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Excess heat capacities of 3He films adsorbed on Grafoil
Physica B 284}288 (2000) 228}229
Excess heat capacities of He "lms adsorbed on Grafoil Masashi Morishita *, Hiroshi Nagatani , Hiroshi Fukuyama Institute of Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan Department of Physics, Graduate School of Science, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
Abstract Excess heat capacities (C ) both in the "rst- and second-layer He "lms adsorbed on Grafoil substrate have been measured at temperatures down to 100 lK. With increasing density, the high-temperature C increases rather abruptly somewhat before the second-layer promotion in the uniform "lm. Otherwise, C is roughly density-independent. The results are consistent with the model that C arises from nuclear-spin degrees of freedom in the amorphous He adsorbed on substrate heterogeneities and that the amorphous He has also a layered structure. 2000 Elsevier Science B.V. All rights reserved. Keywords: 2D helium; Amorphous; Heat capacity; He 2D
1. Introduction In many previous heat-capacity measurements of He thin "lms adsorbed on Grafoil (exfoliated graphite) substrate, almost temperature (¹)-independent excess heat capacities (C ) have been observed below several tens mK besides heat capacities of the uniform two-dimensional (2D) #uid and solid He [1}3]. C is believed to arise from nuclear-spin degrees of freedom in the amorphous He adsorbed on substrate heterogeneities such as boundaries of graphite platelets from comparison with the data for thoroughly heterogeneous substrates such as Vycor glass or silver powders [2,4]. However, detailed areal density- and ¹-dependencies of C are not known until now. In this paper we discuss layer promotion in the amorphous He as well as the ¹-dependence of C deduced from heat-capacity data for the He "lms extended to a wide coverage range.
2. Experimental The apparatus and experimental techniques used in this work are the same as those in an accompanied paper * Corresponding author. E-mail address: [email protected] (M. Morishita)
[5]. Note that the total surface area (390 m) of Grafoil here is smaller by 13% and the ratio of the heterogeneous surface to the homogeneous one (15%) is larger by about a factor of two compared to those in our previous work [2].
3. Results and discussion Heat capacities of the He "lms were measured at 0.1(¹(80 mK at several di!erent areal densities (o) between 2 and 12 nm\. The excess heat capacity C extracted from these data are shown in Fig. 1. At o"2.1 and 4.1 nm\, C was obtained by subtracting C , the heat capacity of the uniform submonolayer 2D $ #uid, from the measured total heat capacity C . C was $ determined with good accuracy by "tting the C data to the formula c¹#b¹ [6] at high temperatures where C $ (the dashed line in Fig. 1) dominates over C . While, at 8.9, 9.8 and 10.5 nm\, the nuclear-spin heat capacity C of the uniform submonolayer 2D solid is so small that ( we can neglect it at ¹'0.2 mK. The dash}dot line in the "gure is an expected high temperature C at 8.4 nm\ ( assuming that the exchange frequency J is 9.3 lK [7]. Since, the promotion to the second-layer #uid occurs at 10.9 nm\ in the uniform "lm, C at 12.3 nm\ was deduced as was done for the submonolayer #uids.
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 4 6 4 - 3
M. Morishita et al. / Physica B 284}288 (2000) 228}229
229
that C does exist even in the "rst layer. It has a high temperature tail falling much faster than the second-layer one while they approach each other at the lowest temperature. Within the model by Golov and Pobell [4] this would indicate that the density in the second-layer amorphous solid distributes only in a low-density (or higher exchange energy) region. This is why it used to be considered that C exists only in the second layer, i.e., the "rst-layer C has not been detected in experiments done only down to a few mK.
Fig. 1. The excess heat capacities (C ) extracted from heat capacity data for the "rst- and second-layer He adsorbed on a Grafoil substrate. C seems to be classi"ed to two categories denoted by the solid lines, which suggests the layered structure. The layer promotion takes place between 8.9 and 9.8 nm\. The dashed line is a heat capacity of the uniform "rst-layer #uid at o"4.1 nm\, and the dash}dot line is that of the uniform "rst-layer solid at o"8.4 nm\ (see text).
Acknowledgements
The data in Fig. 1 fall into two categories denoted by the solid lines. We explain this by assuming a layered structure in the amorphous solid, i.e., the two lines correspond to the "rst- and second-layer placed between 8.9 and 9.8 nm\, which is somewhat below to that in the uniform "lm. One important conclusion is that C is not ¹-independent unlike the previous assumption but decreases gradually up to 20 mK with increasing temperature for the second-layer C . This ¹-dependence is similar to the observations in Vycor [4] and sintered silver powders [8] except that the cuto! temperature is slightly lower in Grafoil. Another important "nding is
References
This work is supported by the Grants-in-Aid for Scienti"c Research from the Ministry of Education, Science and Culture, Japan, the NEDO International Joint Research Grant and by the Cryogenics Center of University of Tsukuba.
[1] [2] [3] [4] [5]
D.S. Greywall, P.A. Busch, Phys. Rev. Lett. 65 (1990) 64. K. Ishida et al., Phys. Rev. Lett. 79 (1997) 3451. M. Morishita et al., J. Low Temp. Phys. 110 (1998) 351. A. Golov, F. Pobell, Phys. Rev. B 53 (1996) 12 647. M. Morishita, H. Nagatani, Hiroshi Fukuyama, in these Proceedings (LT-22), Physica B 284}288 (2000). [6] S. Misawa, in preparation. [7] H. Ikegami, K. Obara, D. Ito, H. Ishimoto, Phys. Rev. Lett. 81 (1998) 2478. [8] H. Kambara, S. Kishishita, T. Matsushita, T. Mamiya, Europhys. Lett. 46 (1999) 499.
