514. All four boules were 60° crystals. The 0.5V samples

were adjacent pieces from a red Verneuil ruby of unknown origin.

Corresponding samples cut from the three boules are identified by

parentheses. Slices number (1) through (7) are adjacent pieces near one end of the boule, and (3) was cut to have large parallel (001) faces.

Slice (8) was cut perpendicular to the boule axis several inches below

the above mentioned pieces. Slice (9) was near the opposite end from(l),

The optical values, in most cases, seem to be considerably smaller

than the activation determinations and consistently larger than those

the susceptibility method gives. The reasons for these discrepancies

are not understood. The optical method is designed to measure only

3+

Cr ion. Other valence states, or other transition metal ion impurities, would either not be detected or would introduce errors unless

they resulted in well-defined extraneous bands. We assume that for

3+

laser quality ruby, Cr ions are the principle source of the optical

absorption bands and that the only likely error would arise because of

the presence of Cr in other valence states, which would not be separa3+

tely identified if present in small amounts. (A loss or gain of Cr

m a given sample would be measurable under favorable circumstances.)

Within these limitations, optical absorption offers a very convenient

method for the analysis of Cr in ruby.

The precision available from optical absorption is 2 to 3% and the

method permits, when small apertures are used, the study of sample

inhomogeneity. Some idea of the inhomogeneity has been indicated in

Table I, although little effort at detailed "mapping" has been

68
attempted. The series (3) slice permitted measuring three places and a variation of several per cent was observed; the series (8) disks were

measured in the center and four places around the edges. In the latter,

the edge values were 5 or 6% higher than the center values. Average

values were used in Table I. The accuracy of the method is determined

largely by the reliability of the absorption coefficients that must be

determined by other analyses.

69
TABLE I

Chromium Analysis (Wt% Cr

2

°'5^ of Rut>y Crystals by Activation Analysis,

Cr

; Optical Absorption, C j and Magnetic Susceptibility Measurements,

C . X

METHODS

Crystal and

Sample

Cn

C

o C

X

C /C

o X

05 -NA

05 "i" cube

05 "x"

0.0443

0.0462*

0.055

0.054 0.044 1.21

050 - (4) 0.059

050 - (3) 0.048

050 - (8) 0.053

0.072

050 - (9) 0.065

075 - (4) 0.078

075 - (3) 0.067

075 - (8) 0.072

075 - (9) 0.086

100 - (4) 0.104

100 - (3) 0.083

100 - (1) 0.0832* 0.088 0.073 1.21

100 - (5) 0.085

100 - (8) 0.087

100 - (9) 0.098

°-5V 0.44 0.37 1.20

0.5V - NA 0.441*

The quoted \i values (1) were assigned standard deviations of about

10%. One other determination can be cited (2) for the 0.56 urn band in

-1

which a value equivalent to 55 cm was reported (to be contrasted with

the 47.1 cm used in Table I). This uncertainty together with the

70
convenience and higher "precision" of the optical method, would make a more accurate re -de termination of absorption coefficients desirable.

Previous analyses (1, 2) in principle give total Cr as do the activation

analyses reported here, as opposed to the optical method which probably

3+

responds only to the Cr ions in the calibrating samples. The magnetic susceptibility method is believed to be particularly favorable

3+

for determining the normal unpaired Cr ions in laser quality ruby.

This method is described in another section of this report on "The

3+

Analysis of Cr in Orange Ruby by Magnetic Susceptibility Measurement." It offers apparent precision on these samples of about 2% and

in principle is an absolute method; that is, the measured susceptibility is expressed as a known formula containing well determined

3+

physical constants, temperature, and the number of Cr spins.

Further, in the three samples measured, the ratio of the optical value

to the susceptibility value (both made on the same sample) was constant

within 2%, with an average of 1.21.

The lower concentrations for the susceptibility measurements as compared with the other chemical analyses (directly or indirectly)

raises several interesting questions which might warrent further investigation. Such questions are exemplified by the possibility of an 3+ appreciable fraction of the Cr not being in the Cr state or that an appreciable fraction of the ions are strongly coupled into anti-ferromagnetic pairs. Also the possibility of fortuitous sample inhomogeneity confusing much of the data cannot be ruled out.

The excellent tracking of the ratio C /C adds considerable confio X

dence in the susceptibility method. If one then assumes that the concentrations so determined (column 3 of Table I),'are correct, new values of

the calibration coefficients can be calculated. The quoted equality of

the E ±c constants for the 0.40 and 0.56 um bands seems reasonable. Other

relative checks were made on the "^" cube, which had parallel faces

containing the c-axis thus permitting E//c measurements. From these and

the measurements of Table I we calculate: 56.8, 56.8, 104.7, and

18.2 cm respectively for u . , [X

r

. r , u . n, and u rr ,, . .4,x' .56,1 -Ml ,56

>ll

71
REFERENCES

1. D. M. Dodd, D. L. Wood, and R. L. Barns, J. Appl. Phys . 35^

1183 (1964).

