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 γ⊥, 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 γ⊥ 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 ωD(n) of the Debye distributions having the same nth moments 〈ωn〉 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) =Σγjωjn /Σωjn corresponding to γ∥(n) and γ⊥(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.