Intermediate statistics in thermoelectric properties of solids
We study the thermodynamics of a crystalline solid by applying intermediate statistics manifested by q-deformation. We based part of our study on both Einstein and Debye models, exploring primarily deformed thermal and electrical conductivities as a function of the deformed Debye specific heat. The results revealed that the q-deformation acts in two different ways but not necessarily as independent mechanisms. It acts as a factor of disorder or impurity, modifying the characteristics of a crystalline structure, which are phenomena described by q-bosons, and also as a manifestation of intermediate statistics, the B-anyons (or B-type systems). For the latter case, we have identified the Schottky effect, normally associated with high-Tc superconductors in the presence of rare-earth-ion impurities, and also the increasing of the specific heat of the solids beyond the Dulong-Petit limit at high temperature, usually related to anharmonicity of interatomic interactions. Alternatively, since in the q-bosons the statistics are in principle maintained the effect of the deformation acts more slowly due to a small change in the crystal lattice. On the other hand, B-anyons that belong to modified statistics are more sensitive to the deformation.