Excess heat capacities of He "lms adsorbed on Grafoil Masashi Morishita *, Hiroshi Nagatani , Hiroshi Fukuyama Institute of Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan Department of Physics, Graduate School of Science, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
Abstract Excess heat capacities (C ) both in the "rst- and second-layer He "lms adsorbed on Grafoil substrate have been measured at temperatures down to 100 lK. With increasing density, the high-temperature C increases rather abruptly somewhat before the second-layer promotion in the uniform "lm. Otherwise, C is roughly density-independent. The results are consistent with the model that C arises from nuclear-spin degrees of freedom in the amorphous He adsorbed on substrate heterogeneities and that the amorphous He has also a layered structure. 2000 Elsevier Science B.V. All rights reserved. Keywords: 2D helium; Amorphous; Heat capacity; He 2D
1. Introduction In many previous heat-capacity measurements of He thin "lms adsorbed on Grafoil (exfoliated graphite) substrate, almost temperature (¹)-independent excess heat capacities (C ) have been observed below several tens mK besides heat capacities of the uniform two-dimensional (2D) #uid and solid He [1}3]. C is believed to arise from nuclear-spin degrees of freedom in the amorphous He adsorbed on substrate heterogeneities such as boundaries of graphite platelets from comparison with the data for thoroughly heterogeneous substrates such as Vycor glass or silver powders [2,4]. However, detailed areal density- and ¹-dependencies of C are not known until now. In this paper we discuss layer promotion in the amorphous He as well as the ¹-dependence of C deduced from heat-capacity data for the He "lms extended to a wide coverage range.
2. Experimental The apparatus and experimental techniques used in this work are the same as those in an accompanied paper * Corresponding author. E-mail address: [email protected] (M. Morishita)
[5]. Note that the total surface area (390 m) of Grafoil here is smaller by 13% and the ratio of the heterogeneous surface to the homogeneous one (15%) is larger by about a factor of two compared to those in our previous work [2].
3. Results and discussion Heat capacities of the He "lms were measured at 0.1(¹(80 mK at several di!erent areal densities (o) between 2 and 12 nm\. The excess heat capacity C extracted from these data are shown in Fig. 1. At o"2.1 and 4.1 nm\, C was obtained by subtracting C , the heat capacity of the uniform submonolayer 2D $ #uid, from the measured total heat capacity C . C was $ determined with good accuracy by "tting the C data to the formula c¹#b¹ [6] at high temperatures where C $ (the dashed line in Fig. 1) dominates over C . While, at 8.9, 9.8 and 10.5 nm\, the nuclear-spin heat capacity C of the uniform submonolayer 2D solid is so small that ( we can neglect it at ¹'0.2 mK. The dash}dot line in the "gure is an expected high temperature C at 8.4 nm\ ( assuming that the exchange frequency J is 9.3 lK [7]. Since, the promotion to the second-layer #uid occurs at 10.9 nm\ in the uniform "lm, C at 12.3 nm\ was deduced as was done for the submonolayer #uids.
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 4 6 4 - 3
M. Morishita et al. / Physica B 284}288 (2000) 228}229
229
that C does exist even in the "rst layer. It has a high temperature tail falling much faster than the second-layer one while they approach each other at the lowest temperature. Within the model by Golov and Pobell [4] this would indicate that the density in the second-layer amorphous solid distributes only in a low-density (or higher exchange energy) region. This is why it used to be considered that C exists only in the second layer, i.e., the "rst-layer C has not been detected in experiments done only down to a few mK.
Fig. 1. The excess heat capacities (C ) extracted from heat capacity data for the "rst- and second-layer He adsorbed on a Grafoil substrate. C seems to be classi"ed to two categories denoted by the solid lines, which suggests the layered structure. The layer promotion takes place between 8.9 and 9.8 nm\. The dashed line is a heat capacity of the uniform "rst-layer #uid at o"4.1 nm\, and the dash}dot line is that of the uniform "rst-layer solid at o"8.4 nm\ (see text).
Acknowledgements
The data in Fig. 1 fall into two categories denoted by the solid lines. We explain this by assuming a layered structure in the amorphous solid, i.e., the two lines correspond to the "rst- and second-layer placed between 8.9 and 9.8 nm\, which is somewhat below to that in the uniform "lm. One important conclusion is that C is not ¹-independent unlike the previous assumption but decreases gradually up to 20 mK with increasing temperature for the second-layer C . This ¹-dependence is similar to the observations in Vycor [4] and sintered silver powders [8] except that the cuto! temperature is slightly lower in Grafoil. Another important "nding is
References
This work is supported by the Grants-in-Aid for Scienti"c Research from the Ministry of Education, Science and Culture, Japan, the NEDO International Joint Research Grant and by the Cryogenics Center of University of Tsukuba.
[1] [2] [3] [4] [5]
D.S. Greywall, P.A. Busch, Phys. Rev. Lett. 65 (1990) 64. K. Ishida et al., Phys. Rev. Lett. 79 (1997) 3451. M. Morishita et al., J. Low Temp. Phys. 110 (1998) 351. A. Golov, F. Pobell, Phys. Rev. B 53 (1996) 12 647. M. Morishita, H. Nagatani, Hiroshi Fukuyama, in these Proceedings (LT-22), Physica B 284}288 (2000). [6] S. Misawa, in preparation. [7] H. Ikegami, K. Obara, D. Ito, H. Ishimoto, Phys. Rev. Lett. 81 (1998) 2478. [8] H. Kambara, S. Kishishita, T. Matsushita, T. Mamiya, Europhys. Lett. 46 (1999) 499.