Representing crystal orientations

 

See also: Euler angles, orientation matrix, misorientation

 

Crystal orientation measurement  is a major application of EBSD.  This refers to the orientation of the crystal lattice with respect to a coordinate system fixed in the sample (see figure below). The orientations can be represented in a number of ways.

 

A common method for representing a crystal orientation is to use the ideal orientation nomenclature (hkl)[uvw]. Directions in the crystal are referred to a set of coordinates fixed in the sample. Using the terminology of rolled sheet metals, these are the sample normal (ND), rolling direction (RD) and transverse direction (TD). (See the figure below). In the ideal orientation nomenclature the normal to the crystal plane (hkl) is parallel to the sample normal and the crystal direction [uvw] parallel to the rolling direction. The notation {hkl}<uvw> denotes the symmetrically related set of directions which represent the texture.

 

The orientation in the figure can also be represented by three Euler angles φ1Φφ2 with φ1=135, Φ=90 and φ2=90.  The orientation can also be represented by the  orientation matrix.

 

 

Find out more about the ways of measuring crystal orientations with our orientation simulation applet here.