Theory of Preferred Crystal Orientation Developed by Crystallization under Stress

Abstract

The thermodynamic theory of equilibrium under non-hydrostatic stress, developed by Gibbs, is applied to linearly elastic crystals under infinitesimal strain and is worked out in detail for several examples of practical importance, mostly situations of uniaxial stress. The conditions for preferred orientation are shown to depend only on the stress deviators and are thus invariant to a change in hydrostatic pressure. For equilibrium across a given interface between crystal and fluid, the preferred crystal orientation under any non-hydrostatic stress is in most cases that for which the elastically weakest direction in the crystal is perpendicular to the interface. When recrystallization takes place by solution and redeposition, the preferred orientation is that which minimizes the chemical potential required for equilibrium across the plane normal to the greatest principal pressure axis. Thus the weakest axis of a crystal (c-axis of calcite) tends to align with the greatest principal pressure axis, or axes, while the strongest axis (c-axis of quartz) tends to align perpendicular thereto. Hexagonal and rhombohedral crystals are classified into four types on the basis of the c-axis preferred orientation expected to develop under uniaxial stress. Quartz is unique among the common hexagonal and rhombohedral minerals in that the theory predicts that under some conditions a small girdle of quartz c-axes should develop about the unique stress axis. The theory accounts for several main features of quartz fabrics observed in tectonites. An isometric crystal in a uniaxial stress field tends to align either [100] or [111] parallel to the unique stress axis (whether tensional or compressional), depending on how the crystal deviates from elastic isotropy. When recrystallization takes place without solution and deposition, that is, by the growth of some crystals directly at the expense of adjacent ones of the same composition, an extension of Gibbs's theory is necessary to predict the preferred orientation that develops. It is found that if the initial grain shapes are equant, the condition for preferred orientation is obtained simply by averaging the conditions given by Gibbs's theory for the three principal stress planes. Rhombohedral or hexagonal crystals in a uniaxial stress field develop preferentially in most cases with their weakest axis perpendicular to the unique stress axis (whether tensional or compressional) or their strongest axis parallel to the unique axis. For recrystallization of glacier ice in situ during glacier flow, the theory predicts, under the likely assumption that $$s_{44}$$ for single ice crystals is relatively large, several main features of the observed c-axis fabrics of temperate glacier ice.