Historically powder X-ray diffraction was the go-to method for reconstructing crystal structure. X-ray sources were limited in intensity and emittance and so to collect data in a reasonable amount of time one would use a (nearly) monochromatic beam and a large area detector (originally photographic emulsion, now 2D position-sensitive gas counters or solid stat devices) to collect those beautiful ring images shown above.

To analyze a true powder (uniformly random distribution in crystal orientations) one would reduce this to a single 1D plot of intensity vs radius, then apply something like a Rietveld refinement to deduce relative reflection intensities for structure determination and maybe some information on grain size or micro-strain.

The rings would sometimes be lumpy due to failure to achieve uniform, isotropic orientations of the grains of the powder, often due to wall effects in the container and other mechanical packing and correlation effects.

Then both metallurgy and thin films used in semiconductor manufacture came along. For example the thin films might be silicides used to make ohmic contact between metal layers and the semiconductor material, or nitrides (e.g. TiN) for seed layers before electrodeposition of copper for interconnects.

For polycrystalline metals and semiconductor thin films, pole figures were generated from area detector X-ray diffraction data for a given reflection plane.

Pole figures could be used (along with other Rietveld refinement results ) to put together a picture of crystallographic texture.

The pole figures show the distribution in directions that the normal to a given crystal plane is pointing. It doesn't tell you anything about how the crystallites contributing to a given spot on the pole figure are rotationally oriented around the normal direction.

For that information you combine results of several pole figures for several different reflections.

For example you might also have a fixed X-ray incident angle and area detector position, and rotate the sample around the sample normal to get more information.

Finally, based on the amount and variety of data you've collected, one builds up a model orientations of the crystallites in 3D space - the texture of the polycrystalline film or material.

Question: Starting from a series of area detector images taken at different rotations of a sample about its normal, how does one generate pole figures from limited amounts of data? "Explain it like I'm five years old" means a wall of equations is not as helpful as a step-by-step overview of how do to the calculation from scratch.

So "Use MAUD" or "Use Program X" are not helpful because the actual calculations I'm curious about are mostly hidden in those packages.

File:MAUD-MTEX-TiAl-hasylab-2003-Liss https://commons.wikimedia.org/wiki/File:MAUD-MTEX-TiAl-hasylab-2003-Liss.png

Source: File:MAUD-MTEX-TiAl-hasylab-2003-Liss

"Minerals at 'Rocknest' and 'John Klein'" https://commons.wikimedia.org/wiki/File:Minerals_at_%27Rocknest%27_and_%27John_Klein%27.jpg

Source: Minerals at 'Rocknest' and 'John Klein'



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