- Email: [email protected]
Solidification of 3He in a porous glass
Volume 102A, number 9
PHYSICS LETTERS
11 June 1984
SOLIDIFICATION OF 3He IN A POROUS GLASS M. SHIMODA, T. MIZUSAKI, T. SUZUKI, A. HIRAI Department of Physics, Kyoto University, Kyoto, 606, Japan and K. EGUCHI Government Industrial Research Institute, Osaka, Ikeda, 536, Japan Received 14 March 1984
NMR relaxation measurements of 3He in porous high silica glass within a temperature range of 0.5 to 4.2 K at various applied pressures up to 14.6 MPa are reported. The onset of solidification of 3He in the pores was observed at excess pressures ~2.3 -4.7 MPa above the bulk melting pressure between 1.3 and 2.1 K. The specific heat of 3He in the porous glass was measured to supplement the NMR measurements and the result confirmed the solidification.
There has been much interest in the properties o f helium confined in very small geometries at low temperatures. There is a wide variety of phenomena in this system. Superfluidity o f 4He in restricted geometries has been investigated theoretically [ 1 ] and experimentally [ 2 - 8 ] . In the case o f 3 He, the Fermi liquid properties in restricted geometries have been studied [ 9 - 1 1 ]. The transport coefficients such as thermal conductivity and spin diffusion have been studied in the collisionless or Knudsen regime. Another interesting problem is the solidification of 4He in confined geometries [ 5 - 8 , 1 2 ] . Several experimental works related to this problem include the flow measurements o f liquid 4 He in packed powders of various sizes [6], the specific heat [7] and torsional-osciUator measurement [5] taken in porous Vycor glass. It has been reported that the 4He in the pores remained liquid at excess pressures as large as 1.5 MPa. The onset o f solidification of 4 He in porous Vycor was recently identified by the change in the transverse sound velocity measurement [8]. An excess pressure of 2 - 3 MPa above bulk melting pressures between 1 and 2 K was observed. This paper reports the investigation of the solidi426
fication o f 3 He in a porous high silica glass* ~ by the NMR relaxation measurement and the specific heat measurement. The results are compared with those for 4He. The porous glass was cylindrical in shape with a 7.3 mm diameter and 9.5 mm length and was fitted tightly within the lower part o f the NMR sample cell made of an epoxy. The mean pore diameter o f the porous glass was 52 A and the volume o f the pores was 0.14 cm 3 (35% porosity). The upper part of the sample cell outside the porous glass was filled with bulk 3He. A NMR detection coil was wound just around the boundary between the porous glass and the bulk 3 He, and therefore, the observed signal came equally from 3He in the pores and the bulk 3He. We chose this geometry because NMR signals in the pores could be measured and compared with those for the bulk 3He. The 3 He sample was made by the blocked capillary method so that below the temperature o f the block point the total amount of sample in the sample cell was kept constant. ,1 A porous high silica glass is a material similar to porous Vycor glass produced by Corning Glass Works. The pore distribution and the porosity were determined from the isothermal absorption measurement of nitrogen. 0.375-9601/84/$ 03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 102A, number 9
PHYSICS LETTERS
The spin-lattice relaxation time T l was measured by using the standard pulsed NMR where we observed the free induction decay signal after 9 0 0 - 9 0 ° pulse sequences. NMR frequency was fixed at 10.7 MHz. The magnetization recoveries could be expressed by a sum o f two exponential functions. Two T 1 s (T 1 B for the bulk 3He and Tip for that in the pores) were determined by a least squares fit to data, assuming that the ratio of intensities of two exponential functions was constant for all temperatures. There were a few difficulties in the above analysis. In a solid-liquid coexistence of bulk 3He, three kinds o f signals were observed. The magnetization recoveries in the pores seemed to be non-exponential at least when the sample was in the liquid phase (similar results have been observed for the submonolayer samples of absorbed 3He in a porous Vycor glass [13]). In this case Tip was determined as the time when the magnetization recovered to the value of 1/e. The temperature dependence o f Tlp and T 1B for two representative samples are shown in fig. 1. A
