Anisotropic Thermal Expansion of Pyrolytic Graphite at Low Temperatures

Abstract

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.

Quantum mechanics based force field for carbon (QMFF-Cx) validated to reproduce the mechanical and thermodynamics properties of graphite

“…Below room temperature, we find good agreement with the experimental in-plane coefficients of thermal expansion, 16,80 not surprising considering the agreement in the specific heat at this temperature observed previously. From 300 to 100 K, the X6 potential overestimates the thermal expansion coefficient by 40%, although convergence is observed at higher temperatures.…”

Energetics of interlayer binding in graphite: The semiempirical approach revisited

“…As for the experimental interlayer distance, the zeroand room-temperature values are consistent if we take into account the c-axis thermal expansion. 54 We confirm in Table I that the GGA yields an in-plane lattice constant in an almost complete agreement with experiment but badly fails in predicting interlayer characteristics including d, U coh , and c 33 . In contrast, the agreements between the LDA calculations and experiments for all these interlayer characteristics are much better, with an almost perfect agreement for d. We also find that the vdW-DF yields a much better result for U coh than LDA and GGA, but predicts too large d, and there is still room for improvement.…”

“…The experimental lattice parameters at room temperature obtained by several authors 48,[50][51][52][53] are consistent with one another. The in-plane negative thermal expansion at low temperatures 25,54 implies that the zero-temperature value of a is at most 0.001 Å larger than the room-temperature one and a Ϸ 2.462-2.464 Å. These values are slightly larger and possibly more accurate than that of Baskin and Meyer 48 ͑Table I͒.…”

Large negative linear compressibility of Ag 3 [Co(CN) 6 ]

“…The opposite behavior is seen in layered anisotropic materials, such as graphite, where a compression perpendicular to the carbon layers produces a very different microscopic strain to a parallel compression (Fig. 4B); indeed, the ␥ i even have different signs in this case (38).…”