2. R. P. Bashuk, et al., Zhurnal Prikladnoi Spektroskpoii 5_, 172 (1966).

3+

4.3.3.3. Analysis of Cr in Orange Ruby by

Magnetic Susceptibility Measurements

R. F. Blunt, G. A. Candela, R. A. Forman, and A. H. Kahn

Inorganic Materials Division

Institute for Materials Research

Objective

The objective of this work was the investigation of the magnetic

3+ susceptibility of paramagnetic spins in ruby as a method of Cr determination. The following experiments were planned:

1. Precision bulk magnetic susceptibility measurements on each of

several crystals containing different concentrations of Cr.

2. Simultaneous and selective microwave saturation of the ground

3+

state levels of Cr to give a positive identification of the

3+ contribution to the susceptibility of the Cr ions.

ftO 3. The measurements to be repeated on the same samples after Co

3+

irradiation as a possible means of determining loss of Cr

associated with the resulting coloration.

This work has been supported in part by the Advanced Research

Projects Agency.

Experimental Results

Pure sapphire is diamagnetic and hence paramagnetic centers such as 3+ substitutional Cr can be expected to give predictable and measurable

susceptibility even when present in concentrations such as

72
0.05 wt % Cr„0 . Additional paramagnetic centers can, of course, make

appreciable contributions and have to be allowed for if susceptibility

is to be used as an analytical tool.

Theoretical derivations (1, 2) give expressions applicable to our case 3+

using the assumption of isolated substitutional Cr ions in the

trigonal Oi - A1.0 lattice. In our experimental conditions, the susceptibility, Xj is given to a good approximation by: NC where C

X ~ T + A

is a quantity involving only fundamental constants and the g value for

the ions and N is the number of ions in the sample. The g values for

3+

Cr in ruby are very precisely known. A can be considered, in this

simple discussion, as a constant that can be determined by making

3+

measurements at several temperatures, and it is anisotropic. The Cr

concentration is calculated from the sample weight and the value of N

obtained from the above.

The apparatus used has been described previously (3) . It employs the

Faraday method but in addition has the sample suspended in the Ka-band

microwave cavity thus permitting simultaneous microwave resonance. The

conditions for resonance in these measurements were B j_ c-axis with

3+

B = approximately 0.05 tesla, such that one Cr resonance occurs at a microwave frequency of 14.1 GHz. Under these conditions it is possible

to resonate one transition and get some "pumping" to all levels via

cross relaxation. Thus when the spin-lattice relaxation time is long

enough, all four ground state levels can be saturated, thereby removing

these ions from the spin system available for susceptibility.

Three samples about 300 mg each were measured, having nominal concentrations of 0.05, 0.10, and 0.50 wt "L Cr. Bulk susceptibility was measured at 300K, 78K, and several temperatures between 4.2 and 2K. The

concentration of paramagnetic ions was sufficiently low so that the

(diamagnetic) susceptibility measured at 300K could be used for the

lattic diamagnetic correction. The corrected x values for low temper3+

atures thus contained normal Cr contributions from which the

73
concentration could be calculated plus additions from extraneous paramagnetic centers. The diamagnetic susceptibilities agreed well with

published values for sapphire. Finally, a sample of extremely pure

sapphire grown at NBS by H. S. Parker was measured down to 2 K. A

susceptibility value of -0.32 x 10 cm gm was obtained. The expected,

essentially temperature independent diamagnetism also confirmed the

corrections made on the ruby.

Microwave saturation experiments were performed on each of the

three ruby samples at 4.2 K and below. The degree of saturation was

taken as the fraction of the total bulk paramagnetic susceptibility

that was removed at the maximum microwave power used. Both high temperature and high concentration would tend to decrease spin-lattice re- laxation time and limit the degree of saturation. Extraneous para3+ magnetic ions, i.e. ions other that Cr in normal substitutional sites,

would not be expected to resonate and hence could not be removed from

the spin system. These ions would, therefore, reduce the degree of

saturation. The 0.57o sample showed considerable saturation, ever, at 4.2K.

At naar 2 K, the following values were obtained for the degree of

saturation: 99.6%, 97.4%, and 94% for the 0.05, 0.1, and 0.5 samples,

respectively. In the case of the 0.05% sample the saturation was essentially 100% at only about 1/3 of the maximum power with no further

change with power increase. The saturation of the 0.1% sample may not

have reached its maximum value at the maximum microwave power, while

this was quite clearly the case for the 0.5% sample. We attribute the

lack of approximately 100% saturation in all three samples to fast

relaxation in the more concentrated samples or to the danger of over- heating the sample, rather than to the presence of extraneous ions.

