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Third-order elastic constants of indium antimonide at 300° and 80°K
Solid State Communications, Vol. 21, pp. 701—703, 1977.
Pergamon Press.
Printed in Great Britain
THIBD..ORD1~RELASTIC CONSTANTS OF INDIUM ANTIMONID~AT 300°AND ~)0K V. Sundara Raja and P. Jayarama 1~ddy Physics Department, Sri Venkateswara University, Tirupati, India (Revised received 29 November 1976 by A.R. Verma) The six third—order elastic constants of single crystal indium antimonide have boon determined at 3000 and ~Oe)K, using pulse interference technique. ThOUEh there is a slight variation in the constants with change in temperature the variations are not very significant. These are the hrst measurements to be made at R0°K, The six independent third—order elastic constants(TOEC) of single cry— stal indium ~ntimon1dehave been deter— mined at 300 and 80°Kfrom thermea— sured velocities of ultrasonic waves propagated through the unlaxially stressed sample. The pulse interference technique at 10 MHz based 9fl the prin— ciple of Williams and Lamb’ Is employed, The details of this technique have been discussed elsewhere2, The indium antimonide specimen is n—type, ~th a carrier concentration, 1.5 x 1~)’~ electrons~ m~and having a resistivity, 8 x 10 ohm—rn at room temperature. The electrical resistivity Table 1.
(001). The orie~tattons were held to well within 1/3 by X—ray Lane back reflection method. Sufficient care was taken in preparing plane and para].1.1 faces in order b~achieve the desired accuracy In the measurement of transit timeg, X—cut and Y—cut quartz trane— ducere of resonant frequency 10 MHz were used to excite longitudinal and shear waves respectively. To msaaurs the ultrasonic wave velocities at 80°!, the crystal was cooled at a very slow rate, to avoid the breakage of the bond— ing film due to the differential con— traction of the specimen and the trane— ducers. The temperature was measured by
Measured Zero pressure sound wave velocities in single crystal Indlue antimonide at 300°and 80°K
Propagation
Polarisation
Measured velocity in ml see
Velocity
--
direction
direction
300°K
90°K
001
001
2~08.l0
001
110
2284.03
23l~.94
3767.77 2284.1
3R2~,R9 1649.02
V 2 V3
110
110
V4
110
001
‘15
110
l~24.05
V6
110
ilo iTo
V7
110
001
228~.23
23l5.R6
V8
110
110
1624.18
1649.22
2~lF.7l
3767.49
is low enough to assure zero field pro— pagation conditions for this piezoelec— trio material. The crystal ingot with growth direction nearly parallel to ( 111 > , was ground to a rectangular block with external faces (110),O.lo) arid *Pregent address: Department of Agricultural Agricultural College, Tirupati. 701
a copper—constantan thermocouple in conjunction with a potentiometer capa— ble of reading to ±ifr%V. Measurements at room temperature were normalised to 300°K. The adiabatic longitudinal and Chemistry and Physics, S,V.
ELASTIC CONSTANTS OF INDIUM ANTIMONIDE AT 300° AND 80’K
702
shear wave velocities at 3000 and 80°K measured along <0O1>,<1t0> arid directions are shown in Table 1. it is
Vol. 21, No. 8
are averages of a number of pressure runs made with increasing arid decreas— ing stresses. Of these, th. first six modes were used to compute the six
~p(J~~14
)~at 300°ani
Table 2.
Tiniaxial stress
Stress
Propagation
Polarisation
%p
direction
direction
direction
300°K
1 2. 3.
001 001 001
110 110 110
110 110 001
-1.88±0,05 ~i.89±0.04 +0.87±0.02
-1.83±0.05 ~l.8R±0.o4 +0.86±0.02
4. 5. 6,
110 110 110
110 110 110
110 110 001
~0,74~004 -0.85±0.03 +0.28±0.02
+0.83±0.05 -0.86±0.02 +0.30±0.02
7. 8, 9.
110 110 110
001 001 001
001 110 110
~2,29~O.06 —1.23±0.05 -0.22±0.03
+2.40±0.07 -l.2~0.05 -0.21±0.02
i~xpt. N0,
derivatIves
seen that there is a good degree of internal consistency among the measured velocities. to calculate These second—order velocitieselastic are used con~ stants. In order to determine TOEC, the crystal was stressed normal to the direc —tion of propagation and the natural velocity3 W ‘ was measured as a func— tion of applied uniaxial stress. The Table
~.
R0°K
(F0w~)~_0 80°K
Independent TOEC using the explicit 3 and the other three wereandused relations develored by Thruston Brugger for a cross check. The TOEC obtained at 800 and 3000K are presented in Table 3 along with associated errors. It is seen that though there is an increase In the magnitude of ~he conat— ants as we go from 3000 to 80 K, the
Third order elastic constants of Indium antimonide at 800 and 200°K (In units of Present study
Constant
io~N.tn”2). Drabble and Brarniner
--
(Room
temperature).
