Quartz: structural and thermodynamic analyses across the α ↔ β transition with origin of negative thermal expansion (NTE) in β quartz and calcite
Bibliographic record
Abstract
The temperature variation, T, of the crystal structure of quartz, SiO2, from 298 to 1235 K was obtained with synchrotron powder X-ray diffraction data and Rietveld structure refinements. The polymorphic transformation from P3221 (low-T, α quartz) to P6222 (high-T, β quartz) occurs at a transition temperature, Ttr = 847 K. The T variations of spontaneous strains and several structural parameters are fitted to an order parameter, Q, using Landau theory. The change in Si atom coordinate, Six, gives Ttr - Tc = 0.49 K, which indicates an α ↔ β transition that is weakly first order and nearly tricritical in character (Q(4) ∝ T). Strains give higher Ttr - Tc values (≃ 7 K). Other fitted parameters are the oxygen Oz coordinate, Si-Si distance, Si-O-Si and ϕ angles, and intensity of the (111) reflection, I111. In α quartz, the Si-Si distance increases with T because of cation repulsion, so the Si-O-Si angle increases (and ϕ decreases) and causes the thermal expansion of the framework structure that consists of corner-sharing distorted rigid SiO4 tetrahedra. The Si-Si distances contract with T and cause negative thermal expansion (NTE) in β quartz because of increasing thermal librations of the O atom in the Si-O-Si linkage that occur nearly perpendicular to the Si-Si contraction. In calcite, CaCO3, the short Ca-Ca distance expands with T, but the next-nearest Ca-Ca distance, which is of equal length to the a axis, contracts with T and causes NTE along the a axis. The thermal librations of the atoms in the rigid CO3 group increase with T along the c axis.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 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".