Chemical Physics of Phonons & Superconductivity: A Heuristic Approach - Bucknum, Michael J. (2008)
Several potential heuristic angles are explored with regard to the parametrization of the superconducting transition temperature, T(c), and its relationship to the chemical physics of bonding. Fruitful angles explored in this paper include the relationship of the gas of Cooper pairs in a superconductor to a van der Waals equation of state for such a fluid and how it may be controlled and exploited through the consideration of such variables as pressure, P, and volume, V, of the fluid of Cooper pairs resident in a superconductor. Other angles explored, in an attempt to get a heuristic handle on the superconducting transition temperature, T(c), for superconducting compositions across the Periodic Table, include the introduction of a Morse’s anharmonic chemical bond potential for the Debeye frequency of the phonons as it emerges from the central result for T(c) in superconductors from the Bardeen-Cooper-Schreifer (BCS) formulation of superconductivity. Yet another angle explored in this heuristic reasoning, is the use of a Badger’s relationship between chemical bond force constant, k, and equilibrium internuclear distance, r(ₑ), to try to gain some understanding of the nature of the electron-phonon coupling mechanism in superconductors. A relationship between r(ₑ) and D(e) emerges as a result of this line of thought, given as r(ₑ)D(ₑ) = “critical temperature constant”, from which examination of spectroscopic data across the Periodic Table may yield a compositional solution of the appropriate chemical bonding, with the assumption of the proper electron-phonon coupling constant, C, and density of states, N(0), that ultimately may be yield more desirable superconductivity transition temperatures.