First-principles study of lattice dynamics of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">TiO</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>in brookite and cotunnite structures
Bibliographic record
Abstract
The zone-center phonons and dielectric properties of orthorhombic brookite and cotunnite structures ${\mathrm{TiO}}_{2}$ were studied in the framework of density functional perturbative theory. The dielectric properties of brookite and anatase structures are similar. The calculated static dielectric permittivity of brookite is found to be slightly higher than that of anatase, but far lower than that of the rutile structure. This is in contrast with the recent experimental report on brookite flowers. Our study suggests that the static dielectric constant of cotunnite structure is smaller than those of rutile and brookite structures. We obtained the full phonon band structure and elastic properties of these structures. The bulk modulus and Debye temperature of brookite are intermediate between those of the anatase and rutile structures. The obtained value of 301 GPa for the bulk modulus of cotunnite is in good agreement with the stiffness of the material reported experimentally. Because of the similarity in $z$-direction packing of the ${\mathrm{TiO}}_{6}$ tetrahedron between brookite and rutile structures, the elastic constants associated with the $z$-polarized movement of atoms in brookite are similar to those of the rutile structure. The elastic constants of brookite associated with the movement of the atoms in $x$-$y$ plane, are similar to the corresponding constants in anatase and rutile structures. This demonstrates the similarity between the packing character of the brookite structure with both anatase and rutile structures. So, the lattice dynamics of brookite is intermediate between those of anatase and rutile polymorphs. The calculated phonon density of states of cotunnite shows that it is stable at ambient pressure.
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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) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".