A statistical model approximation for perovskite solid-solutions: A Raman study of lead-zirconate-titanate single crystal
Bibliographic record
Abstract
Lead titanate (PbTiO3) is a classical example of a ferroelectric perovskite oxide illustrating a displacive phase transition accompanied by softening of a symmetry-breaking mode. The underlying assumption justifying the soft-mode theory is that the crystal is macroscopically sufficiently uniform that a meaningful free energy function can be formed. In contrast to PbTiO3, experimental studies show that the phase transition behaviour of lead-zirconate-titanate solid solution (PZT) is far more subtle. Most of the studies on the PZT system have been dedicated to ceramic or powder samples, in which case an unambiguous soft-mode study is not possible, as modes with different symmetries appear together. Our Raman scattering study on titanium-rich PZT single crystal shows that the phase transitions in PZT cannot be described by a simple soft-mode theory. In strong contrast to PbTiO3, splitting of transverse E-symmetry modes reveals that there are different locally ordered regions. The role of crystal defects, random distribution of Ti and Zr at the B-cation site and Pb ions shifted away from their ideal positions, dictates the phase transition mechanism. A statistical model explaining the observed peak splitting and phase transformation to a complex state with spatially varying local order in the vicinity of the morphotropic phase boundary is given.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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) | 0.000 | 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".