C 111
—3.71±0.38
—2.56±0.36
—3.l’1±0.2
c112
-2.83±0.19
-2.66±0.15
-2,lotr).2
C123
—1.15±0,12
—1.00±0.11
.-0.48±0.l
C144
~0.21±0,13
~0.l6t0.l2
+009~01
0166
—1.41±0.08
-1.39±0.08
—1,18±0.1
C456
+0.03±0.06
-0.004±0.07
~o.002~o.o1
2 calculated from the variation is not very significant. The measured as a function of changes involved in most of the con— quantity, velocity W applied uniaxial stress was linear upto stants are within the experimental the highest stress employed. The den— errors. Even in the case of germanium sity 1~0 In the unstre~sed stateAwas the variation in TOEC ac the temperature taken as 5.7747 kg/rn° at 25~’C . The changed from 300° to 80”K was not very uniaxial stress derivatives %~(Aw~)~... 0 significant. The earlier measurement of thus obtained for the nine possible TOEC at6room temperature by Drabbie and modes with different directions of Brammer using an Improved version of propagation, polarisation and applied sing around technique are also Included stress are shown in Table 2. The slopes in Table 3 for comparison. The agree—
P0
Vol. 21, No. 8
ELASTIC CONSTANTS OF
INDIUM
ANTIMONIDE AT
3000
AND
80°K
merit is quite satisfactory inspite of the fact that the measurements were made with different techniques on d~ffe— rent specimens. No comparison at 80 K has been possible since these are the
made on indium antimonide at this temperature.
first measurements, we believe, to be
Industrial Research, for the award of
Acknowledgement— One of us (VS) is thankful to Council of Scientific and Junior Research Fellowship.
RE~F3RSNC3S WILLIAMS 3 and LAMB 3,, 3. Acoust. Soc. Am. ~Q, 308 (1958). SA~AV.P.N. and BEDDY P.3., Phys. Stat, SolIdi. (a) ~, 562 (l9’2). 3, THRTJSTON R.N. and BR~JGGERK., Phys. Rev, ~, A i6O~ (1964). 1 2
4, STPAUMANIS M.E. and KIM D,, 3, Appi. Phys. ~, 3822 (1965). 5. DRABBLB~ J.R. and F~NDLEY 3., 3. Ph~, Chem. Solids, 6f~9 (1967). 6~DRABBLE J.R. and BRAMM~ A.J., Proc. Phys. Soc, ~21, 959 (l9~7).
~.a,
703
Pergamon Press.
Printed in Great Britain
THIBD..ORD1~RELASTIC CONSTANTS OF INDIUM ANTIMONID~AT 300°AND ~)0K V. Sundara Raja and P. Jayarama 1~ddy Physics Department, Sri Venkateswara University, Tirupati, India (Revised received 29 November 1976 by A.R. Verma) The six third—order elastic constants of single crystal indium antimonide have boon determined at 3000 and ~Oe)K, using pulse interference technique. ThOUEh there is a slight variation in the constants with change in temperature the variations are not very significant. These are the hrst measurements to be made at R0°K, The six independent third—order elastic constants(TOEC) of single cry— stal indium ~ntimon1dehave been deter— mined at 300 and 80°Kfrom thermea— sured velocities of ultrasonic waves propagated through the unlaxially stressed sample. The pulse interference technique at 10 MHz based 9fl the prin— ciple of Williams and Lamb’ Is employed, The details of this technique have been discussed elsewhere2, The indium antimonide specimen is n—type, ~th a carrier concentration, 1.5 x 1~)’~ electrons~ m~and having a resistivity, 8 x 10 ohm—rn at room temperature. The electrical resistivity Table 1.
(001). The orie~tattons were held to well within 1/3 by X—ray Lane back reflection method. Sufficient care was taken in preparing plane and para].1.1 faces in order b~achieve the desired accuracy In the measurement of transit timeg, X—cut and Y—cut quartz trane— ducere of resonant frequency 10 MHz were used to excite longitudinal and shear waves respectively. To msaaurs the ultrasonic wave velocities at 80°!, the crystal was cooled at a very slow rate, to avoid the breakage of the bond— ing film due to the differential con— traction of the specimen and the trane— ducers. The temperature was measured by
Measured Zero pressure sound wave velocities in single crystal Indlue antimonide at 300°and 80°K
Propagation
Polarisation
Measured velocity in ml see
Velocity
--
direction
direction
300°K
90°K
001
001
2~08.l0
001
110
2284.03
23l~.94
3767.77 2284.1
3R2~,R9 1649.02
V 2 V3
110
110
V4
110
001
‘15
110
l~24.05
V6
110
ilo iTo
V7
110
001
228~.23
23l5.R6
V8
110
110
1624.18
1649.22
2~lF.7l
3767.49
is low enough to assure zero field pro— pagation conditions for this piezoelec— trio material. The crystal ingot with growth direction nearly parallel to ( 111 > , was ground to a rectangular block with external faces (110),O.lo) arid *Pregent address: Department of Agricultural Agricultural College, Tirupati. 701
a copper—constantan thermocouple in conjunction with a potentiometer capa— ble of reading to ±ifr%V. Measurements at room temperature were normalised to 300°K. The adiabatic longitudinal and Chemistry and Physics, S,V.
