Thermoelectric power in alloys with phase separation (composites)

A thermopower formula is derived for composites: Sigma(i) upsilon(i)/kappa(i)/S(i)-kappa/S/kappa(i)/S(i)+2 kappa/S = 0 (kappa(i) and kappa are the specific thermal conductivities, S(i) and S are the Seebeck coefficients of the phase i and the composite, respectively, and upsilon(i) is the volume fraction of the phase i). This formula can be applied for calculating the Seebeck coefficient (thermoelectric power) of amorphous transition-metal-metalloid alloys, for which amorphous phase separation occurs for large ranges of concentration. There are two contributions to Si, a scattering term and a contribution due to electron transfer between the phases maintaining a common electrochemical potential mu. The theory predicts discontinuities in the concentration dependence of the Seebeck coefficient of metallic composites. It is argued that in amorphous composites these discontinuities occur very precisely at upsilon(i) = 1/3. This phenomenon can be used to characterize the crystallization kinetics of amorphous alloys. The theory is applied to a-Cr(1-x)Si(x) alloys for calculation of S versus x. Both the calculated S(x) dependence and the discontinuities agree very well with the experimental data, as long as x < 0.67; the deviations at x > 0.67 are interpreted to be caused by the p-d bonds at the phase boundaries.