THE LOW TEMPERATURE HEAT CAPACITY OF 3He IN A 37 Å 4He FI LM

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THE LOW TEMPERATURE HEAT CAPACITY OF

3He IN A 37 Å 4He FI LM

M. Di Pirro, F. Gasparini

To cite this version:

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JOURNAL DE PHYSIQUE

_Colloque

_{C6, supplkment au no 8, Tome 39, aoiit 1978, page C6-3 12}

4

THE

LOW

TEMPERATURE HEAT CAPACITY

OF

3 ~ e I N A 37

A

He

FILM

t

M.J. Di Pirro and F.M. Gasparini

Department of Physics, S t a t e University o f New York a t Buffalo, Amherst, N.Y. 14260, USA

R6sumd.- Nous avons mesurd la capacitd calorifique d'un film dl'He avec des quantitds variables dI3He afin de determiner la chaleur spdcifique des dtats de surface de lt3He. Nous trouvons des structures imprdvues dans la capacitd calorifique qu'on ne peut pas expliquer d'aprss le modsle dlAndreev d'un gaz iddal bidimensionnel de quasi-particules.

Abstract.- We have measured the heat capacity of a 'He film with various amounts of 3 ~ e to deter- mine the specific heat of the 3 ~ e surface states. We find unexpected structures in the heat capacity which cannot be explained on the basis of the Andreev model of an ideal two dimensional gas of quasi-particles.

Theexistenceof a bound state for3He atoms on monolayer as 6.4 x IOl4 ~ m - ~ , /4/ and the "mono- the surface of 'He was first suggested by Andreev /I/ layer" designation refers to the situation when all to explain a drop in the low temperature surface ten- of the He would be on the surface. Of course the sion of '~e 121. Subsequent, more detailed measure- actual number on the surface will vary with tempe- ments of surface tension /3,4/, and surface second ratllre In a way determined by the experimental

sound 151 have supported a model of the surface 3 ~ e

as a weakly interacting fermi gas of quasiparticles r A I I

with effective mass m* 2 1.3 m, bound at the surface with an energy E = 2.3 K below the bulk states.

We report first measurements of the specific

-

k heat of a 37 A 'He film and sufficient 3 ~ e to form

w

0.1, 0.3 or 1.0 layers on the surface. To achieve a

-

w

large signal for the 3 ~ e in a controlled geometry we

U

have chosen as a substrate Nuclepore filters. The 4

4

formation of helium films on this substrate has been +

4

studied in conjunction with the work on finite size W I

scaling near the 1 transition /6,7/. On a filter with 2000 diameter pores one is able to form 'He

e

films up to about 56 A in thickness before the onset of capillary condensation. For the heat capacity data

0 0 37 % ~e~ FILM AND CALORIMETER 0 1.00 LAYER OF HZ ADDED 8 I I 100 200 300 TEMPERATURE (mK)

near T1 it has been shown that these thick films can Fig. 1 : The hgat capacity of the calorimeter with

be prepared with good size homogeneity. Our calori- a 37 A 'He film and the heat capacity upon addition of a monolayer of 3 ~ e meter consists of 2000 filters giving us a surface

area of 1 14 m2

.

It is suspended from the mixing chamber of a dilution refrigerator by a graphite rod, and thermally anchored to the mixer via a Zn switch. The heat capacity of the 'He film plus the experimental cell, and the heat capacity upon addition of a monolayer of 3 ~ e is shown in figure 1. We define a

surface to volume ratio. From figure 3 we can clearly see the 3 ~ e signal above the film "background" This signal shows two interesting structures : a sudden drop near 60 mK and a very steep rise near

180 mK. In figure 2 we have plotted the data for three coverages after subtracting the background contribution. The rise in the specific heat can be

+

Work supported in part by Research Corporation seen to proceed from a suggestive inflection at 0.1 and N.S.F. under grants DMR 7711325, and

DMR 7509498101 layers to a well defined step at 0.3 layers and a

very rapid rise at 1 layer. For this data, which we

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786138

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TEMPERATURE ImKl

Fig. 2 : The heat capacity at three coverages with the background contribution subtracted. The top datum for 1 layer should be plotted at 74.0 erg

have not at this time followed to higher temperatures, the point shown as going off the graph has a heat capacity more than an order of magnitude higher than

TEMPERATURE ImK)

functions of temperature in a way unique to our experimental surface to volume ratio. We have assumed the film to act as bulk helium, and the 3 ~ e as an i- deal gas of quasi-particles with appropriate effective mass and surface binding energy. The 3 ~ e in the film for the 0.3 layer case is Boltzmann within the region of our calculation and is degenerate on the surface. The result of our calculation is shown in figure 3. FJe also show here the percent of 3 ~ e on the surface. The calculation clearly does not reproduce the data. Indeed, agreement can be obtained only above 200 mK and this by assuming an effective mass for the 3 ~ e on the surface equal to the bare mass. The important conclusion is that three seems

to be no way within this model to reproduce the sharp rise in the specific heat, or for that matter, the maximum exhibited by the one layer data at low temperature. This conclusion is in sharp contrast to the success of the two dimensional fermi gas model in explaining the surface tension data. To be sure these data are for the surface of bulk helium, while we are dealing with a film. In addition our system differs in the fact that the film is formed in a cylindrical geometry. This fact could play a role. At present we have no explanation for our data, and are continuing our measurements.

References

/ I / Andreev, A.F., 2h.Eksp.Teor.Fiz.

50

(1966) 1415

(Sov.Phys.-JETP

3

(1966) 939)

/ 2 / Atkins, K.R. and Narahara, Y., Phys.Rev.

138A

(1966) 437

/ 3 / Zino'eva, N.K. and Boldarev, S.T., Zh.Eksp.Teor. Fig. 3 : The 0.3 layer data and the expected heat Fig.

56

(1969) 1089, (Sov.Phys. JETP

2

(1969)

capacity calculated from and ideal fermi gas model 585)

with bulk and surface effective masses as shown. The

top curve represents the amount of 3 ~ e on the surface 1 4 1 GUO, H - M - , Edwards, D.O., Sarwinski, R.E. and as calculated from the same model Tough, J.T., Phys.Rev.Lett.

7

(1971) 1959

in the 100-150 mK region. The specific heat maximum is barely suggestive at 0.3 layers and is buried in the "noise" for the 0.1 layer case. The behavior is completely different from that of 3 ~ e films formed on Grafoil /8/

.-

In an attempt to understand these data we have calculated the heat capacity from the expression for the total entropy

b b

S=N'S'+N

s

,

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151

Eckardt, J.R., Edwards, D.O., Fatouros, P.P., Gasparini, F.M. and Shen, S.Y., Phys.Rev.Lett.

3 2 (1974) 7 0 6

-

/ 6 / Chen, T.P., Di Pirro, M.J., Gaeta, A.A. and Gasparini,F.M., J.Low Temp.Phys. 26 (1977) 927 / 7 / Chen, T.P., Gasparini, F.M., Phys.Rev.Lett. 4 0

(1978) 331

/ 8 / Hickernell, D.C., Mc Lean, E.O. and Vilches,O.E.

28 (1972) 789

-

where the amount of 3 ~ e on the surface, N,' or in the b