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Theoretical modelling of the elastic properties of forsterite: A polyhedral approach

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Abstract

A modified rigid-ion model is developed based on coordination polyhedra as the fundamental modelling units in a crystal structure. A crystal structure is represented by its constituent coordination polyhedra that are treated as three-dimensional elastic continua. Elastic moduli, experimentally determined or otherwise assumed, are ascribed to these coordination polyhedra. Finite element analysis is applied to retrieve the interatomic force information implicit in the elastic moduli of these polyhedra. The polyhedral approach provides a framework to model noncentral and many-body forces in a conventional lattice calculation because the elastic moduli contain much information on the nature of static interatomic forces within a crystal structure. The polyhedral model of the single-crystal elastic moduli of forsterite compares very well with the observed data; the average deviation of the calculated elastic moduli from the measured elastic moduli is within 6 percent.

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Author notes

  1. Andrew Y. Au

    Present address: Interferometrics Inc., 8150 Leesburg Pike, 22180, Vienna, VA, USA

Authors and Affiliations

  1. Department of Earth and Space Sciences, State University of New York at Stony Brook, 11794, Stony Brook, New York, USA

    Andrew Y. Au & Donald J. Weidner

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  1. Andrew Y. Au
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  2. Donald J. Weidner
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Additional information

Also at Geophysical Laboratory, Carnegie Institution of Washington, 2801 Upton Street, N.W., Washington, DC 20008, USA, where part of the research was performed during a postdoctoral fellowship

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Au, A.Y., Weidner, D.J. Theoretical modelling of the elastic properties of forsterite: A polyhedral approach. Phys Chem Minerals 13, 360–370 (1986). https://doi.org/10.1007/BF00309181

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  • DOI: https://doi.org/10.1007/BF00309181

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