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NASA 

Reference 

Publication 

1131 


September 1984 


Engineering and Design 
Properties of Thallium- 
Doped Sodium Iodide and 
Selected Properties of 
Sodium-Doped Cesium Iodide 


K. Forrest, C. Haehner, 
T. Heslin, M. Magida, 

J. Uber, S. Freiman, 

G. Hicho, and R. Polvani 


NASA 


NASA 

Reference 

Publication 

1131 


1984 


Engineering and Design 
Properties of Thallium- 
Doped Sodium Iodide and 
Selected Properties of 
Sodium-Doped Cesium Iodide 


K. Forrest, C. Haehner, 
T. Heslin, M. Magida, 
and J. Uber 
Goddard Space Flight Center 
Greenhelt, Maryland 

S. Freiman, G. Hicho, 
and R. Polvani 
National Bureau of Standards 
Washington, D.C. 



National Aeronautics 
and Space Administration 


Scientific and Technical 

Information Branch 



All measurement values are expressed in the International System of 
Units (SI) in accordance with NASA Policy Directive 2220.4, paragraph 4. 



CONTENTS 


Page 

INTRODUCTION 1 

TEST REQUIREMENTS 2 

SUMMARY OF RESULTS 3 

MATERIALS, SPECIMENS, AND TEST METHODS 9 

TEST RESULTS AND STATISTICAL ANALYSIS 38 

CONCLUSIONS 65 

RECOMMENDED TESTING FOR DESIGNERS 67 

ACKNOWLEDGMENTS 67 


REFERENCES 


69 



ENGINEERING AND DESIGN PROPERTIES OF 
THALLIUM-DOPED SODIUM IODIDE AND 

SELECTED PROPERTIES OF SODIUM-DOPED 

CESIUM IODIDE 


K. Forrest, C. Haehner, T. Heslin, M. Magida, J. Uber 

NASA /Goddard Space Flight Center 
Green belt, Maryland 20771 

S. Freiman, G. Hicho, R. Polvani 

National Bureau of Standards 
Washington, D. C. 20234 


INTRODUCTION 

The experiments selected for the Gamma Ray Observatory (GRO) will utilize over 1000 kg of 
inorganic Nal(Tl) and CsI(Na) scintillators. Many of the individual blocks of scintillators will be 
larger than any that have previously been launched in a space vehicle. The Energetic Gamma Ray 
Experiment (EGRET) scintillator, for example, is a composite assembly of Nal(Tl) approximately 
0.76 m square by 20 cm thick, and the Oriented Scintillation Spectrometer Experiment (OSSE) 
uses a 0.33 m diameter cylinder composed of a 10 cm thick piece of Nal(Tl) and a 7.6 cm thick 
piece of CsI(Na). Proper mechanical systems design for the encapsulation, bonding, and support of 
these large scintillator blocks is necessary if performance degradation from cracking near support 
regions or failure because of creep or clouding from hydration are to be avoided. On the other hand, 
overdesigned support systems that result in large weight penalties are also to be avoided. 

Although the alkali halides have been studied for years, most of the work in the 1950’s and 1960’s 
centered on NaCI, KCI, LiF, and cubic materials such as MgO because these materials were model 
systems for delineating solid-state theories about defect structures that were the subject of extensive 
research at the time. Other than some work on Csl done for the High Energy Astronomy Observa- 
tory in the early 1970’s (references 1 and 2), the only engineering properties study of Nal was a 
report of limited circulation by Stanford University (reference 3) and undoped, single-crystal elastic 
constant data in Landolt-Bornstein (reference 4). 

To optimize the mechanical design of the scintillator supports and housings for experiments, the 
GRO systems team authorized a program for determining accurate and statistically significant values 
for the mechanical and thermal properties of Nal(Tl) and selected properties of CsI(Na). The 


1 



ensuing materials evaluation program was conducted by the Materials Control and Applications 
Branch of the Goddard Space Flight Center (GSFC) and the Fracture and Deformation Division of 
the National Bureau of Standards under contract to GSFC. Emphasis of the program was placed on 
the needs of the EGRET and OSSE programs. This test report was compiled from the results of this 
test program. In addition, other test results and literature data that were not developed in this pro- 
gram are cited to make this compilation as comprehensive as possible for those who wish to use 
these two materials in mechanical designs. Enough test description and analysis of the data is 
presented to facilitate comparative testing in the future. 

In the following section, a series of ten test requirements are outlined, beginning with coefficient of 
linear thermal expansion and ending with ingot variation of strength. This sequence of properties is 
the topic outline for each succeeding section in this report, beginning with summary of results and 
ending with the conclusions. 

TEST REQUIREMENTS 

The following properties of single-crystal and polycrystalline Nal(Tl) were required for meeting the 
needs of the various GRO experiments: 

1 . Coefficient of linear thermal expansion 

2. Thermal conductivity 

3. Thermal-shock resistance 

4. Heat capacity 

5. Elastic constants 

a. Density 

b. Young’s modulus 

c. Shear modulus 

d. Mechanical damping efficiency (internal friction) 

6. Ultimate strengths 

a. Modulus of rupture 

b. Shear 

c. Compressive 

d. Critical stress intensity factor (K IC ) 

7 . Creep 

a. Bending 

b. Compression 


2 



8. Hardness 

9. Susceptibility to subcritical crack growth 

10. Ingot variation of strength 

In addition, it was determined that compressive strength and compressive creep measurements were 
necessary for single-crystal CsI(Na). 

Material for all tests was purchased from the Harshaw Chemical Company, Solon, Ohio, and the 
Bicron Corporation, Newbury, Ohio. 

SUMMARY OF RESULTS 

This section summarizes the test results for single-crystal and polycrystalline Nal(Tl) and single- 
crystal CsI(Na). After each property heading, the symbol subsequently used to refer to the property 
is listed, and the range of values measured for that property is given without regard to the values 
referring to single-crystal or polycrystalline material unless otherwise stated. 

Finally, an evaluated average, plus or minus one standard deviation, is given when applicable along 
with the number (n) of data points used to arrive at the standard deviation. The evaluated average is 
arrived at in the section entitled “Test Results and Statistical Analysis” and usually represents the 
average of the largest group of specimens that cannot be statistically differentiated from each other 
using a pair-wise t-test of the equality of means at the 90- or 95-percent confidence level. In the 
short text after each heading, some details on the effects of orientation and position are given for 
single-crystal and Polyscin* materials, and the effects of ingot variation are cited. An abbreviation 
key referring to position and orientation designations for Polyscin and single-crystal material appears 
in Table 4. 

Coefficient of Linear Thermal Expansion, a 

• Range 45.65 X 10' 6 K 1 to 50.20 X 10' 6 K 1 at 253 to 323 K 

® Evaluated average (47.21 ± 0.44) X 10' 6 K' 1 at 297 to 323 K, n = 9 

Measurements were made on three oriented single-crystal and four Polyscin Nal(Tl) specimens. 
Single-crystal material exhibited the same coefficient of linear thermal expansion in the <100>, 
<01 1>, and <1 1 1> directions. The coefficient of linear thermal expansion of Polyscin is slightly 
less in the direction perpendicular to the extrusion axis than in the direction parallel to it, and there 
is no significant difference between similarly positioned material taken from the beginning or end 
of an extrusion. 

Literature values are as follows: 

® Single-crystal, undoped Nal 44.7 X 10' 6 K' 1 , 293 K (reference 5, page 1116) 

• Single-crystal, undoped Csl 48.3 X 10' 6 K' 1 , 293 K (reference 5, page 1098) 

*“Polyscin” is a polycrystalline form of Nal(Tl) produced by the Harshaw Chemical Company. 


3 



Thermal Conductivity, k 


• Range 1 .47 X 1 O' 2 to 1 .9 1 X 1 O’ 2 W/cm K at 300 K 

® Evaluated average (1.71 ± 0.28) X 10' 2 W/cm K at 300 K, n = 43 

Measurements were made on three oriented single-crystal Nal(Tl) specimens and four Polyscin 
specimens. Single-crystal material exhibited the same thermal conductivity in the <100> and 
<01 1> directions, but exhibited a lower value in the <1 1 1> direction. Polyscin material from the 
interior of the initial end of an extrusion exhibited the highest measured thermal conductivity in 
the direction parallel to the extrusion axis. Measurements made on the other three Polyscin speci- 
mens and the <100> and the <01 1> single-crystal specimens were statistically indistinguishable 
at the 90-percent confidence level. 

Literature values are as follows : 

• Single crystal, undoped Nal, 1 .53 X 10" 2 W/cm K at 300 K (reference 3, page 2) 

® Single crystal, undoped Csl, 1.05 X 10' 2 W/cm K at 296 K (reference 6, page 561) 

Thermal Shock Resistance, AT c 

In oil-quench tests of 23 Nal(Tl) specimens, AT c ranged from 18.5 to 33.5 K for material with a 
surface area to volume ratio of 1 .83 and 3.4 cm -1 , respectively. In air-quench tests of four Nal(Tl) 
specimens, AT, ranged from 59.5 to 67 K for material with a surface area to volume ratio of 
1 .83 cm' 1 and 3.4 cm' 1 , respectively. 

Analysis indicates that, for initial crack sizes in the range of 2.5 mm (which was average in the 
Polyscin examined), AT c ranges from a low of 3.3 K for a very high heat-transfer coefficient and 
Biot modulus (h -> °°, j3 > > 100) to a high of about 25 K for oil quenching (h* = 0.037 W/cm 2 K, 
j3* = 0.628) and 67 K for air quenching (h* = 0.012 W/cm 2 K, ( 5 * = 0.23). 

Heat Capacity, C p 

© Range 0.346 to 0.350 J/gK at 310 K 

® Evaluated average 0.348 ± 6.61 X 10' 3 J/gK, at 310 K, n = 28 

Four Nal(Tl) specimens were measured; two single-crystal and two Polyscin specimens. No signifi- 
cant difference was observed between the specimens. 

Literature values are as follows: 

® Nal (undoped) 0.347 J/gK at 273 K 

(reference 7, page 2273) 

0.355 J/gK at 323 K 

® Csl (undoped) 0.203 J/gK at 298 K (reference 8, page 496) 


*Calculated values. 


4 



Elastic Constants, p, E, G, C.., Q' 1 , all at 300 K 

IJ 

p — range 3.657 to 3.675 g/cc 

evaluated average 3.67 ± 5.61 X 10' 3 g/cc, n = 35 

E - range 1.9129 X 10 4 MPa (E <in> )to 2.6263 X 10 4 MPa (E <100> ) 

evaluated average 2.01508 X 10 4 MPa ± 0.06258 X 10 4 MPa (Polyscin), n = 50 

G - range 7.35 X 10 3 MPa (G <100><010> )to 1.07 X 10 4 MPa (G <on><oIl> ) 
evaluated average 7.6470 X 10 3 MPa ± 0.2857 X 10 3 MPa (Polyscin), n = 50 

C u - range 3.0250 to 3.0747 X 10 4 MPa 

evaluated average 3.0418 X 10 4 ± 0.01 17 X 10 4 MPa, n = 36 

C 12 - range 8.7790 to 9.1125 X 10 3 MPa 

evaluated average 8.9581 X 10 3 ± 0.1035 X 10 3 MPa, n = 36 

C 44 - range 7.3305 to 7.4368 X 10 3 MPa 

evaluated average 7.3601 X 10 3 ± 0.0262 X 10 3 MPa, n = 36 

Q’ 1 - range 2.80 X 10' 4 to 5.30 X 10' 4 at 750 Hz 

evaluated average 5.12 X 10' 4 ± 1.3 X 1 O' 4 , n = 8 

The average value for Young’s, shear, and bulk moduli for Polyscin are 2.01 X 10 4 , 7.64 X 10 3 , and 
1.80 X 10 4 MPa, respectively, and Poisson’s ratio is 0.314, there being a 4.2 to 7.3-percent differ- 
ence in the value of these constants corresponding to the degree that the material has been work- 
hardened in the forming operation. Material tested from two separate logs of Polyscin had the same 
elastic constants, p, E, and G. Material from two different single-crystal ingots had the same elastic 

constants, p and C.. . 

’ r u 

Literature values are as follows: 

• Nal at 300 K 

p = 3.667 g/cc (reference 7, page 656) 

E = 2.08 X 10 4 MPa (Polyscin) (reference 3, page 1) 

G = 7.86 X 10 3 MPa (Polyscin) (reference 3, page 1) 

C u = 3.03 X 10 4 MPa (reference 4, page 8) 

C 12 = 8.9 X 10 3 MPa (reference 4, page 8) 

C 44 = 7.34 X 10 3 MPa (reference 4, page 8) 

• Csl at 300 K 

p = 4.510 g/cc (reference 7, page 656) 

E = 1.39 X 10 4 MPa (Polycrystal) (reference 2, page 4) 

G = 6.9 X 10 3 MPa (Polycrystal) (reference 2, page 4) 


5 



Cjj = 2.45 X 10 4 MPa (reference 4, page 8) 

C 12 = 6.7 X 10 3 MPa (reference 4, page 8) 

C 44 = 6.3 X 10 3 MPa (reference 4, page 8) 

Ultimate Strength 

Nal(TI) at 300 K 

• Modulus of rupture (MOR) 

<100> cleavage, range =1.57 to 2.71 MPa 
Polyscin, range = 2.85 to 6.49 MPa 

• Shear 

<100> cleavage, range = 6.42 to 9.74 MPa 
Polyscin, range = 5.71 to 8.00 MPa 

• Compression 

<100> cleavage, range = 1 1.19 to 16.72 MPa 
Polyscin, range = 9.1 1 to 23.12 MPa 

• K 

ic 

Polyscin, range = 0.304 to 0.436 MPa m 1/2 
Evaluated average = 0.382 ± 0.042 MPa m 1/2 , n = 9 

Material from two separate logs of Polyscin and nine different Nal(Tl) single-crystal ingots was 
tested. Although Polyscin is homogeneous with respect to elastic moduli, its MOR strength in one 
extrusion varied significantly (a factor of 1 .4 on average) with position in the log, whereas in the 
second extrusion, MOR strength was homogeneous. Single-crystal strengths are ingot-dependent 
within the ranges cited. 

Csl(Na) at 300 K (0.2-percent yield) 

• <100> single crystal, range = 3.27 to 7.49 MPa 

• Polycrystal, average = 2.98 ± 0.22 MPa, n = 5 

Material from three single-crystal ingots and one polycrystal ingot of CsI(Na) was tested. Yield 
strength varied extensively from ingot to ingot (as much as a factor of 2.3), but strength within an 
ingot was homogeneous. 


6 



Literature values are as follows: 


• Nal(Tl) 

MOR = 6.45 MPa (reference 3, Part 2, page 1 ) 

• CsI(Na) 

Proportional limit = 0.276 to 2.35 MPa (reference 2, page 14) 

K IC = 0.279 to 1 .206 MPa m 1/2 , single crystals* 

Creep 

Nal(TI) at 300 K 

• Compression 

Less than 0.005 percent in 2000 hours at 1 .38 MPa (Polyscin) 

Less than 0.017 percent in 3000 hours at 1.08 MPa (<100> single crystal) 

• Bending (four point) 

12.7- by 2.54- by 2.54-cm specimens, 10.6-cm outerspan, 3.386-cm inner span 
Less than 5.08 X 1 0' 5 cm in 4000 hours at 1 .93 MPa (Polyscin) 

Less than 7.62 X 10" 4 cm in 4000 hours at 1 .48 MPa (<100> single crystal) 

Compressive and flexural creep in Nal(Tl) at 300 K can be expressed linearly using a t 1/3 plot, 
where t is time. An indication of creep rate is measured in terms of the slope of such a linear plot. 
An increasing slope indicates an increasing creep rate. Significant creep is considered to be the point 
of maximum rate of change in a plot of slope versus applied stress (Figure 19). 

