Time evolution of twin domains in cordierite: a computer simulation study

Blackburn, John; Salje, Ekhard K. H.

doi:10.1007/s002690050188

Cited by 11 publications

(6 citation statements)

References 19 publications

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“…Of the several theories [12][13][14][15][16] dealing with these materials, only that of Wen et al 16 found patterns consistent with some of those observed. Their phase-field kinetic theory is however highly phenomenological, being based on order parameters with no direct physical interpretation; an expansion to sixth order is necessary, and even the scaled theory requires at least five parameters.…”

Section: Introductionmentioning

confidence: 56%

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Statics and dynamics of domain patterns in hexagonal-orthorhombic ferroelastics

Curnoe

Jacobs

2001

Phys. Rev. B

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We study the statics and the dynamics of domain patterns in proper hexagonal-orthorhombic ferroelastics; these patterns are of particular interest because they provide a rare physical realization of disclinations in crystals. Both our static and dynamical theories are based entirely on classical, nonlinear elasticity theory; we use the minimal theory consistent with stability, symmetry and ability to explain qualitatively the observed patterns. After scaling, the only parameters of the static theory are a temperature variable and a stiffness variable. For moderate to large stiffness, our static results show nested stars, unnested stars, fans and other nodes, triangular and trapezoidal regions of trapped hexagonal phase, etc observed in electron microscopy of Ta4N and Mg-Cd alloys, and also in lead orthovanadate (which is trigonal-monoclinic); we even find imperfections in some nodes, like those observed. For small stiffness, we find patterns like those observed in the mineral Mg-cordierite. Our dynamical studies of growth and relaxation show the formation of these static patterns, and also transitory structures such as 12-armed bursts, streamers and striations which are also seen experimentally. The major aspects of the growth-relaxation process are quite unlike those in systems with conventional order parameters, for it is inherently nonlocal; for example, the changes from one snapshot to the next are not predictable by inspection.

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Section: Introductionmentioning

confidence: 56%

“…We assume that the dissipation is large and drop the inertial term ρü i ; the equations of motion are then (15) where G i = δF/δe i :…”

Section: Dynamicsmentioning

confidence: 99%

Statics and dynamics of domain patterns in hexagonal-orthorhombic ferroelastics

Curnoe

Jacobs

2001

Phys. Rev. B

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“…The parameters for X-ray data collection and structure refinement are given in Table 2 . Orthorhombic Fe-cordierite shows pseudo-hexagonal micro-scale twinning and twinnig in synthetic orthorhombic Mg-cordierite has been described in literature (e.g., Putnis 1980 ; Armbruster 1985a ; Blackburn and Salje 1999 ). The refinement of the orthorhombic Fe-cordierite was performed assuming three twin-domains, related to each other by a 60° rotation around c .…”

Section: Experimental Methodsmentioning

confidence: 94%

Structural investigations of the two polymorphs of synthetic Fe-cordierite and Raman spectroscopy of hexagonal Fe-cordierite

Haefeker¹,

Kaindl

Tropper³

et al. 2013

Miner Petrol

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The crystal structures of synthetic hexagonal and orthorhombic Fe-cordierite polymorphs with the space groups P6/mcc and Cccm were refined from single-crystal X-ray diffraction data to R1, hex = 3.14 % and R1, ortho = 4.48 %. The substitution of the larger Fe2+ for Mg leads to multiple structural changes and an increase of the unit cell volumes, with a, c (hex) = 9.8801(16) Å, 9.2852(5) Å and a, b, c (ortho) = 17.2306(2) Å, 9.8239(1) Å, 9.2892(1) Å in the end-members. Furthermore Fe incorporation results in an increase of the volumes of the octahedra, although the diameters of the octahedra in direction of the c-axis decrease in both polymorphs. X-ray powder diffraction analysis indicates a high degree of Al/Si ordering in the orthorhombic polymorph, the Miyashiro distortion index is ~0.24. Estimations of site occupancies based on the determined tetrahedral volumes result in the following values for hexagonal Fe-cordierite: ~73 % Al for T1 and ~28 % Al for T2. For the first time Raman spectroscopy was performed on the hexagonal Fe-cordierite polymorph. In the hexagonal Fe-cordierite polymorph most Raman peaks are shifted towards lower wavenumbers when compared with the Mg-end-member.Electronic supplementary materialThe online version of this article (doi:10.1007/s00710-013-0313-3) contains supplementary material, which is available to authorized users.

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“…We have no information regarding the atomic structure of such twin walls, but we may speculate that the same principles, which were discussed in this paper, also apply. An atypical example is the twinning in cordierte that contains ferroelastic and topological aspects [116]. This means that these twinned minerals may contain a multitude of 'emerging' properties that we simply do not know.…”

Section: Discussionmentioning

confidence: 99%

Ferroelastic Twinning in Minerals: A Source of Trace Elements, Conductivity, and Unexpected Piezoelectricity

Salje

2021

Minerals

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Ferroelastic twinning in minerals is a very common phenomenon. The twin laws follow simple symmetry rules and they are observed in minerals, like feldspar, palmierite, leucite, perovskite, and so forth. The major discovery over the last two decades was that the thin areas between the twins yield characteristic physical and chemical properties, but not the twins themselves. Research greatly focusses on these twin walls (or ‘twin boundaries’); therefore, because they possess different crystal structures and generate a large variety of ‘emerging’ properties. Research on wall properties has largely overshadowed research on twin domains. Some wall properties are discussed in this short review, such as their ability for chemical storage, and their structural deformations that generate polarity and piezoelectricity inside the walls, while none of these effects exist in the adjacent domains. Walls contain topological defects, like kinks, and they are strong enough to deform surface regions. These effects have triggered major research initiatives that go well beyond the realm of mineralogy and crystallography. Future work is expected to discover other twin configurations, such as co-elastic twins in quartz and growth twins in other minerals.

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Time evolution of twin domains in cordierite: a computer simulation study

Cited by 11 publications

References 19 publications

Statics and dynamics of domain patterns in hexagonal-orthorhombic ferroelastics

Statics and dynamics of domain patterns in hexagonal-orthorhombic ferroelastics

Structural investigations of the two polymorphs of synthetic Fe-cordierite and Raman spectroscopy of hexagonal Fe-cordierite

Ferroelastic Twinning in Minerals: A Source of Trace Elements, Conductivity, and Unexpected Piezoelectricity

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