Open AccessLattice Dynamics of MgO, Al 2 MgO 4 and Mg 2 SiO 4 Spinel
Author(s) -
Sammis Charles
Publication year - 1972
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1972.tb06148.x
Subject(s) - spinel , periclase , dimensionless quantity , ionic bonding , stishovite , lattice constant , thermodynamics , ion , chemistry , materials science , mineralogy , physics , diffraction , metallurgy , organic chemistry , high pressure , optics
Summary The method of long waves is used to compute the volume dependence of the elastic properties of MgO, γ‐Al 2 MgO 4 (spinel), and γ‐Mg 2 SiO 4 (spinel structure) from a rigidion, central force model. A comparison of theoretical and experimental elastic constants for the first two compounds shows that the neglect of non‐central forces and ionic polarization severely limits the application of the model for oxides and silicates. The Coulombic contributions to the elastic constants for both the 3–2 spinel (γ‐Al 2 MgO 4 ) and the 2–4 spinel (γ‐Mg 2 SiO 4 ) are expressed as dimensionless Madelung‐like constants and are computed as a function of the oxygen parameter. The distortion of the two spinels from c.c.p. is shown to be primarily an electrostatic effect. The elastic properties of γ‐Mg 2 SiO 4 are predicted using the bond parameters for Mg‐O found from data on periclase and for Si‐O found from stishovite. Although the rigid‐ion model is too restrictive to give geophysically useful predictions, it shows how lattice dynamics may be used as a framework through which laboratory data may be used to interpret seismic velocity and density profiles.