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Continuous Invariant-Based Maps of the Cambridge Structural Database.

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The crystal isometry principle (CRISP) uses atomic geometry to uniquely define periodic crystals. New continuous maps, based on pointwise distance distributions (PDD), locate all crystals invariantly, aiding future discoveries.

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Area of Science:

  • Crystallography
  • Materials Science
  • Computational Chemistry

Background:

  • The Cambridge Structural Database (CSD) is a key resource for crystallographic data.
  • The crystal isometry principle (CRISP) posits that crystal structures are uniquely defined by atomic geometry, irrespective of atomic types.
  • Previous work introduced pointwise distance distributions (PDD) as invariant descriptors for crystals.

Purpose of the Study:

  • To develop continuous, geographically-styled maps for visualizing the entire landscape of periodic crystals.
  • To present analytic formulas and physical interpretations for these invariant coordinates.
  • To demonstrate that these maps can uniquely locate existing crystals and accommodate new discoveries.

Main Methods:

  • Utilizing the crystal isometry principle (CRISP) and ignoring atomic types to create a common space for crystal analysis.
  • Applying pointwise distance distributions (PDD) as invariant structural descriptors under isometric transformations (translation, rotation, reflection).
  • Developing continuous mapping techniques based on these invariant coordinates.

Main Results:

  • The first continuous maps of the Cambridge Structural Database (CSD) and its subsets were generated in invariant coordinates.
  • These maps provide analytic formulas and physical interpretations for crystal locations.
  • Each periodic crystal occupies a unique, stable position on these maps, regardless of its discovery time.

Conclusions:

  • Continuous mapping of crystal structures in invariant coordinates offers a powerful new visualization and analysis tool.
  • The developed method provides a stable framework for organizing and understanding the vast diversity of known and future crystalline materials.
  • This approach facilitates the study of crystal structures independent of specific atomic identities, focusing on fundamental geometric principles.