Sublimation of a volatile component as a possible mechanism for thermoelectric material degradation

A physical model of the sublimation of a volatile component from a thermoelectric material has been developed. On its basis, two versions of the mathematical description of the degradation process of thermoelectric material are presented. The first of them takes into account only the diffusion of tellurium as a volatile impurity to the evaporation surface, on which the pressure and, consequently, the concentration of atoms of the volatile component are considered to be known. The second explicitly takes into account the volatility of the evaporating component and, hence, the boundary flux on the evaporation surface. In both cases, an analytical solution of the one-dimensional diffusion equation is obtained taking into account the presence of a temperature gradient along the length of the leg. Further, by computer methods in the Mathcad environment, the time dependence of the thickness of the layer with a reduced concentration of the volatile component and the nature of the distribution of the concentration of this component in it was determined. On this basis, the degradation time of thermoelectric material due to the loss of volatile components is estimated and the requirements for the protective coating of thermoelectric branches are established.