Twinning relationships in coexisting cubic and tetragonal phases of ferroelectrics
Bibliographic record
Abstract
Many ferroelectric materials undergo thermally driven transitions between cubic and tetragonal phases. Despite being well-known for decades, such transitions still pose unresolved questions, particularly about the role of domains in shaping the transition pathway. It is understood that tetragonal domain assemblages are crucial for mismatch-free coexistence of both tetragonal and cubic phases, as described by the Weschler—Lieberman—Read (WLR) crystallographic theory. However, direct experimental characterization of domain patterns during the phase transition remains challenging. Here, we enhance the single-crystal X-ray diffraction to investigate domain microstructures during cubic-tetragonal phase transition, leveraging the bulk-penetrating and non-destructive character of this method. We extend the WLR model by the analytical expressions for the orientation relationships between the real and reciprocal bases of the cubic phase and tetragonal domains. We systematically catalogue the Bragg peak separations for 24 possible coexistence variants and validate these predictions using 3D reciprocal space maps from a piezo-/ferroelectric PMN-35PT crystal at phase coexistence temperatures. Our results provide a framework for interpreting domain configurations during the phase transition and offer insights applicable to other systems involving orientation relationships in coexisting phases.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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".