Structure Topology and Graphical Representation of Decorated and Undecorated Chains of Edge-Sharing Octahedra
Bibliographic record
Abstract
ABSTRACT Infinite chains of edge-sharing octahedra occur as fundamental building blocks (FBBs) in the structures of several hundred mineral species. Such chains consist of a backbone of octahedra to which decorating polyhedra may be attached. The general, stoichiometric formula of such chains may be written as c[MATxФz] where M is any octahedrally coordinated cation, T is any cation coordinated by a decoration polyhedron (regardless of coordination geometry), Ф is any possible ligand [O2–, (OH)–, (H2O), Cl–, or F–], and c indicates the configuration of backbone octahedra. In the minerals in which they occur, these types of chains will commonly (though not exclusively) form part of the structural unit (i.e., the strongly bonded part) of a mineral. Hence, investigating the topology, configuration, and arrangement of such chains may yield fundamental insights into the stability of minerals in which they occur. A discussion of the topological variability of chains is presented here, along with the formulae necessary for their characterization. It is shown that many aspects of chain topology can be efficiently communicated by a pair of values with the form ([x], [Bopqrst]), where [x] summarizes the symmetry operations necessary to characterize the configuration of backbone octahedra, B indicates the length of the topological repeat, and o through t indicate the number of individual decorations (related to B). A methodology for developing finite graphical representations for infinite chains is presented in detail, showing that for any given chain, a single, irreducible finite graph exists that contains all topological information. Such a graph, however, can correspond to multiple chain topologies, highlighting the importance of geometrical isomerism. The utility of the graphical approach in facilitating the development of a hierarchy of chains and chain-bearing structures is also discussed.
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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) | 0.000 | 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) | 0.000 | 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".