Euler angles and the orientation matrix

In this video I talk about the Euler angles and the orientation (or rotation) matrix. The orientation matrix (g) can be used to describe the relationship between two coordinate systems by 3 consecutive rotations, which are based on the 3 Euler angles. These 2 coordinate systems can be the specimen coordinate system (RD, TD, ND) and the crystal coordinate system in the case of a flat piece of metal sheet.

The orientation matrix can be used to represent an external stress within the crystal (grain) or represent the misorientation between two grains or two points. The latter is very useful when we for example try to find grain boundaries.

This method is used in different diffraction techniques. I will focus on electron backscattered diffraction (EBSD).