The solutions of the Frank-Bilby equation for the dislocation content of symmetric tilt grain boundaries were analyzed for a number of grain and twin boundaries. Based on this analysis, the geometrical model of grain boundary migration - shear coupling was extended to evaluate the coupling factor (amount of shear) for twin and grain boundaries in various crystal structures. The coupling factors calculated according to the proposed general formula are in excellent agreement with respective experimental and simulation data known from literature. For a given grain/twin boundary the coupling factor was found to result from a combination of two elementary coupling modes, the balance between which is constituted by an introduced weighting factor. Hence, the coupling factor (or the twinning shear) depends not only on the tilt angle of the grain/twin boundary, but also on the weighting factor, which may vary for crystallographically equivalent boundaries. With respect to deformation twinning, the weighting factor is intimately linked to the amount and direction of twinning shear produced by the boundary. A variation of the weighting factor for the same boundary can be interpreted as a result of a structural change of the grain/twin boundary, i.e. grain boundary phase transformation.

分析了Frank-Bilby方程的对称倾斜晶界的位错含量的解，其中包含了许多晶界和孪晶界。在此基础上，扩展了晶界迁移-剪切耦合的几何模型，以评估各种晶体结构中孪晶和晶界的耦合因子（剪切量）。根据所提出的通式计算的耦合因子与文献中已知的各个实验和模拟数据非常吻合。对于给定的晶粒/孪晶边界，发现耦合因子是由两种基本耦合模式的组合产生的，两者之间的平衡由引入的加权因子构成。因此，耦合因子（或孪生剪切）不仅取决于晶粒/孪晶边界的倾斜角，而且取决于权重因数，对于结晶学上等价的边界，权重因数可能会发生变化。对于变形孪生，加权因子与边界产生的孪生剪切的量和方向紧密相关。对于相同边界的加权因子的变化可以解释为晶粒/孪晶边界的结构变化（即晶粒边界相变）的结果。