<i>Ab initio</i> constrained crystal-chemical Rietveld refinement of Ca<sub>10</sub>(V<sub> <i>x</i> </sub>P<sub>1 − <i>x</i> </sub>O<sub>4</sub>)<sub>6</sub>F<sub>2</sub> apatites
Bibliographic record
Abstract
Extraction of reliable bond distances and angles for Ca10(VxP1-xO4)6F2 apatites using standard Rietveld refinement with Cu Kalpha X-ray powder data was significantly impaired by large imprecision for the O-atom coordinates. An initial attempt to apply crystal-chemical Rietveld refinements to the same compounds was partly successful, and exposed the problematic determination of two oxygen-metal-oxygen angles. Ab initio modeling with VASP in space groups P6(3)/m, P2(1)/m and Pm showed that both these angular parameters exhibited a linear dependence with the vanadium content. Stable crystal-chemical Rietveld refinements in agreement with quantum results were obtained by fixing these angles at the values from ab initio simulations. Residuals were comparable with the less precise standard refinements. The larger vanadium ion is accommodated primarily by uniform expansion and rotation of BO4 tetrahedra combined with a rotation of the Ca-Ca-Ca triangular units. It is proposed that the reduction of symmetry for the vanadium end-member is necessary to avoid considerable departures from formal valences at the AII and B sites in P6(3)/m. The complementarity of quantum methods and structural analysis by powder diffraction in cases with problematic least-squares extraction of the crystal chemistry is discussed.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".