Maximally localized rigid unit modes and structural diversity of cristobalite-like crystals


  • Mikhail B. Smirnov Physical department, Saint-Petersburg State University, Russian Federation
  • Pierre Saint-Gregoire CAL, 34110 Frontignan, France


silica, polymorphism, rigid unit modes, cristobalite


It is shown that the particular feature of the ideal beta-cristobalite “C9 lattice” (with
space group Fd3m) is the existence of Chain Tilting Modes (CTM) localized within infinite
linear chains of the linked tetrahedra. Within a CTM the tetrahedra forming the chain may
concordantly rotate without perturbing the rest of the lattice. It is shown that arbitrary Rigid
Unit Mode (RUM) of the C9 structure can be represented as a combination of C?Ms. It is
also shown that all experimentally determined cristobalite-like crystal structures can be
represented as originated from the ideal C9 lattice by a distortion represented as linear
combinations of CTMs.


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How to Cite

Smirnov, M. B., & Saint-Gregoire, P. (2021). Maximally localized rigid unit modes and structural diversity of cristobalite-like crystals. OAJ Materials and Devices, 5(1). Retrieved from