Abstract
Aluminum, indium, and lead fine particles with free surfaces were made by evaporation in helium gas to study the size dependence of the superconducting transition temperatureT c in very small particles. The transition temperature was determined from the change of diamagnetic susceptibility with temperature. The present experiment shows thatT c rises with decrease of the average diameter\(\bar d\) for aluminum and indium, while it remains nearly constant for lead. The enhancement factorsT c /T b c (T b c isT c for the bulk material) in the case of\(\bar d = 100 {\AA}\) are determined as 1.45, 1.15, and 1.0 for aluminum, indium, and lead, respectively. The effect of the soft phonon mode arising from the increasing fraction of surface satisfactorily explains the experiment with respect to both the size dependence and the difference among elements by a rather simple model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. Kubo,J. Phys. Soc. Japan 17, 975 (1962).
R. Denton, B. Mühlschlegel, and D. J. Scalapino,Phys. Rev. Lett. 26, 707 (1971).
J. P. Hurault, K. Maki, and T. Béal-Monod,Phys. Rev. B 3, 762 (1971); B. Mühlschlegel, D. J. Scalapino, and R. Denton,Phys. Rev. B 6, 1767 (1972).
T. Fujita, K. Oshima, N. Wada, and T. Sakakibara,J. Phys. Soc. Japan 29, 797 (1970).
S. Kobayashi, T. Takahashi, and W. Sasaki,J. Phys. Soc. Japan 31, 1442 (1971); S. Kobayashi, T. Takahashi, and W. Sasaki,J. Phys. Soc. Japan 32, 1234 (1972).
P. Townsend, S. Gregory, and R. G. Taylor,Phys. Rev. B 5, 54 (1972); P. N. Chubovet al., Soviet Phys.—JETP 28, 389 (1969); O. A. E. Churney and J. Shewchun,Can. J. Phys. 47, 1101 (1969); I. S. Khurkhareva,Soviet Phys.—JETP 16, 828 (1963).
B. Abeleset al., Phys. Rev. Lett. 17, 632 (1966); W. Buckel and R. Hilsch,Z. Phys. 138, 109 (1954).
J. H. P. Watson,Phys. Rev. 148, 223 (1966).
J. H. P. Watson,Phys. Rev. B 2, 1282 (1970).
K. K. Man'kovskiiet al., Soviet Phys.—JETP 32, 404 (1971).
M. Stronginet al., Phys. Rev. B 1, 1078 (1970).
N. Wada,Japan J. Appl. Phys. 6, 555 (1967).
K. Kimoto and I. Nishida,Japan J. Appl. Phys. 6, 1047 (1967).
S. Matsuo, H. Miyata, and S. Noguchi,Japan J. Appl. Phys. 13, 351 (1974).
S. Matsuo, S. Hayashi, and S. Noguchi,J. Phys. Soc. Japan 31, 1593 (1971).
A. Rothwarf,Phys. Lett. 30A, 55 (1969).
R. H. Parmenter,Phys. Rev. 166, 392 (1968).
R. E. Allen and F. W. de Wette,Phys. Rev. 187, 883 (1969).
J. Appel,Phys. Rev. Lett. 21, 1164 (1968).
W. L. McMillan,Phys. Rev. 167, 331 (1968).
J. M. Dickey and A. Paskin,Phys. Rev. B 1, 851 (1970).
W. B. Pearson, Handbook of Lattice Spacings and Structures of Metals (Pergamon, London, 1958) p. 124.
J. W. Garland and P. B. Allen,Physica 55, 669 (1971).
A. A. Maradudin,et al., Solid State Physics, Suppl. 3,Theory of Lattice Dynamics in the Harmonic Approximation, 2nd ed. (Academic, 1971), p. 438.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Matsuo, S., Sugiura, H. & Noguchi, S. Superconducting transition temperature of aluminum, indium, and lead fine particles. J Low Temp Phys 15, 481–490 (1974). https://doi.org/10.1007/BF00654622
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00654622