Least-squares thermal expansion tensor of vanadate and arsenate triclinic apatites derived from laboratory X-ray powder diffraction cell data
Bibliographic record
Abstract
Cell data for triclinic end-member Ca10(VO4)6F2and Ca10(AsO4)6F2apatites were measured in the temperature range from 303 to 773 K. Reversible phase transitions at, respectively, 453 and 583 K are shown and attributed to mobility of contact surfaces for triclinic twins within a mosaic block at about the transition temperature. The simple method developed here is based on 12 separate linear regressions. The first six regressions are on observations for individual lattice parametersa,b,c, α, β or γ. The last six are on linear data sets, each involving a single expansion coefficient α11, α22, α33, α12, α13or α23. Singular-value decomposition of the least-squares thermal expansion tensors obtained below the transition temperatures shows that both materials actually contract considerably along [2\bar14] upon heating. Expansion in the plane perpendicular to this direction differs somewhat for the two materials. In contrast, the expansion above the transition temperature is barely anisotropic in both materials. The ability to measure thermal expansion tensors for triclinic materials with decent accuracy from routine powder data is demonstrated. This possibility extends the applications of the powder method because some samples may not be readily available in single-crystal form.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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 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".