Material from one extrusion of Polyscin was tested in flexure and in compression. Material from one 
single crystal was tested in compression while material from another single crystal was tested in 
flexure. 

In general, single-crystal material crept more than Polyscin for the same test. Compressive and flex- 
ural creep was greatest for single-crystal material stressed in a principal-axis, <100> direction, com- 
pared to material stressed in the other symmetry-axis directions, <01 1> and <1 1 1>. 

For Polyscin, compressive creep is very small (<0.005 percent in 2000 hours) at stresses below 
1.38 MPa. Material from the end of an extrusion, near the surface, creeps less than material from 
the interior of an extrusion near the beginning by a factor of about 0.72. This is attributed to a dif- 
ference in the degree of work-hardening in these two regions. 

In either case, relatively large creep rates (slope >10 microstrain/hr 1 /3 ) do not occur until the 
proportional limit of the material is exceeded, which is, on the average, 2.43 MPa for interior 
material and 3.44 MPa for surface material. Maximum compressive creep was measured in a single 
crystal loaded in a principal-axis <100> direction. A strain of 0.135 percent was measured in 350 
hours at 2.89 MPa. 


*D. Lewis, Personal Communication, Ceramics Branch, Naval Research Laboratory, Washington, D.C. 


7 



In flexure, creep in Polyscin begins when the maximum flexural stress exceeds 1.93 MPa. Below this 
stress level, no observable creep was detected in 4000 hours with a sensitivity of 5.08 X 10' 5 cm. In 
contrast with compressive creep, flexural creep in Polyscin is homogeneous with respect to position 
and orientation in an extrusion. Relatively large creep rates (slope >5.08 X 10' 6 cm/hr 1/3 ) do not 
occur until the proportional limit of the material is exceeded, which is, on the average, 3.03 MPa. 
Maximum flexural creep was measured in a single crystal loaded in a principal-axis <100> direction. 
A displacement of 7.62 X 10‘ 4 cm was measured after 4000 hours at 1 .72 MPa. 

Csl(Na) at 300 K (Compression) 

« Less than 0.858 percent in 979 hours at 2.25 MPa (polycrystal) 

• Less than 0.139 percent in 1126 hours at 2.69 MPa (<100> single crystal) 

The dominant feature of creep behavior of the CsI(Na) is the high variability between crystal ingots. 
Vickers Hardness, H 

• Range 7.74 to 9.5 kg/mm 2 (single crystal) 

• Evaluated average 8.12 ± 0.6 kg/mm 2 

The hardness of single-crystal Nal(Tl) is independent of crystallographic direction. 

Susceptibility to Subcritical Crack Growth 

Stress-rate tests indicate that Polyscin Nal(Tl) is not susceptible to subcritical crack growth in the 
stress-rate range from 0.132 to 63.8 MPa/second. Plastic deformation behavior is observed in this 
stress-rate range. At higher rates, in excess of 1 .4 X 1 0 4 MPa/second, strength increased relative to 
the values exhibited at the lower stress rates by a factor of 2 to 5 times, and brittle fracture was 
observed. 

Ingot Variation of Strength 
Nal(TI) 

A study of the MOR, <100> single-crystal cleavage strength of 38 Nal(Tl) specimens from eight 
different ingots indicates that strength is ingot-dependent but homogeneous within an ingot. Aver- 
age strengths varied from 1 .75 to 2.58 MPa. 

A similar study of the MOR strengths of 24 specimens from one extrusion of Polyscin and eight 
specimens from another extrusion indicated that the second extrusion was homogeneous with 
respect to strength, whereas the first one was not. Average MOR strength is extrusion-dependent, 
and varied from 4.03 to 5.6 MPa. The thallium concentration in Nal(Tl) was measured for each of 
the MOR test specimens. No correlation was found to establish a strength dependency on the basis 
of thallium concentration. 



A compressive initial cracking-strength (ICS) study of eight Polyscin specimens from both of two 
extrusions indicates that ICS is ingot-dependent and is not homogeneous within an ingot. Average 
strengths varied from 1 1.4 to 18.9 MPa. 

Csl(Na) 

A study of the 0.2-percent <100> compressive yield strength of nine single-crystal CsI(Na) speci- 
ments from three different ingots indicates that strength is ingot-dependent but homogeneous 
within an ingot. Average strengths varied from 3.50 to 7.36 MPa. 

MATERIALS, SPECIMENS, AND TEST METHODS 

Testing was divided into two general areas. Nal(Tl) testing was performed by GSFC, except for 
stress-rate testing and initial K IC testing, which was addressed by the National Bureau of Standards 
(NBS). CsI(Na) testing was performed by NBS. Three separate specimen orders were received. GSFC 
received two orders of Nal(Tl) about 2 years apart (1980 and 1982), and NBS received one order of 
CsI(Na) and Polyscin Nal(Tl) in 1980. The Polyscin Nal(Tl) material in the NBS order was taken 
from a different extrusion than that of the material in the GSFC order; therefore, including the 
three specimens (two bonded and one solid) tested by Stanford University in 1976 (reference 3), 
four Polyscin extrusions have been sampled and documented. The strength-test results for specimens 
from these four extrusions are summarized and discussed further in the section on “Test Results 
and Statistical Analysis.” 

The first order received by GSFC consisted of 144 Nal(Tl) specimens from the Harshaw Chemical 
Company and 51 specimens from the Bicron Corporation. 

One extrusion of Polyscin and three ingots of single-crystal material were represented in this order. 
The second GSFC order consisted of 16 Polyscin and 24 single-crystal ultimate-strength specimens, 
representing one poly crystalline extrusion and six single-crystal ingots. Including the first order of 
material, nine single-crystal ingots have been sampled and documented. Strength-test results of 
specimens from these nine ingots are summarized and discussed further in the section on “Test Re- 
sults and Statistical Analysis.” 

The Nal(Tl) portion of the NBS order consisted of 68 Polyscin MOR specimens for stress-rate 
testing and six double-cantilever beam specimens for K JC measurements. The CsI(Na) portion of the 
NBS order consisted of 15 single-crystal compression specimens and five poly crystalline specimens. 
The 1 5 single-crystal specimens represented three different ingots and the three symmetry-axis 
directions, as well as top, middle, and bottom positions in an ingot (reference 9). 

Specimens for corroborative K JC testing (measurement No. 6d) hardness (No. 8) and impact testing 
(No. 9) were made and tested at GSFC from unused creep specimens or broken MOR bars. 

Tables 1 , 2, and 3 list the specimens. Table 4 identifies the symbols used in Tables 1 , 2, and 3. 


9 



Table 1 

GSFC Purchase No. 1 (1980) 


Property 

Test 

Number 

Material 

Type* 

Position* 

Orientation* 

Specimen 

Size 

(cm) 

Number of 
Specimens 

Coefficient of 

1 

P 

IH 

// 

5.08 X 0.555 dia 

1 

Linear Thermal 


P 

IS 

i 

5.08 X 0.555 dia 

1 

Expansion 


P 

FH 

// 

5.08 X 0.555 dia 

1 



P 

FS 

1 

5.08 X 0.555 dia 

1 



S,H 

Any 

<100> 

5.08 X 0.555 dia 

1 



S,H 

Any 

<01 1> 

5.08 X 0.555 dia 

1 



S,H 

Any 

<1 1 1> 

5.08 X 0.555 dia 

1 

Thermal 

2 

P 

IH 

// 

0.954 X 5.08 dia 

1 

Conductivity 


P 

IS 

1 

0.954 X 5.08 dia 

1 



P 

FH 

// 

0.954 X 5.08 dia 

1 



P 

FS 

I 

0.954 X 5.08 dia 

1 



S,B 

Any 

<100> 

0.954 X 5.08 dia 

1 



S,B 

Any 

<01 1> 

0.954 X 5.08 dia 

1 



S,B 

Any 

<11 1> 

0.954 X 5.08 dia 

1 

Specific 

3 

P 

IH 

Any 

0.635 dia X 0.127 

1 

Heat 


P 

FS 

Any 

0.635 dia X 0.127 

1 



S,H 

Any 

Any 

0.635 dia X 0.127 

1 

Thermal 

4 

P 

FS 

// 

2.54 X 7.62 X 7.62 

3 

Shock 


P 

IH 

1 

2.54 X 7.62 X 7.62 

3 

Resistance 


S,B 

Any 

<100> 

2.54 X 7.62 X 7.62 

3 

Elastic 

5 

P 

m 

// 

12.7 X 2.54 X 0.475 

2 

Moduli 


P 

1 

1 

1 2.7 X 2.54 X 0.475 

2 

and 


P 

mm 

// 

12.7 X 2,54 X 0.475 

2 

Damping 


P 

FH 

// 

12.7 X 2.54 X 0.475 

2 



P 

FH 

1 

12.7 X 2.54X 0.475 

2 



P 

FS 

// 

12.7 X 2.54 X 0.475 

2 



S,H 

Any 

<100> 

12.7 X 2.54 X 0.475 

2 



S,H 

Any 

<01 1> 

12.7 X 2.54 X 0.475 

2 



S,H 

Any 

<11 1> 

12.7 X 2.54 X 0.475 

2 

Ultimate 

6a 

P 

IH 

// 

12.7 X 2.54 X 2.54 

4 

Bending 


P 

IH 

1 

12.7 X 2.54 X 2.54 

4 

Strength 


P 

IS 

// 

12.7 X 2.54 X 2.54 

4 

(4 point) 


P 

FH 

// 

12.7 X 2.54 X 2.54 

4 



P 

FH 

1 

12.7 X 2.54 X 2.54 

4 



P 

FS 

// 

12.7 X 2.54 X 2.54 

4 



S,H,& B 

Any 

<100> 

12.7 X 2.54 X 2.54 

3 



S,H,& B 

Any 

<01 1> 

12.7 X 2.54 X 2.54 

3 



S,H,& B 

Any 

<1 1 1> 

12.7 X 2.54 X 2.54 

3 


*Table 4 defines symbols that appear in this table. 


10 



















































Table 1 (Continued) 


Property 

Test 

Number 

Material 

Type* 

Position* 

Orientation* 

Specimen 

Size 

(cm) 

Number of 
Specimens 

Ultimate 

6b 

P 

FS 

// 

7.62 X 1.27 dia 

4 

Shear 


P 

IH 

1 

7.62 X 1.27 dia 

4 

Strength 


S,H,& B 

Any 

<100> 

7.62 X 1.27 dia 

3 



S,H,& B 

Any 

<01 1> 

7.62 X 1.27 dia 

3 



S,H,& B 

Any 

<11 1> 

7.62 X 1.27 dia 

3 

Ultimate 

6c 

P 

FS 

// 

2.86 X 2.54 dia 

4 

Compression 


P 

IH 

1 

2.86 X 2.54 dia 

4 

Strength 


S,H,& B 

Any 

<100> 

2.86 X 2.54 dia 

3 



S,H,& B 

Any 

<01 1> 

2.86 X 2.54 dia 

3 



S,H,& B 

Any 

<11 1> 

2.86 X 2.54 dia 

3 

Bending 

7a 

P 

FS 

// 

12.7 X 1.90 X 1.90 

6 

Creep 


P 

IH 

1 

12.7 X 1.90 X 1.90 

6 

(4 point) 


S.B 

Any 

<100> 

12.7 X 1.90 X 1.90 

2 



S,B 

Any 

<01 1> 

12.7 X 1.90 X 1.90 

2 



S.B 

Any 

<11 1> 

12.7 X 1.90 X 1.90 

2 

Compression 

7b 

P 

FS 

// 

2.54 X 0.635 dia 

6 

Creep 


P 

IH 

I 

2.54 X 0.635 dia 

6 



S.B 

Any 

<100> 

2.54 X 0.635 dia 

2 



S.B 

Any 

<01 1> 

2.54 X 0.635 dia 

2 



S.B 

Any 

<1 1 1> 

2.54 X 0.635 dia 

2 


* Table 4 defines symbols that appear in this table. 


Table 2 

GSFC Purchase No. 2 (1982) 


Property 

Test 

Number 

Material 

Type* 

Position* 

Orientation* 

Specimen 

Size 

(cm) 

Number of 
Specimens 

Ultimate 

6c 

P 

IH 

i 

2.86 X 2.54 dia 

4 

Compression 


P 

FS 

// 

2.86 X 2.54 dia 

4 

Ultimate 

6a 

P 

IH 

// 

12.7 X 2.54 X 2.54 

4 

Bending 


P 

FH 

// 

12.7 X 2.54 X 2.54 

4 



S,H 

Any 

<100> 

12.7 X 2.54 X 2.54 

24** 


*Table 4 defines symbols that appear in this table. 
**Four specimens from each of six different ingots. 


11 























































Table 3 

NBS Purchase (1980) 







Specimen 



Test 

Material 



Size 

Number of 

Property 

Number 

Type* 

Position* 

Orientation* 

(cm) 

Specimens 

Ultimate 
Bending 
(3 point) 
Stress-Rate 
Testing 

6a 

P 

Any 

Any 

2.5 X 0.6 X 0.3 

68 

Double 
Cantilever 
Beam, K |C 

6d j 

P 

Any 

Any 

5.0 X 1.9 X 0.2 

6 

— — 

0.2% 

7b 

C 

S 

R 

1 .27 X 0.635 dia 

5 

Compression 



T 

<100> 

1.27 X 0.635 dia 

3** 

Yield and 



M 

<100> 

1.27 X 0.635 dia 

3** 

Creep 



B 

<100> 

1.27 X 0.635 dia 

3** 




B 

<11 0> 

1.27 X 0.635 dia 

3** 




B 

<11 1> 

1 .27 X 0.635 dia 

3** 


*Table 4 defines symbols that appear in this table. 

* *One specimen from each of three different ingots. 


For <100>, <01 1>, and <11 1> specimens, the mutually perpendicular direction pairs <010>, 
<00 1>; <01 1>, <100>;and <ll0>, <11 2>, respectively, were indicated on the specimen, and for 
parallelepiped specimens, these directions were perpendicular to prismatic faces. The 1 2.7- by 2.54-cm 
faces of the elastic moduli and Q' 1 specimens (property No. 5) were perpendicular to the <01 1 > 
direction for <01 1> specimens and perpendicular to the <1 12> direction for <1 1 1> specimens. 

Specimens were received from the manufacturers in sealed cans. The cans were opened, and the 
specimens were inspected in an N 2 gas-purged glove box. The specimens were subsequently inven- 
toried, stored in a bank of file drawers inside the dry glove box, and purged with the dry N 2 boiloff 
from an LN 2 tank as shown in Figure 1 . The dryness of the purged gas was periodically measured 
with a hygrometer (Great Eastern Model 500) and was consistently found to be below a dew point 
of 253 K. 

CsI(Na) specimens were also kept in a dry glove-box facility at the National Bureau of Standards 
similar to the one shown in Figure 1 ; however, precautions to maintain the low humidity necessary 
for testing Nal(Tl) were not necessary for CsI(Na). These specimens were tested in a laboratory 
environment (<5 0-percent relative humidity at 295 K). 

