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Hypersound velocities of solid argon
Solid State Communications,
Vol. 7, pp. 1745—1747, 1969.
Pergamon Press.
Printed in Great Britain
HYPERSOUND VELOCITIES OF SOLID ARGON G. Nath and M. Gsänger Physik Department der Technischen Hochschule Miinchen
Longitudinal sound velocities in solid Argon at 76.8°K have been determined by means of SBS. Relative threshold powers of SBS in solid and liquid Argon are reported.
SOUND velocity measurements on rare gas solids are of great interest because they may give information about the anharmonic potential. ~ rare gas solids many special problems arise if one uses conventional pulse ecboe techniques. The high vapor pressure at the triple point and the large coefficient of expansivity of these substances make the coupling of the transducers to the crystal extremely difficult. Moreover one has to determine precisely the distance between the transducers at low temperatures. Stimulated Brillouin scattering measurements in the backward direction are technically simpler. One has the advantage of access to the sample container through a warm window. Access to the sample is reduced to the problem of preparing one single transparent surface for the beam. When lasers
The backscattered Rrillouin light was detected photographically by means of a Fabry—Pérot spectrometer. (Dispersion range 1/2d = 0.332cmt Former growth experiments2 under similar conditions showed presence of single crystalline grains of 3—4 mm in diameter and preferential growth in [100] direction. By varying the position of the focus throughout the volume of the crystal one should expect different orientations in axis direction. We always found one single sharp Brillouin line. Using this line we thus measured the velicities in single crystalline grains of various orientation, whereas the pulse echoe technique would give the mean sound velocity in the randomly oriented grains between the transducers. The optically determined sound velocity V 1 is given by
with high mode purity are used under carefully controlled operational conditions, the error of the velocity determination can be made as small as a few tenths of 1 per cent.’
Ay
=
XL
A y as measured from the Fabry—Pérot pattern turned out to be 5 Gc. With our multimode laser
Three argon polycrystals have been investigated at 76.8°K. The samples were grown hemispherically from the liquid phase with a growth rate of about 5 mm/hr. They were 4cm in length and 3.5cm inFigure diameter and were transparent. 1 shows our completely experimental setup. A thin liquid layer at the top was made by flushing the solid with clean nitrogen gas. This layer acted as an index match, making the surface of the crystal transparent for the laser beam. Our ruby laser had a peak power of about 100 MW/cm 2•
V1 could only be determined with a resolution of ± 2.5 per cent, which is comparable to the error which we obtained with transducer tech3 The velocity spread lies fairly well within niques at 10the Mc.extremum values given by these measurements (Table 1). At 85°K we observed SBS in liquid argon. The resulting sound velocity agrees with the value reported by Lim et al.4 1745
1746
HYPERSOUND VELOCITIES OF SOLID ARGON
Vol.7, No.24
Loserbeam
/
~omsplitter~, GP
<
~L2 I
•
FR
1 f~~Ocm
GP: Ar(l)
Ground Gloss
C : Camera Ar(l): Liquid Layer of Ar
r(s)
TA
C
L1,2: Lenses FR: Fabry -P4rot -Interferometer (Spacing 1,5 cm)
25
W
Ar(s): Solid Argon N2(L): Liquid Nitrogen W: Plane Window
N211)
FIG.
L
>:
Growth direction
1. Schematic diagram of experimental arrangement.
Table 1. Various data for solid and liquid argon. Solid argon (76.8°K)
Liquid argon (85°K)
p
1.6451 g/cm ~ (Ref 6)
1.401 g/cm ~ (Ref 4)
n (5893 A)
1.271 (Ref 7)
1.231 (Ref 8)
0.2834
0.2630
5.32. 10~cgs
4.03. lO
(1357
...
1427 ±29) rn/s (Ref 3)
(853.0 ±0.02) rn/sec (Ref 4)
(1377
...
