Studies on Transition Temperature of the Superconducting Materials Related to Elastic Constants

Abstract

For a face-centered-cubic structure crystal the parameters like atomic mass M, atomic number Z, lattice spacing are the important factors in the determination of a many body Hamiltonian H. Instead of using fcc lattice spacing we can also utilize atomic volume Ω. Using the superconducting transition temperature expressed as Tc = Tc(M)(Z,Ω), a well defined region in superconducting elements is possible. Tc may also be related to BCS theory through Debye temperature. This Debye temperature is related to elastic constants C11, C12 and C44, atomic weight and atomic volume. Also Tc for five fcc transitions metals is linear in the Cauchy deviation C* = (C12 - C44)/( C12 + C44), such linearity is also seen in bcc transition elements. Finally via elastic constants mass density and atomic volume, a correlation between C* and the Debye Ω temperature has been established for the five fcc transition elements. This correlation indirectly sets up a relation between transition temperature and elastic constant. 
 
 Bangladesh J. Sci. Ind. Res. 42(2), 203-212, 2007