The Hume-Rothery size rule and double-well microstructures in gold-nickel
Bibliographic record
Abstract
The miscibility gap and high critical temperature in Au-Ni together with coherency strain effects in decomposition arise primarily due to the Pauli principle, whereby the fcc lattice parameter of Au is 1.15 times that of Ni, thus acting maximally according to Hume-Rothery against extensive solid solution formation. Since the critical point is only about 100 °C below the solidus, this simplifies the theoretical evaluation of the solubility limitation. It also offers a bridge to spinodal kinetics encompassing a dominant solution effect of local Vegard's law strain, which acts repulsively in bulk clustering and attractively in gradient energy relaxation. Low and high temperature TEM hot stage observations of continuous modulated decomposition spanning the miscibility gap of Au-Ni ( T c ≃1080 K) can be interpreted according to the time-dependent Ginzburg-Landau (TDGL) reaction-diffusion theory modified to include solute conservation and a diffusion-relaxable effect of strain while maintaining full low amplitude coherency. Modulated decomposition structures of order 3 nm, proven through lattice imaging to be spinodal in character by Sinclair et al , have often been reported near the so-called upper limit, coherent critical temperature (~420 K), where the wavelength is supposed to be infinite, while we report here well advanced 10 nm modulations at 350 °C above this. As a crystallographic template, the fine three-dimensional interleaved dendrite-like tweed pattern first decoheres, then locally transforms at 773 K into ~100 nm lamellar spacing intragranular nodules. These coarsened bulk products are modulation-templated, faceted, near-spherical structures, first observed by Underwood between 673 and 973 K and by Cahn at 993 K in 1954, and prove to be consistent with steady state lamellar solutions of the TDGL equation. This three-stage decomposition mode in ~100 nm thick films competes with the well known grain-boundary-nucleated short-circuited lamellar product, which was originally deemed to be unique in bulk samples at higher temperatures.
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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 | 0.000 | 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) | 0.001 | 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 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".