Hall Effect and Magnetoresistivity in Carbons and Polycrystalline Graphites

The Hall constant and magnetoresistance of a carbon (soft type) were investigated as a function of heat treatment temperature, ${T}_{\mathrm{ht}}$, (that is, crystallite size) at two ambient temperatures $T$ (78\ifmmode^\circ\else\textdegree\fi{} and 300\ifmmode^\circ\else\textdegree\fi{}K). The maximum in the Hall constant shifts toward higher heat treatments as the ambient temperature is lowered, in much the same way as does the maximum in the thermoelectric effect. Anomalies in the Hall curves in the range $1600<{T}_{\mathrm{ht}}<1900\ifmmode^\circ\else\textdegree\fi{}$C are shown to be due to impurities. No magnetoresistance is detectable for ${T}_{\mathrm{ht}}<1700\ifmmode^\circ\else\textdegree\fi{}$C; the magnetoresistance was found to be negative in the range $1700<{T}_{\mathrm{ht}}<2300\ifmmode^\circ\else\textdegree\fi{}$C and to be positive and rapidly increasing with ${T}_{\mathrm{ht}}$ above that. For both ambient temperatures the maximum of negative magnetoresistance occurs at about the same ${T}_{\mathrm{ht}}$ as the maximum of the Hall constant. Introduction of acceptors changes the magnetoresistance in the direction of lower ${T}_{\mathrm{ht}}$. The value of magnetoresistance and of Hall constant show a sensitive dependence on the alignment of crystallites in the samples. The results are interpreted in terms of the band model. It is concluded that the lower (full) and upper (empty) bands are slightly overlapping in graphite crystals, and furthermore, that the negative magnetoresistance is due to holes in the lower band and the positive magnetoresistance as well as the high diamagnetic susceptibility are due to electrons in the upper band. Remarks about the thermoelectric effect and electrical resistance are also included.