Predicting the Crystal Structure of Beryl from the Chemical Composition
Bibliographic record
Abstract
Abstract Crystal-structure prediction is a challenging topic. Few models have been developed that use the chemical composition of a known compound to determine a complete crystal structure. A complete structural model should include all major bond lengths and angles, atomic coordinates, polyhedral volumes and distortions, and unit-cell parameters. The mineral beryl is used here to develop such a model. Beryl (Be3Al2Si6O18) is an ideal mineral to show that predicting the crystal structure using chemistry is possible: the framework structure is known, this structure has only two cation sites that experience substitutions, and these substitutions only minimally occur simultaneously. Vacant channel sites are involved in coupled substitutions, allowing alkali cations (typically Na+) to enter the structure, and the channel regularly contains molecular H2O correlated to Na content (Henry et al. 2022). The research employed single-crystal X-ray diffraction and electron probe microanalyses of 80 samples to create a model which was subsequently tested using 33 samples. Results show that the complete crystal structure of beryl can be accurately calculated using the Al-site average ionic radius (Al-SAIR) for octahedrally trending beryl, or the Be-site average ionic radius (Be-SAIR) for tetrahedrally trending beryl. Beryl for which Al-SAIR > (0.45 × Be-SAIR) + 0.414 is considered octahedrally trending and that for which Al-SAIR ≤ (0.45 × Be-SAIR) + 0.414 is considered tetrahedrally trending. Red beryl (differentiated by high Fe and Mn) exhibits a different trend, forming a subset of the octahedrally trending beryl. There is an upper limit to the predictable range of beryl structures of 0.604 Å Al-SAIR or 0.326 Å Be-SAIR. This model makes it possible to explore limitations on the crystal structure of beryl and the potential for unusual cation substitutions, or conversely, to compute the structure of a hypothetical pure endmember beryl. It is robust for true beryl (beryl for which Be and Al are the dominant non-Si cations) up to a high limit of cation substitutions, but not for other beryl-group minerals, including stoppaniite, bazzite, avdeevite, and johnkoivulaite. Future studies on beryl will be able to estimate basic crystal-structure features arising from standard chemical analyses as used in this research. It enables the creation of an extensive beryl database, aids comparisons of natural beryl to synthetics, and helps provide further guidance on provenance studies. It also invites future crystal-structure prediction research. This approach is applicable to broader fields, as crystal structures are linked to the physical characteristics of minerals and rocks in which they form.
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How this classification was reachedexpand
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".