Phase Transitions and Crystal Symmetry

Izyumov, Yu. A.; Syromyatnikov, V. N.

doi:10.1007/978-94-009-1920-4

Cited by 203 publications

(201 citation statements)

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“…, n ), can be approximated by a Landau-type polynomial expansion in the order parameters, which usually is obtained by symmetry and stability consideration. 53,54 The general requirement for the description of sintering is that f(, 1 , 2 , . .…”

Section: (2) Continuum-phase-field Methods and Its Application To Sintmentioning

confidence: 99%

Simulating Microstructural Evolution and Electrical Transport in Ceramic Gas Sensors

Wang

Liu

Ciobanu

et al. 2000

Journal of the American Ceramic Society

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An integrated computational approach to microstructural evolution and electrical transport in ceramic gas sensors has been proposed. First, the particle-flow model and the continuum-phase-field method are used to describe the microstructural development during the sintering of a prototype two-dimensional film. Then, the conductivity of the sintering samples is calculated concurrently as the microstructure evolves, using both resistor lattice models and effective medium theory for electrical transport in porous aggregates of lightly sintered particles. This approach, when combined with the modeling of resistivity at the grain-grain contacts as a function of neck geometry, ambient gas concentration and temperature, could facilitate the development and optimization of novel microstructures for advanced ceramic gas sensors.

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Section: (2) Continuum-phase-field Methods and Its Application To Sintmentioning

confidence: 99%

Simulating Microstructural Evolution and Electrical Transport in Ceramic Gas Sensors

Wang

Liu

Ciobanu

et al. 2000

Journal of the American Ceramic Society

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“…The basis functions %(0 are not only determined by the IR Fj but also depend on the transition type (ordering, displacement etc.) and on the distribution of the crystal's atoms in the original phase over the orbits of the group G. These functions may be constructed either by the standard method of projection operators (see, for example, Izyumov, Naish & Syromyatnikov, 1979) or by the 'direct' method described by Sakhnenko, Talanov, Chechin & Ulyanova (1983). The knowledge of the stationary vector Cj and of the basis functions of the IR Fj fully determines the contribution Aj by this representation to the function 8p(r).…”

Section: Group-theoretical Methods For Studying the Structure Of Low-mentioning

confidence: 99%

Peculiarities of the low-symmetry phase structure near the phase-transition point

Chechin¹,

Ipatova²,

Sakhnenko³

1993

Acta Cryst Sect A

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The structure of the low-symmetry phase near the transition point depends on the number of arbitrary parameters, which is smaller than that determined by the space group GD of this phase. Such a feature gives rise to some nontrivial structural effects in the vicinity of the transition point: there are numerical relationships among the displacements of the atoms belonging to different orbits of the Go group. In some cases, atoms may be displaced in a direction not singled out by symmetry in any of the 230 space groups. These effects are revealed by grouptheoretical methods and the Landau concept of one irreducible representation.

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“…In our case, the natural candidate on the symmetry violating system position is the in-plane transverse optical phonon. The simplest Landau functional containing a certain spatial scale (apart from the lattice spacing) in a crystal without the Lifshitz invariant is the one suggested for incommensurate ferroelectrics [4]:…”

Section: In-plane Phonon Instabilitymentioning

confidence: 99%