Atom transport in random two sublattice structures: analogue of the random alloy sum rule
Bibliographic record
Abstract
A simple and often used model of atom transport by the vacancy mechanism on two physically distinct interpenetrating sublattices assumes that each atom–vacancy exchange frequency depends only on the species of the atom and the sublattice from which it jumps. In the kinetic theory of this model, the phenomenological coefficients can be expressed as sums of partial correlation functions, each labelled by the sublattices associated with the atoms making the first and last jumps in the sequence of correlated jumps which it represents. A sum rule, a set of exact relations among these partial correlation functions, is derived for the model, assuming arbitrary vacancy content and any number of chemical species. It reduces to a widely used sum rule for the random lattice gas [L.K. Moleko and A.R. Allnatt, Phil. Mag. A 58 677 (1988)] in the limit that atom jump frequencies are made independent of sublattice. For the two sublattice model at very low vacancy contents, a more powerful sum rule is also derived; it is essentially the same as that of Belova and Murch [Defect Diffus. Forum 194/199 547 (2001)]. The efficiencies of the three sum rules are briefly compared. The low vacancy concentration sum rule is illustrated by numerical simulations for a binary two sublattice system.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".