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The yield strength of polycrystalline CdTe as a function of grain size
Materials Science and Engineering, 13 (1974) 194--196 © Elsevier Sequoia S.A., Lausanne -- Printed in The Netherlands
Short Communication
The yield strength of polycrystalline CdTe as a function of grain size F. BUCH and C.N. AHLQUIST
Mechanical Engineering Department, University of Colorado, Boulder, Colo. 80302 (U.S.A.)
(Received in revised form March 2, 1973)
The mechanical strength of polycrystalline CdTe is an important factor in determining its
e m p l o y m e n t as a window material. It is expected that relatively fine grained polycrystals
Fig. 1. Typical microstructures of undeformed polycrystalline CdTe (100X).
195
should exhibit enhanced mechanical properties when compared with single crystals. It was the purpose of the present work to experimentally measure the yield strength of polycrystalline CdTe as a function of grain size. Samples approximately 2 × 2 × 3.5 mm were cut from hot pressed CdTe blocks. The loading faces of the samples were masked with stop-off lacquer, and the sides were then polished for 180 see in a solution 1 of 10 ml HNO a, 2 0 m l HzO and 4 g K z C r 2 0 v. This polishing procedure removed approximately 30 pm from each side face of the sample while maintaining the masked loading faces parallel and flat. The masking of the loading faces was done to avoid rounding, which would cause a n o n u n i f o r m load distribution during compression. The grain sizes were determined using the intercept m e t h o d on photomicrographs of u n d e f o r m e d samples, see Fig. 1. The samples were compressed at room temperature (23°C +- 1 deg C) using a model TT Instron machine set at 0.05 m m / m i n crosshead speed. To minimize surface friction, a 30 pm thick Teflon tape was placed between the sample and loading platen. A tungsten filament microscope lamp was focused on the samples after yielding in dark to ascertain whether or not photoplastic effects were present in polycrystalline CdTe as have been observed in single crystal CdTe e. Several samples were tested for each grain size from which a mean yield strength was calculated, see Table 1.
Dislocation pile-up t h e o r y predicts that the yield strength should be inversely proportional to the square root of the average grain diameter 3 -- 5, O=O 0
+Ad-I/2
where oo represents the lattice friction stress and A is a constant*. Figure 2 shows the average yield strength versus d -1/2 for CdTe. These data predict oo = 37.7 N/mm 2 and A = 165
N/mm 2 × pm 1/2 (= 1.65 × 103 Nm--3/2). Since the yield strength is influenced by both grain size and point defect concentration, it would be desirable to normalize the preceding data to a c o m m o n doping level. This is not possible at the present time since the effect of In impurities on yield strength is not known. However, it is known that the yield strength of CdTe is weakly dependent on native point defect concentration 2 and thus we expect the influence of grain size to dominate in the present case. The lattice friction stress, 00, can be independently estimated from the single crystal data of Carlsson 2. Assuming a m i n i m u m impurity concentration of 1 p.p.m. (equivalent to 1016 electrons/cm 3 ) and that these impurities influence the strength of CdTe in the same way as native point defects, we find % = 15 N / m m 21. Taking a typical Schmid factor of 0.5, this predicts a oo = 30.0 N / m m 2 which is in reasonable a ~ e e m e n t with the * A similar r e l a t i o n o b t a i n s in t h e case o f d i s l o c a t i o n initiated cracking w h e r e d = pile-up l e n g t h 6 .
TABLE 1 S u m m a r y o f results Identification
Name Code
A CV 104
B CII82
C CV76
D CII88
Material h i s t o r y
Doping level Dopant Pressing t e m p e r a t u r e Resistivity (~2cm)
10 p . p . m . In 750 °C 6 x 10 s
--750 °C 5 x 10 4
50 p . p . m . In 800 °C 10 7
-750 °C 5 X 105
d--l~2
d (pm) (pm--1/2 )
118.2 0.092
60.4 0.129
55.7 0.134
38.1 0.162
Oy m e a n ( N / m m 2) Oy m e a n (lb./in. 2) Spread* No. o f samples t e s t e d E x p e r i m e n t a l errors Light e f f e c t M a x i m u m light e f f e c t
51.9 7519 19.8% 11 +_4% Neg. --3%
60.8 8808 15.7% 6 +5% Pos. +4.5%
59.9 8674 8.5% 8 ±3% Neg. --2%
63.4 9187 8.5% 8 +-3% Pos. +5%
Grain sizes Test results
* M a x i m u m m i n u s m i n i m u m o b s e r v e d yield s t r e n g t h in % o f m e a n value.
