Metallic Bonding in Close-Packed Structures: Structural Frustration from a Hidden Gauge Symmetry
Bibliographic record
Abstract
Based on its simple valence electron configuration, we may expect lithium to have straightforward physical properties that are easily explained. However, solid lithium, when cooled below 77 K, develops a complex structure that has been debated for decades. A close parallel is found in sodium below 36 K where the crystal structure still remains unresolved. In this Letter, we explore a possible driving force behind this complexity. We begin with the observation that Li and Na form close-packed structures at low temperatures. We demonstrate a gauge symmetry that forces all close-packed structures to have the same electronic energy and, in fact, the very same band structure. This symmetry requires two conditions: (a) bands must arise from s orbitals, and (b) hoppings beyond second-nearest neighbors must be negligible. We argue that both can be reasonably invoked in Li and Na. When these conditions are satisfied, we have extensive degeneracy with the number of competing isoenergetic structures growing exponentially with system size. Weak effects, such as p-orbital admixture, long-range hopping, and phonon zero-point energy, can break this symmetry. These can play a decisive role in "selecting" one particular ordered structure. This point of view may explain the occurrence of ordered structures in Li and Na under pressure. Our results suggest that martensitic transitions may also occur in heavier alkali metals such as potassium.
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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) | 0.001 | 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".