Superconducting transition temperatures of the elements related to elastic constants

TL;DR

This paper explores how superconducting transition temperatures of elements relate to elastic constants, atomic volume, and atomic number, proposing a formal expression and identifying correlations through theoretical and empirical analysis.

Contribution

It introduces a formal expression for Tc based on atomic and elastic properties and establishes correlations between elastic constants and superconducting temperatures for bcc transition metals.

Findings

Superconducting elements occupy a specific region in atomic number vs. volume graph.

Tc is related to elastic constants and atomic properties via BCS theory.

A linear relationship exists between Tc and the Cauchy deviation C* for bcc transition metals.

Abstract

For a given crystal structure, say body-centred-cubic, the many-body Hamiltonian 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, Omega. Since the thermodynamic quantities can be determined from H, we conclude that Tc, the superconducting transition temperature, when it is non-zero, may be formally expressed as Tc = Tc^(M) (Z, Omega). 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) Tc 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) Tc 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.