Theory of the metal-insulator transition in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Pr</mml:mi><mml:msub><mml:mi mathvariant="normal">Ru</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">P</mml:mi><mml:mn>12</mml:mn></mml:msub></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Pr</mml:mi><mml:msub><mml:mi mathvariant="normal">Fe</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">P</mml:mi><mml:mn>12</mml:mn></mml:msub></mml:mrow></mml:math>
Bibliographic record
Abstract
All symmetry-allowed couplings between the $4{f}^{2}$-electron ground state doublet of trivalent praseodymium in $\mathrm{Pr}{\mathrm{Ru}}_{4}{\mathrm{P}}_{12}$ and $\mathrm{Pr}{\mathrm{Fe}}_{4}{\mathrm{P}}_{12}$ and displacements of the phosphorus, iron, or ruthenium ions are considered. Two types of displacements can change the crystal lattice from body-centred cubic to simple orthorhombic or to simple cubic. The first type lowers the point group symmetry from tetrahedral to orthorhombic, while the second type leaves it unchanged, with corresponding space group reductions $Im\overline{3}\ensuremath{\rightarrow}Pmmm$ and $Im\overline{3}\ensuremath{\rightarrow}Pm\overline{3}$, respectively. In former case, the lower point group symmetry splits the degeneracy of the $4{f}^{2}$ doublet into states with opposite quadrupole moment, which then leads to antiquadrupolar ordering, as in $\mathrm{Pr}{\mathrm{Fe}}_{4}{\mathrm{P}}_{12}$. Either kind of displacement may conspire with nesting of the Fermi surface to cause the metal-insulator or partial metal-insulator transition observed in $\mathrm{Pr}{\mathrm{Fe}}_{4}{\mathrm{P}}_{12}$ and $\mathrm{Pr}{\mathrm{Ru}}_{4}{\mathrm{P}}_{12}$. We investigate this scenario using band-structure calculations, and it is found that displacements of the phosphorus ions in $\mathrm{Pr}{\mathrm{Ru}}_{4}{\mathrm{P}}_{12}$ (with space-group reduction $Im\overline{3}\ensuremath{\rightarrow}Pm\overline{3}$) open a gap everywhere on the Fermi surface.
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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 | 0.009 | 0.004 |
| Meta-epidemiology (narrow) | 0.005 | 0.009 |
| Meta-epidemiology (broad) | 0.002 | 0.010 |
| Bibliometrics | 0.002 | 0.006 |
| Science and technology studies | 0.007 | 0.007 |
| Scholarly communication | 0.006 | 0.008 |
| Open science | 0.010 | 0.008 |
| Research integrity | 0.008 | 0.009 |
| Insufficient payload (model declined to judge) | 0.596 | 0.009 |
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; both teacher heads agree on what is shown here.
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".