Bibliographic record
Abstract
Using the ab initio method within the local-density approximation with ultrasoft pseudopotentials and plane-wave basis, calculating the Hellmann-Feynman forces and applying the direct method, the phonondispersion relations for ferroelectric and paraelectric rhombohedral phases of LiNbO 3 crystal have been derived.The calculated phonon frequencies for the ferroelectric phase at the point are compared with Raman, infrared, and neutron-scattering measurements, and they agree very well.The phonon frequencies at the Z, L, and F high-symmetry points are also calculated.It is disclosed that the force constants involving lithium ions are an order of magnitude smaller than the force constants between niobium and oxygen ions.As a consequence, the lithium ions do not contribute to high-frequency optical vibrations.In the paraelectric phase the phonon-dispersion curves show a soft branch with the soft mode of symmetry A 2u at the point.This soft mode leads to the observed paraelectric-ferroelectric phase transition.The LO/TO splitting is considered by assuming formal values of ionic charges, and by fitting the longitudinal infrared active modes to the experimental data.
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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 | 0.000 | 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 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".