Temperature dependence of Raman shifts and line widths for Q0 and Q2 crystals of silicates, phosphates, and sulfates
Bibliographic record
Abstract
The temperature dependence of Raman shifts and line widths (full-width at half maxima or FWHM) for the A 1 symmetric stretch of TO 4 (T = Si, P, S) have been analyzed for nine alkali and alkaline earth silicates, phosphates, and sulfates. In crystalline silicates, the Q 0 and Q 2 species Raman shifts decrease with temperature, whereas FWHM increase. The strikingly similar behavior of Q 0 and Q 2 in silicates and Q 0 in phosphates makes it possible to estimate to within ±4 cm −1 Raman shifts up to ~1000 K. Similarly systematic increases in FWHM with temperature can be estimated to within ±5 cm −1 up to ~1400 K. The type of element centering TO 4 (i.e., Si, P, or S) has no appreciable effect on the temperature dependence of Raman shifts or line widths; the local environment of the Q 0 and Q 2 tetrahedra is the primary determinant of the temperature dependence. The type of cation in the first coordination sphere of the tetrahedron may have a secondary effect by affecting Heisenberg lifetimes of Raman virtual states. Previous theoretical considerations have been modified to include the effect of the Heisenberg (or natural) lifetime on Raman FWHM. This contribution is required to explain the anomalous FWHM of Li 2 SiO 3 relative to the FWHM of isostructural Na 2 SiO 3 and the large Li 2 SO 4 and Li 3 PO 4 FWHM (relative to Ba and Sr phosphates). The theoretically based expressions dictate a necessary, simple relationship among temperature, Raman shift, and FWHM. The relationship is developed and it allows, with one measurement of Raman shift and FWHM (e.g., measured at 298 K), prediction of Raman shifts and FWHM of Q 0 and Q 2 crystals to within 5 cm −1 up to ~1500 K. The properties of the TO 4 moiety (T = Si, P, S) are mostly responsible for the striking regularity of Raman shifts and FWHM, although alkali and alkaline earth cations affect to varying extent Heisenberg lifetimes, hence FWHM.
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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 | 0.001 |
| 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) | 0.002 | 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".