On the mechanism of the α-β phase transformation of quartz

Grimm, H.; Dörner, B.

doi:10.1016/0022-3697(75)90066-9

Cited by 186 publications

(118 citation statements)

References 12 publications

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“…Hence it is reasonable to assume that, for a given chemical composition (SiO 2 or GeO 2 ), l(dsecθ/dR)(dR/dl) will also be approximately equal for both polymorphs if the CTM is valid. dδ/dθ and dθ/dsecθ are purely geometrical and expressions relating δ to θ have been derived elsewhere for α-quartz [31] and α-cristobalite [21] structures containing regular tetrahedra.…”

Section: Poisson's Ratios Of the Undeformed Silica And Germania Polymmentioning

confidence: 99%

“…The Poisson's ratios (ν 31 ) thus calculated with this constraint of rigid SiO 4 tetrahedra are also included in table 3. The analytical model calculations employed the experimentally determined tilt angles of δ = 16.3° and 23.5° for silica α-quartz [31], and α-cristobalite [32], respectively and 26.5° and 34.0° for germania α-quartz [33], and α-cristobalite [34], respectively.…”

Section: Poisson's Ratios Of the Undeformed Silica And Germania Polymmentioning

confidence: 99%

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Deformation mechanisms leading to auxetic behaviour in the α-cristobalite and α-quartz structures of both silica and germania

Alderson¹,

Evans²

2008

J. Phys.: Condens. Matter

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Analytical expressions have been developed in which the elastic behaviour of the α-quartz and α-cristobalite molecular tetrahedral frameworks of both silica and germania are modelled by rotation, or dilation or concurrent rotation and dilation of the tetrahedra. Rotation and dilation of the tetrahedra both produce negative Poisson’s ratios (auxetic behaviour), whereas both positive and negative values are possible when these mechanisms act concurrently. Concurrent rotation and dilation of the tetrahedra reproduces with remarkable accuracy both the positive and negative ν31 Poisson’s ratios observed for silica α-quartz and α-cristobalite, respectively, when loaded in the x3 direction. A parametric fit of the concurrent model to the germania α-quartz experimental ν31 Poisson’s ratio is used to predict ν31 for germania α-cristobalite, for which no experimental value exists. This is predicted to be +0.007. Strain-dependent ν31 trends, due to concurrent rotation and dilation in the silica structures, are in broad agreement with those predicted from pair-potential calculations, although significant differences do occur in the absolute values. With the model of concurrent dilation and rotation of the tetrahedra we predict that an alternative uniaxial stress (σ3)-induced phase exists for both silica, α-quartz and α-cristobalite, and germania, α-cristobalite, having geometries in reasonable agreement with β-quartz and idealized β-cristobalite, respectively.

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Section: Poisson's Ratios Of the Undeformed Silica And Germania Polymmentioning

confidence: 99%

Section: Poisson's Ratios Of the Undeformed Silica And Germania Polymmentioning

confidence: 99%

Deformation mechanisms leading to auxetic behaviour in the α-cristobalite and α-quartz structures of both silica and germania

Alderson¹,

Evans²

2008

J. Phys.: Condens. Matter

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“…The excellent agreement with conventional X-ray results is shown by inclusion of values of ~p calculated from the high-temperature X-ray data (Young, 1962). Also shown, for comparison, are points from Grimm & Dorner's (1975) predicted q~(T) and data from Bachheimer & Dolino's (1975) Maker Experiment measurements of dl 1(73.…”

Section: Methodsmentioning

confidence: 99%

“…The first of these, Grimm & Dorner (1975), identifies ~0 as an order parameter and gives a Landau theory functional form for ~o(T). The other paper, Bachheimer & Dolino (1975), asserts, on the basis of group symmetry properties, that d~lt is itself a representation of the order parameter.…”

Section: Theorymentioning

confidence: 99%

Structural mechanics from nonlinear optics – the α to β phase transition in quartz

Crane¹,

Bergman²

1976

J Appl Cryst

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“…The hettotypes of the quartz family may be partially collapsed structures, such as o-quartz, and may contain cavity ions. Tilting models have been developed for the quartz family and geometrical relationships between the cell parameters, the size of the tetrahedron and the tilt angle, assuming regular tetrahedra, were reported independently by Taylor (1972), Megaw (1973), and Grimm and Dorner (1975). Grimm and Dorner (1975) also gave an equation for the calculation of the tilt angle of o-quartz in the presence of distorted tetrahedra, but their equation requires knowledge of the atomic co-ordinates.…”

Section: Framework Structures Without Cavity Ions: Each Shared Vertexmentioning

confidence: 99%

The structural behaviour of tetrahedral framework compounds — a review Part II. Framework structures

Taylor¹

1984

Mineral. mag.

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ABSTRACT. Tetrahedral framework compounds, as defined in this paper, generally exist as tilted and distorted versions of ideal fully expanded structures'at room temperature and atmospheric pressure. How pressure, temperature, and composition (P, T, and X) affect the tilting and distortion is critically reviewed. It is shown that although the effects of P, T, and X on the cell parameters are broadly analogous, the underlying structural changes are generally different. An important, and frequently neglected thermal effect is the apparent shortening of the framework bonds by the anisotropic thermal motion of the framework oxygens. Tilting models of framework compounds are critically examined and their failure to match the observed structural behaviour is attributed to changes in tetrahedral distortion. For quartz it appears that during compression the change in tetrahedral distortion is virtually all angular (O-Si-O angles), whereas during thermal expansion the change in distortion is in the Si-O distances. Such behaviour may typify the behaviour of many other framework compounds but the structural data needed to establish this are lacking. The review is illustrated by reference to the quartz and cristobalite analogues; to the sodalite, leucite, nepheline, scapolite, and feldspar families; and to the nitrides and oxynitrides of silicon and germanium. It is concluded that our understanding of the structural behaviour of framework compounds is still superficial and that much theoretical and experimental work remains to be done.

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On the mechanism of the α-β phase transformation of quartz

Cited by 186 publications

References 12 publications

Deformation mechanisms leading to auxetic behaviour in the α-cristobalite and α-quartz structures of both silica and germania

Deformation mechanisms leading to auxetic behaviour in the α-cristobalite and α-quartz structures of both silica and germania

Structural mechanics from nonlinear optics – the α to β phase transition in quartz

The structural behaviour of tetrahedral framework compounds — a review Part II. Framework structures

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