Low-frequency acoustics in solid ${}^4\text{H}\text{e}$ at low temperature

The elastic properties of hcp ${}^4\text{H}\text{e}$ samples have been investigated using low-frequency (20 Hz to 20 kHz) high sensitivity sound transducers. In agreement with the findings of other workers, most samples studied grew very significantly stiffer at low temperature; Poisson’s ratio $\nu$ was observed to increase from 0.28 below 20 mK to $\sim 0.35$ at 0.7 K. The span of the variation in $\nu$ varies from sample to sample according to their thermal and mechanical history. Crystals carefully grown at the melting curve show a different behavior, the change in $\nu$ taking place at lower $T$ and being more abrupt.

Figure 1

(Color online) Schematic drawing of the acoustic cell, The displacement gauge is located at the top and the piezoelectric transducer at the bottom. The drawing is approximately to scale, except for the cut that makes it appear shrunk vertically.

Figure 2

(Color online) Reduced uniaxial compression modulus $M\left(T\right)/M\phantom{(}\left(0.03\right))$ in terms of the temperature, in kelvin. The curves that extend to above 0.55 K pertain to a typical BC sample at a molar volume of $20.45{\text{cm}}^3$ subjected to different thermal histories (bottom curve, fast cooling, top curve, slow cooling followed by rapid warming to 1.05 K), the two remaining curves to two CT samples, grown at 0.8 K (top) and 1.1 K (truncated at 0.15 K) and slowly cooled. The arrow marks the curve break referred to in the text.

Figure 3

(Color online) Acoustic spectra at various temperatures for a QC sample with molar volume $20.45{\text{cm}}^3$; left $y$ axis, relative diaphragm displacement $z_{\text{d}}$ in picometers; right $y$-axis, temperature in Kelvin on a logarithmic scale; $x$ axis, frequency in Hertz. Below 200 mK, the resonance line splits and develops wiggles; a satellite also develops to the left of the main peak.

Figure 4

(Color online) Acoustic resonance peak frequency vs temperature for several BC samples: C1, quenched, same as in Fig. 3; C2, $20.63{\text{cm}}^3$ per mole, slowly cooled, C2a, after thermal shock; C3, $20.06{\text{cm}}^3$ per mole. This last sample exhibits three resonance peaks, one of which disappears below $\sim 0.2\text{K}$.