Nal(Tl) specimens were kept dry and were isolated from ambient humidity at all times. They were 
transported, from dry storage boxes through air locks to the testing facility, in sealed containers 
filled with anhydrous CaS0 4 . 


12 























Table 4 

Symbols Key for Tables 1 , 2, and 3 


Symbol 

Definition 

Material Type Key 


P 

Nal (Tl) Polyscin 

S 

Nal (Tl) single crystal 

C 

Csl (Na) 

H 

Harshaw Chemical Company material 

B 

Bicron Corporation material 

Position Key 


1 

Initial end of extrusion 

F 

Final end of extrusion 

H 

Heart of extrusion 

S 

Surface of extrusion 

T 

Top portion of a single-crystal ingot 

M 

Middle portion of a single-crystal ingot 

B 

Bottom portion of a single-crystal ingot 

Orientation Key 


// 

First dimension parallel to extrusion direction 

i 

First dimension perpendicular to extrusion direction 

<100> 

First dimension parallel to a Miller index <100> crystallographic direction 

<01 1> 

First dimension parallel to a Miller index <01 1> crystallographic direction 

<1 1 1> 

First dimension parallel to a Miller index <1 1 1> crystallographic direction 

R 

Random (orientation unknown) 


Three methods of humidity reduction were necessary for maintaining moisture levels below a dew- 
point of 253 K, depending on the size of the enclosure. Small enclosures were continuously purged 
with dry N 2 from LN 2 tanks or compressed-gas bottles. Larger enclosures maintained a dry N 2 
purge coupled with open containers of anhydrous CaS0 4 . Because of the size of the creep facility, 
however, it was necessary to install a drying train to maintain sufficiently low humidity levels. In 
some cases, polished scrap pieces of Nal(Tl) were used as a visual moisture indicator; cloudiness 
indicates unacceptably high moisture levels. 

Coefficient of Linear Thermal Expansion 

Measurements were made according to ASTM E228-71 with a Custom Scientific Instruments 
Company model CS-128, quartz push-rod dilatometer. A National Bureau of Standards copper 
standard reference specimen was used to calibrate the instrument. The smallest displacement mea- 
surable with the apparatus was 7.62 X 10' 5 cm. 


13 











Figure 1 . Receiving/storage station. 


14 


Thermal Conductivity 


A model TPRC 100 thermal comparator made by McClure Park Corporation, West Lafayette, 
Indiana, was used for all thermal conductivity measurements. 

The essential part of the thermal comparator is an insulated probe with a projecting tip. The probe 
is integral with a thermal reservoir held at a temperature about 1 5 to 20 K above room temperature. 
A surface thermocouple is mounted at the tip of the probe and is differentially connected to the 
thermal reservoir for measuring the temperature difference between the reservoir and the tip. In 
operation, the probe is gently placed on the surface of the test material. On contact of the probe tip 
of known thermal conductivity (k t ) and originally at temperature T x with the surface of the test 
material of unknown thermal conductivity (k 2 ) and at room temperature (T 2 ), the temperature of 
the probe tip drops quickly to an intermediate temperature (T), giving the expression: 

AT = ( T -T) = ( T 

\ k i- k 2 

This temperature difference is registered as the electromotive force (emf) reading of the differ- 
ential thermocouple after a brief transient period (1 to 2 seconds) has elapsed. 

From the emf readings of the test on a series of reference specimens of known thermal conduc- 
tivity, a calibration curve is obtained, and the thermal conductivity of an unknown specimen can 
thus be determined graphically from the emf reading, using the calibration curve. Ebonite, Corn- 
ing code 7740 glass, fused silica, A1 10AT titanium, 316 stainless steel, and Armco iron specimens 
supplied by the instrument manufacturer were used to calibrate the instrument. Precision of emf 
readings was 4 percent for the standards and 5.3 percent for all the Nal(Tl) measured. Because of 
the nonlinear relationship of thermal conductivity and the emf read from a calibration curve, a 5- 
percent emf precision resulted in a much larger (16 percent) uncertainty in measured thermal con- 
ductivity. 

Thermal Shock 

Thermal-shock resistance of single-crystal Nal(Tl) and Polyscin was determined by using oil- and 
air-quench tests to measure the critical temperature gradient at crack initiation (AT c ). The extent of 
consequent crack propagation was noted and used as an indication of crack propagation resistance. 
Results were compared with predictions made by using known or derived material constants for 
Nal(Tl) in an equation derived by Hasselman (reference 10) and elaborated on in references 11 
through 16. 

Oil Quenching 

The nine-plate specimens described in Table 1 were about one-tenth the size of the crystal proposed 
for the EGRET scintillator. In addition, five 7.62- by 1 .27-cm diameter rod specimens were tested. 
These specimens were duplicate ultimate shear rods. Four of these specimens were Polyscin, and 


15 



one was a single crystal. In addition, two 3.81- by 1.27-cm diameter Polyscin rods were tested. 
These specimens were made from broken ultimate shear specimens. Finally, nine 6.35-cm long by 
2.54-cm square bars were made from broken MOR specimens and were tested. Five of these speci- 
mens were single crystals, and the remaining four were Polyscin. 

Oil testing was done by using Penetone TPC cutting fluid as a medium. This fluid is a very low- 
viscosity oil in which Nal(Tl) is quite insoluable and is used by manufacturers as a coolant in 
machining this material. Haake type FS and FK constant temperature hot and cold circulating 
baths were used for heating and quenching. Capacity of each unit was about 1.5 liters of fluid. The 
volume of the largest specimen was 0.15 liters. Both baths had a <1 K thermal gradient across the 
10 centimeters from one side of the bath to the other. Temperatures of the bath fluid were mea- 
sured to within ±0.5 K. 


Before testing, all specimens were closely inspected for flaws such as edge, face, or corner cracks. 
Flaw size and location were recorded for later use in fracture analysis. 

The testing involved heating the specimens for 30 minutes to allow them to thermally equilibrate, 
then transferring them as rapidly as possible to the cold bath, increasing the temperature difference 
between the two baths, if necessary, by 2 K increments until fracture first occurred. The difference 
temperature between the two baths at fracture was assumed to be equal to the thermal gradient at 
the specimen surface. 


Measured values of AT, at fracture were compared with predicted values for the various geometries 
and critical flaw sizes using the relation (reference 10): 


AT 


C 


ffG(1 - 2i;)2 \ L + 16 (1 - v 2 ) Nfl 3 \ ,y / Bk \ 
2E a 2 (1 -v 2 )/ \ 9(1 - 2v) / \ah c / 


( 1 ) 


where 

E = Young’s modulus = 2 X 10 10 N/m 2 
v = Poisson’s ratio = 0.314 

K IC = critical stress intensity factor = 0.382 X 10 6 N/m 3/2 
G = fracture energy = K 2 , /2E = 5.1 J/m 2 
a = coefficient of linear thermal expansion = 47 X 10' 6 K 1 

N = number of cracks per unit volume = 3 X 1 0 s m' 3 

£ = crack length (m) 

B = a geometric factor (4.67 for rods, 4 for square bars, and 3.25 for 
square plates, reference 1 2) 

k = thermal conductivity of Nal(Tl) = 1.71 X 10' 2 W/cm K 


16 



a = characteristic length of specimen (volume to surface-area ratio) = 0.75, 

0.54, and 0.29 cm for plate, bar, and rod specimens, respectively 

h c = calculated average surface heat-transfer coefficient, assuming forced convection 

in light oil = 0.019, 0.024, and 0.037 W/cm 2 K for plate, bar, and rod, respectively 

As agreement between observed and calculated AT c was good, the foregoing equation was used to 
calculate an average heat-transfer coefficient in still air, assuming a crack size equal to the average 
in Polyscin and an average AT c observed for rod specimens tested hi air. 

Air Quenching 

Two Polyscin rod and two Polyscin bar specimens were tested in air by heating the specimens in a 
convection oven for 30 minutes and then quenching into still room-temperature air (297 K). Tem- 
perature in the oven was read with a thermometer. The oven temperature was raised by 5 K incre- 
ments until fracture occurred on quenching. The critical temperature (AT,) was taken as the 
difference between oven temperature and room temperature. Thermal gradients in the oven were 
negligible over the dimensions of the specimen. 

The effects of specimen size were evaluated by plotting AT, versus surface area to volume ratio for 
both oil- and air-tested specimens. 

Heat Capacity 

The heat capacity of single-crystal and poly crystalline Nal(Tl) was measured at 310 K using a 
Perkin-Elmer differential scanning calorimeter model DSC-1B with a heat capacity kit (P-E part 
No. 219-0136). This instrument uses a comparative method to measure the amount of heat required 
to raise the temperature of a specimen to a specified temperature at a predetermined rate. In the 
determination, a sapphire standard, the specific heat of which is accurately known and documented, 
is used as a comparison material. The measurement is based on the electrical power required for 
maintaining the temperature control of a specimen and a reference pan embedded in a specimen- 
holder assembly block. The system monitors and controls the average temperature of the specimen- 
holder assembly block and the difference temperature between the reference holder and the speci- 
men holder. Thus, by increasing the temperature of the specimen-holder assembly block to a 
specified value at a predetermined rate and monitoring the differential power needed for maintain- 
ing the same temperature in the specimen holder as in the reference holder, a measure of the energy 
supplied to the specimen and its holder is obtained relative to the reference holder and its contents, 
as a function of time or temperature. 

In practice, the average temperature of the specimen-holder assembly block is recorded on the 
abscissa while the differential power needed for maintaining an equivalent temperature between the 
reference holder and the specimen holder is recorded on the ordinate of the system’s chart recorder. 
This method involves (1) heating the specimen-holder assembly block to a predetermined tempera- 
ture at a specified rate, using sapphire and an empty reference pan, (2) making a blank determina- 
tion with both pans empty, and finally, (3) scanning the same range using the specimen and an 


17 



empty reference pan. In each determination, an ordinate pan shift from one baseline to a new base- 
line occurs. After correcting the ordinate amplitudes recorded for the specimen and the reference 
holder in light of the blank determination, the heat capacity of the specimen is calculated as: 

A 

S 

C p (specimen) = — 

where 

A s = ordinate amplitude (specimen) 

A r = ordinate amplitude (sapphire) 

W r = weight (sapphire) 

W s = weight (specimen) 

Precision (standard deviation divided by the mean) of the measurement was less than 2 percent. 
Table 1 describes the specimens. 

Elastic Constants 

Density was determined for Nal(Tl) compression specimens from first and second shipments by 
measuring their weight and dimensions inside the dry glove-box storage facility. 

The elastic stiffness constants for single crystals, and Young’s modulus and shear modulus for Poly- 
scin specimens, were measured in two ways. The first and most accurate method used a Panametric 
model 5054 time intervalometer to measure the transmit time of an ultrasonic pulse in the material, 
using a technique called pulse-echo overlap. In this technique, an acoustic transducer is used to inject 
a shear or longitudinal wave packet into a specimen. The same transducer is then used to pick up 
the echo of the wave packet after it is reflected from a surface that is perpendicular to the transmis- 
sion direction and that is situated at an accurately known distance from, and parallel to, the intro- 
duction plane. The transducer signal is applied to the vertical axis of an oscilloscope, and the 
horizontal axis of the oscilloscope is swept sinusoidally at a frequency whose period is the round- 
trip transit time of the wave packet, thus superposing the injected wave packet with its echo. Because 
the horizontal drive frequency can be generated and measured accurately, the time of flight of the 
wave packet can be determined accurately. The time between wave-packet injections was large and 
the period of vibrations within a wave packet was small compared with the round-trip time of a 
wave packet. This enabled multiple echoes to die out before new echoes were generated and enabled 
the injected wave packet and its reflections to be well-defined entities on the oscilloscope rather 
than interferring with one another. Longitudinal and shear wave transducers had a period of 0.44 jus. 
The time between wave-packet introductions was 0.01 or 0.001 times the typical round-trip flight 
times, which were 20 to 40 /jls. Accuracy and precision of the measurement was 0.03 percent and 
was limited by the accuracy and precision of the measurement of specimen dimensions and density. 
Ultimate compression and MOR bend-test specimens were used for this measurement (Table 1 ). 


W 

X ' — X C p (sapphire) 

W s 


18 



The second method used to measure elastic moduli employed a Nametre model XV acoustic spec- 
trometer to measure resonance frequencies of appropriately held specimens. In this technique, 
electromagnetic pickup and drive units (Airpax 1- 0055) are used to excite and monitor specimen 
vibrations. Small soft-iron contacts cemented to the specimen provide electromechanical coupling 
with the transducers. The specimens were supported on wire or point supports at nodal points 
using a chrome-plated brass frame designed for this use by Nametre. The frame itself was mounted 
on rubber and styrofoam padding to isolate it from spurious vibrations. The lathe-like specimens 
listed in Table 1 (measurement No. 5) were driven in flat-flexural and torsional resonance by 
appropriate placement of the driver and pickup transducers with respect to the specimen. Mechan- 
ical damping efficiency or internal friction (Q" 1 ) was also measured with the Nametre acoustic 
spectrometer, using the same lathe-like specimens. In the second shipment of material (Table 2), 
elastic moduli of only the eight Polyscin specimens were measured, and the method used the 
pulse-echo overlap technique. 

The stiffness constants (C u , C J2 , and C 44 ) can be determined from the sound velocities of three 
independent waves in a single crystal using the pulse-echo overlap technique. The three types of 
waves that are most economical of specimens are those derived by measuring the longitudinal and 
two perpendicular shear velocities in the <01 1> direction on an ultimate compression specimen. 
For such specimens (reference 17, page 371), 

C 44 = V S! P 

Cn = (Vl + 2Vg 2 - Vgj)p 

c i2 = <yi - - v| a )P 


where 

V gl = shear wave velocity in a face-diagonal direction such as <01 1> with displacement in 
a principal-axis direction such as <100> 

V g2 = shear wave velocity in a face-diagonal direction such as <01 1> with displacement in a 
face-diagonal direction, such as <011 > 

V L = longitudinal wave velocity 

p = density 

The other approach to specimen utilization was to use both <100>and <1 11> ultimate compres- 
sion specimens. In this case, the longitudinal and shear velocities were measured along the specimen 
axes. For these specimens, the shear wave velocity is rotationally invariant. In this case, for <100> 
specimens, 


C 


i i 



c 


44 



19 



and for <1 1 1> specimens, using C and C 44 calculated from the <100> specimen (reference 17, 
page 371), 


C„ = 0PV L 2 - C u - 4C 44 )/2 


and 


C 12 C 11 + C 44 " 3pV S 2 

Both values of C 12 were determined, and an average value was calculated. In both approaches to 
specimen utilization for measuring C 1:l , C 12 , and C 44 , values for the anisotropy constant (A) and 
the bulk modulus (B) were calculated as: 

A = 2C 44 /(C u - C 12 ) 

B = 1/3 (C n + 2C n ) 

Values for Young’s modulus in <100> principal-axis, <01 1> face-diagonal, and <11 1> body- 
diagonal directions were calculated using the following formula (reference 18, page 183): 

E hki = S u + ( 2S 12 - 2S n + S 44 )( h2k2 + h 2 l 2 + k 2 l 2 ) ( 2 ) 

where hkl are the direction cosines of the longitudinal displacement, or the axis of an axially stres- 
sed rod, and S y are the elastic compliances. The elastic compliances are related to the stiffness con- 
stants, Ch, by: 

s n - ( c n + c .2>/< c n - C|jXC n + 2C„) 

S n ’ - C 1 2 « C U " c uXC u + 2C 12 ) 

S 44 - i/c 44 

The shear modulus (G) and Poisson’s ratio (v) are dependent on crystallographic orientation in a 
manner similar to Young’s modulus. The shear modulus is given by (reference 18, page 106): 

^12 = ^44 + 4 ( 2!3 12 “ 2 ^11 + ^ 44 ^ 1 k l E 2 k 2 + E 1 ^ 1 E 2^2 + k l ^ l k 2 ^ 2 ^ 

where the subscript 1 on G' 1 and on the direction cosines refers to the direction around which rota- 
tion occurs or along which a shear wave propagates, and subscript 2 refers to the direction of dis- 
placement (or more properly, for torsion, to the direction of the tangent to the displacement). 