100
'
'
'
'
I
'
'
'
'
I
sample for 2.6 MPa ia believed to be in the liquid phase at all temperatures and data for T1B and Tip are shown by the broken line and solid line, respectively. Tip depends weakly on the temperature and is nearly constant at about 1 s. It should be mentioned that Tip did not depend much on the initial pressure if the sample in the pores was in the liquid phase. The weak temperature and pressure dependence o f T 1 were reported for such samples as the saturated and unsaturated 3He confined in a very narrow space [14]. It is apparent from the data for an initial pressure o f 8.8 MPa that the temperature dependence of Tip is quite different from that of T1B and indicates a large hysteresis between the cooling curve (A ~ D t E ~ F) and the warming curve (F ~ E-+ D 2 ~ A). It is just a coincidence in this sample that T1B in the socalled exchange plateau region [15] is very close to Tip in the solid phase. The phase transition takes place around 2 K in the bulk 3 He. If we know the temperature Tc at which the
'
'
~++ ---
(2 oo i
'
'
+
I
'
'
'
'
I
'
'
+
+
+
"~------- ~ - -
•
•
•
•
'
'
I"2.6MPa]
Tm
B
Tte 1"2.6MPa] 10
11 June 1984
+
Tm
[8.8MPm]
•
TIp
[8.SMPa]
---
eool lng
o
Tip CS.8MPa]
---
warming
i
Dl
L..~'o~
1.0
000
F alllallili
0.1~
' 1.0
D2
•
•
Iq
+
1
+++ ++$
a
I
÷
I
I
I
,
2.0
Temperature
,
,
I
,
,
3.0
,
,
I
,
1
I
I
4.0
[K]
Fig. 1. Temperature dependence of Tlp and TIB for two typical samples. For the sake of clarity data of TIB and Tip for an initial pressure of 2.6 MPa are shown by the broken line and solid line, respectively. TIB for an initial pressure of 8.82 MPa are shown by pulses and Tip for the cooling curve and that for the warming curve are shown by solid circles and open circles, respectively. 427
Volume 102A, number 9
PHYSICS LETTERS
bulk sample is solidified completely, we could estimate the corresponding pressure Pc by using the 3 He phase diagram [16]. We assume that the pressure of the sample in the pores is the same as Pc and determine the P - T p h a s e diagram in the pores. It is not accurate to determine T e from the plot of T1B against temperatures in fig. 1. We exploited a handy and sensitive method to estimate T c as follows. We measured the magnetization recoveries repeatedly every ten seconds and therefore the signal from the bulk liquid was saturated. We then derme Tl* by the time when the total magnetization recovered to the value of 1/10. When we plot TI* as a function of temperatures, Tc was determined very accurately. In the figure we indicate both the onset point of solidification by B and the completion point of that by C determined by the above method. Tlp does not change down to TD1 = 1.34 K in the cooling process and thus 3 He in the pores should be in the liquid until TD1. The sharp decrease of Tlp between D 1 and E can be attributed to the phase transition from the liquid to the solid phase in the pores. This interpretation is supported by the existence of a large hysteresis which implies that the transition is of
11 June 1984
the first order. The point D 1 should be regarded as the onset of solidification in the pore. On the other hand, T1)2 = 1.70 K should correspond to the temperature of the completion of melting in the pores in the warming curve. Assuming that PD 1 = PD2 = PC, the points (TD1, PD1 ) and (TD2 ,PD2) for various samples are plotted in fig. 2, In order to confirm the phase transition both of the bulk 3He and 3He in the pores, FT-NMR was performed at some representative temperatures, where the free induction signal under the linear field gradient (sometimes the spin echo signal) was Fourier transformed and thus the signal of 3He in the pores was separated in space from that for the bulk part. FTNMR results of T1B and Tip agreed very well with the above results. The typical result of the specific heat of 3 He in the porous glass at an initial pressure of 10.3 MPa is shown in fig. 3. The specific heat was measured by using a separate sample cell. The volume of the bulk 3He for this sample cell was so small that the contribution of the specific heat from the bulk 3He except for the latent heat was negligible compared with that from the sample in the pores. The large peak around 2.5 K
",J
15
/
r'~
~10
• |•
L.
