Crystal structure and crystal chemistry of the τ-Mg32(Al,Zn)49 solid solution using first-principles calculations and thermodynamic modelling
Bibliographic record
Abstract
This paper presents a study of the crystal structure and crystal chemistry of the τ-Mg32(Al,Zn)49 phase. We first performed DFT calculations to resolve conflicting data concerning the occupancy of site 2a of the solid solution crystal structure. Subsequently, 16 ordered configurations derived from the mixing of Al/Zn on sites 24g1, 24g2 and 48h of the solid solution structure, as well as the mixing of Mg/Zn on site 12e1 were generated. We then used DFT calculations to derive the formation enthalpies of all the end-members of the solid solution, their elastic constants by imposing 51 finite deformations for each end-member, and their energies as a function of volume. These calculations were used in a Debye-Wang model (in Slater form) to calculate the heat capacities of the 16 end-members and to obtain in fine their Gibbs energies. At last, these calculations were used to support a thermodynamic model based on the Bragg-Williams approximation, enabling all mixed sites occupancies to be calculated at any temperature and chemical composition. For instance, the predictions we carried out at 633 K and 800 K are in very good agreement with the available measurements. On the basis of these new results, we have determined the chemical ordering of the solid solution over a very wide range of chemical composition and temperature, which has enabled us to propose a new sublattice model for the τ-Mg32(Al,Zn)49 solid solution. This sublattice model is both simpler and more accurate than all the other models used in the literature since it agrees with the crystal structure and the crystal chemistry of the τ-Mg32(Al,Zn)49 phase in a large range of temperature and chemical composition.
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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".