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Journal ArticleDOI

Rigid-unit phonon modes and structural phase transitions in framework silicates

01 Oct 1996-American Mineralogist (Mineralogical Society of America)-Vol. 81, pp 1057-1079
TL;DR: The rigid unit mode model as discussed by the authors has been used to explain the phase transitions in cristobalite and the diferent feldspar, sodalite, and leucite structures.
Abstract: The rigid-unit mode model provides many new insights into the stability and physical properties of framework silicates. In this model the SiOo and AlO4 tetrahedra are treated as very stifl to a first approximation as completely rigid, in comparison with intertetrahedral forces. In this paper we apply the model to several important examples. The model is reviewed by a detailed study of quarlz, and it is shown that the a-B phase transition involves a rigid-unit mode that preserves the Si-O-Si bond angle. The model is used to explain the phase transitions in cristobalite and the diferent feldspar, sodalite, and leucite structures. We also use the model to explain the nature of the high-temperature disordered phases of cristobalite and tridymite, to interpret the observations of streaks of diffuse scattering in electron diffraction patterns, to interpret the structures in the kalsilite-nepheline solid solution, to explain volume anomalies in the cubic leucite structures, and to explain qualitatively the negative linear thermal expansion in cordierite. The results for the highest symmetry sodalite structure show that there is a rigid-unit mode at every wave vector, a finding with significant implications for the understanding of the sorption and catalytic behavior of zeolites.
Citations
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Journal ArticleDOI
TL;DR: In this article, the authors give an overview of some of the physical phenomena that can give rise to negative thermal expansion and some of their unusual structural properties, and discuss the structural properties of such materials.
Abstract: The vast majority of materials have a positive coefficient of thermal expansion and their volume increases on heating. There has been considerable recent interest in materials which display the unusual property of contracting in volume on heating; i.e. those with a negative coefficient of thermal expansion. This Perspective gives an overview of some of the physical phenomena that can give rise to this unusual effect. Recent insights into negative thermal expansion materials and some of their unusual structural properties are discussed.

487 citations

Journal ArticleDOI
Koshi Takenaka1
TL;DR: This review briefly summarizes materials and mechanisms of NTE as well as composites containing NTE materials, based mainly on activities of the last decade.

429 citations

Journal ArticleDOI
TL;DR: In this paper, the wave-vector and polarization properties of amorphous Si have been analyzed and diffusivity has been characterized by calculating phase auotient and spadal polarization memory.
Abstract: Numerical studies of amorphous Si show that the lowest 4% of vibrational modes are piane wave like (‘propagons’) and the highest 3% of modes are localized (‘locons’). The rest are neither piane wave like nor localized. We cali them ‘diffusons’. Since diffusons are by far the most numerous, we try to characterize them by calculating such properties as the wave-vector and polarization (which do not seem to be useful), ‘phase auotient’ (a measure of the change of vibrational phase between first-neighbour atoms), spadal polarization memory and diffusivity. Localized states are characterized by finding decay lengths, inverse participation ratios and coordination numbers of the participating atoms.

396 citations

Journal ArticleDOI
TL;DR: The methodology is shown at work, illustrating its various possibilities for improving the characterization of distorted structures, for example: detection of hidden structural correlations, identification of fundamental and marginal degrees of freedom, reduction of the effective number of atomic positional parameters.
Abstract: The description of displacive distorted structures in terms of symmetry-adapted modes is reviewed. A specific parameterization of the symmetry-mode decomposition of these pseudosymmetric structures defined on the setting of the experimental space group is proposed. This approach closely follows crystallographic conventions and permits a straightforward transformation between symmetry-mode and conventional descriptions of the structures. Multiple examples are presented showing the insight provided by the symmetry-mode approach. The methodology is shown at work, illustrating its various possibilities for improving the characterization of distorted structures, for example: detection of hidden structural correlations, identification of fundamental and marginal degrees of freedom, reduction of the effective number of atomic positional parameters, quantitative comparison of structures with the same or different space group, detection of false refinement minima, systematic characterization of thermal behavior, rationalization of phase diagrams and various symmetries in families of compounds etc. The close relation of the symmetry-mode description with the superspace formalism applied to commensurate superstructures is also discussed. Finally, the application of this methodology in the field of ab initio or first-principles calculations is outlined. At present, there are several freely available user-friendly computer tools for performing automatic symmetry-mode analyses. The use of these programs does not require a deep knowledge of group theory and can be applied either a posteriori to analyze a given distorted structure or a priori to parameterize the structure to be determined. It is hoped that this article will encourage the use of these tools. All the examples presented here have been worked out using the program AMPLIMODES [Orobengoa et al. (2009). J. Appl. Cryst. 42, 820–833].