Q)
L n
5 -•
J
I
I
I
]
1.0
I
I
I
I
[
I
2.0 Temperature
I
I
• A
I
:
NMR
:
Specific
I
3.0
I
I
I
Heat
I
I
I
I
4.0
[K]
Fig. 2. P-Tphase diagram for Dt and D2 determined by NMR and by the specific heat measurements. Solid lines show the phase diagram of bulk 3He. 428
Volume 102A, number 9
PHYSICS LETTERS
'
'
'
'
I
'
'
'
'
I
'
'
'
25
11 June 1984
'
I
'
'
P
!
'
'
I
10.3
=
'
MPa
.y.
I
-0 2 0
i
l
E
\
''15
-rio
! -
t
I
iI
¢.t-
k,'
I!
D2CB
1.0
2.0
i
,
I
i
3.0
Temperature
R
A
,
,
,
I
,
4.0
[K]
Fig. 3. The specific heat of 3He in the porous glass for an initial pressure of 10.3 MPa. The solid line is a straight line to fit data between A and B and the broken lines indicate the phase transition in the bulk 3He. can be attributed to the latent heat of the transition in the bulk sample. Without this peak, there is no anomaly in the region between A and D 2. This clearly indicates that 3He in the pores between A and D 2 is in the liquid phase. Since the specific heat of bulk solid 3He should be smaller than that of liquid 3He, the broad peak below D 2 may be attributed to the latent heat of the phase transition of 3He in the pores. Both measurements of the NMR and the specific heat were in good agreement with each other. The onset of solidification was observed at excess pressures of 2.3--4.7 MPa between 1.3 and 2.1 K above the bulk melting curve. The two models have been proposed to explain the large excess pressure necessary to solidify the liquid helium in the restricted geometries. The excess contribution of the surface energy between solid and liquid boundary was attributed to the excess pressure [6]. If solid 3 He does not wet the surface of the pores, similar to the case of solid 4He [17], the excess pressure AP required to form a stable droplet of radius R is given by a t , = ( 2 ~ s d R ) v~ /( Vs - v O ,
(1)
where as~ is the interfacial tension between the liquid and solid, V~ and Vs are the liquid and solid molar volumes and R = 26 A for our sample. Since the large hysteresis was observed in the phase transition in the pores, it is not clear which point, D 1 or D2 represents the true equilibrium phase boundary. For the sake of comparison with the result of 4He [8], we apply eq. (2) to the onset of solidification (point Dr) and calculate C~s~. as~ changes from 0.13 to 0.25 erg/cm 2 between 1.3 and 2.1 K. These values are close to those obtained in 4He [8,18]. Dash [12] has proposed another model in which excess pressure is attributed to the grain boundary energy between the crystallites in the small pores. AP is given by Aao ~ 0.05c~pa/l,
(2)
where/a is the shear modulus of solid 3 He, a is the latI tice spacing and l is the volume to surface ratio (= ~R for the porous glass). The surface roughness parameter ais not known. If we u s e t ~ 10 [ 8 ] , g t = l X 108 dyn/ cm 2 [19] ,a = 3 A andR = 26 A, this model gives AP 1 MPa which is of the correct order of magnitude we observed. 429
Volume 102A, number 9
PHYSICS LE'I'rERS
The solidification or melting in the pores was qualitatively very similar to the case of 4He. It is difficult so far to determine which model is applicable to the solidification of He in the pores. This work was supported in part by the Coming Research Grant.
