Quantum-thermodynamic treatment of intrinsic anharmonicity; Wallace’s theorem revisited |
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Authors: | Michel HG Jacobs Bernard HWS de Jong |
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Institution: | (1) Department Theoretical Geophysics, Faculty of Geosciences, Utrecht University, Budapestlaan 4, 3584 CD Utrecht, The Netherlands;(2) Petrology Group, Faculty of Geosciences, Utrecht University, Budapestlaan 4, 3584 CD Utrecht, The Netherlands |
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Abstract: | Wallace (in Thermodynamics of crystals, 1972) developed a theorem, rooted in rigid lattice dynamics, which incorporates intrinsic anharmonic effects in solids. The practical
application of this theorem in mineral physics is computationally involved and this is the main reason for the theorem not
getting the attention it deserves. Because intrinsic anharmonicity is an important issue at the extreme conditions in planetary
mantles, we derived a method which removes the computational obstacles in applying this theorem. We extended the theorem to
incorporate details of the phonon spectrum and tested our algorithm on forsterite (Mg2SiO4). Using a least squares inversion technique applied to all available experimental data, we show that it results in an accurate
representation of thermodynamic properties and sound wave velocities of Mg2SiO4 in its complete pressure–temperature stability range. We also show that the accuracy of our results is not significantly
affected by the use of a different equation of state. |
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Keywords: | Sound velocity Anharmonicity Equation of state Forsterite Thermal expansivity |
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