We conclude, therefore, that the measured bulk susceptibility is due

3+ almost entirely to largely isolated substitutional Cr ions, and th

the measured x can be used to calculate the concentration.

The 0.05 and 0.10% samples were colored orange by a "saturation"

ft n irradiation by Co and measured. No detectable change in bulk susceptibility was observed. Attempts at microwave saturation yielded very

74
small reductions in x> which we attribute to very fast relaxation processes produced by the irradiation damage, hence giving no useful information. The susceptibility data for the orange ruby were plotted on the

corresponding graph obtained for the samples before irradiation and the

agreement was clearly within 1% at worst. One possible model for the

Q 1^ 0_|_ / _|_ damage would be one in which Cr was converted to Cr and/or Cr

Both of these are expected to have susceptibilities distinctly different

3+

from Cr , the first higher and the second lower. It would ve very at3+ tractive to conclude from the small change, that the loss in Cr would

be less than 1%. However, when one considers various possible defects

that could be generated by the y -irradiation, the magnetic properties of

which are unknown, it is obvious that no real conclusion about valence

change can be made. A large reduction in x would certainly have been

3+

suggestive of Cr loss. The only conclusion that can be drawn is that

the lack of change does put a considerable constraint on the magnetic

properties of any model proposed. It does seem most unlikely that any

appreciable changes in, additions to, or deletions from the paramagnetic

centers originally present would result in a net negligible overall

susceptibility change. Such coincidences are unlikely but could happen.

Figure 1 is a plot of x vs. T. The extrapolation of x to zero

gives a value of A at the intercept with the abcissa. The slope of each

curve is in fact the product NC from which the concentration can be calculated. Plotted along with the B± c-axis data are two sets of data

taken for B|| c-axis. It is seen that A = -4K and An = K. Theory (1)

predicts that these values should be -.1 and+. 2K, respectively, and data

in the literature (4) is reported to be in accord with these. An additional measurement was made as a check on this apparent discrepancy. It was done on an adjacent piece of the same 0.1% boule at essentially zero

field by the mutual inductance method. The measurement was kindly

performed by B. W. Mangum of the NBS Low Temperature Section. This

method does not afford an absolute calibration hence the data was

plotted to a convenient arbitrary scale, but the intercept is in agreement with that obtained at a much higher field.

75
The apparent discrepancy between the theory for isolated ions and

the observed behavior at low temperature is not understood at this

time. It should be pointed out that the difference, from the standpoint of Fig. 1, is equivalent to the addition of an isotropic antiferromagnetic susceptibility of such magnitude as to shift the curves

over about 0.2 K. The total anisotropy, that is An - A , is observed

as 0.4 K rather than the predicted 0.3 K. However, there is no reason,

that we can see, how the above difficulty could have appreciable effect

3+

on the validity of the determination of the number of Cr spins in

these samples.

The sensitivity and reproducibility of the susceptibility measurements at 4.2 K and below were sufficiently good to give a resultant

3+

Cr determination that appears to be good to 1%. The values obtained

were: 0.044, 0.073, and 0.37 wt % Cr„0 , respectively for the 0.05,

0.10, and 0.5% samples. These were consistently lower than the values

(respectively 0.054, 0.088, and 0.44%) obtained on these identical

samples by the optical absorption method discussed in another section

of this report. This latter method, although capable of excellent re- producibility, is only relative and requires a calibrating constant

which might very well be in error. It is interesting to note that the

ratios of the optical to susceptibility values were constant within

2% for the three samples.

These analyses, as well as neutron activation analyses are summarized

in Table I of the section of this report on "The Optical Absorption

Determination of Cr in Ruby."

We believe that this susceptibility method offers a precise and

3+ direct method of determining the Cr concentration in ruby. It very

likely has potential use in other systems in which a dilute ion of

appropriate configuration is in a diamagnetic lattice.

USCOMM-NBS-DC

76
REFERENCES

1. M. H. L. Price, Nuovo cimento Suppl. 6_, 817 (1957).

2. H. L. Davis, Z. Physik. Chem. 16_, 213 (1958).

3. G. A. Candela and R. E. Mundy, Rev. Sci. Instr. 36, 338 (1965)

4. K. Brugger and J. G. Daunt, Z. Physik. Chem. 16_, 203 (1958).

77
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(J 2

V) • TJ

fD I/)

O z CD • i

+J -a 4-> >*

"O to

+->

M

a; +-> c CD o •—

+j c/j o •—

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