Cláudio A. Perottoni, Atilio Minotto Neto, Janete E. Zorzi
{"title":"Vibrational Density of States-Weighted Grüneisen Parameters of Graphite","authors":"Cláudio A. Perottoni, Atilio Minotto Neto, Janete E. Zorzi","doi":"10.1007/s13538-024-01502-1","DOIUrl":null,"url":null,"abstract":"<p>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 (<span>\\(G_{a}(\\Theta )\\)</span> and <span>\\(G_{c}(\\Theta )\\)</span>) from the temperature-dependent linear thermal expansion coefficients parallel to the crystallographic <i>a</i>- and <i>c</i>-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 <span>\\(G_{a}(\\Theta )\\)</span>, centered around <span>\\(\\Theta\\)</span> = 100 K and <span>\\(\\Theta\\)</span> = 1200 K, and one narrow peak in <span>\\(G_{c}(\\Theta )\\)</span> centered around <span>\\(\\Theta\\)</span> = 100 K. The low-energy, narrow peak of negative amplitude in <span>\\(G_{a}(\\Theta )\\)</span> 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 <i>a</i>-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 <span>\\(G_{a}(\\Theta )\\)</span> and <span>\\(G_{c}(\\Theta )\\)</span>, plus an asymmetric Gaussian peak with positive amplitude in <span>\\(G_{a}(\\Theta )\\)</span>, is proposed which still captures the main features of graphite’s thermal expansion.</p>","PeriodicalId":499,"journal":{"name":"Brazilian Journal of Physics","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Brazilian Journal of Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s13538-024-01502-1","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
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 (\(G_{a}(\Theta )\) and \(G_{c}(\Theta )\)) 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 \(G_{a}(\Theta )\), centered around \(\Theta\) = 100 K and \(\Theta\) = 1200 K, and one narrow peak in \(G_{c}(\Theta )\) centered around \(\Theta\) = 100 K. The low-energy, narrow peak of negative amplitude in \(G_{a}(\Theta )\) 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 \(G_{a}(\Theta )\) and \(G_{c}(\Theta )\), plus an asymmetric Gaussian peak with positive amplitude in \(G_{a}(\Theta )\), is proposed which still captures the main features of graphite’s thermal expansion.
期刊介绍:
The Brazilian Journal of Physics is a peer-reviewed international journal published by the Brazilian Physical Society (SBF). The journal publishes new and original research results from all areas of physics, obtained in Brazil and from anywhere else in the world. Contents include theoretical, practical and experimental papers as well as high-quality review papers. Submissions should follow the generally accepted structure for journal articles with basic elements: title, abstract, introduction, results, conclusions, and references.