Assessment of the Holland model for silicon phonon-phonon relaxation times using lattice dynamics calculations
Bibliographic record
Abstract
We assess the ability of the Holland model to accurately predict phonon-phonon relaxation times from bulk thermal conductivity values. First, lattice dynamics calculations are used to obtain phonon-phonon relaxation times and thermal conductivities for temperatures ranging from 10 K to 1000 K for Stillinger-Weber silicon. The Holland model is then fitted to these thermal conductivities and used to predict relaxation times, which are compared to the relaxation times obtained by lattice dynamics calculations. We find that fitting the Holland model to both total and mode-dependent thermal conductivities does not result in accurate mode-dependent phonon-phonon relaxation times. Introduction of Umklapp scattering for longitudinal modes resulted in improved prediction of mode-dependent relative contributions to thermal conductivity, especially at high temperatures. However, assumptions made by Holland regarding the frequency-dependence of phonon scattering mechanisms are found to be inconsistent with lattice dynamics data. Instead, we introduce a simple method based on using cumulative thermal conductivity functions to obtain better predictions of the frequency-dependence of relaxation times.
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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".