A practical method to determine the five-parameter orientation of intragranular boundaries in polycrystals

Abstract

Intragranular boundaries are important features of polycrystalline materials and impact on many physical and chemical properties. Knowledge of their physical orientation is often crucial to explain such properties. However, it has proved difficult to determine the complete orientation of intragranular boundaries, which involves the misorientation angle and axis about which the adjacent crystal lattices need to be rotated to bring them into coincidence and also the physical orientation of the boundary plane, expressed by the plunge and azimuth of its normal; five parameters in total. Here we present a simple and practical manual method to determine the complete intragranular boundary orientation in any crystal system. The method is developed on geometrical relationships exhibited between electron channelling patterns across a common boundary but then extended for use with electron backscattered diffraction patterns. The method recognises the channelling/diffraction band, equivalent to a crystal lattice plane, not displaced across a boundary; the boundary rotation axis must be the normal to this plane. Geometrical relationships between the boundary trace, the non-displaced band/plane and their respective plane normals constrain boundary orientation to two alternative symmetrically equivalent solutions and are evaluated via stereographic projection. The choice of solution is guided by comparison with the presence or absence of a similarly oriented band/plane observed in the original channelling/diffraction patterns. The method therefore conforms to the low-index crystallographic lattice plane and dislocation model for intragranular boundary formation and defines boundary orientation in terms of total angular misorientation due to tilt and twist components and the orientation of the boundary plane. Examples of intragranular boundary orientation determination using this method are provided in olivine. Results are compared to and differ from those obtained via conventional misorientation analysis, which only rotates adjacent crystal lattices into parallelism and does not consider boundary plane orientation. Potential extrapolation of the new method to intergranular boundaries is also considered