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Surface states of 3He on an adsorbed3He4He film at low temperatures
Volume 35A, number 4
PHYSICS LETTERS
14 June 1971
3He ON AN ADSORBED SURFACE OF LOW TEMPERATURES 3He - 4HeSTATES FILM AT D. F. BREWER, A. EVENSON* and A. L. THOMSON School of Mathematical and Physical Sciences, University of Sussex, Falmer, Brighton BN 1 9 QH, UK Received 26 April 1911
An adsorbed 3He — 4He mixture filling a porous material has a constant specific heat between O.5°Kand 1 °K. With partial fillings, when a free surface is present, this is replaced by a temperature—dependent term, attributable probably to 3He surface states.
The existence of a surface contribution to the specific heat of pure helium films is well established [1-3], We report here a new phenomenon in the specific heat of adsorbed 3He - 4He mixture films at low temperatures, which may be
of 3He atoms at the free surface of the film. This is probably interpreted as thethe result mostofdirect a highevidence concentration so far produced for the existence of surface states of 3He in an isotopic liquid helium solution, which have previously been proposed to explain certain experiments on surface tension and others with negative ions [4,5]. The adsorbed film was formed on Vycor p0rous glass which had an effective mean pore diameter of 62.4 A and a surface area of 580m2 [1,3]. Nearly all of the original gas sample was condensed, a negligible amount remaining in the vapour phase in equilibrium with the adsorbate, so that the nominal concentration is essentially the average concentration of the adsorbate. The results have been corrected for heat of desorption, calculated from separate adsorption data [6]. Fig. 1 shows the specific heat of a film mixture of 3He molar concentration X = 0.09, at two coverages. The larger coverage relates to a situation in which the pores are full, while in the smaller one they are partly empty and a free surface is present. The two cases show a striking difference in behaviour at the lower temperatures. Three features are specially notable: (i) The residual “~mbefr~” anomaly. In bulk liquid He solutions, the temperature of the maximum in the specific heat decreases with addition *
Present address: Unilever Research Laboratories,
Isleworth, 455 London Road, London, Middlesex.
a
I ~.,
-
•
I
Fraction
~
592 cm3
-
2
—
o
0.5
T3~~
1.0
1.5
~MP~AThP~
2.0 ,
K
Fig. 1. Specific heat of adsorbed He mixture film with (I) and without (0) a free surface. TA and T 4He and of a 9% 3He in 4He bulktemperatures solution, Tsize is the temperature 3ofare the the lambda of pure maximum in the specific heat of pure 4He filling the pores of the same adsorbent. of 3He, and in pure 4He films it both decreases and is less well defined. In this film mixture, to a fair approximation the impurity effect and the size effect are additive; (ii) The full-pore specific heat reaches a constant value at low temperatures (between 0.9 °Kand 0.5 °K); (iii) The “film” specific heat (i.e., in the presence of a free surface) is strongly temperature dependent and decreases rapidly below the full-pore value at the lower temperatures. We restrict further remarks to the two last
observations, which we partly interpret as 30’?
Volume 35A, number 4
PHYSICS
4He contribution to the follows. Below 1 °K, the specific heat is negligibly small, and the constant full-pore value is presumed to be a result of a classical independent-particle motion of the 3He atoms or quasiparticles. A similar result has been found before in bulk liquid solutions rich in 4He [7], in which the constant value is very nearly ~ k~per 3He atom. In our case, the value is (1.95±3%)kBper atom, and has no such obvious interpretation as in the bulk liquid experiments. This constant specific heat very largely or entirely disappears in the presence of a free surface, and is replaced by a strongly temperature-dependent term, which, in the ternperature range 0.5 °Kto 1 °K,is linear through the point (0, 0.23 °K). One has, therefore, to assume that much of the 3He has left the body of the film; and since it is known that 4He is preferentially adsorbed at the substrate surface [3,6j it must have migrated to the free surface, where it takes part in some other form of thermal excitation. This observation forms a rather direct confirmation of the existence of surface states of 3He on an isotopic He mixture. The results do not permit a determination of the nature of the surface excitations. A very similar linear variation has been found with pure 4He monolayers on the same adsorbent preplated with nitrogen [8]. In magnitude and ternperature dependence the results are also very similar to the surface contributions which can be identified in films of pure 3He [2,3] and 4He [1,3] which we have noted might be attributed to ripplon modes. In the case of surfaces of 3He atoms, however, it is not at present clear that ripplons are not highly attenuated by Landau damping, as thermal phonons are in bulk liquid 3He at low temperatures, although this could be calculated. Andreev’s theory [9] which gives a successful explanation of the temperature variation of the surface tension of 3He - 4He liquid solutions [101, gives no reason for the existence of surface states, but treats them as non-degenerate fermions. According to this theory, the number of surface states is strongly temperature dependent, and at 0.5 °Kabout 90% of the 3He atoms present in the film would be concentrated at the surface, which is consistent with our result. However, an
LETTERS
l4June 1971
areal number density of this magnitude would imply, assuming the effective mass given by the surface tension experiments [10], that the surface states had some degree of degeneracy, so that the theory is not immediately applicable. Moreover, in the case of films the concentration far from the surface, which for bulk liquid and in the theory is practically constant, becomes temperature dependent since it is greatly affected by migration of 3He atoms to the surface. Neither Lekner’s theory [4], which treats a single fermion, nor Bowley’s [11], which is concerned with 4He, appears directly relevant to these observations. Nuclear resonance experiments, which we are now carrying out, may give more information on the state of degeneracy of the surface atoms. We are grateful to A.J. Legett, J. Lekner and J. A. Plaskett for helpful discussions. The work was carried out with the help of an SRC equipment grant and Research Studentship (A.E.), and was also partly supported by the U.S. Air Force Office of Scientific Research through the European Office of Aerospace Research under Grant EOOAR 68-0023
References [1] D. F. Brewer, A.J.Symonds and A. L. Thomson, Phys. Rev. Letters 15 (1965) 182. [2] L.T.Sun, M.Sc.Thesis, University of Sussex 1969 (unpublished). [3] D. F. Brewer, J.Low Temp. Phys. 3 (1970) 205.
