New ion radii for oxides and oxysalts, fluorides, chlorides and nitrides
Bibliographic record
Abstract
Ion radii are derived here from the characteristic (grand mean) bond lengths for (i) 135 ions bonded to oxygen in 459 configurations (on the basis of coordination number) using 177 143 bond lengths extracted from 30 805 ordered coordination polyhedra from 9210 crystal structures; and (ii) 76 ions bonded to nitrogen in 137 configurations using 4048 bond lengths extracted from 875 ordered coordination polyhedra from 434 crystal structures. There are two broad categories of use for ion radii: (1) those methods which use the relative sizes of cation and anion radii to predict local atomic arrangements; (2) those methods which compare the radii of different cations (or the radii of different anions) to predict local atomic arrangements. There is much uncertainty with regard to the relative sizes of cations and anions, giving rise to the common failure of type (1) methods, e.g. Pauling's first rule which purports to relate the coordination adopted by cations to the radius ratio of the constituent cation and anion. Conversely, type (2) methods, which involve comparing the sizes of different cations with each other (or different anions with each other), can give very accurate predictions of site occupancies, physical properties etc. Methods belonging to type (2) can equally well use the characteristic bond lengths themselves (from which the radii are derived) in place of radii to develop correlations and predict crystal properties. Extensive quantum-mechanical calculations of electron density in crystals in the literature indicate that the radii of both cations and anions are quite variable with local arrangement, suggesting significant problems with any use of ion radii. However, the dichotomy between the experimentally derived ion radii and the quantum-mechanical calculations of electron density in crystals is removed by the recognition that ion radii are proxy variables for characteristic bond lengths in type (2) relations.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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".