A kinetic model of oriented nucleation under nonhydrostatic stress: Implications for the preferred orientation of columnar and platy minerals in metamorphic rocks

Abstract

We propose a kinetic model for the nucleation rate of columnar and platy minerals in nonhydrostatically stressed metamorphic rocks. Nucleation rate I in our model is expressed as IT,σn=Aexp−ΔU∗−TΔS∗+σnΔV∗kBT, Where ΔU∗, ΔS∗ and ΔV∗ are the internal energy, entropy and volume of activation, respectively, kB is the Boltzmann constant, T is absolute temperature, σn is the magnitude of the normal stress applied to the site of heterogeneous nucleation, and A is a constant. As σn varies with respect to the spatial orientation of the nucleation site in nonhydrostatically stressed rocks, the nucleation rate I also varies accordingly. As the number of nucleated grains is proportional to I, anisotropic nucleation can produce a preferred orientation of mineral grains. The model predicts the von Mises distributions of the long axes of columnar mineral grains and poles to the basal planes of platy mineral grains on any plane cut perpendicular to the principal-stress axes. The model also uses the exponential form of the Lamé’s stress ellipsoid to plot contoured equal-area stereographic fabric diagrams. As the generated patterns are similar to those observed in metamorphic rocks, the model is likely useful for analyses of natural deformation.