[4] J. Lekner, Phil. Mag. 22 (1970) 669. [5] A.J.Dahm, Phys. Rev. 180 (1969) 259. [61 A. Evenson, D.F.Brewer and A. L.Thomson,
Eleventh Conf. temperature physics, eds. J. F.Tnt. Allen, D. on M. Low Finlayson and D. M. McCall (St. Andrews, 1968) Vol. 1, p.125. [7] R.de Bruyn Ouboter, K. W. Taconis, C. Ic Pair and J.J.M.Beenakker, Physica 26(1960) 853; D.O.Edwards, D.F.Brewer, M. Skertic and M. Yagub, Phys.F.Seligman, Rev. Letters 15
(1965) 773. [8] A. L. Thomson, D. F. Brewer and E. Evenson, Proc. Tenth Tnt. Cod, on Low temperature physics (Moscow 1968) Vol.1, p.507. [9] A. F. Andreev, J. Exptl. Theoretic. Phys. (USSR) 50 (1966) 1415; Soviet Phys.JETP 23 (1966) 939. [10] K. N. Zinovieva and A. T. Boldarev, J. Expt.
Theoret. Phys. (USSR) 56 (1969) 1089.
[11]R. M. Bowley, J. Phys. C. 3 (1970) 2012.
308
PHYSICS LETTERS
14 June 1971
3He ON AN ADSORBED SURFACE OF LOW TEMPERATURES 3He - 4HeSTATES FILM AT D. F. BREWER, A. EVENSON* and A. L. THOMSON School of Mathematical and Physical Sciences, University of Sussex, Falmer, Brighton BN 1 9 QH, UK Received 26 April 1911
An adsorbed 3He — 4He mixture filling a porous material has a constant specific heat between O.5°Kand 1 °K. With partial fillings, when a free surface is present, this is replaced by a temperature—dependent term, attributable probably to 3He surface states.
The existence of a surface contribution to the specific heat of pure helium films is well established [1-3], We report here a new phenomenon in the specific heat of adsorbed 3He - 4He mixture films at low temperatures, which may be
of 3He atoms at the free surface of the film. This is probably interpreted as thethe result mostofdirect a highevidence concentration so far produced for the existence of surface states of 3He in an isotopic liquid helium solution, which have previously been proposed to explain certain experiments on surface tension and others with negative ions [4,5]. The adsorbed film was formed on Vycor p0rous glass which had an effective mean pore diameter of 62.4 A and a surface area of 580m2 [1,3]. Nearly all of the original gas sample was condensed, a negligible amount remaining in the vapour phase in equilibrium with the adsorbate, so that the nominal concentration is essentially the average concentration of the adsorbate. The results have been corrected for heat of desorption, calculated from separate adsorption data [6]. Fig. 1 shows the specific heat of a film mixture of 3He molar concentration X = 0.09, at two coverages. The larger coverage relates to a situation in which the pores are full, while in the smaller one they are partly empty and a free surface is present. The two cases show a striking difference in behaviour at the lower temperatures. Three features are specially notable: (i) The residual “~mbefr~” anomaly. In bulk liquid He solutions, the temperature of the maximum in the specific heat decreases with addition *
Present address: Unilever Research Laboratories,
Isleworth, 455 London Road, London, Middlesex.
a
I ~.,
-
•
I
Fraction
~
592 cm3
-
2
—
o
0.5
T3~~
1.0
1.5
~MP~AThP~
2.0 ,
K
Fig. 1. Specific heat of adsorbed He mixture film with (I) and without (0) a free surface. TA and T 4He and of a 9% 3He in 4He bulktemperatures solution, Tsize is the temperature 3ofare the the lambda of pure maximum in the specific heat of pure 4He filling the pores of the same adsorbent. of 3He, and in pure 4He films it both decreases and is less well defined. In this film mixture, to a fair approximation the impurity effect and the size effect are additive; (ii) The full-pore specific heat reaches a constant value at low temperatures (between 0.9 °Kand 0.5 °K); (iii) The “film” specific heat (i.e., in the presence of a free surface) is strongly temperature dependent and decreases rapidly below the full-pore value at the lower temperatures. We restrict further remarks to the two last
observations, which we partly interpret as 30’?
