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Superconducting transition temperatures of the elements related to elastic constants



For a given crystal structure, say body-centred-cubic, the many-body Hamiltonian H in which nuclear and electron motions are to be treated from the outset on the same footing, has parameters, for the elements, which can be classified as (i) atomic mass M , (ii) atomic number Z , characterizing the external potential in which electrons move, and (iii) bcc lattice spacing, or equivalently one can utilize atomic volume, . Since the thermodynamic quantities can be determined from H , we conclude that T c , the superconducting transition temperature, when it is non-zero, may be formally expressed as T c = . One piece of evidence in support is that, in an atomic number vs. atomic volume graph, the superconducting elements lie in a well defined region. Two other relevant points are that (a) T c is related by BCS theory, though not simply, to the Debye temperature, which in turn is calculable from the elastic constants C 11 , C 12 , and C 44 , the atomic weight and the atomic volume, and (b) T c for five bcc transition metals is linear in the Cauchy deviation C * = ( C 12 - C 44 )/( C 12 + C 44 ). Finally, via elastic constants, mass density and atomic volume, a correlation between C * and the Debye temperature is established for the five bcc transition elements.



The European Physical Journal B - Condensed Matter and Complex SystemsSpringer Journals

Published: Jun 1, 2004

DOI: 10.1140/epjb/e2004-00213-y

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