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The Semiempirical Method for Finding Thermal Characteristics of Simple Crystals

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A method for ab initio (using density functional theory) study of thermal properties of crystalline solids, based on the quasiharmonic approximation, is briefly summarized. On that basis the semiempirical method is proposed which combines the ab initio calculation of the static total energy with the Einstein model of crystal vibration. The Murnaghan equation of states is used as an analytical model for the static total energy. An exponential form of the phonon energy versus volume dependence is introduced which was proved to perform very well. Two parameters appearing in the model are found by fitting to easily available experimental data (tabular or measured). The method then provides thermodynamic characteristics in a large range of temperatures and pressures. On the other hand, the corrections due to the zero-point vibration are provided to some first principles results, like lattice parameters or bulk modulus. An interesting outcome of the model is the pressure dependence of the overheating temperature, for relatively low pressures. Tests performed on the example of fcc aluminum show remarkably good agreement of the results with experimental data. Therefore the method offers a handy tool for fast analysis of thermodynamics of simple crystalline systems, omitting the first principles evaluation of the phonon energies.
  • Institute of Physics, Wrocław University of Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
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