On the Physical Meaning of the Hall-Petch Constant
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Bibliographic record
Abstract
In order to solve the contradiction found in the Hall-Petch behavior in the ultra-finegrained- and nano-grained- materials, reinvestigation of the physical meaning of Hall-Petch constants has become necessary. The present work is hence attempted to theoretically construct the Hall-Petch slope constant, KH-P. This was carried out based on the principle of image analysis and previous internal energy approach. After analyzing several influencing factors on the KH-P, a model was established with 95% accuracy in predicting the KH-P value. In other words, this model, for the first time, has related the KH-P value to grain boundary surface energy,γ , shear modulus, G, and lattice constant, a0, via 1/ 2 0 K β G(2a γ ) H P = − .
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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 | 0.001 | 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it