First principles investigation on how site preference and entropy affect the stability of (Eu<sub><i>x</i></sub>M<sub>1–</sub><sub><i>x</i></sub>)<sub>2</sub>Ge<sub>2</sub>Pb (M = Ca, Sr, Ba) polar intermetallics
Bibliographic record
Abstract
Density functional theory calculations have been carried out to analyze the factors contributing to the stabilities of a set of recently synthesized quaternary polar intermetallic compounds, (Eu x M 1– x ) 2 Ge 2 Pb with M = Ca, Sr, and Ba. Experiments showed that these preferentially crystallized with Pbam (M = Ca) or Cmmm (M = Sr, Ba) symmetry. We systematically explored how the electronic energies of these structures depended on how they were “colored” by the europium/M ions for a wide composition range. It was found that whereas there was very little site preference in the Cmmm structure, the “B” site in the Pbam structure strongly preferred smaller cations. The configurational entropy was also found to play a role in determining which structures might be preferred. However, the experimentally obtained product ratios could only be fully rationalized by the Gibbs free energies of structures containing M:Eu ratios resembling those that were synthesized experimentally. Our results highlight the importance of calculating vibrational contributions to the entropy for realistic structure models (in terms of coloring and composition) to explain product ratios for syntheses carried out at high temperatures.
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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 | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.002 | 0.003 |
| 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; both teacher heads agree on what is shown here.
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".