196 O-
%
x I000
O"
~/em2
Ibf~n 2
xlO00
8O
Ib~n2
9
POLYCRYSTALLrNE
/ /
J
CdTe
60
23eC 0.0~ mifl"1
D
50
A ~ /
CdTe
I
0.014
23 °C
it
~ 40" W O~
~ 20"
min - I
$~N6LE CRYSTAL
]
/
40
/ I / /
/ •
o.~5
o~
~,'6 d_~ (.~)
Fig. 2. The 0.05% offset yield strength vs. reciprocal of the square root of the average grain diameter of CdTe tested in compression at 23°C. Each data point represents the average of at least 6 tests.
CROSSHEAD DISPLACEMENT
Fig. 3. Typical flow stress vs. time curves for single and polycrystalline CdTe tested in light and darkness at
value extrapolated from Fig. 2 (o 0 = 37.7 N/ mm 2). Better agreement would be fortuitous in view of the assumptions made in arriving at the estimated ~0 and the experimental error bars in Fig. 2. Single crystal CdTe doped with native point defects exhibits strong increases in strength when tested in light v e r s u s dark 2. Relatively small photoplastic effects were observed in polycrystalline CdTe as shown in Fig. 3. In addition, CdTe compensated by doping with In exhibited a negative light effect. This light-induced weakening has still to be explained. The authors thank Dr. L. Carlsson for many stimulating discussions and critical reading of the manuscript. This research was sponsored by the Air Force Office of Scientific Research, Air Force
23°C.
Systems Command, USAF, under Grant No. AFOSR 72-2172. The United States Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation hereon.
REFERENCES 1 M. Inoue, I. Termoto and S. Takayanagi, J. Appl. Phys., 33 (1962) 2578. L. Carlsson and C.N. Ahlquist, J. Appl. Phys., 43 (1972) 2529. 3 E.O. Hall, Proc. Phys. Soc. (London), B64 (1951) 747. 4 N.J. Petch, J. Iron S t e e l Inst. ( L o n d o n ) , 174 (1953) 25. 5 R.W. Armstrong, A d v a n c e s in Materials S c i e n c e IV, Wiley, New York, 1970, p. 101. 6 R.W. Davidge and A.G. Evans, Mater. Sci. Eng., 6 (1970) 281.
Short Communication
The yield strength of polycrystalline CdTe as a function of grain size F. BUCH and C.N. AHLQUIST
Mechanical Engineering Department, University of Colorado, Boulder, Colo. 80302 (U.S.A.)
(Received in revised form March 2, 1973)
The mechanical strength of polycrystalline CdTe is an important factor in determining its
e m p l o y m e n t as a window material. It is expected that relatively fine grained polycrystals
Fig. 1. Typical microstructures of undeformed polycrystalline CdTe (100X).
195
should exhibit enhanced mechanical properties when compared with single crystals. It was the purpose of the present work to experimentally measure the yield strength of polycrystalline CdTe as a function of grain size. Samples approximately 2 × 2 × 3.5 mm were cut from hot pressed CdTe blocks. The loading faces of the samples were masked with stop-off lacquer, and the sides were then polished for 180 see in a solution 1 of 10 ml HNO a, 2 0 m l HzO and 4 g K z C r 2 0 v. This polishing procedure removed approximately 30 pm from each side face of the sample while maintaining the masked loading faces parallel and flat. The masking of the loading faces was done to avoid rounding, which would cause a n o n u n i f o r m load distribution during compression. The grain sizes were determined using the intercept m e t h o d on photomicrographs of u n d e f o r m e d samples, see Fig. 1. The samples were compressed at room temperature (23°C +- 1 deg C) using a model TT Instron machine set at 0.05 m m / m i n crosshead speed. To minimize surface friction, a 30 pm thick Teflon tape was placed between the sample and loading platen. A tungsten filament microscope lamp was focused on the samples after yielding in dark to ascertain whether or not photoplastic effects were present in polycrystalline CdTe as have been observed in single crystal CdTe e. Several samples were tested for each grain size from which a mean yield strength was calculated, see Table 1.
