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Deformations of Crystal Frameworks
Ciprian S. Borcea,Ileana Streinu +1 more
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In this article, the deformation space of periodic bar-and-joint frameworks for tetrahedral crystal structures is investigated in detail for frameworks modelled on quartz, cristobalite and tridymite.Abstract:
We apply our deformation theory of periodic bar-and-joint frameworks to tetrahedral crystal structures. The deformation space is investigated in detail for frameworks modelled on quartz, cristobalite and tridymite.read more
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Proceedings Article
Flexible Crystal Frameworks.
Ciprian S. Borcea,Ileana Streinu +1 more
TL;DR: It is shown that quartz and cristobalite have smooth three-dimensional configuration spaces, but ideal high tridymite is a singular configuration with a six-dimensional tangent space, and the topology around this singularity is explicitly described.
Posted Content
Geometric deformations of sodalite frameworks
Ciprian S. Borcea,Ileana Streinu +1 more
TL;DR: In this paper, the authors study combinatorial, geometric and kinematic properties for frameworks modeled on sodalite and show that the properties of these materials can be computed from their geometric representation.
Geometric deformations of sodalite frameworks
Ciprian S. Borcea,Ileana Streinu +1 more
TL;DR: In this paper, the authors study combinatorial, geometric and kinematic properties for frameworks modeled on sodalite and show that the properties of these materials can be computed from their geometric representation.
References
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Journal ArticleDOI
Theory of displacive phase transitions in minerals
TL;DR: In this paper, a soft-mode model for displacive phase transition in silicates is presented, in which the phase-transition mechanism involves a phonon frequency that falls to zero at the transition temperature.
Journal ArticleDOI
The structure of some sodium and calcium aluminosilicates.
TL;DR: Two years ago it was pointed out that the electrostatic valence rule requires that the aluminum ions in alkali aluminum silicates have the coordination number 4 rather than 6, oxygen ions in the crystal then being common to a silicon tetrahedron, an aluminum tetraherron, and one or more alkali-ion polyhedra.
Journal ArticleDOI
Periodic frameworks and flexibility
Ciprian S. Borcea,Ileana Streinu +1 more
TL;DR: In this paper, a concise deformation theory for periodic bar-and-joint frameworks in R d was formulated and illustrated on frameworks related to various crystalline structures, such as tectosilicates and perovskites.
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