Maximum disorientation angles between crystals of any point groups and their corresponding rotation axes
Bibliographic record
Abstract
The symmetry-reduced misorientation,i.e.disorientation, between two crystals is represented in the angle–axis format, and the maximum disorientation angle between any two lattices of the 32 point groups is obtained by constructing the fundamental zone of the associated misorientation space (i.e.Rodrigues–Frank space) using quaternion algebra. A computer program based on vertex enumeration was designed to automatically calculate the vertices of these fundamental zones and to seek the maximum disorientation angles and respective rotation axes. Of the C_{32}^2 = 528 possible combinations of any two crystals, 129 pairs give rise to incompletely bounded fundamental zones (i.e.zones having at least one unbounded direction inR3); these correspond to a maximum disorientation angle of 180° (the trivial value). The other 399 pairs produce fully bounded fundamental zones that lead to nine different nontrivial maximum disorientation angles; these are 56.60, 61.86, 62.80, 90, 90.98, 93.84, 98.42, 104.48 and 120°. The associated rotation axes were obtained and are plotted in stereographic projection. These angles and axes are solely determined by the symmetries of the point groups under consideration, and the only input data needed are the symmetry operators of the lattices.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.007 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".