Elasticity,crystal structure and phase transitions

It is demonstrated that in many cases the ratio of elastic velocities of polymorphs of a material depends primarily on the crystal structures involved, and only secondarily on the composition. Crucial to this demonstration is the use of estimates, from the Hashin-Shtrikman bounds, of the elastic properties of mixtures of simple oxides isochemical to particular compounds. Normalization to the oxide mixture properties displays the interrelationships between the densities and velocities of different crystal structures. A wide range of velocity-density trends through possible phase transitions is found. Transitions involving increases of Si coordination from 4 to 6 tend to have lower slopes. Velocity-density correlations are reasonably consistent with the average trends through phase transitions.Comparison of models of the transition zone with the characteristics of the olivine-spinel-oxides transitions indicates that in some studies the lower mantle density may have been underestimated or the mean atomic weight of the lower mantle overestimated. The transition zone of Model B1 of Jordan and Anderson, which was derived entirely from seismic data, is consistent, overall, with the olivine-oxides transition and uniform composition, but the individual discontinuities are not consistent with the olivine-spinel and spinel-oxides transitions.