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Calculation of crystal field splittings in distorted coordination polyhedra: spectra and thermodynamic properties of minerals

Published online by Cambridge University Press:  05 July 2018

Bernard J. Wood  and
R. G. J. Strens
Bernard J. Wood
Affiliation:
Department of Geology, The University, Manchester M13 9PL, England
R. G. J. Strens
Affiliation:
School of Physics, The University, Newcastle NE1 7RU, England
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Summary

A simple method has been developed for calculating the d-orbital energy levels of transition-metal ions in coordination polyhedra with both orthogonal and non-orthogonal distortions, using equations based on those derived by Ballhausen (1954). The input data are atomic coordinates, a standard value of the crystal field splitting parameter Δ at known metal-ligand distance, and the ratio of radial integrals B2/B4, which is approximately constant for a given ion. The method can be applied to polyhedra containing different ligands.

Application of the equations to the Mn3+ (M3) site in piemontite and the Fe2+ (M2) site in orthopyroxene gives calculated transition energies in good agreement with the observed band energies.

The calculations permit definite assignment of the great majority of d-d absorption bands even in multi-site phases, and enable discrimination of crystal-field and charge-transfer bands in mineral spectra. They also throw light on the fine structures of both oxygen → metal and metal → metal charge-transfer bands, and allow the calculation of crystal-field stabilization enthalpy and electronic entropy. The latter is a previously neglected energy term that contributes significantly to the energetics of reactions within and between phases containing transition-metal ions.

Type
Research Article
Information
Mineralogical Magazine , Volume 38 , Issue 300 , December 1972 , pp. 909 - 917
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 1972

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