20 



Similarly, Poisson’s ratio is given by (reference 18, page 184): 


* 12 = - E i [S 12 - l/2(2S 12 -2S u +S 44 )ai^+k^ + l*l* ) ] 

where, in this case, the subscripts on v, E and the direction cosines (hkl) again refer to directions. 
Subscript 1 refers to the direction of axial strain, subscript 2 refers to the direction of lateral strain, 
and v is the ratio of lateral strain along direction 2 to axial strain along direction 1. In terms of 
the measured Cy, the formulas for E hkg , G 12 , and i> 12 are: 

E hKi = kSoo + k 0-A)n| 1 

L c 44 J 


7' 1 

"< 100 > 


( C ll +C 12> 

(C u+ 2C 12 )(C 11 - C i 2 ) 


S2 = h 2 k 2 + h 2 l 2 + k 2 l 2 


G 12 = 


G <iooxoio> + p (1-A)J2 

X4 


12 


p-1 

< 100 X 010 *'~44 


= i/c d 


«12 = h l k l h 2 k 2 + V1V2 + k l\ k 2 l 2 


P 12 = E 1 


12 


(C u +2Ci2)(Cn- C i2) 2C 


(1 - A) S2 


12 


44 


«12 = h ? h 2 + k i k 2 + W 

For polycrystalline specimens, the shear wave velocity is rotationally invariant, and only one longi- 
tudinal velocity (V L ) and one shear velocity (V s ) were measured. The formulas used to determine 
Young’s modulus, the shear modulus, Poisson’s ratio, and bulk modulus for these specimens were as 
follows (reference 19, page 18): 

R = V l/V s 

v = (R 2 - 2)/2 (R 2 - 1) 

F = [(1 -v)Kl + i/)(l -2v)] x ' 2 


21 



E = V L 2 p/F 
G = V s 2 p 

B = P (V L 2 - j V/) 

The other technique for measuring elastic constants and moduli was to determine resonant fre- 
quencies of vibration of appropriately held specimens, using an acoustic spectrometer. The elastic 
modulus calculations using measured resonant frequencies, specimen dimensions, and density are 
an iterative process and were done on a computer. 

For a rectangular bar of material, Young’s modulus (E) and shear modulus (G) are calculated from 
the flat-flexural fundamental and'torsional fundamental as (reference 18, pages 84 and 90): 

2 

E = 0.94642 l “j— j p T 3 

G = 4 p R £ 2 f 2 /n 

where 

E = Young’s modulus (dynes/cm 2 ) 

G = shear modulus (dynes/ cm 2 ) 
p = density (g/cc) 
n = order of vibration = 1 
f E = flat-flexural fundamental (Hz) 

F q = torsional fundamental (Hz) 

v = Poisson’s ratio 
£ = specimen length (cm) 

h = specimen height (cm) 
b = specimen breadth (cm) 

T 3 and R are finite length correction factors. 


22 



3 


1 + 6.585 (1 + 0.0752 p + 0.8109 i 


2 ,/h\ fh\ 

'v 2 ) - - 0.8681 — I 

W W 

a /h\ 4 

8.340 (1 + 0.2023 v + 2.173 v 2 ) ( — I 


1 + 6.338 (1 +0.14081 + + 1.536 


4) 


R = 


( 


1 + (b/h) 2 


4 - 2.521 (h/b )(1 


/l .99 1 ' 
\e nb/h + 1 



1 +0.00851 n 2 b 2 


'(H 


From these values of E and G, Poisson’s ratio is calculated as (reference 19, page 89): 

E 

v - — - 1 
2G 

Since v appears in the calculation for E, the procedure for calculating Young’s modulus is to assume 
an arbitrary value of v equal to 0.3 in the calculation for E, then determine G and calculate v from 
the above equation, and iteratively arrive at a value for E. This iterative process is done by computer 
to less than 0.1 -percent change in v. The accuracy and precision of the measurement was limited by 
how closely the resonant frequency could be read and by positioning the specimen grips. It is esti- 
mated that an accuracy and precision of about 1 percent was obtained. 

For single-crystal specimens, E and G are calculated as for Polyscin above. The elastic compliances 
are then calculated from the directional Young’s modulus and shear modulus given by equations 2 
and 3. For <100> specimens, 


E <ioo> Sn and G <100><010> 


= S 


44 


This gives two of the three elastic compliances. Compliance S 12 is calculated by using the values of 
E iteratively derived for the <01 1> and <11 1> specimens and using the above-determined values 


for S n and S 44 


from a <100> specimen. For a <01 1> specimen, 


12 


2 ( E <011> 


-- S 


li 


4 S 4+) 


23 



Similarly, for a <1 1 1> specimen, 


S 12 2 ( E <m> 3 S 11 3 S 44^ 

With S n , S 12 , and S 44 so determined, values of C n , C 12 , and C 44 are now available as (reference 
23, page 147): 

C„ = (S„ + S„)/(S n - S n )(S n + 2S n ) 

= -S, 2 /(S, , - S^HS,, + 2 S 12 ) 
c 44 = 1/S 44 

This method is more complex and not as accurate as the pulse-echo overlap method that can be 
used to determine the stiffness constants (CL) directly from velocity data without first computing 
the elastic compliances (S..). 

Internal friction (Q’ 1 ) was determined at flexural, torsional, and longitudinal fundamentals and their 
overtones by two independent methods, using the Nametre model XV acoustic spectrometer as 
described in reference 20. One method used forced vibration at resonance, relating internal friction 
to the half-peak width of the resonance curve of frequency versus amplitude. The second method 
used the log-decrement of amplitude as a measure of the damping of free vibrations in the specimen 
at resonance. These methods generated internal friction data in the 700- to 50,000-Hz range. The 
same setup used to measure elastic properties was used to measure damping. 

The forced-vibration measurement of Q' 1 involves obtaining a spectrum of vibrational amplitude 
(indicated by the output voltage of the pickup detector) as a function of frequency while the speci- 
men is driven through a range of frequencies around resonance. Internal friction (Q 1 ) is calculated 
from the width of the resonance peak at half its maximum height, as follows (reference 20, page 
121): 


where 

f = resonance frequency (Hz) 

Af = width of the resonance peak at half-height (Hz) 

To measure Q' 1 by the free-vibration method involves measuring the decay of free vibrations at 
resonance after the driving force is removed. The drop in amplitude as a function of time is used to 
calculate Q" 1 as follows (reference 18, page 121): 

In A 2 /Aj 

Q-l _ 

■ree jrf At 

r 



24 



where 


A 2 / Aj = ratio of amplitudes of any two successive vibrations 
At = time elapsed between A and A 2 (sec) 

The results of forced-vibration measurements of Q' 1 were used to assess material effects on Q' 1 
because these measurements reflect Q' 1 measured at the maximum amplitude attained by the speci- 
men. Free- and forced-vibration measurements were averaged to assess the frequency dependence 
of Q _1 , using free-vibration estimates of Q' 1 at maximum amplitude. Finally, in describing observed 
amplitude dependence of Q' 1 , only the free-vibration results were used because they yield a decay 
curve from which Q 1 can be correlated easily with relative vibrational amplitude. 

Ultimate Strength 

Modulus of rupture, ultimate shear, and compression strength measurements and K IC of Nal(Tl) 
were all done with a floor-model 1125 Instron universal tester that had been modified to provide 
a low-humidity environment. The modification enclosed the loading frame with sealed acrylic 
sheets that had two gloved ports for manipulating specimens and a flapped iris port for specimen 
entry. Dry N 2 from a liquid nitrogen dewar was used to purge the test region. In addition, a dryer 
train continuously recirculated the chamber atmosphere through anhydrous CaS0 4 . The method 
provided a less than 3-percent RH environment at room temperature. Stress-rate testing and the 
critical stress-intensity factor (K IC ) of Polyscin Nal(Tl) was measured at NBS using a similarly 
enclosed Instron testing machine. The NBS system, however, did not require the CaS0 4 recir- 
culation system because of its smaller size. 

The equipment used for the GSFC MOR tests is a modification of the four-point bending fixture 
shown in Figure 2. Extensions were built onto the lower bearing rollers of the fixture, and a dummy 
specimen was mounted on these extensions during each test to account for fixture compliance. The 
motion of the fixture was electronically subtracted from the motion of the specimen by subtracting 
the dummy specimen linear variable-differential transformer (LVDT) output from the Nal(Tl) 
specimen LVDT output. The fixture had a 10.15-em outer span and a 3.39-cm inner span. Speci- 
mens were broken using a crosshead speed of 0.00508 cm/minute. The specimens tested are des- 
cribed in Tables 1 and 2. Nominally, the specimens were 12.7- by 2.54- by 2.54 cm prisms. For 
these specimens, the calculated applied stress rate is 0.1956 MPa/s. For single-crystal material, 
specimens were oriented with their long axis along one of the three crystallographic symmetry axis 
directions, <100>, <01 1>, or <11 1> and were pushed in the<001>, <01 1>, and <1 1 0> direc- 
tions, respectively, as shown in Figure 3. The observed failure tensile stress was resolved into a com- 
ponent normal to the observed failure plane. The properties measured from the loading curves and 
LVDT data were modulus of rupture, proportional limit, and maximum deflection before failure. 
After failure pieces of the specimen were dissolved hi nitric acid and thallium concentration, mea- 
surements were made using a Perkin-Elmer model 403 atomic-absorption spectrometer. 

The purpose of NBS MOR stress-rate testing was to assess the susceptibility of Nal(Tl) to subcritical 
crack growth. If subcritical crack growth occurs, specimens broken at a high stress rate appear to be 
stronger than specimens broken at a low stress rate due to crack extension during the loading pro- 
cess. The NBS modulus-of-rupture equipment was similar to that of the GSFC facility except that 


25 






DIRECTION OF PUSH 
AND DIRECTION OF 
VELOCITY MEASUREMENT 


< 01 1 > 




(a) <100>MOR SPECIMEN (b) <01 1 > MOR SPECIMEN 

< 111 > 



(c) <111> MOR SPECIMEN 


Figure 3. Diagram of single-crystal MOR 
specimen orientations. 


the test fixture had three-point loading with a span of 2.15 cm. In addition, the specimens were 
smaller (Table 3), being nominally 2.5 by 0.6 by 0.3 cm. Crosshead rates of 5.08 X 10' 1 , 5.08 X 
10- 2 , 5.08 X 10' 3 , and 10.16 X 10' 4 cm/minute were used. In addition to the modulus of rupture, 
the 0.2-percent offset proportional limit was determined for loading rates of 5.08 X 10' 1 , 5.08 X 
10' 3 , and 10.16 X 10' 4 cm/minute. 

Shear-strength tests were made by using a double-shear fixture that is shown schematically in Fig- 
ure 4a. The fixture could also be used in single shear as shown in Figure 4b. Machine crosshead 
speeds of 0.0127 cm/min and 0.0508 cm/min were used. The specimens were nominally 1.27-cm 
diameter, 7.62-cm long rods, as indicated in Table 1. 

Compression testing of Nal(Tl) at GSFC was performed in the enclosed Instron facility with a self- 
aligning loading fixture shown schematically in Figure 5. To prevent localized crushing from occur- 
ring at the ends, each specimen was placed into 0.158-cm thick end plate. At the beginning of each 
test, a crosshead speed of 0.00508 cm/minute was used until the 0.2-percent yield point had been 
reached. As the test continued, the crosshead speed was incrementally increased from 0.00508 to 
0.127 cm/minute until cracking began and, finally, load-bearing capability was lost. Initial cracking 
was observed visually, using a high-intensity lamp. The increase in strain rate was necessary because 
most specimens exhibited a total strain greater than 20 percent. From load-deflection curves recorded 


27 





(b) SINGLE-SHEAR FIXTURE 


Figure 4. Full-scale drawing of test fixtures. 


28 






Figure 5. Schematic of loading fixtures used in compression 
testing of sodium iodide. 

by the testing machine, proportional elastic limit stress, 0.2-percent compressive yield stress, ulti- 
mate compressive stress, initial cracking stress, and total compressive strain were determined for 
first-shipment material (Table 1 ), but only initial cracking stress was determined for second-ship- 
ment material (Table 2). 

Compressive testing of CsI(Na) at NBS was performed with equipment similar to that used at GSFC 
except that again the specimens were smaller, nominally 1.27 cm long by 0.635 cm in diameter 
(Table 3). These specimens were not stressed to the point of load-bearing loss as were the Nal(Tl) 
specimens. The 0.2-percent offset yield stress was the only property measured because these speci- 
mens were subsequently used for creep measurements. Although no purged dry N 2 enclosures were 
used for CsI(Na) testing, the specimens were dip-coated in silicone oil (Dow Corning type 704) to 
provide a vapor barrier. Tests were performed using a table-model Instron TM-M-L. A crosshead 
travel rate of 0.5 cm/minute was used. A specimen fixture, based on a V-block, was developed to 
locate the test specimen on and parallel to the axis of the test frame. After the yield measurement, 
the specimens were examined for evidence of distortion. 

The critical stress-intensity factor (K JC ) of Polyscin Nal(Tl) was measured in two ways: (1) using 
the double-cantilever-beam technique, and (2) using the notched-beam technique. The measurement 
was initially made at NBS using the double-cantilever-beam method that is described in reference 21 , 


29 





page 24. A schematic diagram of the specimen' and the formula used to calculate K„ are shown in 
Figure 6. Specimens were nominally 0.2- by 1.9- by 5.0-cm plates (Table 3). The load was applied 
through wire hooks epoxied to the end of the plate. The specimens were placed in the Instron test 
chamber at a dev/ point of 240 K. A beginning crack was introduced into the specimen by tapping a 
razor blade into one end. The specimens were stressed in the test machine at a crosshead speed of 
0.0508 cm/minute until the crack propagated. Although all the cracks propagated out to the side 
rather than down the center of the specimens, a value of K IC was calculated for the initial stages of 
growth from the peak load, specimen dimensions, and crack length using the formula shown in 
Figure 6. 



Figure 6. Double-cantitever-beam specimens 
(reference 21 ) 

The second method for measuring K IC was a single-edge notched-beam test performed at GSFC 
using broken MOR specimens. The technique is discussed in reference 22, page 13, and a schematic 
diagram of a specimen with the formula used to calculate K IC is shown in Figure 7. The test is a 
three-point bend test with a notch at the center of the tensile face. Specimens of various sizes, but 
geometrically similar, were tested. Geometric similarity was maintained by keeping the ratio of 
span-to-specimen thickness and notch-depth-to-specimen thickness constant at 4 and 0.30, respec- 
tively. 

To preclude geometric effects and ensure accurate measurement of K IC , a In In plot of failure stress 
versus notch depth was made, and the slope was compared to -1/2. Specimens were notched with a 
0.043 cm thick watering wheel and were tested in a variable-span three-point bend fixture at a cross- 
head speed of 0. 1 27 cm/minute. Tests were conducted in less than 3-percent RH at room temperature. 

