Journal of Low Temperature Physics, Vol. 136, Nos. 1/2, July 2004 ( 2004)

Liquid Helium up to 160 bar

F. Werner, G. Beaume, A. Hobeika, S. Nascimbe`ne,C. Herrmann, F. Caupin, and S. Balibar*

Laboratoire de Physique Statistique de lEcole Normale Superieure, associe aux UniversitesParis 6 et 7 et au CNRS, 24 Rue Lhomond, 75231 Paris Cedex 05, France

E-mail: balibar@lps.ens.fr

(Received December 19, 2003; revised April 10, 2004)

We have used an acoustic technique to pressurize liquid helium 4 up to 163 20 bar. This is far above the liquidsolid equilibrium pressure Pm, whichis 25.3 bar in the low, temperature domain, where the experiment was per-formed (0.05K

94 F. Werner et al.

away from any wall. The static pressure Pstat in the experimental cell wasclose to 25 bar, and the positive swings of the waves were as large as140 bar. This amplitude was far more than necessary to produce cavitationin the negative swings of the wave. The calibration of the wave amplitudewas obtained by studying the dependence of the cavitation threshold onthe static pressure in the cell, as explained in a previous publication.4

When reaching 163 bar, we have achieved a much larger overpressurethan ever done before. If liquid helium is compressed in ordinary cells,heterogeneous nucleation of helium crystals occurs a few millibars onlyabove the liquidsolid equilibrium pressure Pm = 25.3 bar.5 Balibar et al.1

suggested that this was due to the presence of graphite dust particles inordinary cells. On a clean glass plate, Chavanne et al.2,3 found that nucle-ation of crystals occurred 4.3 bar above Pm and showed that it took placeon one particular defect at the surface of the glass. After removing theglass plate from Chavannes setup, we expected this nucleation to occurnear 65 bar, the prediction from the standard homogeneous nucleation the-ory.6 Our results show that the standard theory fails to predict the nucle-ation pressure of solid helium.

In this article, we rst present experimental techniques, including thecalibration method from an analysis of cavitation (Section 2). In Section 3we describe our search for the nucleation of crystals. At the end ofthis article, we discuss possible reasons why the standard nucleation the-ory fails. We also discuss the possible existence of an instability around200 bar,7 and how we could reach it. In fact, our experiments explore anew region in the phase diagram where the properties of metastable liquidhelium are rather unknown. Of particular interest is the pressure variationof its superuid transition temperature.

2. EXPERIMENTAL METHOD

The present results were obtained with an experimental setup similarto the one previously used by Chavanne et al.2,3 We have focused burstsof 1MHz acoustic waves and studied the possible nucleation of bubblesor crystals by shining laser light through the acoustic focal region (seeFig. 1), a technique which was rst introduced by Nissen et al.8 The soundemitter was the same hemispherical piezoelectric transducer as in Refs. 2and 3. In Refs. 2 and 3, the transducer was pressed against a glass platein order to measure the instantaneous density, i.e. the sound amplitudeat the focus. In the course of this former study, it was veried that thesize of the acoustic focal region was one acoustic wavelength, 0.36mmin liquid helium at Pm = 25.3 bar. The threshold pressure for the nucle-ation of helium crystals was found to be P =Pm +4.3bar. When the pres-

Liquid Helium up to 160 bar 95

Fig. 1. The present experimental setup is only slightly modied with respect to the one usedby Chavanne et al.3. A hemispherical piezoelectric transducer emits and focuses bursts ofultrasound at its center. A green Ar+ laser is used to detect the possible nucleation of bub-bles by the negative swings or crystals by the positive swings at the acoustic focus.

sure exceeded this pressure during the positive swings of the acoustic wave,crystals grew with a large velocity before melting during the following neg-ative swing.9 The observed growth velocity was a signicant fraction of thesound velocity, so that crystals could grow up to several microns in timesof order 100 ns, a fraction of the sound period. The details of the growthand melting mechanisms were not fully understood,9 but the ability ofhelium crystals to grow very fast from superuid helium at low enoughtemperature is well known.1012

Chavanne et al. showed that the light scattering technique was a fastdetection method, sensitive enough to detect crystals of micrometer size,not only bubbles.3 As compared to the experiments by Caupin et al.,4

Chavannes detection sensitivity had been improved by focusing the lightat the acoustic focus with a lens inside the experimental cell (see Fig. 1).As done in the present work, Chavanne et al. detected the light transmit-ted through the acoustic focal region with a photomultiplier tube (PMT)whose response time was of order 100 ns. In the focal region, the highintensity acoustic wave scatters light at small angle, so that more andmore light is missing in the forward direction as the acoustic amplitude isincreased. Bubbles or crystallites scatter light more strongly and at largerangle. In order to detect nucleation, one could measure either a decreasein the intensity of light along the optical axis in the forward direction oran increase in light intensity a few degrees away from this axis (see Fig. 2).Some nucleation events were detected with a larger signal to noise ratioaway from the axis, but detecting in the forward direction guaranteed thatno nucleation event was missed. A clear signature of the sound amplitudereaching a nucleation threshold was the observation of a random changeto a different shape of the scattered light amplitude.4 This is because the