Dislocation pile-up t h e o r y predicts that the yield strength should be inversely proportional to the square root of the average grain diameter 3 -- 5, O=O 0
+Ad-I/2
where oo represents the lattice friction stress and A is a constant*. Figure 2 shows the average yield strength versus d -1/2 for CdTe. These data predict oo = 37.7 N/mm 2 and A = 165
N/mm 2 × pm 1/2 (= 1.65 × 103 Nm--3/2). Since the yield strength is influenced by both grain size and point defect concentration, it would be desirable to normalize the preceding data to a c o m m o n doping level. This is not possible at the present time since the effect of In impurities on yield strength is not known. However, it is known that the yield strength of CdTe is weakly dependent on native point defect concentration 2 and thus we expect the influence of grain size to dominate in the present case. The lattice friction stress, 00, can be independently estimated from the single crystal data of Carlsson 2. Assuming a m i n i m u m impurity concentration of 1 p.p.m. (equivalent to 1016 electrons/cm 3 ) and that these impurities influence the strength of CdTe in the same way as native point defects, we find % = 15 N / m m 21. Taking a typical Schmid factor of 0.5, this predicts a oo = 30.0 N / m m 2 which is in reasonable a ~ e e m e n t with the * A similar r e l a t i o n o b t a i n s in t h e case o f d i s l o c a t i o n initiated cracking w h e r e d = pile-up l e n g t h 6 .
TABLE 1 S u m m a r y o f results Identification
Name Code
A CV 104
B CII82
C CV76
D CII88
Material h i s t o r y
Doping level Dopant Pressing t e m p e r a t u r e Resistivity (~2cm)
10 p . p . m . In 750 °C 6 x 10 s
--750 °C 5 x 10 4
50 p . p . m . In 800 °C 10 7
-750 °C 5 X 105
d--l~2
d (pm) (pm--1/2 )
118.2 0.092
60.4 0.129
55.7 0.134
38.1 0.162
Oy m e a n ( N / m m 2) Oy m e a n (lb./in. 2) Spread* No. o f samples t e s t e d E x p e r i m e n t a l errors Light e f f e c t M a x i m u m light e f f e c t
51.9 7519 19.8% 11 +_4% Neg. --3%
60.8 8808 15.7% 6 +5% Pos. +4.5%
59.9 8674 8.5% 8 ±3% Neg. --2%
63.4 9187 8.5% 8 +-3% Pos. +5%
Grain sizes Test results
* M a x i m u m m i n u s m i n i m u m o b s e r v e d yield s t r e n g t h in % o f m e a n value.
196 O-
%
x I000
O"
~/em2
Ibf~n 2
xlO00
8O
Ib~n2
9
POLYCRYSTALLrNE
/ /
J
CdTe
60
23eC 0.0~ mifl"1
D
50
A ~ /
CdTe
I
0.014
23 °C
it
~ 40" W O~
~ 20"
min - I
$~N6LE CRYSTAL
]
/
40
/ I / /
/ •
o.~5
o~
~,'6 d_~ (.~)
Fig. 2. The 0.05% offset yield strength vs. reciprocal of the square root of the average grain diameter of CdTe tested in compression at 23°C. Each data point represents the average of at least 6 tests.
CROSSHEAD DISPLACEMENT
Fig. 3. Typical flow stress vs. time curves for single and polycrystalline CdTe tested in light and darkness at
value extrapolated from Fig. 2 (o 0 = 37.7 N/ mm 2). Better agreement would be fortuitous in view of the assumptions made in arriving at the estimated ~0 and the experimental error bars in Fig. 2. Single crystal CdTe doped with native point defects exhibits strong increases in strength when tested in light v e r s u s dark 2. Relatively small photoplastic effects were observed in polycrystalline CdTe as shown in Fig. 3. In addition, CdTe compensated by doping with In exhibited a negative light effect. This light-induced weakening has still to be explained. The authors thank Dr. L. Carlsson for many stimulating discussions and critical reading of the manuscript. This research was sponsored by the Air Force Office of Scientific Research, Air Force
23°C.
Systems Command, USAF, under Grant No. AFOSR 72-2172. The United States Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation hereon.
REFERENCES 1 M. Inoue, I. Termoto and S. Takayanagi, J. Appl. Phys., 33 (1962) 2578. L. Carlsson and C.N. Ahlquist, J. Appl. Phys., 43 (1972) 2529. 3 E.O. Hall, Proc. Phys. Soc. (London), B64 (1951) 747. 4 N.J. Petch, J. Iron S t e e l Inst. ( L o n d o n ) , 174 (1953) 25. 5 R.W. Armstrong, A d v a n c e s in Materials S c i e n c e IV, Wiley, New York, 1970, p. 101. 6 R.W. Davidge and A.G. Evans, Mater. Sci. Eng., 6 (1970) 281.