Creep 

The creep apparatus and enclosure for Nal(Tl) testing was custom-built. It was determined that 
nine flexure tests and nine compression tests were required over a 6-month period. A schematic 
diagram of the test facility is shown in Figure 8. The facility was continuously purged with dry N 2 . 
However, because of its size and the permeability of the acrylic enclosure to moisture, a gas-recir- 
culating system was built. Humidity and temperature control was achieved at less than 1 -percent 


30 





Y = K x BW 2 /6Ma 1/2 

= A 0 + A t (a/W) + A 2 (a/W) 2 + A 3 (a/W) 3 + A 4 (a/W) 4 
The coefficients A have the following values: 

A 0 A 1 A 2 A 3 A 4 


Pure bending +1.99 -2.47 +12.97 -23.17 +24.80 

Three-point: 

S/W = 8 +1.96 -2.75 +13.66 -23.98 +25.22 

S/W = 4 +1.93 -3.07 +14.53 -25.11 +25.80 


Figure 7. K calibrations for bend specimens (reference 22). 

RH and 300 K with two removable dryer/heater units, one of which is depicted in Figure 9. Each 
unit contained 4 pounds of anhydrous calcium sulfate. Two fans within each dryer recirculate the 
atmosphere within the RTV-sealed acrylic enclosure that covers the creep facility. Also within the 
recirculating unit is a thermostatically controlled cone heater for maintaining the temperature with- 
in the enclosure at 300 K. Sliding doors seal off the dryers from the enclosure for servicing and for 
regenerating the dryer material every 72 hours. Two units, one at each end of the enclosure, are 
capable of dropping the humidity of the N 2 gas in the enclosure from 25- to 0.5-percent RH in 2 
hours. 

Inside the creep facility, fixtures were suspended from an I-beam frame mounted on a 1.22- by 
1.83-m pneumatically suspended isolation table. The fixtures were dead-weight loaded. To accom- 
modate 18 simultaneous tests, six multiple-specimen fixtures were made, each designed to allow test- 
ing three specimens with one set of weights, as shown in Figure 1 0, In each case, the load is applied 
at the bottom of the fixture and is transferred through the lower specimen to the middle specimen, 


31 





Figure 8. Multiple-creep-test facility. 

through to the upper specimen, and finally to the upper fixture in a chain-like fashion. Creep dis- 
placements were measured with a Pickering model 7303W-4A0, 6-volt input dc-dc linear variable- 
differential transformer, which gives a 0 - to 2-volt dc output for a 0 - to 0.508-mm displacement 
with a sensitivity of 0.508 X 10‘ 3 mm. 

Initially, the middle fixture in each assembly was loaded to twice the nominally expected maximum 
service stress for the EGRET scintillator. The maximum expected service stresses were 1.29 MPa in 
flexure and 0.710 MPa in compression. In compression, stresses applied by the top and bottom fix- 
tures in a loading chain were about 20 percent more and less, respectively, than the stresses applied 
by the middle fixture in an assembly. In bending, loading of the top and bottom fixtures in a chain 
differed from the middle fixture by about 30 percent. 


The loading schedule for the assembly is shown in Table 5. As time progressed and some of the 
specimens were not observed to creep, the applied load was increased. Creep behavior was analyzed 
in terms of (time) 1/3 equations: 


e - a + bt 1 ^ compression 

8 = a + bt 1/3 flexure 


32 





33 










Table 5 

Creep Loading Schedule 


Type 

Test 

Specimen 

Number 

Specimen 

Designation 

A: Applied 
Stress 
(MPa) 

B: Initial 
Cracking 
Stress 
(MPa) 

% of Initial 
Cracking 
Stress 

(A/B) X 100 

C 

: Proportional 
Limit 
(MPa) 

% of Proportional 
Limit 

(A/C) X 100 



1 

FS// 

1.65 



8.7 



48 



2 

FS// 

1.38 


18.88 

7.3 


3.44 

40 



3 

FS// 

1.10 

) 


5.8 

) 


32 

C 

c 


4 

IH1 

1.65 

) 


13 



68 

& 

5 

IH 1 

1.38 


12.46 

11 


l 2.43 

56 

a 




l 








6 

IHI 

1.10 



8.8 



45 

o 










7 

<11 1> 

1.65 


3.3 

4.37 

38 



8 

<01 1> 

1.38 


3.5 

4.94 

28 



9 

<100> 

1.10 

13.45 

8.1 

1.63 

67 



10 

FS// 

3.36 



86 



116 



1 1 

FS// 

2.60 


> 3.92 

66 


2.89 

90 



1 

FS// 

1.85 



47 



64 

(3 


■Si 

IHI 

3.36 



70 

) 


100 

3 

X 

14 

IHI 

2.60 


> 4.79 

54 


3.35 

78 

LL 

15 

IHI 

1.85 



39 

J 


55 



16 

<1 1 1> 

3.36 

6.79 

49 

2.21 

152 



17 

<01 1> 

2.60 

3.70 

70 

1.93 

135 



18 

<100> 

1.85 

2.50 

74 

1.91 

96 


where 

t = time 
e = strain 

5 = midspan deflection 

b = slope of a t 1 / 3 plot 
a = intercept of a t 1/3 plot 

Flexure fixtures used four-point bending with an inner and outer span of 3.38 and 10.16 cm, re- 
spectively. Specimens were nominally 12.7 cm long with a 1.9-cm-square cross section (Table 1). 

Compressive creep of CsI(Na) was measured by the NBS. However, a purged dry N 2 enclosure was 
not required as it was with Nal(Tl). Specimens were coated in silicone oil as for MOR measure- 
ments. The apparatus for this measurement was also custom-built and is shown in Figure 1 1 . Four 


35 





























Figure 1 1 . A one-half scale cross-sectional view of the 
Csl(Na) creep test frame. 


36 



test frames were built. The displacement transducers were LVDT-type transducers (Schaevitz 
Engineering model PCA-220-100), which have a displacement resolution of 0.003 mm and a less 
than 0.1 percent deviation from linearity. The use of a wobble-plate linkage to couple the specimen 
and the transducer provides a means of averaging out errors in the signal that result from misalign- 
ment of the specimen. 

The CsI(Na) creep data were collected manually and were plotted using Dataplot (reference 9). 
Dataplot is an NBS-developed statistics, curve-fitting, and graphics program. The data were plotted 
in terms of a natural logarithm of time equation: 

e = a 1 + a 2 In (1 +t/a 3 ) 

where a x , a 2 , and a 3 are curve-fitting parameters. 

To perform extrapolations of the test results, another computer program, Runnonlin, was developed 
(reference 9). Using Runnonlin, the test results were extrapolated to times outside the test data 
base with confidence limits based on the test-data scatter. 

Hardness 

Vickers microhardness of Nal(Tl) was measured using loads of 100, 300, and 500 g. The specimens 
were cleaned with toluene before indenting to remove any surface hydration, and no attempt was 
made to control relative humidity below laboratory ambient. The specimens were oriented so that 
their surface was perpendicular to the indenter and were aligned so that dimensions of the square- 
shaped surface impression were parallel to known crystallographic directions. Vickers hardness (H y ) 
was calculated using the equation: 


H y = 18.54 P/d 2 [kg/mm 2 ] 


where 

P = load in grams 

d = mean diagonal of indentation in pm 
Susceptibility to Subcritical Crack Growth 

In addition to the stress-rate testing of Polyscin performed by NBS and described under modulus- 
of-rupture ultimate strength testing, GSFC performed three-point instrumented impact tests on 
single crystals of Nal(Tl). An analog oscilloscope trace of the impact event was recorded as a load- 
time trace and was evaluated to obtain load to failure and time to failure. From these measurements, 
failure stresses and stress rates were calculated. Most specimens were cleaved from broken MOR bars. 
In addition, four 76- by 13- by 13-mm specimens were provided gratis from Bicron Corporation 
specifically for this test. Impact specimens of various dimensions were cleaved from these single- 
crystal bars by hand using a razor blade. After cleaving, the specimens were wet-ground and polished 


37 



by hand using a fixture to maintain parallel sides. Pentone Corporation’s TPC solvent and General 
Electric’s silicone (SF97-50) oil were used for grinding and polishing mediums, respectively. Speci- 
men edges were chamfered. The long axis of a specimen was in the <1QQ> direction, and prismatic 
surfaces were perpendicular to the other two principal axes. The majority of specimens were nomi- 
nally 6.4 by 6.4 by 64 mm. A total of 22 of these specimens were tested. 

The impact tester was a modified Custom Scientific Instruments, Incorporated, pendulum-type 
tester. The machine was modified by changing the impact mode from tension to three-point bending 
with a 50.8-mm span. A piezoelectric quartz load cell (Kister model 910) was used to pick up the 
impact event. The oscilloscope was externally triggered by the interruption of a helium/neon laser 
beam to a solar cell by a metal flag attached to the pendulum head. The impact tester was enclosed 
in a sealed acrylic chamber that had four flapped-iris ports for access. Surgical gloves were worn 
when handling the specimens. Specimens were broken at stress rates ranging from 1.0 X 10 4 to 
4.0 X 10 4 MPa/s, compared with quasi-static stress rates of about 0.1956 MPa/s measured with 
a universal testing machine. 

Ingot Variation 

For Nal(Tl), ingot variation was investigated in a controlled manner (i.e., the same specimen sizes, 
test equipment, personnel, etc.) in terms of elastic moduli, modulus of rupture (MOR), and com- 
pressive initial cracking strength. This was done by measuring these properties for two Polyscin 
extrusions and by measuring the MOR of material from eight single-crystal ingots and the elastic 
constants for material from two of these single-crystal ingots. An uncontrolled measure of ingot 
variation of strength was obtained by comparing MOR values measured at GSFC with MOR values 
measured at NBS in stress rate testing to assess susceptibility to subcritical crack growth and with 
some early Polyscin strength measurements performed by Stanford University. 

For CsI(Na), ingot variation was investigated by comparing compressive strength (0.2-percent yield) 
and creep for three single-crystal ingots and for poly crystalline material from a fourth ingot. 

TEST RESULTS AND STATISTICAL ANALYSIS 

Specimens were classified and differentiated on the basis of: 

• Material type— Nal, Csl, polycrystal, or single crystal 

• Ingot-Four Polyscin ingots, eight single-crystal ingots 

® Position within an ingot— Initial and final end, surface, or interior of a Polyscin extrusion 
or top, middle, and bottom of a Csl ingot as designated in Table 4 

® Orientation— Specimen dimensions relative to symmetry axes as designated in Table 4 

In most cases, a statistical analysis determined whether observed differences in the mean value of a 
property for various classifications of material were significant. This analysis was done by pair-wise 
t-testing for significance of differences in mean values, after an F-test for equality of variances was 


38 



performed to ensure the validity of the t-test (reference 24, pages 61-65). In cases in which vari- 
ances are not equal, another statistic (t') is used rather than the t-variable for testing the hypothesis 
of equality of means (reference 25, page 264). In the following, the letter s refers to the square root 
of a sample variance, commonly called the standard deviation. 

The F-test is as follows: 


hypothesis H q : S 2 X = S 2 2 versus Hj : S 2 j A S 2 2 

where S 2 j and S 2 2 are population variances. 

Accept H q if : 


S r 2 

— < F c (T.iq - l,n 2 - 1) 


where S t 2 and S 2 2 are sample variances with S 1 2 /S 2 2 > 1, n equals the number of data points in 
each sample, and y is the confidence level. 

If the test statistic (S 2 /S 2 2 ) is less than F c , then H q is accepted, and the mean value for each set of 
observations is compared using the t-test of equality of means. In this test, the hypotheses are: 

H o : Xj = X 2 versus Hj: X x A X 2 

where X : and X 2 are means of samples X and X 2 . 

H o can be rejected if 


t (v, y) < 


Vi 


[ l r 

Vn, + m 


where 


t = the test statistic 

O 

v = number of degrees of freedom = n t + n 2 - 2 


S p 2 = pooled sample of variance : 


(n x - 1) S 2 + (n 2 - 1) S 2 /(n 1 + n 2 - 2) 


39 



If the test statistic S 2 /S 2 is greater than F , then the mean value for each set of observations is 

1 2 * C 

compared using test statistic t' rather than t u in the t-test of equality of means, where: 


with S 2 = Sj/iij , S 2 - S 2 /n 2 

Coefficient of Linear Thermal Expansion (Nal(TI) 253 to 323 K) 

Measurements were made on three oriented single-crystal and four Polyscin Nal(Tl) specimens. Two 
determinations and a 2 were made for each specimen and the results are shown in Table 6. 


N/i 


+ Sf 


Table 6 
a X 10 6 (K 1 ) 


^"-'Orientation* 

Group 1 

Group 2 

Group 3 

Comment 

IH// FH// 

IS1 FS1 

<100> 

<11 1> 

<01 1> 

Temperature 

Range 

253 - 297 K 

253 - 297 K 

253 - 297 K 

a l 

49.7 

49.7 

48.9 48.8 

50.0 

50.2 

50.0 

a 2 

49.6 

48.9 

50.3 

50.4 

50.3 

a 

49.65 

49.7 

48.9 48.85 

50.15 

50.3 

50.15 

Total Number 
of Measurements 

n = 3 

n = 3 

n = 6 

5 + S 

49.67 ± 0.06 

48.87 +0.06 

50.20 + 0.17 

Temperature 

Range 

297 - 323 K 

297 - 323 K 

297 - 323 K 

a l 



45.3 45.8 

47.5 

47.6 

47.8 

a 2 



46.0 45.5 

- 

46.6 

47.3 

a 


46.9 

45.65 45.65 

47.5 

47.1 

47.55 

Total Number 
of Measurements 

n = 4 

II 

C 

n = 5 

S± S 

47.02 + 0.38 

45.65 ±0.31 

47.36 ± 0.46 


*Refer to symbols key in Table 4. 


40 































In the temperature range 297 to 323 K, groups 1 and 3 do not differ significantly at the 90-percent 
confidence level. The grand average for these five material types is a = 47.21 ± 0.44, n = 9. 

Thermal Conductivity (Nal(TI) at 300 K) 

Multiple measurements were made on three oriented single-crystal Nal(Tl) specimens and fourPoly- 
scin specimens, and the results are summarized in Table 7. 


Table 7 

Summary of Nal(TI) Thermal Conductivity Measurements 


Material 

Description* 

Number of 
Observations 

Thermal Conductivity ±S (W/cm K) 

IH // 

9 

(1.91 +0.37) X 10" 2 

IS1 

9 

1.77 ±0.24 

FH// 

9 

1.64 ±0.21 

FSI 

9 

1 .77 ± 0.24 

<100> 

6 

1.77 ±0.38 

<01 1> 

20 

1.62 ±0.31 

<111> 

10 

1.47+0.26 


*Refer to symbols key in Table 4. 


There is no significant difference between IS1, Vtl// , FSI, <100>, and <01 1> specimens at the 90- 
percent confidence level. A grand average for these specimens is k = (1.71 ± 0.28) X 10‘ 2 W/cm K, 
n = 43. 


