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Generalized Einstein-Model for High-T, P Thermal Properties of Al Crystal

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Due to intricate calculations for phonon density-of-states (p-dos), full-lattice dynamics are hardly ever used to derive thermodynamics at high-T condition. Instead, either continuum Debye-model or mono-frequency Einsteinmodel (EM) at the quasi-harmonic level is frequently employed with desirable accuracy. Conventional EM assumes crystal as identical independent harmonic oscillators and p-dos is replaced by delta function. Thus, EM ignores correlation between vibrating atoms/ions in a crystal. We propose new method to estimate generalized (single) Einstein frequency ωE or equivalent temperature E. It is based on the fact that the interaction potential and thus the binding energy are asymmetric about the equilibrium lattice constant. This asymmetry in the binding energy is the cause of thermal expansion, and based on this energy functional E is deduced. Anharmonicity in E is parameterized and it is shown to be related to Gr√ľneisen parameter. This generalized EM is used to deduce various high-T thermal properties of fcc-Al, and the shock Hugoniot. Results are compared and discussed in light of other findings.
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Keywords: Aluminum; Einstein-Model; Shock Hugoniot; Thermal Properties

Document Type: Research Article

Affiliations: 1: Department of Physics, Sardar Patel University, Vallabh Vidyanagar 388120, Gujarat, India 2: Department of Physics, School of Sciences, Gujarat University, Ahmedabad 380009, Gujarat, India

Publication date: November 1, 2016

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