1453 ±35) rn/s
(850 ±20) rn/sec
Elasto-optical coefficients = (,~2 1)(nz + 2) —
3~4
Elasto-optical parameters (Ref 5) p pV, .n
5cgs
V 1 V1 (5Gc) (this work)
With our device we determined the threshold power for SBS in liquid argon and2 quartz in the glass. unWe found laser it to be 35 ±10MW/cm focussed beam for both substances. The threshold in solid argon was about 2 times higher
than that of the liquid, putting the ratio in only qualitative agreement the existing of elasto-optic parameterswith ~ (Table 1). Thistheory may be due to light scattering at the uneven solid liquid interface. As is well known, giant pulse lasers
Vol.7, No.24
HYPERSOUND VELOCITIES OF SOLID ARGON
with passive Q-switch sometimes emit two or three giant pulses of different frequencies with delays of about 107_106 sec. In this case the Brillouin lines on the Fabry—Pérot records had doublet or triplet structure, demonstrating the possibility of generating SBS without damage in the interior of the crystal. We feel that SBS is a good tool for precise determinations of longitudinal sound velocities of dielectric crystals with low melting points like the rare gas solids, because of its technical simplicity. Moreover it is superior to other tech-
1747
niques when large single crystals are not available. One can also obtain information about the anisotropy of the longitudinal sound velocity when coarse grained samples are available. We are working to extend our measurements to lower temperatures, to use oriented single crystals of argon and to use a single mode laser. Acknowledgements The authors are grateful to Prof. K. Dransfeld, Prof. E. Lüscher, W. Heinicke and G. Winterling for helpful discussions and H. Egger and H. Meixner for experimental assistance. —
This work was partly supported by the Deutsche Forschungsgomeinschaft.
REFERENCES 1.
GOLDBLATT N.R. and LITOWITZ T.A., J. acoust. Soc. Am. 41, 1301 (1967).
2. 3.
GSANGER M., EGGER H., FRITSCH G. and LUSCHER E., Z. angew. Phys. 26, 334 (1969). GSANGER M., EGGER H. and LUSCHER E., Phys. Lett. 27A, 695 (1968).
4.
LIM C.C. and AZIZ R.A., Can. J. Phys. 45, 1275 (1967).
5.
PINE A.S., Phys. Rev. 149, 1113 (1966).
6. 7. 8.
PETERSON O.G., BATCHELDER D.N. and SIMMONS R.O., Phys. Rev. 150, 703 (1966). EATWELL A.J. and JONES G.O., Phil. Mag. 10, 1059 (1964). JONES G.O. and SMITH B.L., Phil. Mag. 5, 355 (1960).
Mit stimulierter Brillouinstreuung wurden longitudinale Schallgeschwindigkeiten von festem Argon bei 76,8°K gemessen und die relativen Schwellwerte für SBS in festem und filissigem Argon bestimmt.
Vol. 7, pp. 1745—1747, 1969.
Pergamon Press.
Printed in Great Britain
HYPERSOUND VELOCITIES OF SOLID ARGON G. Nath and M. Gsänger Physik Department der Technischen Hochschule Miinchen
Longitudinal sound velocities in solid Argon at 76.8°K have been determined by means of SBS. Relative threshold powers of SBS in solid and liquid Argon are reported.
SOUND velocity measurements on rare gas solids are of great interest because they may give information about the anharmonic potential. ~ rare gas solids many special problems arise if one uses conventional pulse ecboe techniques. The high vapor pressure at the triple point and the large coefficient of expansivity of these substances make the coupling of the transducers to the crystal extremely difficult. Moreover one has to determine precisely the distance between the transducers at low temperatures. Stimulated Brillouin scattering measurements in the backward direction are technically simpler. One has the advantage of access to the sample container through a warm window. Access to the sample is reduced to the problem of preparing one single transparent surface for the beam. When lasers
The backscattered Rrillouin light was detected photographically by means of a Fabry—Pérot spectrometer. (Dispersion range 1/2d = 0.332cmt Former growth experiments2 under similar conditions showed presence of single crystalline grains of 3—4 mm in diameter and preferential growth in [100] direction. By varying the position of the focus throughout the volume of the crystal one should expect different orientations in axis direction. We always found one single sharp Brillouin line. Using this line we thus measured the velicities in single crystalline grains of various orientation, whereas the pulse echoe technique would give the mean sound velocity in the randomly oriented grains between the transducers. The optically determined sound velocity V 1 is given by
with high mode purity are used under carefully controlled operational conditions, the error of the velocity determination can be made as small as a few tenths of 1 per cent.’