Thermal Shock Resistance (IMal(TI) at 300 K) 

Critical thermal gradient (AT c ), as a function of crack length (£), was calculated for plate, bar, and 
rod specimens of Nal(Tl) tested in light oil and for the condition of infinite heat transfer coeffi- 
cient using equation 1 (Figure 12). A minimum in the critical temperature gradient occurs at a 
crack length of about 4.5 mm. The median edge-crack size observed in Polyscin is 2.5 mm. The area 
above a curve is a region of crack instability, and the area below a curve is a region of stability. 

Critical thermal gradient results for oil quenching are shown in Table 8. Comparison of these results 
with AT c determined from Figure 12 shows generally good agreement of predicted and observed 
results when the median flaw size is known. 

Effects of specimen size were extrapolated by plotting AT c versus surface-area-to-volume ratio for 
both oil- and air-quenched specimens (Figure 13). 

As agreement between observed and calculated AT, was generally good, equation 1 was used to cal- 
culate an average heat transfer coefficient in still air, assuming a crack size equal to the median in 


41 




AT (K) 


rod specimen, h c = 0.037 W/cm 2 K 

bar specimens, h c = 0.024 W/cm 2 K 
plate specimens, h = 0.019 W/cm 2 K 


Figure 1 2. AT c versus £, specimen size, and specimen 
geometry for Nal(TI) quenched in light oil. 


Table 8 

Results of Oil-Quench Testing of Nal(TI) 


Specimen 

Number of 

C 

Average AT c 

Predicted AT c 

Description 

Specimens 

(mm) 

Observed (K) 

(K) 

<100> 

3 

<0.4 

32 

35 

IHi 

3 

~2.5 

9 

14 

FS// 

3 

~2.5 

10 

14 










Figure 13. AT c surface-area-to-volume ratio for Nal(Tl) 
in air- and oil-quench tests. 

Polyscin (2.5 mm) and the average AT c observed for rod specimens tested in air (67 K). A value of 
h= 1.2 X 10' 2 W/cm 2 K was calculated. 

Heat Capacity (Nal(TI) at 300 K) 

Multiple measurements were made on two single-crystal and two Polyscin specimens, and the results 
are summarized in Table 9. 

Pair-wise hypothesis testing for equality of the means indicates that the means are equal at the 90- 
percent confidence level. A grand average is C p = 0.347 ±6.61 X 10" 3 J/gK, n = 28. 

Elastic Constants (Nal(TI) at 300 K) 

Results of the density measurements for Polyscin Nal(Tl) are summarized in Table 10. 

An F-test for equality of variances fails at the 95-percent confidence level. A t'-test for equality of 
means indicates that the means are equal at the 95-percent confidence level, giving: 

p = 3.67 ± 5.61 X 10" 3 , n = 35 


43 




Table 9 

Summary of Nal(TI) Heat Capacity Data 


Specimen 

Number 

Specimen 

Description* 

Average Heat 
Capacity ±S 
(J/gK) 

Number of 
Observations 

1 

IH 

0.346 ±3.96 X 10' 3 

7 

2 

FS 

0.350 ± 1.05 X 10' 2 

7 

3 

Single crystal 

0.348 ± 8.66 X 10' 3 

7 

4 

Single crystal 

0.346 ± 1.91 X 10 -3 

7 


* Refer to symbols key in Table 4. 


Table 10 

Density of Polyscin Nal(TI) 


Extrusion No. 

Average Density ±S (g/cc) 

No. of Specimens 

1 

3.67 +3.97 X 10' 3 

27 

2 

3.66 ± 9.48 X 10" 3 

8 


Results for the measurement of Young’s modulus and shear modulus for Polyscin Nal(Tl) are sum- 
marized in Table 1 1 . 

The mean values for ingot 1 , groups 1 through 9, were found to be equal at the 9 5 -percent confi- 
dence level, giving an ingot 1 sample size of 34 specimens. The mean values for groups 1 1 through 
14 were found to be equal at the 95-percent confidence level, giving an ingot 2 sample size of 16 
specimens. The mean value for these two groups, representing ingot 1 and ingot 2 material, were 
found to be equal at the 95-percent confidence level, giving a sample size of 50 with the following 
mean values: 


E = (2.01508 ± 0.06258) X 10 4 MPa 

,n= 50 

G = (7.64700 ± 0.28570) X 10 3 MPa 

When tested against the means for specimens measured using the resonance method (group 1 0), this 
sample was found to be unequal at the 95-percent confidence level. 

The results of elastic-stiffness-constant measurements performed on single crystals of Nal(Tl) are 
summarized in Table 12. 


44 





Table 1 1 

Young's Modulus (E) and Shear Modulus (G) of Polyscin 



Position 

Type 

Number in 

E+S 

G ±S 

Group No. 

Orientation* 

Specimen' 

Sample 

(MPa) 

(MPa) 

Extrusion 1, PEO Method (Groups 1-9) 




1 

IH// 

MOR 

4 

(1.9864 ± 0.0454) X 10 4 

(7.581 6 ± 0.4221 )X 10 3 

2 

IHi 

MOR 

4 

1.9771 ±0.0613 

7.4867 ±0.2109 

3 

IS// 

MOR 

3 

2.0035 ± 0.0227 

7.6465 ±0.1323 

4 

FH// 

MOR 

4 

1.9821 ±0.0176 

7.5807 +0.1115 

5 

FH1 

MOR 

3 

2.0244 ± 0.0449 

7.6685 ± 0.2001 

6 

FS// 

MOR 

4 

1.9710 ±0.0305 

7.4748 ± 0.0872 

7 

IH//, ISi 
FH //, FS 1 

TC 

4 

2.0257 ± 0.0335 

7.7102 ±0.1600 

8 

FS// 

UC 

4 

1.9589 ±0.0290 

7.3869 ±0.1 153 

9 

IHI 

UC 

4 

2.0715 ±0.0240 

7.9535 ± 0.0951 

Extrusion 1, Resonance Method (Group 10) 




10 

IH//, IHi 
IS//, FH// 
FH i, FS// 

Q' 1 

12 

(2.138 ± 0.072) X 10 4 

(8.295 ±0.324) X 10 3 

Extrusion 2, PEO Method 

(Groups 11-14) 




11 

IHI 

UC 

4 

(2.0359 + 0.091 12) X 10 4 

(7.7461 +0.34966) X 10 3 

12 

FS// 

UC 

4 

1 .9693 ± 0.06658 

7.4660 ± 0.33760 

13 

IHI 

MOR 

4 

2.0937 ±0.04315 

7.9012 + 0.15579 

14 

FH i 

MOR 

4 

2.0975 ± 0.12773 

7.81 60 ±0.48633 


*Refer to symbols key in Table 4. 

+ .1 
MOR = modulus of rapture; TC = thermal conductivity; UC = ultimate compression; and Q = internal friction. 


The mean values for material groups tested by using the PEO method were found to be equal at the 
95-percent confidence level, giving a sample of 36 specimens with: 

C n = (3.0418 ±0.0117) X 10 4 MPa 

C 12 = (8.9581 ± 0.1035) X 10 3 MPa, , n = 36 

C 44 = (7.360 ± 0.0262) X 10 3 MPa 

Testing the mean of this sample against the mean of specimens measured by using the resonance 
method indicates that the means are not equal at the 95 -percent confidence level. The PEO method 
is considered to be the most accurate and reliable method. 


45 








Table 12 

Elastic Stiffness Constants 


Ingot No. 

Type 
Sped men 

‘ 

No. in 
Sample 

Cn±S 

(MPa) 

c 12 ±s 

(MPa) 

C 44 ±S 
(MPa) 

PEO Method 






1 

UC 

7 

(3.0283 ± 0.0049) X 10 4 

(8.8579 ± 0.093) X 10 3 

(7.3573 ±0.019) X 10 3 

1 

MOR 

9 

3.0407 ±0.0137 

8.9262 ±0.1399 

7.3573 ± 0.0233 

2 

UC 

6 

3.03215 + 0.0036 

8.9427 ± 0.0684 

7.3437 ± 0.0044 

2 

MOR, TC 

14 

3.0536 ±0.0133 

9.0354 ± 0.0679 

7.4017 ±0.0251 

Resonance 

Method 






1 

CT 1 

6 

(2.902 ± 0.099) X 10 4 

(8.066 ± 1 .43) X 10 3 

(7.323 ±0) X 10 3 


Mechanical damping efficiency (internal friction) was measured by using forced- and free-vibration 
measurements. Forced-vibration measurements of Q' 1 were used to assess material effects onQ' 1 . 
These measurements reflect Q' 1 measured at the maximum amplitude attained by the specimen, 
and these results are shown hi Table 13. Free- and forced-vibration measurements for single-crystal 
material and for Polyscin were averaged to assess the frequency dependence of Q' 1 , using free- 
vibration estimates of Q' 1 of maximum amplitude. These results are shown in Table 14. Finally, 
strain amplitude dependence of Q' 1 was observed for many specimens at the flexural, torsional, and 
longitudinal fundamental frequencies, manifest as a nonlinear decay curve of log amplitude versus 
time in the free-vibration method. Internal friction was highest at maximum amplitude and dropped 
to a low limiting value with time as the vibrational amplitude dropped to zero. 

Ultimate Strengths 

Nal(TI) at 300 K 

Tables 15 and 16 summarize single-crystal bending strengths for Nal(Tl) and Tables 17 and 18 
summarize Polyscin bending strengths. All the specimens tested were of the large variety (12.7 by 
2.54 by 2.54 cm). Although smaller Polyscin bend specimens (2.5 by 0.6 by 0.3 cm) were also 
tested, the results for them are summarized in the section on “Susceptibility to Subcritical Crack 
Growth.” Figures 14 and 15 with Tables 19 and 20 give Weibull analyses for Polyscin and single- 
crystal material, respectively. 

Thallium ion concentration measured by atomic absorption using pieces of the fracture surfaces 
ranged from 416 to 1423 ppm. No correlation of strength to thallium ion concentration was ob- 
served. 

Tables 21 and 22 summarize single-crystal compressive strength results for Nal(Tl), and Tables 23 
and 24 summarize the results for Polyscin. 


46 
















Table 13 

Material Effects on Qfg rcect of IMal(Ti) Resonance Specimens 
at Fundamental Resonance Frequencies 


Material 

Designation* 

No. of 
Specimens 

Flexural F 1 
@ 750 Hz 

Torsional T 1 
@2100 Hz 

Longitudinal L 1 
@ 9500 Hz 

<100> 

1 

5.30 X 1C 4 

3.05 X 10' 4 

— 

<01 1> 

2 

2.80 X 10' 4 

1.35 X 10' 4 

8.66 X 10- 5 

<11 1> 

2 

3.70 X 10' 4 

2.45 X 10' 4 

1.63 X 10' 5 

Polyscin 

8 

5.12 X 10‘ 4 



IH, IS, FS 



2.58 X 10' 4 

1.57 X 10' 4 

Polyscin 

4 

3.32 X 10’ 4 



FH 






*Refer to symbols key in Table 4. 


Table 14 

Internal Friction of Nal(TI) at Various Frequencies 


Vibration 

Mode 

and 

Overtone 

Frequency 

(Hz) 

No. of 
Specimens 

Q’ 1 

(free) 

Q' 1 

(forced) 

cr 1 ±s 

F 1 

750 

31 

(3.29 ± 1.9) X 10' 4 

(4.21 ± 1.9) X 1 0' 4 

(3.74 ± 1.9) X 10 -4 

F 2 

2100 

9 

t 1 ’ 08 -0'.4o) X 10 ‘ 3 

- 

( 1 - 08 -oi«) x 10 ' 3 

F 4 

6000-7000 

3 

(6.53 ± 2.0) X 10’ 3 

- 

(6.53 ±2.0) X 10‘ 3 

F 6 

14000 

3 

(2.84 ± 1.8) X 10" 3 

- 

(2.84 ± 1.8) X 10' 3 

T 1 

2100 

32 

(2.82 ± 1.6) X 1 0' 4 

(2.66 ± 1.7) X 10' 4 

(2.74 + 1.7) X 10' 4 

T 3 

6000-7000 

6 

(6.24 t 1 5‘|) X 10 ’ 4 

- 

6.24 t X 10 ’ 4 

T 5 

11000-12000 

3 

(8.36 ± 1.0) X 10" 4 

- 

(8.36 ± 1.0) X 10' 4 

L 1 

9500 

31 

(1.17 ± 0.4) X 10' 4 

(l.48 + 1;g)xi0- 4 

f 1 -32! Ml) XI O' 4 

L 1 

15000 

3 

(5.11 +1.6JX 10‘ 4 

- 

(5.11 ± 1.6) X 10' 4 

l 2 

28000 

2 

(7.35 ±0.9) X 10" 4 

- 

(7.35 ±0.9) X 10' 4 

L 3 

42000 

3 

(4.32 ± 1.0) X 10‘ 4 

- 

(4.32 ± 1.0) X 10 4 
























Table 15 

Nai(TI) Single-Crystal Critical Resolved Tensile Stress in Bending 


Ingot No. 

Specimen 

Type* 

Average Critical 
Resolved Tensile 
Stress ±S 
(MPa)** 

No. 

Specimens 

Group 

Number 

1 

<100> 

2.38 ± 0.04 

3 

1 

1 

<01 1> 

2.36 ±0.1 7 

3 

2 

1 

<1 1 1> 

2.32 ±0.23 

3 

3 

2 

<100> 

2.50 ±0.08 

3 

4 

2 

<01 1> 

1.85 ±0.19 

3 

5 

2 

<1 1 1> 

2.27 ±0.07 

3 

6 

3 

<100> 

1.65 ±0.13 

3 

7 

4 

<100> 

2.58 ±0.12 

4 

8 

5 

<100> 

2.45 ±0.15 

4 

9 

6 

<100> 

2.32 ±0.13 

4 

10 

7 

<100> 

2.16 ± 0.15 

4 

11 

8 

<100> 

2.52 ±0.16 

4 

12 

9 

<100> 

2.06 ±0.20 

4 

13 


•Refer to symbols key in Table 4. 
••Applied stress rate of 0,1956 MPa/s. 


Table 16 

Results of Pair-Wise t-Testing of Groups 8 Through 13 
from Table 15 


Group 

8 

9 

10 

11 

12 

13 

8 

— 

t 

X 

X 

t 

X 

9 


- 

t 

X 

t 

X 

10 



— 

t 

t 

X 

11 




- 

X 

t 

12 





— 

X 

13 






- 


t signifies arithmetic means are equal at 90-percent confidence level. 

X signifies arithmetic means are not equal at 90-percent confidence level. 


48 


















Extrusion No. 


Nal(TI) Polvscin Modulus of Rupture Results 


Position 
Orientation * 


No. of 
Specimens 


Average MOR ±S 
(MPa)** 


3.74+0.66 
4.78 + 1.85 
3.70 + 0.41 
3.92 + 0.43 
5.82 + 0.95 
5.37 +0.78 
5.13 ± 1.47 
5.22 + 1.11 


Group No. 


1 


Refer to symbols key in Table 4. 
Applied stress rate of 0.1956 MPa/s. 


Group 


Table 18 

Results of Pair-Wise t-Testing for Polyscin MOR Data 
from Table 17 


3 


t t 


5 

6 

X 

X 

X 

X 

X 

X 

X 

X 


t signifies arithmetic means are equal at 95-percent confidence level . 

