The Estimation of Elastic Properties from Analogue Compounds

Abstract

The concept of isostructural compounds as elastic analogues is extended to include some new correlations involving the bulk modulus, K, the shear modulus, p, and their pressure derivatives, K and p', and these are combined here with some previously demonstrated correlations. For many simple compounds, K correlates with the mole atomic volume, V, according to the well-known relation KV" = C , , where C1 is a constant characteristic of crystal structure, and n is usually about 1. An analogous relation, pV" = Cz, is shown here to be an equally accurate approximation. C2 is again characteristic of crystal structure and m is usually about $. Some exceptions are related to the presence of transition metal ions, and possibly to magneto-elastic coupling and non-stoichiometry. These relations are poorer approximations for more complex compounds. Much of the irregularity can be attributed either to the presence of more than one dominant bond type or to the presence of transition metal ions and associated effects. For complex compounds, an alternative correlation, previously demonstrated, is updated and refined using the above insights into simple compound properties: the ratios of elastic velocities and density of a compound to those of its isochemical mixture of simple compounds are characteristic of the crystal structure of the compound.

Interaction of mantle dregs with convection: Lateral heterogeneity at the core‐mantle boundary

“…Empirical estimates of these parameters are 1 -1.3 for Vp and 1 -2 for Vs [Davies, 1976]. thickness of 0.033D (100 km), which is closer to the usual seismological estimates.…”

Pyroxenes and Olivines: Structural Implications of Shock-Wave Data for High Pressure Phases

“…Incidentally, though we discuss the direct transformation from pyroxene to perovskite structures under shock, this obviously represents a metastable phase boundary (based on our current knowledge from Liu's work Estimates of the bulk modulus K O and K0, dF ! '^ê mpirical correlation with density.with particular emphasis given to data for perovskite-structured compounds [Davies, 1976;Beattie and Samara, 19711.…”

Seismic velocities in mantle minerals and the mineralogy of the upper mantle

“…By treating a large, diverse data set it is possible to see trends with ionic radius, Ks/G, and "f [Anderson, 1988]. These trends are often not evident if attention is limited to "geophysically relevant" compounds (silicates) because of the small range and small number of measured samples and the low precision of data on relatively incompressible compounds [Davies, 1976].…”

“…Relationships involving the pressure derivative of the shear modulus are, surprisingly, less ambiguous. Theoretical considerations suggest that the pressure derivative of the shear modulus G' should depend on coordination and Poisson's ratio [Anderson, 1968;Davies, 1976]. Anderson [1988] pointed out additional relationships involving the dimensionless logarithmic anharmonic (DLA) parameter, { G}r, which is given by…”

“…Systematics among derivatives of elastic properties have proven to be rather elusive [e.g., Davies, 1976] particularly for the oxides and silicates. The bulk modulus pressure derivative (dK/dP or K1) is particularly resistant to description by convincing systematics.…”