Lattice dynamics, inelastic neutron scattering and thermodynamic properties of minerals
Narayani Choudhury, Samrath L. Chaplot, Subrata Ghose, Mala N. Rao, Ranjan Mittal, 2002. "Lattice dynamics, inelastic neutron scattering and thermodynamic properties of minerals", Energy Modelling in Minerals, Carlo Maria Gramaccioli
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Understanding the structure of the Earth's interior, only indirectly inferred from seismic observations, requires modelling based on structural data, and the thermodynamic properties and phase relations of minerals at high pressures and temperatures. Since experimental studies under these conditions are often limited, particularly on high pressure phases that can be synthesised in only very small amounts, an important objective of earth sciences is to develop the capability of predicting these properties under various pressure and temperature conditions prevalent in the Earth. It is now possible to theoretically explore the entire spectrum of thermal vibrations of crystals using lattice dynamical methods. The vibrational average, known as the phonon density of states, is the basis for the calculation of the various thermodynamic properties. The accuracy of the theoretical calculations of the phonon density of states and the phonon dispersion relations can be evaluated by comparison with their experimental measurements by inelastic neutron scattering on large powder and single crystal samples, respectively. In this paper, the theory of lattice dynamics and inelastic neutron scattering and the experimental measurements using neutrons from reactor and spallation sources are reviewed, along with the derivation of thermodynamic properties from the calculated phonon density of states. Work accomplished in this area, both theoretical and experimental, on a number of major rock forming silicate minerals, including olivine (forsterite and fayalite), enstatite, various garnets and the aluminium silicate polymorphs (andalusite, sillimanite and kyanite) are discussed. We start with a discussion of lattice dynamics in a single crystal.
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