References [1] [2] [3] [4]
T.C. Padmore, Phys. Rev. Lett. 28 (1972) 1512. F.D.M. Pobell et al., Phys. Rev. Lett. 28 (1972) 542. R.H. Tait and J.D. Reppy, Phys. Rev. B20 (1979) 997. G. Ahlers, in: The physics of liquid and solid helium, Vol. 1, eds. K.H. Bennemann and J.B. Ketterson (Wiley, New York, 1976). [5] D.F. Brewer, C. Liezhao, C. Girit and J.D. Reppy, Physica 107B (1981) 583. [6] E.N. Smith, D.F. Brewer, C. Liezhao and J.D. Reppy, Physiea 107B (1981) 585.
430
11 June 1984
[7] A.L. Thomson, D.F. Brewer, T. Naji, S. Haynes and J.D. Reppy, Physica 107B (1981) 581. [8] J.R. Beamish, A. Hikata, L. Tell and C. Elbaum, Phys. Rev. Lett. 50 (1983) 425. [9] M.J. Rice, Phys. Rev. 165 (1968) 288. [10] D.S. Betts, D.F. Brewer and R.S. Hamilton, J. Low Temp. Phys. 14 (1974) 331. [11] D.F. Brewer and J.S. Rolt, Phys. Lett. 48A (1974) 141. [12] J.G. Dash, Phys. Rev. B25 (1982)508. [ 13 ] D.F. Brewer et al., in: Monolayer and submonolayer helium films, eds. J.G. Daunt and E. Lerner (Plenum, New York) p. 101. [ 14] B.P. Cowan, J. Low Temp. Phys. 50 (1983) 135. [ 15] R.A. Guyer, R.C. Richardson and L.I. Zane, Rev. Mod. Phys. 43 (1971) 532. [16] E.R. Grilly and R.L. Mills, Ann. Phys. 8 (1959) 1. [ 17 ] S. Balibar, D.O. Edwards and C. Laroche. Phys. Rev. Lett. 42 (1979) 782. [18] J. Landau, S.G. Lipson, L.M. Maattanen, L.S. Balfour and D.O. Edwards, Phys. Rev. Lett. 45 (1980) 31. [19] S.B. Trickey, W.P. Kirk and E.D. Adams, Rev. Mod. Phys. 44 (1972) 668.
PHYSICS LETTERS
11 June 1984
SOLIDIFICATION OF 3He IN A POROUS GLASS M. SHIMODA, T. MIZUSAKI, T. SUZUKI, A. HIRAI Department of Physics, Kyoto University, Kyoto, 606, Japan and K. EGUCHI Government Industrial Research Institute, Osaka, Ikeda, 536, Japan Received 14 March 1984
NMR relaxation measurements of 3He in porous high silica glass within a temperature range of 0.5 to 4.2 K at various applied pressures up to 14.6 MPa are reported. The onset of solidification of 3He in the pores was observed at excess pressures ~2.3 -4.7 MPa above the bulk melting pressure between 1.3 and 2.1 K. The specific heat of 3He in the porous glass was measured to supplement the NMR measurements and the result confirmed the solidification.