X signifies arithmetic means are not equal at 95-percent confidence level 






















































Table 19 

Polyscin Weibull Analysis of Large Specimens 


n 

a 1 (MPa) 

In a 

In In (1/1 - P) f 

i 

2.85 

1.049 

-2.800 

2 

3.16 

1.150 

-2.080 

3 

3.17 

1.154 

-1 .640 

4 

3.20 

1.162 

-1.310 

5 

3.26 

1.182 

-1 .050 

6 

3.59 

1.281 

-0.832 

7 

3.62 

1.286 

-0.634 

8 

4.02 

1.391 

-0.452 

9 

4.03 

1.395 

-0.283 

10 

4.05 

1.398 

-0.119 

11 

4.10 

1.411 

-0.041 

12 

4.14 

1.420 

0.202 

13 

4.16 

1.426 

0.369 

14 

4.52 

1.508 

1.775 

0.551 

15 

5.90 

0.761 

16= N 

6.76 

1.910 

1.040 


*12.7 by 2.54 by 2.54 cm. 
t P = n/(N + 1}. 

Table 20 

Single-Crystal Weibull Analysis of Large Specimens 


n 

a (MPa) 

In a 

i 

2.13 

0.756 

2 

2.19 

0.785 

3 

2.23 

0.804 

4 

2.25 

0.810 

5 

2.28 

0.825 

6 

2.36 

0.855 

7 

2.36 

0.858 

8 

2.40 

0.875 

9 

2.41 

0.881 

10 

2.43 

0.887 

11 

2.54 

0.934 

12 

2.55 

0.936 

13 

2.55 

0.936 

14 = N 

2.56 

0.942 


In In (1/1 -P)' 


-0.0874 

0.0940 

0.279 

0.476 

0.700 

0.996 


12.7 by 2.54 by 2.54 cm, 
P = n/(N + 1). 





















Table 21 

Nal(TI) Single-Crystal Compressive Strength 


Ingot No. 

Orientation 

Designation* 

Average Unresolved 
Initial Cracking 
Strength ±S 
(MPa) 

No. of 
Specimens 

Group No. 

1 

<100> 

13.45 ±2.26 

3 

1 


<01 1> 

38.51 ± 0.49 

3 

2 


<1 1 1> 

50.02 ± 3.63 

3 

3 

2 

<100> 

13.87 ±2.48 

3 

4 


<01 1> 

39.51 ± 0.41 

3 

5 


<1 1 1> 

49.73 ±5.37 

3 

6 


* Refer to symbols key in Table 4, 


Table 22 

Results of Pair-Wise t-Testing of Groups 1-6 from Table 21 


Group 

1 

2 

3 

4 

5 

6 

1 

— 

X 

X 

t 

X 

X 

2 


- 

X 

X 

t 

X 

3 



- 

X 

X 

t 

4 




— 

X 

X 

5 





— 

X 

6 






- 


t signifies arithmetic means are equal at 95-percent confidence level. 

X signifies arithmetic means are not equal at 95-percent confidence level. 

Table 23 

Nal(TI) Polyscin Compressive Strength Data 


Extrusion No. 

Position 

Orientation* 

Average Initial 
Cracking Strength ±S 
(MPa) 

No. of 
Specimens 

Group 

No. 

1 

FS// 

18.88+1.46 

4 

1 

1 

IH i 

12.45 ±1.36 

4 

2 

2 

FS// 

11.38 ±2.51 

4 

3 

2 

IH i 

1 8.02 ± 3.59 

4 

4 


Refer to symbols key in Table 4. 
























Table 24 

Pair-Wise t-Test Results 
of Groups 1-4 


Group 

1 

2 

3 

4 

1 

- 

X 

X 

t 

2 


- 

t 

X 

3 




X 

4 




— 


t signifies arithmetic means are equal at 95-percent confidence level. 

X signifies arithmetic means are not equal at 95-percent confidence level. 


Tables 25 and 26 summarize single-crystal and Polyscin shear strength results, respectively. 

The Nal(Tl) critical-stress intensity factor was measured by using two methods: the double canti- 
lever beam method and the notched-beam method. Tables 27 and 28 summarize the test results for 
the double-cantilever-beam method and the notched-beam method, respectively. Using the data 
from Table 28, Figure 1 6 is a log plot of the stress intensity equation, 

K ic = Y 


where Y -a geometry constant 
cr f = the stress at failure 
a f = flaw size at failure 

Csl(Na) at 300 K 

Tables 29 and 30 summarize 0.2-percent compression yield strength results for CsI(Na). 

In addition to the single-crystal results, five polycrystalline specimens from ingot 1 had an average 
yield strength of 2.98 ± 0.22 MPa. 

Creep 

Nal(TI ) at 300 K 

Table 31 and Figures 17 and 18 summarize flexural creep results for Polyscin and single-crystal 
Nal(Tl) materials. The equation that was fitted to the creep data was: 

5 = a + bt 1/3 


53 




Table 25 

Nal(TI) Single-Crystal Shear Strengths 




Average Initial 




Cracking Stress ±S 

No. of 

Ingot No. 

Orientation* 

(MPa) 

Specimens 

1 

<100> 

2.16 ±0.738 

2 

2 

<100> 

3.68 ± 3.51 

2 


*Refer to symbols key in Table 4. 


Table 26 

Nal(TI) Polyscin Shear Strengths 



Position 

Average Initial 
Cracking Stress ±S 

No. of 

Extrusion No. 

Orientation* 

(MPa) 

Specimens 

1 

FS// 

3.03 ± 0.45 

4 

1 

IH1 

1 .79 ± 0.50 

4 


*Refer to symbols key in Table 4. 


Table 27 

Double-Cantilever-Beam K |C forNal(TI) 


Specimen 

K |C (MPa m 1/2 } 

1 

0.43 

2 

0.31 

3 

0.52 

4 

0.58 

5 

0.33 

6 

0.54 

Average 

0.45 + 0.11 


54 
























(MPa) 


Table 28 

Notched-Beam K JC for Nal(TI) 


Specimen 

a f (MPa) 

a f (cm) 

K |C (MPa m 1/2 ) 

1 

4.46 

0.571 

0.304 

2 

10.14 

0.175 

0.384 

3 

9.22 

0.170 

0.345 

4 

9.88 

0.173 

0.371 

5 

11.52 

0.165 

0.423 

6 

10.58 

0.160 

0.385 

7 

7.59 

0.378 

0.423 

8 

8.20 

0.345 

0.463 

9 

7.91 

0.256 

0.363 



Average 

0.382 ±0.042 



Figure 16. Nal(TI) K |c notched-beam data. 


55 













Table 29 

Csl(Na) Single-Crystal 0.2-Percent Compressive Yield Strength (MPa) 


Ingot No. 

Location* 

Orientation* 

<00 1> 

<01 1> 

<1 1 1> 

2 

T 

3.85 




M 

3.27 




B 

3.37 

3.89 

3.05 



Ave ±S 3.49 ± 0.33 



3 

T 

5.03 





5.27 




B 

5.02 

5.68 

2.57 



Ave ±S 5.11 ±0.14 



4 

T 

7.49 




M 

7.34 




B 

7.24 

6.18 

2.84 



Ave ±S 7.36 ±0.1 2 




*Refer to symbols key in Table 4, 


Table 30 

Increase in Average Compressive 0.2-Percent Yield Strength of 
Csl(Na) with Time 



<100> Compressive Yield Strength (MPa) 

Increase 

(%) 

Ingot No. 

Tested 2/1 2/80 

Tested 11/18//81 

1* 

2.98 ± 0.22 

5.45 

182 

2 

3.49 ± 0.33 

4.37 

125 

3 

7.36 + 0.12 

15.51 

211 

4 

5.11 ±0.14 

7.34 

144 


*Five polycrystalline specimens. 



























Table 31 

Summary of Nal(TI) Flexural Creep Results 


Specimen 

Identification* 

Applied 

Stress 

(MPa) 

Slope 

(cm/hr 1/3 ) 

Intercept 

(cm) 

Correlation 

Coefficient 

FS// 

3.36 

1 5.32 X 10' 6 

79 X 10~ 6 

0.879 


2.58 

4.60 

58 

0.590 


1.82 

No perceptible cr 

eep «5.08 X 10' 5 

cm/4000 hr) 

IH1 

3.42 

4.44 

66 

0.609 


2.61 

8.99 

48 

0.842 


1.85 

No perceptible cr< 

3ep (<5.08 X 10' 5 

cm/4000 hr) 

IH -17 

3.75 

12.70 

5 

0.853 


2.93 

14.32 

15 

0.806 


2.19 

1.37 

23 

0.139 

<100> 

1.48 

34.16 

190 

0.977 


0.765 

10.74 

66 

0.738 

<11 1> 

3.32 

17.88 

84 

0.939 

<01 1> 

2.59 

22.58 

35 

0.966 

<100> 

1.86 

4.77 

89 

0.413 

<1 1 1> f 

3.65 

22.05 

140 

0.901 

<01 1> + 

2.92 

5.43 

574 

0.442 

<100^ 

2.19 

2.23 

13 

0.176 


*Refer to symbols key in Table 4. 

'Second loading after initial creep at lower stresses. 


where 

5 = midpoint deflection (cm) 

t = time (hours) 

a = intercept constant in a t 1/3 plot of S 
b = slope constant in a t 1/3 plot of 6 

Tables 32 and 33 summarize compressive creep results for Polyscin and single-crystal Nal(Tl) ma- 
terial, respectively. The equation that was fitted to the creep data was: 

e = a + bt 1 / 3 


57 





O FS/ 

□ 1H1 


3 5 10 15 20 25 

Slope x 10 6 (cm/hr 1 /3 ) 

Figure 17. Flexural creep of Polyscin Nal(TI). 


SYMBOL ORIENTATION 
0 < 100 > 

A <11 1> 

0 < 01 1 > 


POLYSCIN CURVE 




o 


0 


i 





Table 32 

Polyscin Nal(TI) Compressive Creep Summary 


Specimen 

Identification* 

Applied 

Stress 

(MPa) 

Slope 

(microstrain/h 1/3 ) 

Intercept 

(microstrain) 

Correlation 

Coefficient 

FS// 

1.65 

No perceptibl 

e creep «0.005%/20C 

Ohr) 


2.48 

0.62 

46 

0.184 


4.16 

8.19 

66 

0.844 


6.12 

33.83 

196 

0.963 

FS// 

1.34 

No perceptible creep «0.005%/2000 hr) 


2.17 1 ' 

No perceptible creep «0.005%/2000 hr) 


3.82 f 

No perceptible creep (<0.005%/2000 hr) 


5.74 t 

18.55 

112 

0.973 

FS// 

1.07 

No perceptib! 

e creep (<0.005%/2000 hr) 


1.90 + 

No perceptible creep «0.005%/2000 hr) 


3.55 + 

9.44 

401 

0.896 


5.47 + 

13.34 

18 

0.859 

IH1 

1.65 

No perceptible creep «0.005%/2000 hr) 


2.49 + 

No perceptible creep (<0.005%/2000 hr) 


4.18 t 

1.86 

2 

0.214 


6.14 1- 

11.61 

32 

0.706 


7.86 + 

44.31 

242 

0.945 

IH1 

1.37 

2.08 

-6 

0.591 


2.21 f 

1.16 

-12 

0.329 


3.89 + 

6.57 

50 

0.632 


5.86 f 

1.00 

-15 

0.120 


7.40 t 

5.53 

303 

0.512 

IH1 

1.09 

1.23 

-7 

0.673 


1 ,92 t 

0.89 

1 

0.372 


3.60 f 

2.05 

13 

0.625 


5.56 f 

7.47 

29 

0.941 


7.09 t 

13.14 

118 

0.981 


*Refer to symbols key in Table 4. 

'Progressively increasing stresses applied on the same specimen. 


59 










Table 33 

Single-Crystal Nal(Ti) Compressive Creep Summary 


Specimen 

Identification* 

Applied 

Stress 

(MPa) 

Slope 

(microstrain/hr 1/3 ) 

Intercept 

(microstrain) 

Correlation 

Coefficient 

<1 1 1> 

1.65 

7.01 

33 

0.917 


2.36 f 

10.41 

32 

0.841 


3.48 + 

18.76 

230 

0.973 

<01 1> 

1.36 

No perceptible creep (<0.005%/2000 hr) 


2.05 t 

No perceptible creep (<0.005%/2000 hr) 


3.1 7 f 

No perceptib 

e creep «0.005%/2000 hr) 

<100> 

1.08 

9.13 

34 

0.976 


1 .78 t 

No perceptible creep «0.005%/2000 hr) 


2. 89* 

523.6 

946 

0.9757 


*Refer to symbols key in Table 4. 

^Progressively increasing stress on the same specimen. 


where 

e = microstrain 
t = time (hours) 
a = intercept in a t 1 / 3 plot of e 
b = slope in a t 1 / 3 plot of e 

Figure 19 graphically summarizes the Polyscin creep data. 

Cs/(Na) at 300 K 

Table 34 summarizes creep results for polycrystal and single-crystal CsI(Na). The equation that was 
fitted to the data was: 

e = a 1 + a 2 In (1 + t/a 3 ) 

where 

e = microstrain 

= instantaneous creep strain (occurs in <1 minute) 


60 




STRESS (MPa) 



Figure 19. Compressive creep summary for Polyscin. 


Table 34 

Summary of Constants and Residual Standard Deviations 
for Csl(Na) Creep Curves 

















a 2 = a dimensionless fitting parameter (microstrain) 

a 3 = a fitting parameter with the dimensions of time (hours) 

Hardness (NalfTI) at 300 K) 

Table 35 summarizes the hardness values for single-crystal Nal(Tl). 


Table 35 

Vickers Hardness Values for Single-Crystal Nal (Tl) 


Measurement 

Face 

Diagonal 

Direction 

Vickers Hardness Number (kg/mm 2 ) 

100 g f 

300 g + 

500 g 1 " 

(100) 

<100> 

9.50 

8.62 

8.19 

(100) 

<100> 

8.69 

7.55 

7.74 

(111) 

<1 10> 

8.69 

7.82 

8.11 

(011) 

<100> 

8.51 

8.01 

7.67 


+ Load. 


The mean value for Vickers hardness is 8.12 ± 0.600 kg/mm 2 . 

Susceptibility to Subcritical Crack Growth (Nal(TI) at 300 K) 

Tables 36 through 39 summarize the results of the stress-rate testing for Polyscin Nal(Tl). Figure 20 
and Table 38 give a Weibull analysis of groups 3 and 4 from Table 36. 

Ingot Variation 

Nal(TI) at 300 K 

In extrusion 1 , Polyscin material from the beginning of an extrusion is consistently weaker than 
material from the end of an extrusion, whereas in the second extrusion, this distinction is not so 
clear cut. Analysis of the results of the single-crystal Nal(Tl) MOR indicates that each ingot exhibits 
a characteristic strength with a small standard deviation. On the other hand, Polyscin groups exhibit 
higher average strength and a rather large standard deviation relative to <100> cleavage strengths. 
This difference can be explained in terms of the rather small Weibull modulus for Polyscin (~4) 
relative to the Weibull modulus measured for single-crystal material (~17). Materials with a large 
Weibull modulus typically exhibit a characteristic strength because of the rather small range in the 
magnitude of worst flaws. Such materials typically exhibit very little size effect on strength. In con- 
trast, materials with a low Weibull modulus exhibit a large amount of scatter in strength values be- 
cause of the large range in magnitude of worst flaws. Such materials typically exhibit a significant 
size effect on strength since the adequate sampling of a flaw population with a large range in the 
magnitude of worst flaws becomes difficult with small specimens. 