Ay
=
XL
A y as measured from the Fabry—Pérot pattern turned out to be 5 Gc. With our multimode laser
Three argon polycrystals have been investigated at 76.8°K. The samples were grown hemispherically from the liquid phase with a growth rate of about 5 mm/hr. They were 4cm in length and 3.5cm inFigure diameter and were transparent. 1 shows our completely experimental setup. A thin liquid layer at the top was made by flushing the solid with clean nitrogen gas. This layer acted as an index match, making the surface of the crystal transparent for the laser beam. Our ruby laser had a peak power of about 100 MW/cm 2•
V1 could only be determined with a resolution of ± 2.5 per cent, which is comparable to the error which we obtained with transducer tech3 The velocity spread lies fairly well within niques at 10the Mc.extremum values given by these measurements (Table 1). At 85°K we observed SBS in liquid argon. The resulting sound velocity agrees with the value reported by Lim et al.4 1745
1746
HYPERSOUND VELOCITIES OF SOLID ARGON
Vol.7, No.24
Loserbeam
/
~omsplitter~, GP
<
~L2 I
•
FR
1 f~~Ocm
GP: Ar(l)
Ground Gloss
C : Camera Ar(l): Liquid Layer of Ar
r(s)
TA
C
L1,2: Lenses FR: Fabry -P4rot -Interferometer (Spacing 1,5 cm)
25
W
Ar(s): Solid Argon N2(L): Liquid Nitrogen W: Plane Window
N211)
FIG.
L
>:
Growth direction
1. Schematic diagram of experimental arrangement.
Table 1. Various data for solid and liquid argon. Solid argon (76.8°K)
Liquid argon (85°K)
p
1.6451 g/cm ~ (Ref 6)
1.401 g/cm ~ (Ref 4)
n (5893 A)
1.271 (Ref 7)
1.231 (Ref 8)
0.2834
0.2630
5.32. 10~cgs
4.03. lO
(1357
...
1427 ±29) rn/s (Ref 3)
(853.0 ±0.02) rn/sec (Ref 4)
(1377
...
1453 ±35) rn/s
(850 ±20) rn/sec
Elasto-optical coefficients = (,~2 1)(nz + 2) —
3~4
Elasto-optical parameters (Ref 5) p pV, .n
5cgs
V 1 V1 (5Gc) (this work)
With our device we determined the threshold power for SBS in liquid argon and2 quartz in the glass. unWe found laser it to be 35 ±10MW/cm focussed beam for both substances. The threshold in solid argon was about 2 times higher
than that of the liquid, putting the ratio in only qualitative agreement the existing of elasto-optic parameterswith ~ (Table 1). Thistheory may be due to light scattering at the uneven solid liquid interface. As is well known, giant pulse lasers
Vol.7, No.24
HYPERSOUND VELOCITIES OF SOLID ARGON
with passive Q-switch sometimes emit two or three giant pulses of different frequencies with delays of about 107_106 sec. In this case the Brillouin lines on the Fabry—Pérot records had doublet or triplet structure, demonstrating the possibility of generating SBS without damage in the interior of the crystal. We feel that SBS is a good tool for precise determinations of longitudinal sound velocities of dielectric crystals with low melting points like the rare gas solids, because of its technical simplicity. Moreover it is superior to other tech-
1747
niques when large single crystals are not available. One can also obtain information about the anisotropy of the longitudinal sound velocity when coarse grained samples are available. We are working to extend our measurements to lower temperatures, to use oriented single crystals of argon and to use a single mode laser. Acknowledgements The authors are grateful to Prof. K. Dransfeld, Prof. E. Lüscher, W. Heinicke and G. Winterling for helpful discussions and H. Egger and H. Meixner for experimental assistance. —
This work was partly supported by the Deutsche Forschungsgomeinschaft.
REFERENCES 1.
GOLDBLATT N.R. and LITOWITZ T.A., J. acoust. Soc. Am. 41, 1301 (1967).
2. 3.
GSANGER M., EGGER H., FRITSCH G. and LUSCHER E., Z. angew. Phys. 26, 334 (1969). GSANGER M., EGGER H. and LUSCHER E., Phys. Lett. 27A, 695 (1968).
4.
LIM C.C. and AZIZ R.A., Can. J. Phys. 45, 1275 (1967).
5.
PINE A.S., Phys. Rev. 149, 1113 (1966).
6. 7. 8.
PETERSON O.G., BATCHELDER D.N. and SIMMONS R.O., Phys. Rev. 150, 703 (1966). EATWELL A.J. and JONES G.O., Phil. Mag. 10, 1059 (1964). JONES G.O. and SMITH B.L., Phil. Mag. 5, 355 (1960).
Mit stimulierter Brillouinstreuung wurden longitudinale Schallgeschwindigkeiten von festem Argon bei 76,8°K gemessen und die relativen Schwellwerte für SBS in festem und filissigem Argon bestimmt.