Elasticity of polycrystals and rocks

A compilation of the best available elasticity data on single crystals and polycrystalline aggregates shows that the ‘Voigt-Reuss-Hill average’ is neither proven nor disproven experimentally. Because the average of the bounds has no theoretical significance, the true moduli may lie anywhere between them. The ambiguity is removed by Kröner's recent theory for a perfectly disordered aggregate, which specifies a unique modulus for an idealized geometry. Theoretical calculations on aggregates of geophysically interesting crystals, and on mixtures of such crystals (i.e., rocks), shows that the ‘perfectly disordered’ theory differs numerically from the VRH average. In cases where this difference is small, the VRH average is thereby given some theoretical support; however, in certain situations of interest, it is large (e.g., in a highly porous rock, where data confirm Kröner's theory). The seismic parameter Φ of a multicomponent aggregate is not equal to the molar-averaged Φ's of the components; the difference is significant for mixtures of the simple oxides: stishovite, MgO, wüstite. The bulk modulus K of an aggregate, like its shear modulus, depends on the time scale of the experiment that determines it. The short-term (acoustic) K is Kröner's Keff; the long-term (static) K is Reuss' KR, which is ≤Keff. Hence the seismic parameter Φ and the density gradient within the earth are only indirectly related. Where arguments are given to show the near-equality of short- and long-term Φ's, the conclusion follows that the material cannot contain major fractions of widely different phases, such as stishovite and MgO.