4.2 Article

Nets with collisions (unstable nets) and crystal chemistry

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INT UNION CRYSTALLOGRAPHY
DOI: 10.1107/S0108767313020655

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  1. World Class University program [R-31-2008-000-10055-0]
  2. US National Science Foundation [DMR 1104798]
  3. Ministry of Education and Science of Russia [14.B25.31.0005]
  4. Division Of Materials Research
  5. Direct For Mathematical & Physical Scien [1104798] Funding Source: National Science Foundation

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Nets in which different vertices have identical barycentric coordinates (i.e. have collisions) are called unstable. Some such nets have automorphisms that do not correspond to crystallographic symmetries and are called non-crystallographic. Examples are given of nets taken from real crystal structures which have embeddings with crystallographic symmetry in which colliding nodes either are, or are not, topological neighbors (linked) and in which some links coincide. An example is also given of a crystallographic net of exceptional girth (16), which has collisions in barycentric coordinates but which also has embeddings without collisions with the same symmetry. In this last case the collisions are termed unforced.

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