Symmetry-general least-squares extraction of elastic coefficients from<i>ab initio</i>total energy calculations
Bibliographic record
Abstract
A symmetry-general scheme for the simultaneous least-squares extraction of the elastic coefficients and of the residual strain components from ab initio total energy calculations on crystal structure models of materials is proposed. It is quite efficient and avoids error propagation. An appropriate, but usually singular, set of normal equations is first formulated in a triclinic framework, with 21 stiffness coefficients and 6 residual strain components. Rank reduction of this $27\ifmmode\times\else\texttimes\fi{}27$ least-squares system of normal equations is then performed through systematic implementation of the constraints corresponding to the known symmetry of the material. A regular $p\ifmmode\times\else\texttimes\fi{}p$ matrix is obtained through this process, where p is the total number of independent coefficients and components. This computationally robust approach to the extraction of elastic coefficients and their standard deviations can be used to analyze any number of adequately selected and weighted values of the total energy that is larger than the number of independent parameters. It also provides values for the minimum energy and for the corresponding cell data, again with standard errors. The present work enables the automated calculation of elastic coefficients from crystals with any symmetry through a single logical flow. Examples are given for a few cubic, hexagonal, rhombohedral, tetragonal, and orthorhombic materials with known experimental stiffness values. It would be difficult to exaggerate the convenience of the automated implementation of this symmetry-general approach based on total energy calculations.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.003 |
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 source (direct Gemma or distilled Codex), 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".