Heat flux rectification in graded Si_c Ge_{1-c} : Longitudinal and radial heat flows

We evaluate the rectification coefficient of the heat flux in graded SicGe1-c for longitudinal and radial heat flows, and for different stoichiometric spatial distributions c(z), either in the full stoichiometric range c is an element of [0, 1], and in the ranges with steepest variation of heat conductivity with composition, namely c is an element of [0, 0.1] and c is an element of [0.9, 1]. It turns out that rectification is more efficient in the mentioned ranges than in the full stoichiometric range. In the cylindrical case, the inhomogeneity in the length of internal and external perimeters of the system (geometrical inhomogeneity) is combined with the material inhomogeneity of the concentration profile, in contrast to the rectilinear situation, and influences the rectification coefficient, enhancing or reducing it, depending on the situation.