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 $I\left(T,{\sigma }_n\right)=A\exp \left(-\frac{\text{Δ}{U}^{\ast }-T\text{Δ}{S}^{\ast }+{\sigma }_n\text{Δ}{V}^{\ast }}{k_{B}T}\right),$ Where $\Delta U^{\ast }$, $\Delta S^{\ast }$ and $\Delta V^{\ast }$ are the internal energy, entropy and volume of activation, respectively, $k_B$ is the Boltzmann constant, $T$ is absolute temperature, ${\sigma }_n$ is the magnitude of the normal stress applied to the site of heterogeneous nucleation, and $A$ is a constant. As ${\sigma }_n$ 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.

我们提出了非静水应力变质岩中柱状和板状矿物成核速率的动力学模型。成核率$\mathrm{一世}$ 在我们的模型中表示为 $\mathrm{一世}\left(Ť，{\sigma }_{ñ}\right)=\mathrm{一个}\mathrm{经验值}\left(-\frac{\text{Δ}{ü}^{\ast }-Ť\text{Δ}{\mathrm{小号}}^{\ast }+{\sigma }_{ñ}\text{Δ}{\mathrm{伏特}}^{\ast }}{{ķ}_{乙}Ť}\right)，$ 在哪里 $\Delta {ü}^{\ast }$， $\Delta {\mathrm{小号}}^{\ast }$ 和 $\Delta {\mathrm{伏特}}^{\ast }$ 分别是内部能量，熵和激活量， ${ķ}_{乙}$ 是玻耳兹曼常数， $Ť$ 是绝对温度 ${\sigma }_{ñ}$ 是施加到异质形核位点的法向应力的大小，并且 $\mathrm{一个}$是一个常数。作为${\sigma }_{ñ}$ 在非静水应力岩石中，相对于成核位置的空间取向而变化，成核速率 $\mathrm{一世}$也相应地变化。由于有核晶粒的数量与$\mathrm{一世}$各向异性成核可以产生矿物晶粒的优选取向。该模型预测了在垂直于主应力轴切割的任何平面上，柱状矿物颗粒和极点的长轴在板状矿物颗粒基面的冯·米塞斯分布。该模型还使用Lamé应力椭球体的指数形式绘制等值轮廓的立体结构图。由于生成的模式与在变质岩中观察到的模式相似，因此该模型可能对分析自然变形有用。