ELASTIC CONSTANTS OF INDIUM ANTIMONIDE AT 300° AND 80’K
702
shear wave velocities at 3000 and 80°K measured along <0O1>,<1t0> arid
Vol. 21, No. 8
are averages of a number of pressure runs made with increasing arid decreas— ing stresses. Of these, th. first six modes were used to compute the six
~p(J~~14
)~at 300°ani
Table 2.
Tiniaxial stress
Stress
Propagation
Polarisation
%p
direction
direction
direction
300°K
1 2. 3.
001 001 001
110 110 110
110 110 001
-1.88±0,05 ~i.89±0.04 +0.87±0.02
-1.83±0.05 ~l.8R±0.o4 +0.86±0.02
4. 5. 6,
110 110 110
110 110 110
110 110 001
~0,74~004 -0.85±0.03 +0.28±0.02
+0.83±0.05 -0.86±0.02 +0.30±0.02
7. 8, 9.
110 110 110
001 001 001
001 110 110
~2,29~O.06 —1.23±0.05 -0.22±0.03
+2.40±0.07 -l.2~0.05 -0.21±0.02
i~xpt. N0,
derivatIves
seen that there is a good degree of internal consistency among the measured velocities. to calculate These second—order velocitieselastic are used con~ stants. In order to determine TOEC, the crystal was stressed normal to the direc —tion of propagation and the natural velocity3 W ‘ was measured as a func— tion of applied uniaxial stress. The Table
~.
R0°K
(F0w~)~_0 80°K
Independent TOEC using the explicit 3 and the other three wereandused relations develored by Thruston Brugger for a cross check. The TOEC obtained at 800 and 3000K are presented in Table 3 along with associated errors. It is seen that though there is an increase In the magnitude of ~he conat— ants as we go from 3000 to 80 K, the
Third order elastic constants of Indium antimonide at 800 and 200°K (In units of Present study
Constant
io~N.tn”2). Drabble and Brarniner
--
(Room
temperature).
C 111
—3.71±0.38
—2.56±0.36
—3.l’1±0.2
c112
-2.83±0.19
-2.66±0.15
-2,lotr).2
C123
—1.15±0,12
—1.00±0.11
.-0.48±0.l
C144
~0.21±0,13
~0.l6t0.l2
+009~01
0166
—1.41±0.08
-1.39±0.08
—1,18±0.1
C456
+0.03±0.06
-0.004±0.07
~o.002~o.o1
2 calculated from the variation is not very significant. The measured as a function of changes involved in most of the con— quantity, velocity W applied uniaxial stress was linear upto stants are within the experimental the highest stress employed. The den— errors. Even in the case of germanium sity 1~0 In the unstre~sed stateAwas the variation in TOEC ac the temperature taken as 5.7747 kg/rn° at 25~’C . The changed from 300° to 80”K was not very uniaxial stress derivatives %~(Aw~)~... 0 significant. The earlier measurement of thus obtained for the nine possible TOEC at6room temperature by Drabbie and modes with different directions of Brammer using an Improved version of propagation, polarisation and applied sing around technique are also Included stress are shown in Table 2. The slopes in Table 3 for comparison. The agree—
P0
Vol. 21, No. 8
ELASTIC CONSTANTS OF
INDIUM
ANTIMONIDE AT
3000
AND
80°K
merit is quite satisfactory inspite of the fact that the measurements were made with different techniques on d~ffe— rent specimens. No comparison at 80 K has been possible since these are the
made on indium antimonide at this temperature.
first measurements, we believe, to be
Industrial Research, for the award of
Acknowledgement— One of us (VS) is thankful to Council of Scientific and Junior Research Fellowship.
RE~F3RSNC3S WILLIAMS 3 and LAMB 3,, 3. Acoust. Soc. Am. ~Q, 308 (1958). SA~AV.P.N. and BEDDY P.3., Phys. Stat, SolIdi. (a) ~, 562 (l9’2). 3, THRTJSTON R.N. and BR~JGGERK., Phys. Rev, ~, A i6O~ (1964). 1 2
4, STPAUMANIS M.E. and KIM D,, 3, Appi. Phys. ~, 3822 (1965). 5. DRABBLB~ J.R. and F~NDLEY 3., 3. Ph~, Chem. Solids, 6f~9 (1967). 6~DRABBLE J.R. and BRAMM~ A.J., Proc. Phys. Soc, ~21, 959 (l9~7).
~.a,
703