About Misorientation Angle Distribution
Misorientation angle distribution describes how crystal or vector orientations differ across paired observations. It is useful in texture analysis, grain boundary study, and rotation based quality checks. The calculator converts each orientation pair into rotation matrices, compares them, and groups the resulting angles into bins. A small angle often suggests similar alignment. A larger angle suggests stronger change between two measured frames.
Why This Calculation Matters
Raw orientation data can be hard to read. A distribution makes the pattern clearer. You can see whether most pairs are near zero degrees, spread across the full range, or concentrated around a special boundary range. The summary table also gives mean, median, deviation, minimum, maximum, and modal bin. These values help compare samples, processes, or simulation runs with one consistent method.
Input Options
The form accepts Bunge Euler angles or quaternions. Euler rows need six values. They are phi one, Phi, phi two, then the same three values for the paired orientation. Quaternion rows need eight values. They are scalar first, followed by three vector terms for each orientation. Data may be pasted from a spreadsheet, with one pair per line.
Symmetry and Bins
Crystal symmetry can reduce equivalent rotations. Select none for plain matrix comparison. Select cubic when orientations belong to a cubic crystal family and equivalent cube rotations should be tested. The tool then reports the lowest equivalent angle. The bin width controls the histogram resolution. Smaller bins show more detail, while larger bins give a smoother distribution.
Reading the Result
After calculation, the result appears above the form. The pair table lists every computed angle. The distribution table lists bin limits, counts, percentages, and density values. CSV output is best for spreadsheets. PDF output is useful for saving a compact report. Always check units, convention, and symmetry before comparing studies. Also review outlier rows. Unexpected angles can reveal data entry mistakes, indexing errors, or true local rotation changes.
For advanced work, keep metadata with each row. Note specimen name, scan step, phase, and preprocessing choice. Consistent notes make distributions easier to audit later. When several datasets are compared, reuse the same bin width, maximum angle, and symmetry setting across every run for fair visual comparison today.