Anisotropic Thermal Expansion of Pyrolytic Graphite at Low Temperatures

Interferometric measurements of the linear thermal‐expansion coefficients α∥ and α⊥ in the ``c'' and ``a'' axial directions of well‐oriented pyrolytic graphite between approximately 20° and 270°K are reported. Grüneisen parameters γ∥ and ${\gamma }_{\perp }$ , defined for strain coordinates parallel and perpendicular to the ``c'' axis, respectively, have been calculated from the present thermal expansion coefficients and related data. Between 30° and 270°K γ∥ is positive, indicating the preponderance of longitudinal modes of vibration, while ${\gamma }_{\perp }$ is negative, indicating the predominance of transverse modes. The quasiharmonic approximation has been applied to calculate the characteristic temperatures θ(n) corresponding to the maximum frequencies ω<sub>D</sub>(n) of the Debye distributions having the same nth moments ${\mathrm{〈\omega }}^n〉$ as the specimens, which vary between approximately 420° and 2270°K as n increases from −3 to +6. The dimensional dependence of the moments, defined by γ(n) =Σγ<sub>j</sub>ω<sub>j</sub><sup>n</sup> /Σω<sub>j</sub><sup>n</sup> corresponding to γ∥(n) and ${\gamma }_{\perp }\mathrm{(n)}$ , and their variations with n, are consistent with the existence of low‐frequency modes of vibration between planes of atoms perpendicular to the ``c'' axis, and high‐frequency modes within the planes, a result supported by calculations of the rms displacements of the atoms.