329 citations


Cites background from "Rigid-unit phonon modes and structu..."

  • ...One may argue that the remarkable “rigidity” of the polarization vectors of the distortion modes is due to the fact that they correspond to rigid unit modes (RUMs) ((Giddy et al., 1993), (Hammonds et al., 1996)) of the tetrahedral framework in the leucite structure....

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  • ...For these simple structures with rather rigid BX6 octahedra, a mode description is quite simple; many normal modes are fully determined by symmetry and can be identified with tilts or RUMs (Giddy et al. (1993), Hammonds et al. (1996)) of the framework of octahedra....

    [...]

References
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Journal ArticleDOI
TL;DR: In this paper, the authors examine the differences between covalent random networks with high and low average coordination and make rigorous assumptions about the number of continuous deformations (i.e., zero frequency modes) allowed within the network.
Abstract: We examine some current ideas concerning the differences between covalent random networks with high and low average coordination. These ideas can be made rigorous by considering the number of continuous deformations (i.e. zero frequency modes) allowed within the network. In the transition from one kind of network to another, rigidity percolates through the system. This leads to a picture in which random networks with low average coordination (polymeric glasses) have large floppy or spongy regions with a few rigid inclusions. On the other hand in random networks with high average coordination (amorphous solids) the rigid regions have percolated to form a rigid solid with a few floppy or spongy inclusions.

1,202 citations

Journal ArticleDOI
TL;DR: In this paper, the orientation of domain walls in full ferroelastic materials has been investigated based on the same criterion of spontaneous strain compatibility defined by Fousek and Janovec for ferroelectric crystals.
Abstract: The orientations of domain walls in ferroelastic materials are theoretically investigated. The procedure followed is based on the same criterion of spontaneous strain compatibility defined by Fousek and Janovec for ferroelectric crystals. Two given domains in a ferroelastic are found to be separated by a planar wall whose orientation belongs to a set of two mutually perpendicular orientations. Domain walls are not always crystallographically prominent planes of fixed indices ($W$ planes) and can instead be determined by the relative magnitude of the components of the second-rank tensor representing the spontaneous strain (${W}^{\ensuremath{'}}$ walls). In the latter case the orientation is expected to be temperature dependent. It is also shown that symmetry considerations are sufficient to find all $W$ planes. According to the considered ferroelastic species the pair of permissible walls between two domains can be two $W$ planes, or a $W$ plane and a ${W}^{\ensuremath{'}}$ plane, or two ${W}^{\ensuremath{'}}$ planes. The situation where no permissible walls are expected is of particular interest and is examined in known crystals. The predicted orientations of walls are given for the 94 species of full ferroelastics. Available experimental data of the literature are all consistent with our results.

674 citations


"Rigid-unit phonon modes and structu..." refers background in this paper

  • ...The theory of coherent domain packets (Sapriel 1975) shows that the strain energy is minimized if the boundaries lie perpendicular to the [,+1,0] axes....

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  • ...Sapriel, J. (1975) Domain wall orientations in ferroelastics....

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Journal ArticleDOI
TL;DR: The first conclusive evidence that covalent glasses can be divided into two classes is presented by calculating the elastic properties of random networks with different average coordination: those with high average coordination and those with low average coordination.
Abstract: It is believed that covalent glasses can be divided into two classes: those with high average coordination (amorphous solids) and those with low average coordination (polymeric glasses). We present the first conclusive evidence that this division is correct by calculating the elastic properties of random networks with different average coordination $〈r〉$. The results show that the elastic constants depend predominantly on $〈r〉$ and go to zero when $〈r〉=2.4$ with an exponent $f=1.5\ifmmode\pm\else\textpm\fi{}0.2$.

508 citations

Journal ArticleDOI

488 citations

Journal ArticleDOI
TL;DR: The results show that additional harmonic excitations coexist with sound waves below 1 THz, and that these excitations correspond to relative rotation of ${\mathrm{SiO}}_{4}$ tetrahedra.
Abstract: Measurements of the elastic and inelastic neutron scattering from vitreous silica in the frequency range 0.3 to 4 THz and with scattering vectors in the range 0.2 to 5.3 A${\r{}}^{\mathrm{\ensuremath{-}}1}$ are analyzed in conjunction with heat-capacity measurements on the same samples to provide a microscopic description of low-frequency vibrational modes. The results show that additional harmonic excitations coexist with sound waves below 1 THz, and that these excitations correspond to relative rotation of ${\mathrm{SiO}}_{4}$ tetrahedra.

405 citations