Coherent phase equilibria of systems with large lattice mismatch
Bibliographic record
Abstract
In many metallurgical applications, an accurate knowledge of miscibility gaps and spinodal decompositions is highly desirable. Some binary systems where the main constituents of the same crystal structures have similar lattice parameters (less than 15% difference) reveal a composition, temperature shift of the miscibility gap due to lattice coherency. So far, the well-known Cahn's approach is the only available calculation method to estimate the coherent solid state phase equilibria. Nevertheless, this approach shows some limitations, in particular it fails to predict accurately the evolution of phase equilibria for large deformation, i.e. the large lattice parameter difference (more than 5%). The aim of this study is to propose an alternative approach to overcome the limits of Cahn's method. The elastic contribution to the Gibbs energy, representing the elastic energy stored in the coherent boundary, is formulated based on the linear elasticity theory. The expression of the molar elastic energy corresponding to the coherency along both directions [100] and [111] has been formulated in the small and large deformation regimes. Several case studies have been examined in cubic systems, and the proposed formalism is showing an appropriate predictive capability, making it a serious alternative to the Cahn's method. The present formulation is applied to predict phase equilibria evolution of systems under other stresses rather than only those induced by the lattice mismatch.
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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) | 0.000 | 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".