Bibliographic record
Abstract
For many materials, the structure of crystalline surfaces or solid-solid interphase boundaries is characterized by an array of mobile steps separated by immobile terraces. Despite the prevalence of step-terraced interfaces a theoretical description of the growth rate has not been completely solved. In this work the boundary element method (BEM) has been utilized to numerically compute the concentration profile in a fluid phase in contact with an infinite array of equally spaced surface steps and, under the assumption that step motion is controlled by diffusion through the fluid phase, the growth rate is computed. It is also assumed that a boundary layer exists between the growing surface and a point in the liquid where complete convective mixing occurs. The BEM results are presented for varying step spacing, supersaturation, and boundary layer width. BEM calculations were also used to study the phenomenon of step bunching during crystal growth, and it is found that, in the absence of elastic strain energy, a sufficiently large perturbation in the position of a step from its regular spacing will lead to a step bunching instability. Finally, an approximate analytic solution using a matched asymptotic expansion technique is presented for the case of a stagnant liquid or equivalently a solid-solid stepped interface.
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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 | 0.001 |
| 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) | 0.001 | 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 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".