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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Anton-Schmidt equation of state ： ウィキペディア英語版 Anton-Schmidt equation of state The Anton-Schmidt equation is an empirical equation of state for crystalline solids, e.g. for pure metals or intermetallic compounds. Quantum mechanical investigations of intermetallic compounds show that the dependency of the pressure under isotropic deformation can be described empirically by :$$ p(V) = - \beta \left(\frac\right)^n \ln\left(\frac\right) . Integration of $p(V)$ leads to equation of the state for the total energy. The energy $E$ required to compress a solid to volume $V$ is :$$ E(V) = - \int_V^\infty p(V^\prime) dV^\prime which gives :$$ E(V) = \frac \left(\frac\right)^ \left(- \frac\right ) - E_\infty . The fitting parameters $\backslash beta,\; n$ and $V\_0$ are related to material properties, where :$\backslash beta$ is the bulk modulus $K\_0$ at equilibrium volume $V\_0$. :$n$ correlates with the Grüneisen parameter $n\; =\; -\backslash frac\; -\; \backslash gamma\_G$.〔Otero-de-la-Roza, et al., Gibbs2: A new version of the quasi-harmonic model code. Computer Physics Communications 182.8 (2011): 1708-1720. DOI: 10.1016/j.cpc.2011.04.016 ()〕〔Jund, Philippe, et al., Physical properties of thermoelectric zinc antimonide using first-principles calculations., Physical Review B 85.22 (2012) ().〕 However, the fitting parameter $E\_\backslash infty$ does not reproduce the total energy of the free atoms.〔Atomic Simulation Environment documentation of the Technical University of Denmark, Department of Physics ()〕 The total energy equation is used to determine elastic and thermal material constants in quantum chemical simulation packages.〔〔Gilgamesh chemical software documentation of the Department of Chemical Engineering of Carnegie Mellon University ()〕 == See also == * Murnaghan equation of state * Rose–Vinet equation of state * Birch–Murnaghan equation of state 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Anton-Schmidt equation of state」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.