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Submitted on 1 Jan 1978
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PHONON TRANSMISSION THROUGH THE SOLID
4He-LIQUID 4He INTERFACE
Sebastien Balibar, C. Laroche, A. Libchaber
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, supplement au n° 8, Tome 39, aout 1978, page C6-248
PHONON TRANSMISSION THROUGH T H E SOLID 4H e - L I Q U I D 4H e INTERFACE
S. Balibar, C. Laroche and A. Libchaber
Groupe de Physique des Solides de I'Eoole Normale Supeviei&e 24 rue Lhamond, 75231 Paris Cedex 05 FRANCE.
Résumé.- Dans des expériences d'impulsions de chaleur, nous avons observé la transmission de phonons balistiques à travers l'interface He solide - He liquide. Les trois modes du solide sont couplés au mode unique du liquide. Nous proposons quelques idées pour interpréter l'amplitude des signaux observés.
Abstract.- Using a heat pulse technique, we observe the transmission ballistic phonons through the solid **He - liquid "*He interface. The three modes of the solid are coupled to the one of the liquid. Some ideas are proposed in order to interpret the amplitude of the observed signals.
We present here preliminary experiments which have been made possible by a specially favorable design of the filling capillary in our dilution re-frigerator : it allows us to grow slowly (! mm/ran) a ''He monocrystal by pressurizing the experimental cell at a constant temperature below 100 mK. The crystal grows in the hydrostatic pressure gradient starting at the bottom of the cell, and the super-fluid makes the temperature very homogeneous so that the solid-liquid interface is probably very horizontal and flat. By pressurizing slowly, or by letting the Helium gas leak slowly, one can easily control the position of this interface with an accuracy of .1 mm. The quality of the crystal does not depend on how many times it has been partly melted or recrystallized.
As schematized in the upper right corner of Fig. 1, two Cu heaters and Zn bolometers are placed in the cell, in order to propagate heat pulses through the interface. The detection technique has already been described elsewhere /l/, and Fig. 1 shows typical recordings of the signal obtained at 58 mK by emitting a,1 erg pulse (20 mW x 5 s) down-wards from the liquid side. The different curves correspond to different levels of the interface, which goes from below the bolometer (curve 1,x < 0)
up to above the heater (curve 8, x > L = 10.5 m m ) . The total heater bolometer distance L is 10.5 mm, in accordance with a velocity of 365 m s- 1 for the liquid phonons (curve 1). The three modes on curve 8 propagate respectively at 477 m s_ 1( L ) , 312 m s- 1 (FT) and 241 m s- 3 (ST), indicating a crystal with a vertical axis 43 ± 2° from the c axis /2/. Curves 2 to 7 show that the longitudinal mode of the liquid can emit the 3 modes of the solid at the interface.
We have obtained similar results by propagating the heat pulse upside down, i.e. from the solid into the liquid.
- . — • — i • i • _ _ • i •.
10 50 T(j|s)
Fig. I : Transmitted signal from the liquid into the solid(heater l, bolometer l) as a function of time. The parameter x is the height of the solid in millimeters above the level of the bolometer I (see upper right corner). The heater-bolometer distance L is 10.5 mm. It is full of liquid for curve I, full of solid for curve 8, partly solid and liquid for curves 2 •*• 7. The notations L, FT, ST refer to longitudinal, fast transverse and slow transverse modes in the solid.
We have summarized on Fig. 2 the variation with the solid height x of the peak amplitude of the signal obtained in a few preliminary experiments :
Fig. 2A corresponds to the L mode and 2B to the ST mode in the solid, the indication L-*S or S+L
referring to the direction of propagation. The main 2 transverse phonons. features shown on this figure are :
1'
-
The amplitude of the longitudinal signal on Fig. 2A is a decreasing function of X (roughlyReferences X
exp
-
=), the same for both directions of propa-/ l / Balibar, S. et al., Phys. Rev. B
17,
(1978).gation (S+L or L+S)
.
2'
-
In the case (Fig. 2B) of slow transverse pho-/ 2 / The sound velocity has been taken in Crepeau, nons in the solid coupled to longitudinal phonons R.H. et al. Phys. Rev. A?, (1971) 1162. in the liquid, the signal increases in the L+S case.
and decreases in the S+L case. This seems to indi- cate some irreversible processes taking place at the interface in this case. The two opposite directions of variations can be obtained, for example, by sup- posing isotropic emission and reception and an iso- tropic diffuse transmission at the interface.
Fig. 2 : Transmitted signal as a function of the height X of solid. Fig. 2A corresponds to the longi- tudinal mode, and Fig. 2 B to the slow transverse mode in the solid, both coupled to the liquid mode. The notations S+L or L+S refer to the direction of propagation (solid+liquid or liquid+solid). T is the temperature in mK, P and t the power and the width of the pulse, tl the angle between the verti- cal and the c axis of the crystal. A few typical error bars are indicated.
In opposition, a transmission following the refraction laws gives the same variation for both directions (it is reversible), and we are tempted to conclude that it is the case forthecoupling of longitudinal solid phonons to longitudinal liquid phonons :
The variation of the signal on Fig. 2A has the same slope for the L+S and S+L cases. Moreover, this slope seems temperature independent, and this sug- gests a variation due to a finite mean free path
