The determination of rigid-unit modes as potential soft modes for displacive phase transitions in framework crystal structures

Giddy, A. P.; Dove, Martin T.; Pawley, G. S.; Heine, Volker

doi:10.1107/s0108767393002545

Cited by 243 publications

(295 citation statements)

References 22 publications

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“…Such modulations are usually due to a displacive phase transition of the lattice involving rotations of SiO 4 tetrahedra without substantial internal distortions of the tetrahedra themselves [9,10,11]. BaCuSi 2 O 6 can be thought of as a 'vierer' single ring cyclosilicate [12], in which isolated Si 4 O 12 rings (composed of 4 corner sharing SiO 4 tetrahedra) are linked by CuO 4 groups in the ab-plane, and separated by Ba cations between successive layers.…”

Section: Discussionmentioning

confidence: 99%

Low-temperature structural phase transition and incommensurate lattice modulation in the spin-gap compoundBaCuSi2O6

et al. 2006

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Results of high resolution x-ray diffraction experiments are presented for single crystals of the spin gap compound BaCuSi2O6 in the temperature range from 16 to 300 K. The data show clear evidence of a transition from the room temperature tetragonal phase into an incommensurately modulated orthorhombic structure below ∼100 K. This lattice modulation is characterized by a resolution limited wave vector qIC =(0,∼0.13,0) and its 2 nd and 3 rd harmonics. The phase transition is first order and exhibits considerable hysteresis. This observation implies that the spin Hamiltonian representing the system is more complex than originally thought.

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Section: Discussionmentioning

confidence: 99%

Low-temperature structural phase transition and incommensurate lattice modulation in the spin-gap compoundBaCuSi2O6

et al. 2006

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“…However, in the previous studies [26,35] the movement of the framework atoms was usually ignored. Our goal was to develop a technique that can predict at different temperatures not only the cation arrangement but also the exact framework atom positioning.…”

Section: Intramolecular/bond Interactionsmentioning

confidence: 99%

“…Coarser descriptions, like the Rigid Unit Model (RUM) [35], which provide interactions between rigid groups of atoms (tetrahedra and octahedra) linked by vibrating oxygen bridges, have been used in the past for the investigation of the zeolite structure deformation, like temperature dependence of the zeolite pore dimension, and negative thermal expansion coefficients.…”

Section: Intramolecular/bond Interactionsmentioning

confidence: 99%

Simulated annealing effects on Na-FAU crystal reconstruction and sorption efficiency

Krokidas

Skouras

Nikolakis

et al. 2008

Molecular Simulation

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“…Thus even though there is a considerable ionic contribution to bonding in a solid, the knowledge of its structure and chemistry can still allow us to map interatomic interactions into a generalized network, albeit with different building blocks: these do not correspond to two-and three-body constraints as in the Phillips theory, but to local rigid units. The modes that propagate in without its constituent units having to distort have been named Rigid Unit Modes (RUMs) [5].In this paper, we discuss the ability of cuprate high-temperature superconductors to support the RUM, which we associate with the lowest non-trivial energy state in CuO 2 plane. A distinct property of the RUM is its infinite (in the idealized model) correlation length.…”

mentioning

confidence: 99%

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confidence: 99%

Structural flexibility of cuprate superconductors

Trachenko

2007

Philosophical Magazine Letters

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We study the lowest energy state in the CuO2 plane of cuprate superconductors, related to the vibration that does not involve distortions of constituent units of the plane, the Rigid Unit Mode (RUM). We discuss the correlated motion in the plane due to RUM on temperature decrease, and possible relevance of this phonon for superconductivity.The existence of the hierarchy of interatomic interactions in a solid can make a substantial reduction in analyzing its properties. If the energy to break a chemical bond between two atoms considerably exceeds the thermal energy, such a bond can be viewed as a Lagrangian constraint, in a sense that it keeps two atoms at a fixed distance. This idea can be made useful in the case of covalent materials, in which two-body stretching and three-body bending forces considerably exceed all others. These short-range interactions can be translated into the building blocks of a mechanical network. This has been the starting point of the Phillips theory of network glasses [1]. By requiring that the number of degrees of freedom is equal to the average number of bonding constraints, this theory predicted the average coordination number of r = 2.4 for which glass forming ability is optimized. Since then, this picture has been widely used to discuss relaxation in covalent glasses and crystals.The constraint theory offers a great reduction in treating the interactions in a solid, by translating static, vibrational and relaxation properties of a solid into those of a mechanical network, with well-developed methods to study it. For example, the procedure known as Maxwell counting can make rigorous predictions about the lowenergy states of the system. Any modes in a mechanical network that keep local constraints (e. g. two-body stretching and three-body bending constraints) intact, have zero frequency because there is no restoring forces to such deformations. According to Maxwell counting, the number of such modes is equal to the difference between the number of degrees of freedom, N f , and the number of bonding constraints, N c . Therefore, the existence of the hierarchy of interactions in a solid can have important implications for the hierarchy of vibrational modes in terms of their frequency. In the simulation study of constraint counting in glasses, "floppy" modes appear when the network becomes under-constrained, N c < N f , or r < 2.4 [2] (the term "floppy" here points to the fact that in real systems, weaker interactions always give a non-zero restoring force associated with propagation of constraintobeying modes, making their frequency not zero exactly, but some small values).By construction, the picture which maps interatomic interactions into a network of mechanical constraints, is limited to solids with short-range covalent interactions. If ionic contribution to bonding is substantial, the mapping of interatomic interactions into a network is problematic due to the long-range nature of Coloumb forces and the absence of the hierarchy of interactions [3]. It is nevertheless still possi...

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The determination of rigid-unit modes as potential soft modes for displacive phase transitions in framework crystal structures

Cited by 243 publications

References 22 publications

Low-temperature structural phase transition and incommensurate lattice modulation in the spin-gap compoundBaCuSi2O6

Low-temperature structural phase transition and incommensurate lattice modulation in the spin-gap compoundBaCuSi2O6

Simulated annealing effects on Na-FAU crystal reconstruction and sorption efficiency

Structural flexibility of cuprate superconductors

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