Volume 35A, number 4
PHYSICS
4He contribution to the follows. Below 1 °K, the specific heat is negligibly small, and the constant full-pore value is presumed to be a result of a classical independent-particle motion of the 3He atoms or quasiparticles. A similar result has been found before in bulk liquid solutions rich in 4He [7], in which the constant value is very nearly ~ k~per 3He atom. In our case, the value is (1.95±3%)kBper atom, and has no such obvious interpretation as in the bulk liquid experiments. This constant specific heat very largely or entirely disappears in the presence of a free surface, and is replaced by a strongly temperature-dependent term, which, in the ternperature range 0.5 °Kto 1 °K,is linear through the point (0, 0.23 °K). One has, therefore, to assume that much of the 3He has left the body of the film; and since it is known that 4He is preferentially adsorbed at the substrate surface [3,6j it must have migrated to the free surface, where it takes part in some other form of thermal excitation. This observation forms a rather direct confirmation of the existence of surface states of 3He on an isotopic He mixture. The results do not permit a determination of the nature of the surface excitations. A very similar linear variation has been found with pure 4He monolayers on the same adsorbent preplated with nitrogen [8]. In magnitude and ternperature dependence the results are also very similar to the surface contributions which can be identified in films of pure 3He [2,3] and 4He [1,3] which we have noted might be attributed to ripplon modes. In the case of surfaces of 3He atoms, however, it is not at present clear that ripplons are not highly attenuated by Landau damping, as thermal phonons are in bulk liquid 3He at low temperatures, although this could be calculated. Andreev’s theory [9] which gives a successful explanation of the temperature variation of the surface tension of 3He - 4He liquid solutions [101, gives no reason for the existence of surface states, but treats them as non-degenerate fermions. According to this theory, the number of surface states is strongly temperature dependent, and at 0.5 °Kabout 90% of the 3He atoms present in the film would be concentrated at the surface, which is consistent with our result. However, an
LETTERS
l4June 1971
areal number density of this magnitude would imply, assuming the effective mass given by the surface tension experiments [10], that the surface states had some degree of degeneracy, so that the theory is not immediately applicable. Moreover, in the case of films the concentration far from the surface, which for bulk liquid and in the theory is practically constant, becomes temperature dependent since it is greatly affected by migration of 3He atoms to the surface. Neither Lekner’s theory [4], which treats a single fermion, nor Bowley’s [11], which is concerned with 4He, appears directly relevant to these observations. Nuclear resonance experiments, which we are now carrying out, may give more information on the state of degeneracy of the surface atoms. We are grateful to A.J. Legett, J. Lekner and J. A. Plaskett for helpful discussions. The work was carried out with the help of an SRC equipment grant and Research Studentship (A.E.), and was also partly supported by the U.S. Air Force Office of Scientific Research through the European Office of Aerospace Research under Grant EOOAR 68-0023
References [1] D. F. Brewer, A.J.Symonds and A. L. Thomson, Phys. Rev. Letters 15 (1965) 182. [2] L.T.Sun, M.Sc.Thesis, University of Sussex 1969 (unpublished). [3] D. F. Brewer, J.Low Temp. Phys. 3 (1970) 205.
[4] J. Lekner, Phil. Mag. 22 (1970) 669. [5] A.J.Dahm, Phys. Rev. 180 (1969) 259. [61 A. Evenson, D.F.Brewer and A. L.Thomson,
Eleventh Conf. temperature physics, eds. J. F.Tnt. Allen, D. on M. Low Finlayson and D. M. McCall (St. Andrews, 1968) Vol. 1, p.125. [7] R.de Bruyn Ouboter, K. W. Taconis, C. Ic Pair and J.J.M.Beenakker, Physica 26(1960) 853; D.O.Edwards, D.F.Brewer, M. Skertic and M. Yagub, Phys.F.Seligman, Rev. Letters 15
(1965) 773. [8] A. L. Thomson, D. F. Brewer and E. Evenson, Proc. Tenth Tnt. Cod, on Low temperature physics (Moscow 1968) Vol.1, p.507. [9] A. F. Andreev, J. Exptl. Theoretic. Phys. (USSR) 50 (1966) 1415; Soviet Phys.JETP 23 (1966) 939. [10] K. N. Zinovieva and A. T. Boldarev, J. Expt.
Theoret. Phys. (USSR) 56 (1969) 1089.
[11]R. M. Bowley, J. Phys. C. 3 (1970) 2012.
308