There has been much interest in the properties o f helium confined in very small geometries at low temperatures. There is a wide variety of phenomena in this system. Superfluidity o f 4He in restricted geometries has been investigated theoretically [ 1 ] and experimentally [ 2 - 8 ] . In the case o f 3 He, the Fermi liquid properties in restricted geometries have been studied [ 9 - 1 1 ]. The transport coefficients such as thermal conductivity and spin diffusion have been studied in the collisionless or Knudsen regime. Another interesting problem is the solidification of 4He in confined geometries [ 5 - 8 , 1 2 ] . Several experimental works related to this problem include the flow measurements o f liquid 4 He in packed powders of various sizes [6], the specific heat [7] and torsional-osciUator measurement [5] taken in porous Vycor glass. It has been reported that the 4He in the pores remained liquid at excess pressures as large as 1.5 MPa. The onset o f solidification of 4 He in porous Vycor was recently identified by the change in the transverse sound velocity measurement [8]. An excess pressure of 2 - 3 MPa above bulk melting pressures between 1 and 2 K was observed. This paper reports the investigation of the solidi426
fication o f 3 He in a porous high silica glass* ~ by the NMR relaxation measurement and the specific heat measurement. The results are compared with those for 4He. The porous glass was cylindrical in shape with a 7.3 mm diameter and 9.5 mm length and was fitted tightly within the lower part o f the NMR sample cell made of an epoxy. The mean pore diameter o f the porous glass was 52 A and the volume o f the pores was 0.14 cm 3 (35% porosity). The upper part of the sample cell outside the porous glass was filled with bulk 3He. A NMR detection coil was wound just around the boundary between the porous glass and the bulk 3 He, and therefore, the observed signal came equally from 3He in the pores and the bulk 3He. We chose this geometry because NMR signals in the pores could be measured and compared with those for the bulk 3He. The 3 He sample was made by the blocked capillary method so that below the temperature o f the block point the total amount of sample in the sample cell was kept constant. ,1 A porous high silica glass is a material similar to porous Vycor glass produced by Corning Glass Works. The pore distribution and the porosity were determined from the isothermal absorption measurement of nitrogen. 0.375-9601/84/$ 03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 102A, number 9
PHYSICS LETTERS
The spin-lattice relaxation time T l was measured by using the standard pulsed NMR where we observed the free induction decay signal after 9 0 0 - 9 0 ° pulse sequences. NMR frequency was fixed at 10.7 MHz. The magnetization recoveries could be expressed by a sum o f two exponential functions. Two T 1 s (T 1 B for the bulk 3He and Tip for that in the pores) were determined by a least squares fit to data, assuming that the ratio of intensities of two exponential functions was constant for all temperatures. There were a few difficulties in the above analysis. In a solid-liquid coexistence of bulk 3He, three kinds o f signals were observed. The magnetization recoveries in the pores seemed to be non-exponential at least when the sample was in the liquid phase (similar results have been observed for the submonolayer samples of absorbed 3He in a porous Vycor glass [13]). In this case Tip was determined as the time when the magnetization recovered to the value of 1/e. The temperature dependence o f Tlp and T 1B for two representative samples are shown in fig. 1. A
100
'
'
'
'
I
'
'
'
'
I
