Vibrational Density of States-Weighted Grüneisen Parameters of Graphite

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发表日期：

2024年5月30日

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Cláudio A. Perottoni,
Atilio Minotto Neto,
Janete E. Zorzi

摘要

The vibrational spectrum determines, to a large extent, a material’s thermal expansion. However, extracting information on the material’s vibrational spectrum from the measured thermal expansion is an ill-conditioned inverse problem whose solution generally involves regularization techniques. In this work, the procedure for extracting the vibrational density of states-weighted Grüneisen parameter spectra ( $G_{a}(\Theta )$ $G_{a} (Θ)$ and $G_{c}(\Theta )$ $G_{c} (Θ)$ ) from the temperature-dependent linear thermal expansion coefficients parallel to the crystallographic a- and c-axis of materials with a hexagonal Bravais lattice is described and then applied to graphite. The resulting spectra, obtained by solving an inverse problem consisting of a pair of coupled Fredholm integrals of the first kind, exhibit two main contributions to $G_{a}(\Theta )$ $G_{a} (Θ)$ , centered around $\Theta$ $Θ$ = 100 K and $\Theta$ $Θ$ = 1200 K, and one narrow peak in $G_{c}(\Theta )$ $G_{c} (Θ)$ centered around $\Theta$ $Θ$ = 100 K. The low-energy, narrow peak of negative amplitude in $G_{a}(\Theta )$ $G_{a} (Θ)$ is in good agreement with a large and negative Grüneisen parameter previously reported for transverse acoustic modes in graphite and accounts for the negative thermal expansion exhibited by graphite along the a-axis up to about 655 K. A simplified vibrational density of states-weighted Grüneisen parameter spectra of graphite, consisting of the two lowest energy, narrow peaks in $G_{a}(\Theta )$ $G_{a} (Θ)$ and $G_{c}(\Theta )$ $G_{c} (Θ)$ , plus an asymmetric Gaussian peak with positive amplitude in $G_{a}(\Theta )$ $G_{a} (Θ)$ , is proposed which still captures the main features of graphite’s thermal expansion.