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Fourth sound experiments on superfluid 3He in aerogel
Physica B 284}288 (2000) 301}302
Fourth sound experiments on super#uid He in aerogel Akira Matsubara *, Tadashi Ukawa , Tomoyuki Takebayashi , Osamu Ishikawa , Tohru Hata , Takao Kodama , Norbert Mulders Graduate School of Science, Osaka City University, Osaka 558-8585, Japan Department of Physics and Astronomy, University of Delaware, Newark, DE 19716, USA
Abstract Fourth sound experiments on super#uid He in aerogel were carried out. Two aerogel samples were prepared, one is 98% porous aerogel and the other is 99%. The aerogel was grown inside a sintered Ag powder to avoid vibration of the aerogel. Fourth sound of super#uid He was observed at several pressures, and the super#uid fraction was estimated from the sound velocity. The super#uid fraction and the transition temperature are more suppressed at lower pressures. 2000 Elsevier Science B.V. All rights reserved. Keywords: Aerogel; Fourth sound; He super#uid
Aerogel, a highly porous material, is expected to act as an impurity for super#uid He. Aerogel is a disordered network of SiO strands. The porosity of aerogel is very large, with more than 99% porosity available. Typical size of silica strands is about 50 As , and the mean distance of strands is approximately 1000 As . The size of silica strands is smaller than the coherence length of super#uid He. This indicates that for super#uid He aerogel acts not as a wall but as an impurity. In aerogel, large suppressions of the transition temperature and the super#uid fraction have been observed, which are di!erent from that in a restricted geometry [1,2]. Fourth sound is a characteristic sound mode of super#uid, in which only the super#uid component propagates. Fourth sound is realized experimentally in a space smaller than the viscous penetration depth d("(2g/uo) of super#uid He. In aerogel d is larger than the mean distance between strands of aerogel. The normal component will be locked on silica strands of aerogel. Recently, a Cornell group reported a sound mode of super#uid He in aerogel [3], they claimed that the aerogel itself can oscillate and the sound mode in aerogel is not fourth sound but a second-sound-like mode. In order to
* Corresponding author. E-mail address: [email protected] (A. Matsubara)
avoid vibration of aerogel we have grown aerogel in sintered Ag powder, and carried out sound experiments. The sound cell consists of a stainless-steel cylinder and sintered Ag powder inside. The cell body is 15 mm long, and the inner diameter is 8 mm. The average grain size of the Ag sinter is 100 lm, which is large enough to avoid size e!ect of super#uid He. We have prepared two aerogel samples with di!erent porosities, 98% and 99%. For propagation and detection of sound we used a pair of condenser-type transducers, which were attached at both ends of the sample cell. The transducer consists of a metal electrode and Al-plated Mylar sheet. To each transducer was added a DC bias, approximately 200 V. The sound resonance signal was recorded on a computer as a function of frequency. The velocity of fourth sound was calculated from the frequency of a resonance peak. Whole cells were cooled by a nuclear demagnetization cryostat. The temperature was measured by a Pt-NMR thermometer calibrated by a He melting curve thermometer. The temperature was varied by changing the magnetic "eld for demagnetization. Sound modes are observed in super#uid He. Their temperature dependence is the same as fourth sound of super#uid He except for a temperature-independent factor n, which is the index of refraction. We used this n for calculations of velocity of fourth sound C of super#uid He.
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 6 3 6 - 8
302
A. Matsubara et al. / Physica B 284}288 (2000) 301}302
Fig. 1. Phase diagram of super#uid He in aerogel. Solid circles denote transition temperatures in 99% porous aerogel, and open circles are in 98%. Solid lines are the transition temperature of bulk liquid.
Fig. 2. Super#uid fraction of He in 99% porous aerogel obtained from fourth sound measurements.
In super#uid He there exist many resonance peaks. Some of them are spurious, because they are DC bias dependent. Other DC bias-independent peaks disappear at a temperature below the bulk transition temperature ¹ . These peaks show a harmonic relation, and the Q values become larger as the temperature is reduced. This indicates that they are attributed to fourth sound of super#uid He in aerogel. The temperature at which they disappear is the transition temperature in aerogel, ¹ . Fig. 1 shows the phase diagram of He in aerogel. The transition temperatures are more suppressed at lower pressures. This result is similar to those obtained by other methods, torsional oscillator and NMR [1,2]. Regarding the di!erence in porosity, ¹ is reduced more in low porosity. This is consistent with treating aerogel as an impurity for super#uid He.
Fig. 2 shows the super#uid fraction in 99% porous aerogel, calculated from C as o /o"(C /C ). Here C is velocity of "rst sound, which is measured simulta neously with C . In Fig. 2, super#uid fractions show parallel temperature dependence. This result is also similar to those obtained by other methods. The super#uid fraction in 98% porous aerogel, not seen in Fig. 2, shows a di!erent temperature dependence from the 99% porous aerogel. This suggests that more parameters are necessary for super#uid He in aerogel in addition to porosity.
References [1] D.T. Sprague et al., Phys. Rev. Lett. 75 (1995) 661. [2] K. Matsumoto et al., Phys. Rev. Lett. 79 (1997) 253. [3] A. Golov et al., Phys. Rev. Lett. 82 (1999) 3492.
