Generalized electrical conductivity and the melting point of thermionic metals

Abstract

.This work presents a new expression regarding non-equilibrium which generalizes electrical conductivity for metals employed as electron emitters. Also, it shows the connection between the melting point of the metal and a material-dependent coefficient which can be extracted by analyzing its thermionic emission. The Boltzmann transport equation is applied to a Kappa distribution function accounting for the electron population in metals. From this equation we obtain a dynamic conductivity within a modified Ohm law. As a new property, the electrical conductivity evolves with the temperature and then drops when the melting point is reached and completely vanishes. Such disappareance has been observed in many experimental studies such as the phase transition of metals using electrical wire explosions. This work provides additional details about this mechanism and makes a proposal for such experiments. Additionally, the generalized formula could serve to extend the scope of the empirical expressions which are based on polynomial fits and characterises the electrical conductivity. This new formula is tested using experimental data of metals widely employed as thermionic emitters finding a good agreement.