Galvano-thermomagnetic phenomena and the figure of merit in bismuth—I transport properties of intrinsic material

Abstract

Transport theory based on the relaxation time formalism has been applied to bismuth; the results are used in Part II of this paper to determine the figure of merit of Bi in energy conversion processes. Using the Jones-Shoenberg model for bismuth, analytic expressions have been derived for the electrical resistivity, thermal conductivity, and for the Hall, Seebeck and Nernst coefficients. The Boltzmann transport equation was solved for the perturbed distribution function using anisotropic relaxation times. The result was then introduced in the transport integrals for the electric current and for energy flux to obtain the phenomenological equations for each set of charge carriers associated with a given ellipsoid. The contributions of each group of carriers were then added in the common symmetry coordinate system of the crystal to obtain the above-mentioned transport coefficients. To derive analytic expressions, it was necessary to consider the special cases where the magnetic field is aligned with each of the three symmetry axes and to pass to the limit of very low or very high magnetic fields.