Rigid unit modes in crystal structures with octahedrally coordinated atoms

Hammonds, Kenton D.; Bosenick, Anne; Dove, Martin T.; Heine, Volker

doi:10.2138/am-1998-5-607

Cited by 71 publications

(50 citation statements)

References 18 publications

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“…In this glass (or more generally aluminosilicates) the forces within the tetrahedra SiO 4 are much stronger than the forces that act between them [69]: it is easier to rotate two linked tetrahedra than to distort one tetrahedron 8 . This suggests to model such glass as an assembly of linked tetrahedra loosely connected at corners: this is the "rigid unit modes" model [70].…”

Section: Application To Tetrahedral Networkmentioning

confidence: 99%

On the rigidity of amorphous solids

2005

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We poorly understand the properties of amorphous systems at small length scales, where a continuous elastic description breaks down. This is apparent when one considers their vibrational and transport properties, or the way forces propagate in these solids. Little is known about the microscopic cause of their rigidity. Recently it has been observed numerically that an assembly of elastic particles has a critical behavior near the jamming threshold where the pressure vanishes. At the transition such a system does not behave as a continuous medium at any length scales. When this system is compressed, scaling is observed for the elastic moduli, the coordination number, but also for the density of vibrational modes. In the present work we derive theoretically these results, and show that they apply to various systems such as granular matter and silica, but also to colloidal glasses. In particular we show that: (i) these systems present a large excess of vibrational modes at low frequency in comparison with normal solids, called the "boson peak" in the glass literature. The corresponding modes are very different from plane waves, and their frequency is related to the system coordination; (ii) rigidity is a non-local property of the packing geometry, characterized by a length scale which can be large. For elastic particles this length diverges near the jamming transition; (iii) for repulsive systems the shear modulus can be much smaller than the bulk modulus. We compute the corresponding scaling laws near the jamming threshold. Finally, we discuss the implications of these results for the glass transition, the transport, and the geometry of the random close packing.

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Section: Application To Tetrahedral Networkmentioning

confidence: 99%

On the rigidity of amorphous solids

2005

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“…For framework structures, such as perovskites, consisting of concatenated molecular units, there is a small set of external modes of the molecular units, termed Rigid Unit Modes (RUMs) that are consistent with the connectivity of the framework. These occur due to a small excess of degrees of freedom with respect to the number of geometrical constraints in the structure [10,11].…”

Section: Introductionmentioning

confidence: 99%

The ordered phase of methylammonium lead chloride CH3ND3PbCl3

Chi

Swainson

Cranswick

et al. 2005

Journal of Solid State Chemistry

144

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“…A consideration of the constraints [24,25,34,35] imposed by the linkage of the tetrahedra suggests that RUMs may be possible in this structure although the unusually small thermal expansion in willemite is indicative of the extra rigidity from the three-coordinate oxygen atoms. The relationship between low energy vibrational modes such as RUMs and NTE has been well established [26,27,29,[36][37][38] and will be discussed in relation to Zn 2 GeO 4 in a separate contribution [22].…”

Section: Introductionmentioning

confidence: 99%