sample for 2.6 MPa ia believed to be in the liquid phase at all temperatures and data for T1B and Tip are shown by the broken line and solid line, respectively. Tip depends weakly on the temperature and is nearly constant at about 1 s. It should be mentioned that Tip did not depend much on the initial pressure if the sample in the pores was in the liquid phase. The weak temperature and pressure dependence o f T 1 were reported for such samples as the saturated and unsaturated 3He confined in a very narrow space [14]. It is apparent from the data for an initial pressure o f 8.8 MPa that the temperature dependence of Tip is quite different from that of T1B and indicates a large hysteresis between the cooling curve (A ~ D t E ~ F) and the warming curve (F ~ E-+ D 2 ~ A). It is just a coincidence in this sample that T1B in the socalled exchange plateau region [15] is very close to Tip in the solid phase. The phase transition takes place around 2 K in the bulk 3 He. If we know the temperature Tc at which the
'
'
~++ ---
(2 oo i
'
'
+
I
'
'
'
'
I
'
'
+
+
+
"~------- ~ - -
•
•
•
•
'
'
I"2.6MPa]
Tm
B
Tte 1"2.6MPa] 10
11 June 1984
+
Tm
[8.8MPm]
•
TIp
[8.SMPa]
---
eool lng
o
Tip CS.8MPa]
---
warming
i
Dl
L..~'o~
1.0
000
F alllallili
0.1~
' 1.0
D2
•
•
Iq
+
1
+++ ++$
a
I
÷
I
I
I
,
2.0
Temperature
,
,
I
,
,
3.0
,
,
I
,
1
I
I
4.0
[K]
Fig. 1. Temperature dependence of Tlp and TIB for two typical samples. For the sake of clarity data of TIB and Tip for an initial pressure of 2.6 MPa are shown by the broken line and solid line, respectively. TIB for an initial pressure of 8.82 MPa are shown by pulses and Tip for the cooling curve and that for the warming curve are shown by solid circles and open circles, respectively. 427
Volume 102A, number 9
PHYSICS LETTERS
bulk sample is solidified completely, we could estimate the corresponding pressure Pc by using the 3 He phase diagram [16]. We assume that the pressure of the sample in the pores is the same as Pc and determine the P - T p h a s e diagram in the pores. It is not accurate to determine T e from the plot of T1B against temperatures in fig. 1. We exploited a handy and sensitive method to estimate T c as follows. We measured the magnetization recoveries repeatedly every ten seconds and therefore the signal from the bulk liquid was saturated. We then derme Tl* by the time when the total magnetization recovered to the value of 1/10. When we plot TI* as a function of temperatures, Tc was determined very accurately. In the figure we indicate both the onset point of solidification by B and the completion point of that by C determined by the above method. Tlp does not change down to TD1 = 1.34 K in the cooling process and thus 3 He in the pores should be in the liquid until TD1. The sharp decrease of Tlp between D 1 and E can be attributed to the phase transition from the liquid to the solid phase in the pores. This interpretation is supported by the existence of a large hysteresis which implies that the transition is of
11 June 1984
the first order. The point D 1 should be regarded as the onset of solidification in the pore. On the other hand, T1)2 = 1.70 K should correspond to the temperature of the completion of melting in the pores in the warming curve. Assuming that PD 1 = PD2 = PC, the points (TD1, PD1 ) and (TD2 ,PD2) for various samples are plotted in fig. 2, In order to confirm the phase transition both of the bulk 3He and 3He in the pores, FT-NMR was performed at some representative temperatures, where the free induction signal under the linear field gradient (sometimes the spin echo signal) was Fourier transformed and thus the signal of 3He in the pores was separated in space from that for the bulk part. FTNMR results of T1B and Tip agreed very well with the above results. The typical result of the specific heat of 3 He in the porous glass at an initial pressure of 10.3 MPa is shown in fig. 3. The specific heat was measured by using a separate sample cell. The volume of the bulk 3He for this sample cell was so small that the contribution of the specific heat from the bulk 3He except for the latent heat was negligible compared with that from the sample in the pores. The large peak around 2.5 K
",J
15
/
r'~
~10
• |•
L.
Q)
L n
5 -•
J
I
I
I
]
1.0
I
I
I
I
[
I
2.0 Temperature
I
I
• A
I
:
NMR
:
Specific
I
3.0
I
I
I
Heat
I
I
I
I
4.0
[K]
Fig. 2. P-Tphase diagram for Dt and D2 determined by NMR and by the specific heat measurements. Solid lines show the phase diagram of bulk 3He. 428
Volume 102A, number 9
PHYSICS LETTERS
'
'
'
'
I
'
'
'
'
I
'
'
'
25
11 June 1984
'
I
'
'
P
!
'
'
I
10.3
=
'
MPa
.y.
I
-0 2 0
i
l
E
\
''15
-rio
! -
t
I
iI
¢.t-
k,'
I!
