A NEW METHOD TO DETERMINE THE OPTICAL ORIENTATION OF BIAXIAL MINERALS: A MATHEMATICAL APPROACH
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Bibliographic record
Abstract
A mathematical approach has been developed to determine the optical orientation of biaxial minerals by combining spindle stage and X-ray-diffractometer measurements. First, a goniometer head, with crystal affixed, is screwed onto a spindle stage, and its orientation matrix for the biaxial indicatrix is determined. Next, the same goniometer head is transferred to a single-crystal X-ray diffractometer, where the unit cell and, in turn, an orientation matrix for the reciprocal crystallographic axes are determined. The necessary transformations and calculations are then developed to relate these two orientation matrices mathematically. Examples for two orthorhombic minerals of known optical orientation, one monoclinic mineral of unknown optical orientation, and one triclinic mineral of known optical orientation are given. Several measurements were repeated to test the accuracy, reproducibility, and systematic errors of the method; these measurements yielded an accuracy and reproducibility of the method to within 1.0°. Once a suitable crystal has been selected and mounted on a goniometer head, all the required measurements and calculations can be performed in approximately one hour.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it