Electrical properties of transition-metal carbides of group IV

Abstract

Electrical resistivities of six single crystals of group-IVB transition-metal carbides are reported for temperatures between 4 and 1000 K. Hall coefficients of the crystals are reported for temperatures to 350 K. The chemical analyses of the ratio of carbon-to-metal atoms in the crystals (0.89 to 0.99) were verified by an inverse linear relationship between the carbon-vacancy concentration and the low-temperature Hall mobilities. Bloch-Gr\"uneisen theory provides a fit to the temperature dependence of the resistivity data that passes the ${\ensuremath{\chi}}^{2}$ test for ${\mathrm{TiC}}_{\mathrm{x}}$ and ${\mathrm{ZrC}}_{\mathrm{x}}$ but not for ${\mathrm{HfC}}_{0.99}$. The measurements reveal a tendency toward resistivity saturation at high temperature that is well described by a parallel-resistance model in which the saturation resistivity corresponds to a carrier mean free path roughly equal to the lattice constant. The measurements are compared to earlier experimental studies and to predictions of band-structure calculations. Theories of electronic transport are evaluated.