The Matthias Rules : Origins and Influence

Developed by Bernd Matthias, the “Matthias Rules”(MR) offer empirical guidelines that help determine the necessary conditions for the occurrence of superconductivity in elements, compounds, and alloys. Through the analysis of numerous experimental results detailing the discovery of new superconducting compounds, Matthias generalized which parameters are conducive to givising rise to higher superconductive transitions in materials. By simply considering the properties of individual atoms, he empirically deduced a functional form of Tc which depends on the number of valence electrons per atom. Furthermore, he asserted that crystal structure, atomic volume, and atomic mass also play significant roles in inducing superconductive transitions. This helped lead to the understanding that different types of “unconventional” superconductors exist which exhibit mechanisms for superconductivity beyond the electron-phonon interactions described by BCS theory. The origins and impacts of these assertions provided by Matthias are duly discussed. Deviations from these empirical rules are also presented and considered.