Fourth sound experiments on super#uid He in aerogel Akira Matsubara *, Tadashi Ukawa , Tomoyuki Takebayashi , Osamu Ishikawa , Tohru Hata , Takao Kodama , Norbert Mulders Graduate School of Science, Osaka City University, Osaka 558-8585, Japan Department of Physics and Astronomy, University of Delaware, Newark, DE 19716, USA
Abstract Fourth sound experiments on super#uid He in aerogel were carried out. Two aerogel samples were prepared, one is 98% porous aerogel and the other is 99%. The aerogel was grown inside a sintered Ag powder to avoid vibration of the aerogel. Fourth sound of super#uid He was observed at several pressures, and the super#uid fraction was estimated from the sound velocity. The super#uid fraction and the transition temperature are more suppressed at lower pressures. 2000 Elsevier Science B.V. All rights reserved. Keywords: Aerogel; Fourth sound; He super#uid
Aerogel, a highly porous material, is expected to act as an impurity for super#uid He. Aerogel is a disordered network of SiO strands. The porosity of aerogel is very large, with more than 99% porosity available. Typical size of silica strands is about 50 As , and the mean distance of strands is approximately 1000 As . The size of silica strands is smaller than the coherence length of super#uid He. This indicates that for super#uid He aerogel acts not as a wall but as an impurity. In aerogel, large suppressions of the transition temperature and the super#uid fraction have been observed, which are di!erent from that in a restricted geometry [1,2]. Fourth sound is a characteristic sound mode of super#uid, in which only the super#uid component propagates. Fourth sound is realized experimentally in a space smaller than the viscous penetration depth d("(2g/uo) of super#uid He. In aerogel d is larger than the mean distance between strands of aerogel. The normal component will be locked on silica strands of aerogel. Recently, a Cornell group reported a sound mode of super#uid He in aerogel [3], they claimed that the aerogel itself can oscillate and the sound mode in aerogel is not fourth sound but a second-sound-like mode. In order to
* Corresponding author. E-mail address: [email protected] (A. Matsubara)
avoid vibration of aerogel we have grown aerogel in sintered Ag powder, and carried out sound experiments. The sound cell consists of a stainless-steel cylinder and sintered Ag powder inside. The cell body is 15 mm long, and the inner diameter is 8 mm. The average grain size of the Ag sinter is 100 lm, which is large enough to avoid size e!ect of super#uid He. We have prepared two aerogel samples with di!erent porosities, 98% and 99%. For propagation and detection of sound we used a pair of condenser-type transducers, which were attached at both ends of the sample cell. The transducer consists of a metal electrode and Al-plated Mylar sheet. To each transducer was added a DC bias, approximately 200 V. The sound resonance signal was recorded on a computer as a function of frequency. The velocity of fourth sound was calculated from the frequency of a resonance peak. Whole cells were cooled by a nuclear demagnetization cryostat. The temperature was measured by a Pt-NMR thermometer calibrated by a He melting curve thermometer. The temperature was varied by changing the magnetic "eld for demagnetization. Sound modes are observed in super#uid He. Their temperature dependence is the same as fourth sound of super#uid He except for a temperature-independent factor n, which is the index of refraction. We used this n for calculations of velocity of fourth sound C of super#uid He.
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 6 3 6 - 8
302
A. Matsubara et al. / Physica B 284}288 (2000) 301}302
Fig. 1. Phase diagram of super#uid He in aerogel. Solid circles denote transition temperatures in 99% porous aerogel, and open circles are in 98%. Solid lines are the transition temperature of bulk liquid.
Fig. 2. Super#uid fraction of He in 99% porous aerogel obtained from fourth sound measurements.
In super#uid He there exist many resonance peaks. Some of them are spurious, because they are DC bias dependent. Other DC bias-independent peaks disappear at a temperature below the bulk transition temperature ¹ . These peaks show a harmonic relation, and the Q values become larger as the temperature is reduced. This indicates that they are attributed to fourth sound of super#uid He in aerogel. The temperature at which they disappear is the transition temperature in aerogel, ¹ . Fig. 1 shows the phase diagram of He in aerogel. The transition temperatures are more suppressed at lower pressures. This result is similar to those obtained by other methods, torsional oscillator and NMR [1,2]. Regarding the di!erence in porosity, ¹ is reduced more in low porosity. This is consistent with treating aerogel as an impurity for super#uid He.
Fig. 2 shows the super#uid fraction in 99% porous aerogel, calculated from C as o /o"(C /C ). Here C is velocity of "rst sound, which is measured simulta neously with C . In Fig. 2, super#uid fractions show parallel temperature dependence. This result is also similar to those obtained by other methods. The super#uid fraction in 98% porous aerogel, not seen in Fig. 2, shows a di!erent temperature dependence from the 99% porous aerogel. This suggests that more parameters are necessary for super#uid He in aerogel in addition to porosity.
References [1] D.T. Sprague et al., Phys. Rev. Lett. 75 (1995) 661. [2] K. Matsumoto et al., Phys. Rev. Lett. 79 (1997) 253. [3] A. Golov et al., Phys. Rev. Lett. 82 (1999) 3492.