Lattice Vibrations in Graphite

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In both natural and artificial graphites the crystallites are reported to be agglomerates of smaller units, each containing perhaps not more than 12 to 17 well-ordered planes. For atomic displacements perpendicular to a plane the restoring forces are much weaker than for similar displacements in the plane itself. For the latter the restoring forces are so strong that these lattice vibrations will not be excited at low temperatures. In this paper the requisite adaptation of the Debye theory of specific heat is given; it leads to a ${T}^{2}$ law instead of the familiar ${T}^{3}$ law at low temperatures. Unpublished measurements of specific heat between 25\ifmmode^\circ\else\textdegree\fi{} and 60\ifmmode^\circ\else\textdegree\fi{}K by Estermann and Kirkland are cited and compared with the theory; they are found to lead to a value ${\ensuremath{\theta}}_{D}={614}^{\ensuremath{\circ}}$ for the Debye temperature for the vibrations with weak restoring forces. Combining this with a value ${\ensuremath{\theta}}_{D}={2100}^{\ensuremath{\circ}}$ for the remaining modes of vibration is found to represent the specific heat over the whole range of temperature.