Electron Contribution to the Temperature Dependence of the Elastic Constants of Cubic Metals. II. Superconducting Metals

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Abstract
A theory is presented to explain the difference in elastic shear constants between normal and superconducting metals as a function of temperature. The development is based upon the BCS theory of superconductivity in the weak-coupling limit and the quantum mechanical theory of elasticity discussed in the first article of this series. Expressions are presented for the first and second derivatives of the energy gap and critical field with respect to shear strains in terms of parameters for the normal state. Representative calculations are performed to show that the model chosen is capable of giving the correct order of magnitude and sign for the difference in elastic shear constants at absolute zero. It is also found that although the second derivative of the free-energy difference, with respect to shear strains, disappears at the superconducting critical temperature, the corresponding second derivative of the entropy difference is finite at the superconducting critical temperature and is proportional to the difference in elastic shear constants at absolute zero.