62 




Table 36 

Nal(TI) Polyscin Stress-Rate Bend-Test Results 


Crosshead 

Rate 

(cm/s) 

Applied 
Stress Rate 
(MPa/s) 

No. of 
Specimens 

0.2% Yield 
Stress ±S 
(MPa) 

Average Flexural 
Strength ±S 
(MPa) 

Compensated 

Strength* 

(MPa) 

Group 

No. 

1.69 X 10' 5 

0.132 

20 

5.5 ± 0.9 

13.3 ±0.77 

5.56 

1 

8.47 X 10' 5 

0.658 

16 

6.4 ± 1.2 

13.0 + 0.90 

5.44 


8.47 X 10‘ 4 

6.58 

14 

- 

10.3 + 0.98 

4.31 


8.47 X 10' 3 

65.8 

18 

6.0+ 1.3 

10.5 + 0.83 

4.39 

4 


*These specimens were broken in three-point bending with a gauge area of 2.15 by 0.6 cm. Specimens reported in ingot variation 
testing (Table 17) were broken in four-point bending with an inner and outer span of 3.39 and 10.15 cm, respectively. Because for 
brittle materials, strength is a function of specimen size and type of loading, it is necessary to make the measurements comparable 
by using a formula derived from Weibull statistics: 



/m \ 1/m /S 0 \ 1/m /3m + 6\ 

fry (-) M 


where 

o .j = average strength in three-point loading 
ct 2 = average strength in four-point loading 
m = Weibull modulus for Polyscin 

S.j = area of a 2.15- by 0.6-cm tensile face of the small three-point bend specimens 

S 2 = area of a 10.16- by 2.54-cm tensile face of a hypothetical large three-point bend specimen 


The first factor in the above equation converts four-point loading to an equivalent three-point loading. The second factor converts a 
large specimen tensile surface to a smaller one, and the third factor converts a square cross-section specimen to an equivalent rec- 
tangular cross-section specimen (references 26 and 27). 


Table 37 

Pair-Wise t-Testing Results for 
Average Flexural Strengths Listed in 
Groups 1 -4 from Table 36 


Group 

1 

2 

3 

4 

1 

— 

t 

X 

X 

2 


- 

X 

X 

3 



- 

t 

4 




- 


t signifies arithmetic mean strengths are equal at 95-percent confidence level. 

X signifies arithmetic mean strengths are not equal at 95-percent confidence level. 


63 























Table 38 

Poivscin Weibull Analysis of Small Specimens* 


n 

a ( MPa ) 

In a 

In In ( 1/1 - P) t 

i 

5.38 

1.683 

- 3.48 

2 

6.15 

1.817 

- 2.77 

3 

6.28 

1.837 

- 2.35 

4 

6.41 

1.858 

- 2.05 

5 

6.54 

1.878 

- 1.81 

6 

7.36 

1.996 

- 1.61 

7 

7.69 

2.040 

- 1.43 

8 

8.59 

2.151 

- 1.28 

9 

8.97 

2.194 

- 1.14 

10 

9.49 

2.250 

- 1.02 

11 

9.49 

2.250 

- 0.90 

12 

9.74 

2.276 

- 0.79 

13 

9.87 

2.290 

- 0.69 

14 

10.0 

2.303 

- 0.59 

15 

10.0 

2.303 

- 0.50 

16 

10.2 

2.322 

- 0.41 

17 

10.8 

2.380 

- 0.32 

18 

10.8 

2.380 

- 0.24 

19 

10.9 

2.389 

- 0.15 

20 

11.0 

2.398 

- 0.07 

21 

11.1 

2.407 

0.01 

22 

11.8 

2.468 

0.09 

23 

11.9 

2.477 

0.18 

24 

12.0 

2.485 

0.26 

25 

12.4 

2.518 

0.35 

26 

12.8 

2.550 

0.44 

27 

12.8 

2.550 

0.53 

28 

13.1 

2.573 

0.64 

29 

13.6 

2.610 

0.75 

30 

14.3 

2.660 

0.88 

31 

15.0 

2.708 

1.03 

32 = N 

15.7 

2.754 

1.25 


*2.5 by 0.6 by 0.3 cm. 
t P = n/(N + 1). 








Table 39 

Stress-Rate Data for<100> Nal(TI) 
Singie-Crystai impact Specimens" 


Fracture Stress 

Applied Stress Rate 

(MPa) 

(MPa/s) 

5.87 

1.47 X 10 4 

6.15 

1.17 

6.55 

1.56 

6.88 

1.71 

7.14 

1.58 

7.37 

1.19 

7.47 

1.13 

7.74 

1.63 

7.96 

1.06 

8.24 

1.73 

8.32 

1.75 

8.36 

1.04 

8.36 

1.67 

8.61 

1.91 

8.69 

1.39 

9.19 

3.68 

9.34 

1.44 

9.43 

2.22 

10.0 

1.25 

10.6 

3.04 

11.7 

2.60 

11.9 

3.96 

Average: 

Average: 

8.45 ±1.61 

1 .83 X 1 0 4 


*6.4 by 0.64 by 0.64 cm. 


Csl(Na) at 300 K 

CsI(Na) single crystals exhibit extensive ingot variation in 0.2-percent yield strength; however, 
within an ingot, strength appears to be homogeneous. Creep behavior is also ingot-dependent. 

CONCLUSIONS 

1. The tha lli um doping in Nal(Tl) scintillators has little effect on the coefficient of linear 
thermal expansion, thermal conductivity, heat capacity, and elastic stiffness constants 
because measured values for these properties on single crystals were equal to values re- 
ported in the literature for undoped material. 


65 





Figure 20. Weibul! plot of Polyscin MOR data 
(small specimens). 


2. Strength of single-crystal material is ingot-dependent in both Nal(Tl) and CsI(Na), with 
CsI(Na) showing the greatest variation. Strength of material within a single-crystal ingot 
appears to be homogeneous. 

3. Strength of Polyscin Nal(Tl) is extrusion-dependent and dependent on position within an 
extrusion. 

4. Strength of Polyscin Nal(Tl) exhibits a significant size effect as predicted by Weibull 
analysis. 

5. The 0.2-percent yield strength of CsI(Na) appears to become greater with time. 

6. Creep in both Nal(Tl) and CsI(Na) is ingot-dependent. 

7. Although evidence shows that Nal(Tl) does not exhibit subcritical crack growth at stress 
rates of less than 65 .8 MPa/s in less than 3-percent RH room temperature environment, 
there is some mechanism that more than triples its average strength between stress rates ol 
65.8 and 1.0 X 10 4 5 6 7 MPa/s. Possible explanations for this behavior are a susceptibility to 


66 




subcritical crack growth at very high stress rates and/or a strength-enhancing brittle trans- 
ition region between stress rates of 65.8 and 1 .0 X 10 4 MPa/s. 

8. No correlation was found to establish a strength dependency on the basis of thallium con- 
centration. 

RECOMMENDED TESTING FOR DESIGNERS 

Polycrystalline forms of Nal(Tl) and CsI(Na) can be produced by using various forming techniques 
that utilize temperature and pressure to produce a grain structure in material that is originally a 
single crystal. Modulus of rupture and compressive creep are considered to be the most diagnostic 
strength-related measurements for these materials. Creep testing should use a wobble-plate linkage 
to couple the specimen and the transducers as a means of averaging out errors due to specimens mis- 
alignment. These tests, coupled with a K IC measurement and determination of elastic moduli using 
the pulse-echo overlap technique, should provide a good indication of how these newer materials 
compare with extruded Nal(Tl) and single-crystal Nal(Tl) and CsI(Na). 

ACKNOWLEDGMENTS 

This study was initiated by Mr. William Cruickshank who, before his death, contributed greatly to 
its direction and scope. The authors wish to thank Dr. Robert Hartmann, Mr. Earl Angulo, and 
Dr. Carl Fichtel of the Goddard Space Flight Center for their assistance in determining materials 
to be tested and for their continued support. Appreciation is also expressed to Dr. Guy Eubanks 
and Mr. Walter Viehmann for their guidance and critical analysis. Special thanks are given to Messrs. 
Ronald Hunkeler, Edward Sanford, and Carl Walch for their technical support in making measure- 
ments. Helpful suggestions from Drs. Barrie Hughes and Robert Hofstadter of Stanford University, 
Dr. James Kurfess of the United States Naval Research Laboratory, and. personnel from both the 
Harshaw Chemical Company and Bicron Corporation are greatfully acknowledged. 


67 




REFERENCES 


1 . Tidd, John L,, Joseph R, Dabbs, and Norman Levine, Scintillator Handbook with Empha- 
sis on Cesium Iodide, NASA TM X-64741 , April 1973. 

2. Snyder, R. S., and W. N. Clotfelter, Physical Property Measurements of Doped Cesium 
Iodide Crystals, NASA TM X-64898, August 1974. 

3. Hofstadter, R., E. B. Hughes, and B. L. Beron, Final Project Report on Contract N ASS- 
20987, Phase B, Definition Study for EGRET Experiment and Hardware, High Energy 
Physics Laboratory, W. W. Hansen Laboratory of Physics, Stanford University, Stanford, 
California, December 1976. 

4. Landolt-Bornstein, Numerical and Functional Relationships in Science and Technology , 
New Series K. -H. Hellwege, editor in chief, Group III: Crystal and Solid State Physics, 
Vol. 1, Elastic, Piezoelectric, Piezooptic and Electrooptic Constants of Crystals, Springer- 
Verlag, 1966, p. 8. 

5. Thermophysical Properties of Matter, Vol. 13, Thermal Expansion, Nonmetallic Solids, 
Touloukian, Kirby, Taylor and Lee. Plenum Publishing Corporation, New York-Wash- 
ington, 1977. 

6. Touloukian, Powell, Ho and Klemens, Thermophysical Properties of Matter, Vol. 2, 
Thermal Conductivity , Nonmetallic Solids, Plenum Publishing Corporation, New York- 
Washington, 1970. 

7. Handbook of Chemistry and Physics, 42nd Ed., Chemical Rubber Publishing Company, 
Cleveland, Ohio, 1960. 

8. Touloukian, Y. S., and E. H. Buyco, Thermophysical Properties of Matter, Vol. 5, Spe- 
cific Heat Non Metallic Solids, Plenum Publishing Corporation, New York-Washington, 
1970. 

9. Poluani, Robert S., Bruce J. Giza, and Christopher S. Tilghman, Compression Deforma- 
tion Behavior of CsI(Na), Final Technical Report Under Contract S-63970B, Fracture 
and Deformation Division, National Bureau of Standards, Washington, D.C. 

10. Hasselman, D. P. H., “Unified Theory of Thermal Shock Fracture Initiation and Propaga- 
tion in Brittle Ceramics,/. Am. Cer. Soc., 52(1 1), 1969, p. 600. 

1 1. Mason, S. S., and R. W. Smith, “Theory of Thermal Shock Resistance of Brittle Materials 
Based on Weibull’s Statistical Theory of Strength,” /. Am. Cer. Soc., 38(1), 1955, p. 18. 


69 



12. Becker, P. F., et al., Thermal Shock Resistance of Ceramics: Size and Geometry Effects in 
Quench Tests, Bull. Am. Cer. Soc ., 59(5), 1980, p. 542. 

13. Emery, A., and A. Kobayashi, “Transient Stress Intensity Factors for Edge and Corner 
Cracks in Quench Test Specimens,”/. Am. Cer. Soc., 63(7-8), 1980, p. 410. 

14. Satarmurthy, K., J. P. Singh, D. P. H. Hasselman, “Transient Thermal Stresses in Cylinders 
with a Square Cross Section Under Conditions of Convective Heat Transfer,” /. Am. Cer. 
Soc., 63(11-12), 1980, p. 694. 

15. Chapman, Alan J., Heat Transfer, Macmillan Company, New York, 1960. 

16. Kreith, F., Principles of Heat Transfer, First Ed., In-Text Ed. Publishers, New York, 1973. 

17. Mason, Warren P., Physical Acoustics and Properties of Solids, D. Von Nostrand Com- 
pany, Incorporated, Princeton, New Jersey, 1958. 

18. Schreiber, Edward, Orson L. Anderson, and Naohiro Soga, Elastic Constants and Their 
Measurement , McGraw-Hill Company, 1973. 

19. Krautkramer, J., and H. Krautkramer, Ultransonic Testing of Materials, Translation of 
original edition, Springer-Verlag, New York, Incorporated, 1969. 

20. Nowick, A., and B. Berry, Anelastic Relaxation in Crystalline Solids, Academic Press, 
New York and London, 1972. 

21. Bradt, R. C., D. P. H. Hasselman, and F. F. Lange, Ed., Fracture Mechanics of Ceramics, 
Vol. 1, Plenum Press, New York-London, 1974. 

22. Brown, W. F., and J. E. Srawley, Plane Strain Crack Toughness Testing of High Strength 
Metallic Materials , ASTM Special Technical Publication 410, 1967, pp. 1-13. 

23. Nye, J. E., Physical Properties of Crystals, Oxford at the Clarendon Press, 1957. 

24. Hultquist, Robert A., Introduction to Statistics, Holt, Rinehart & Winston, Incorporated, 
New York, 1969. 

25. Wine, R. Lowell, Statistics for Scientists and Engineers, Prentice-Hall, Incorporated, Engle- 
wood Cliffs, New Jersey. 

26. Johnson, C. A., “Fracture Statistics in Design and Application,” General Electric Report 
79 CRD212, December 1979. 

27. Davies, D. G. S., “The Statistical Approach to Engineering Design in Ceramics,” Proc. 
Br. Ceramic Soc., 22, 1973, p. 429. 


70 



2. Government Accession No. 


3. Recipient's Catalog No. 


4. i itle and Subtitle 

Engineering and Design Properties of Thallium -Doped Sodium 
Iodide and Selected Properties of Sodium-Doped Cesium Iodide 

7. Author(s) K. Forrest, C. Haehner, T. Heslin, M. Magida, 

J. Uber, S. Freiman, G. Hicho, and R. Polvani 


9. Performing Organization Name and Address 

Goddard Space Flight Center 
Greenbelt, Maryland 20771 


12. Sponsoring Agency Name and Address 

National Aeronautics and Space Administration 
Washington, D.C. 20546 


5. Report Date 

September 1984 


6. Performing Organization Code 
313 

8. Performing Organization Report No. 
84F0257 


10. Work Unit No. 


1 1 . Contract or Grant No. 


13. Type of Report and Period Covered 
Reference Publication 


14. Sponsoring Agency Code 


15. Supplementary Notes 

K. Forrest, C. Haehner, T. Heslin, M. Magida, and J. Uber: Goddard Space 

Flight Center, Greenbelt, Maryland. 

S. Freiman, G. Hicho, and R. Polvani: National Bureau of Standards, 

Washington, D.C. 


16. Abstract 

Mechanical and thermal properties, not available in the literature but necessary to structural design, using 
thallium-doped sodium iodide and sodium-doped cesium iodide were determined to be coefficient of linear 
thermal expansion, thermal conductivity, thermal-shock resistance, heat capacity, elastic constants, ultimate 
strengths, creep, hardness, susceptibility to subcritical crack growth, and ingot variation of strength. These 
properties were measured for single and polycrystalline materials at room temperature. 


17. Key Words (Selected by Author(s)) 

Alkali halides, Mechanical properties, 
Scintillators, Gamma-ray detectors 


18. Distribution Statement 

STAR Category 31 
Unclassified— Unlimited 


19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of Pages 22. Price* 
Unclassified Unclassified 76 A05 


*For sale by the National Technical Information Service, Springfield, Virginia 221 61 


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