D2CB
1.0
2.0
i
,
I
i
3.0
Temperature
R
A
,
,
,
I
,
4.0
[K]
Fig. 3. The specific heat of 3He in the porous glass for an initial pressure of 10.3 MPa. The solid line is a straight line to fit data between A and B and the broken lines indicate the phase transition in the bulk 3He. can be attributed to the latent heat of the transition in the bulk sample. Without this peak, there is no anomaly in the region between A and D 2. This clearly indicates that 3He in the pores between A and D 2 is in the liquid phase. Since the specific heat of bulk solid 3He should be smaller than that of liquid 3He, the broad peak below D 2 may be attributed to the latent heat of the phase transition of 3He in the pores. Both measurements of the NMR and the specific heat were in good agreement with each other. The onset of solidification was observed at excess pressures of 2.3--4.7 MPa between 1.3 and 2.1 K above the bulk melting curve. The two models have been proposed to explain the large excess pressure necessary to solidify the liquid helium in the restricted geometries. The excess contribution of the surface energy between solid and liquid boundary was attributed to the excess pressure [6]. If solid 3 He does not wet the surface of the pores, similar to the case of solid 4He [17], the excess pressure AP required to form a stable droplet of radius R is given by a t , = ( 2 ~ s d R ) v~ /( Vs - v O ,
(1)
where as~ is the interfacial tension between the liquid and solid, V~ and Vs are the liquid and solid molar volumes and R = 26 A for our sample. Since the large hysteresis was observed in the phase transition in the pores, it is not clear which point, D 1 or D2 represents the true equilibrium phase boundary. For the sake of comparison with the result of 4He [8], we apply eq. (2) to the onset of solidification (point Dr) and calculate C~s~. as~ changes from 0.13 to 0.25 erg/cm 2 between 1.3 and 2.1 K. These values are close to those obtained in 4He [8,18]. Dash [12] has proposed another model in which excess pressure is attributed to the grain boundary energy between the crystallites in the small pores. AP is given by Aao ~ 0.05c~pa/l,
(2)
where/a is the shear modulus of solid 3 He, a is the latI tice spacing and l is the volume to surface ratio (= ~R for the porous glass). The surface roughness parameter ais not known. If we u s e t ~ 10 [ 8 ] , g t = l X 108 dyn/ cm 2 [19] ,a = 3 A andR = 26 A, this model gives AP 1 MPa which is of the correct order of magnitude we observed. 429
Volume 102A, number 9
PHYSICS LE'I'rERS
The solidification or melting in the pores was qualitatively very similar to the case of 4He. It is difficult so far to determine which model is applicable to the solidification of He in the pores. This work was supported in part by the Coming Research Grant.
References [1] [2] [3] [4]
T.C. Padmore, Phys. Rev. Lett. 28 (1972) 1512. F.D.M. Pobell et al., Phys. Rev. Lett. 28 (1972) 542. R.H. Tait and J.D. Reppy, Phys. Rev. B20 (1979) 997. G. Ahlers, in: The physics of liquid and solid helium, Vol. 1, eds. K.H. Bennemann and J.B. Ketterson (Wiley, New York, 1976). [5] D.F. Brewer, C. Liezhao, C. Girit and J.D. Reppy, Physica 107B (1981) 583. [6] E.N. Smith, D.F. Brewer, C. Liezhao and J.D. Reppy, Physiea 107B (1981) 585.
430
11 June 1984
[7] A.L. Thomson, D.F. Brewer, T. Naji, S. Haynes and J.D. Reppy, Physica 107B (1981) 581. [8] J.R. Beamish, A. Hikata, L. Tell and C. Elbaum, Phys. Rev. Lett. 50 (1983) 425. [9] M.J. Rice, Phys. Rev. 165 (1968) 288. [10] D.S. Betts, D.F. Brewer and R.S. Hamilton, J. Low Temp. Phys. 14 (1974) 331. [11] D.F. Brewer and J.S. Rolt, Phys. Lett. 48A (1974) 141. [12] J.G. Dash, Phys. Rev. B25 (1982)508. [ 13 ] D.F. Brewer et al., in: Monolayer and submonolayer helium films, eds. J.G. Daunt and E. Lerner (Plenum, New York) p. 101. [ 14] B.P. Cowan, J. Low Temp. Phys. 50 (1983) 135. [ 15] R.A. Guyer, R.C. Richardson and L.I. Zane, Rev. Mod. Phys. 43 (1971) 532. [16] E.R. Grilly and R.L. Mills, Ann. Phys. 8 (1959) 1. [ 17 ] S. Balibar, D.O. Edwards and C. Laroche. Phys. Rev. Lett. 42 (1979) 782. [18] J. Landau, S.G. Lipson, L.M. Maattanen, L.S. Balfour and D.O. Edwards, Phys. Rev. Lett. 45 (1980) 31. [19] S.B. Trickey, W.P. Kirk and E.D. Adams, Rev. Mod. Phys. 44 (1972) 668.