96 F. Werner et al.

10 15 20 25 30

PMT

signa

l (ar

b. un

its)

time (microseconds)

transmitted light

scattered light

0 5

Fig. 2. Two recordings showing the detection of acoustic cavitation in liquid helium at 25 barand 55mK. A photomultiplier tube (PMT) detects either a decrease in the light transmittedthrough the acoutic focus or an increase of the light scattered by the bubbles away from theoptical axis.

nucleation itself is a random process; the threshold is dened by the soundamplitude which corresponds to a cavitation probability of one-half.

Knowing that, if present, crystals were easy to detect with this setup,we removed Chavannes glass plate and tried to increase the amplitude ofthe sound wave as much as possible, looking for the homogeneous nucle-ation threshold. We started by exciting the transducer at its resonance fre-quency in its fundamental thickness mode (1.013 MHz). We used burstsof 36 oscillations with a repetition rate of 15Hz. For their amplica-tion, we rst used a linear amplier (see Fig. 4), which delivered a voltageamplitude up to 70V on 50 ; the envelope of the bursts was square (seeFig. 3) and the stability was very good (0.1% over several hours, thanks toa temperature regulation of the box containing it). We then used a tunedamplier which was more powerful (up to 265V amplitude) but which hadless stability and some distortion of the burst envelope (Fig. 5).

The upper trace in Fig. 3 shows the excitation voltage applied to thetransducer when using the linear amplier. The lower trace shows a typi-cal signal detected by the PMT when the applied voltage exceeded the cav-

Liquid Helium up to 160 bar 97

-50

0

50

0 5 10 15 20 25 30 35

Exci

tatio

n (V

olt)

Time (microseconds)

Sign

al (a

rb. u

nits)

Fig. 3. The upper trace is a recording of the voltage applied to the transducer. It is a burstof six oscillations at 1.013MHz, the resonance frequency in the thickness mode. The lowertrace shows the amplitude of the scattered light detected by the PMT. The delay of the cav-itation event is due to the ight time of the sound wave from the transducer surface to theacoustic focus. We have carefully analyzed this delay (see text).

itation threshold. In this particular case, the PMT was located off axis soas to detect the light scattered at large angle by the bubbles. The delaybetween the excitation and the detection corresponds to the ight time ofthe acoustic wave from the transducer wall to the acoustic focus. This isan important quantity which is further discussed below.

How did we know that this nucleation event was a bubble, not a crys-tal? Mainly from a study of the nucleation threshold voltage Vc as a func-tion of the static pressure Pstat in the cell. As we decreased Pstat, Vc alsodecreased (see Fig. 6). This behavior was of course consistent with nucle-ation of bubbles, which had to be easier at lower pressure. On the con-trary, the nucleation threshold for crystals would have increased.

In the linear approximation, the sound amplitude at the acousticfocus is given by:

P =P Pstat =R2 L , (1)where R is the inner radius of the transducer, =2f is the angular fre-quency of the wave, L is the density of the liquid, and is the amplitudeof the displacement at the inner surface of the transducer.4 Since is pro-

98 F. Werner et al.

Fig. 4. The electronics of the linear amplier. It uses a PA19 amplier from APEX anddelivers up to 70V of amplitude on a 50 resistor. It amplies bursts of a few oscillationsat 1MHz with a high stability and an accurately square envelope.

portional to the voltage applied to the transducer, one expects the waveamplitude at the acoustic focus to be proportional to the product LVin this linear approximation. Since the cavitation pressure is constant, onethen expects the threshold amplitude LVc to vary linearly with the staticpressure Pstat, and this is indeed what is shown by Fig. 6. Caupin andBalibar4 had already noticed that non-linear effects are small in the caseof hemispherical transducers, while Chavanne et al.14 and Appert et al.15

have shown that they are large in a fully spherical geometry. We have notyet found a robust interpretation for this difference. However, in the spher-ical geometry, the uid velocity has to be zero at the center, by symmetry,while in the hemispherical geometry there is no such constraint. Althoughwe suggest that this is the origin of the difference in behavior, our possibleinterpretation would need to be supported by a calculation of the exactpressure eld at the center in the hemispherical geometry, but this difcultcalculation has not yet been done.

With a few measurements in the small pressure range 0 < Pstat