The relative strengths of deforming mineral phase assemblages: Geometrically necessary deformation mechanisms

The relative strengths of constituent minerals in a deforming poly-mineralic rock depend on the grain size distributions of the various phases, the operating deformation mechanisms in those phases, and the topology of the microstructure. It is observed that more than one deformation mechanism operates, and the resulting constitutive relations (especially for calcite) are extremely variable. To explore such relations, deformation mechanism maps for each mineral are required together with mixing relations for multiple deformation mechanisms. We construct reference deformation mechanism maps for calcite and alkali-feldspars that are based on theoretical expressions for constitutive relations, together with experimental or molecular dynamic estimates of constitutive parameters. A thermodynamically based mixing relation is employed that enables bulk constitutive relations to be established for mixtures of mineral phases and deformation mechanisms with a range of grain sizes. This provides a basis for comparison and understanding of experimental results. We map out fields on deformation mechanism maps where switches in the relative strengths of calcite and quartz and of feldspar and quartz occur. We introduce the concept of geometrically necessary deformation mechanisms that minimise the energy of the system.