Charged lattice gas with a neutralizing background
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
We study a model that was first introduced to describe the ordering of two different types of positive ions in the metal planes of layered hydroxides ${\mathrm{Ni}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}(\mathrm{OH}{)}_{2}({\mathrm{CO}}_{3}{)}_{x/2}\ensuremath{\cdot}y{\mathrm{H}}_{2}\mathrm{O}.$ The ordering is assumed to occur due to long-range Coulomb interactions, and overall charge neutrality is provided by a negative background representing the hydroxide planes and ${\mathrm{CO}}_{3}^{2\ensuremath{-}}$ anions. The previous study was restricted to the ground-state properties. Here we use a Monte Carlo technique to extend the study to finite temperatures. The model predicts that, at some values of the concentration x, the system can exhibit an instability and phase separate. In order to evaluate the precision of these Monte Carlo procedures, we first study a linear chain with finite-range interactions where exact solutions can be obtained using a transfer-matrix method. For a linear chain with infinite-range interactions, we use a devil's staircase formalism to obtain the dependence of the energy of the equilibrium configurations on x. Finally we study the two-dimensional triangular lattice using the same Monte Carlo techniques. In spite of its simplicity, the model predicts multiple first-order phase transitions. The model can be useful in applications such as modeling of the ordering of intercalated metal ions in positive electrodes of lithium batteries or in graphite.
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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 | 0.000 | 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) | 0.005 | 0.008 |
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