The previous slide explains where this formula comes from. Step 4: project the pole onto a point, p, in the plane (stereographic or equal-area):px= tan(/2) cos py= tan(/2) sin.Step 3: convert the rotated pole into spherical angles (to help visualize the result, and to simplify Step 4) where is the co-latitude and is the longitude: = cos-1(h’z),= tan-1(h’y/h’x).Remember - use ATAN2(h’y,h’x) in your program or spreadsheet and be careful about the order of the arguments!.the transpose of the orientation matrix, g, that represents the orientation Rodrigues vectors or unit quaternions can also be used). Step 2: apply the inverse transformation (passive rotation), g-1, to obtain the coordinates of the pole (Miller indices, normalized, crystal axes) in the pole figure (direction in sample axes): h’ = g-1h(pre-multiply the vector by, e.g.In the future, we will use a set of symmetry operators to obtain all the symmetry related copies of a given pole. Each chosen crystal direction is generally specified as a low-index plane normal, e.g.Therefore pole figures represent a projection of the texture information. Since each plane normal is plotted by itself, there is no information in the resulting plot about directions lying in that plane.This definition refers to plane normalsbecause of the standard use of x-ray diffraction to measure pole figures crystal directions can equally well be treated.Think of the rows (not columns) in the orientation matrix, which define the coordinates of each crystal axis with respect to the sample frame. A pole figure (in the context of texture) is a map of a selected set of crystal plane normals plotted with respect to the sample frame.How does one normalize the data for a pole figure to obtain “multiples of a random density (MRD)”?.How do you compute an inverse pole figure?.the orientation matrix), how do you calculate the positions of the poles in a pole figure? How does the equal area projection work?.How does the stereographic projection work?.Why does an experimental pole figure not correspond to a theoretical one at the edges?.Why does a pole figure for a single orientation provide the complete orientation (by contrast to the single crystal case)?. ![]() How can one construct a pole figure for a single orientation?.Why does it not provide complete orientation information for a polycrystalline sample?.Define and explain the inverse pole figure.Explain how to construct a pole figure based on the orientation matrix.Explain how pole figures of single orientations relate to stereographic projections.Explain the stereographic and equal area projections.Provide information on how to measure x-ray pole figures.Intro to X-ray Pole Figures 27-750, Texture, Microstructure & Anisotropy A.D.
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