What do Landau free energies really look like for structural phase transitions?

Giddy, A. P.; Dove, Martin T.; Heine, Volker

doi:10.1088/0953-8984/1/44/005

Cited by 38 publications

(25 citation statements)

References 19 publications

(7 reference statements)

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“…It is also interesting that Giddy, Dove & Heine (1989) suggest the possibility of explaining 'noncritical, non-standard' values of fl exponents by strongly temperature-dependent fourth-order-term coefficients in the conventionally used Landau freeenergy expansion, and raise the question as to whether the polynomial approach is actually appropriate. Salje (1986) points to the importance of nonlinear relationships between microscopic and macroscopic strains in certain structures also giving rise to non-standard exponents.…”

Section: The Cubic-tetragonal Phase Transition Of Sammentioning

confidence: 99%

Phase transition in Sr₈[Al₁₂O₂₄](MoO₄)₂ aluminate sodalite (SAM)

Depmeier¹,

Melzer²,

Hu³

1993

Acta Crystallogr B Struct Sci

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The cubic-tetragonal phase transition at 571 K of the aluminate sodalite Sr8[AI12024](MoO4)2 (SAM) has been studied by following the position of the (pseudo-)cubic {400} reflections as a function of temperature. The high resolution of the synchrotron powder diffraction experiment allowed the temperature dependencies to be followed with good precision. The tetragonal a lattice parameter appears to be a linear extrapolation of the cubic one, with only a small upward shift at the transition, whereas the c parameter decreases strongly below 571 K. These observations can be explained by a model which assumes the superposition of a ferroelastic strain component, and a volume strain component. The volume strain can be rationalized as being the result of a 'shearing' of the sodalite framework. Causes and consequences of the 'shearing' in relation to the sodalite framework are discussed. The weakly first-* Present address:

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Section: The Cubic-tetragonal Phase Transition Of Sammentioning

confidence: 99%

Phase transition in Sr₈[Al₁₂O₂₄](MoO₄)₂ aluminate sodalite (SAM)

Depmeier¹,

Melzer²,

Hu³

1993

Acta Crystallogr B Struct Sci

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“…An advantage of using this model is that its strengths and limits are well known and that other researchers have already attempted to perform such a calculation (8)(9)(10)(11)(12)(13)(14). A system that undergoes a second-order phase transition is described in the GL model by the following free energy, valid in a rotationally invariant one-component real-order parameter scenario,…”

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confidence: 99%

Coarse graining from variationally enhanced sampling applied to the Ginzburg–Landau model

Invernizzi

Valsson

Parrinello

2017

Proc. Natl. Acad. Sci. U.S.A.

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A powerful way to deal with a complex system is to build a coarsegrained model capable of catching its main physical features, while being computationally affordable. Inevitably, such coarsegrained models introduce a set of phenomenological parameters, which are often not easily deducible from the underlying atomistic system. We present a unique approach to the calculation of these parameters, based on the recently introduced variationally enhanced sampling method. It allows us to obtain the parameters from atomistic simulations, providing thus a direct connection between the microscopic and the mesoscopic scale. The coarsegrained model we consider is that of Ginzburg-Landau, valid around a second-order critical point. In particular, we use it to describe a Lennard-Jones fluid in the region close to the liquidvapor critical point. The procedure is general and can be adapted to other coarse-grained models.coarse graining | enhanced sampling | Ginzburg-Landau free energy | second-order phase transitions | Lennard-Jones C omputer simulations of condensed systems based on an atomistic description of matter are playing an everincreasing role in many fields of science. However, as the complexity of the systems studied increases, so does the awareness that a less detailed, but nevertheless accurate, description of the system is necessary.This has been long since recognized, and branches of physics like elasticity or hydrodynamics can be classified in modern terms as coarse-grained (CG) models of matter. In more recent times, a field theoretical model suitable to describe second-order phase transitions has been introduced by Landau (1) and later perfected by Ginzburg (2). In recent decades a number of coarsegrained models that aim at describing polymers or biomolecules have also been proposed (3,4). In all these approaches some degrees of freedom, deemed not essential to study the phenomenon at hand, are integrated out and the resulting reduced description contains a number of parameters that are not easily determined.Here we use the recently developed variationally enhanced sampling (VES) method (5) to suggest a procedure that allows the determination of such parameters, starting from the microscopic Hamiltonian. This illuminates a somewhat unexpected application of VES, which has been introduced as an enhanced sampling method. We show that it also provides a powerful framework for the optimization of CG models, due to the combination of its enhanced sampling capabilities and its variational flexibility. Moreover, VES takes advantage of its deep connection with relative entropy, a quantity that has been shown to play a key role in multiscale problems (6, 7).As a first test case for our procedure we consider the Ginzburg-Landau (GL) model for continuous phase transitions. An advantage of using this model is that its strengths and limits are well known and that other researchers have already attempted to perform such a calculation (8)(9)(10)(11)(12)(13)(14). A system that undergoes a second-order phase transition is desc...

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“…The observation of underdamped soft mode is considered to be an experimental evidence of a displacive type of transition, while in the case of order/disorder transition the transformation occurs from the equal probable distribution of some atoms between several positions to a more ordered configuration with a similar set of atomic positions. The self-consistent phonon approximation, or pseudo-spin models, consecutively, can serve as a starting scheme of the theoretical description in each case [1][2][3][4].…”

Section: Introductionmentioning

confidence: 99%

“…Such approximations serve as a background of the so-called Φ 4 model [1][2][3]. This model can be generalized by including a many-component order parameter, taking into account the interactions with different radii, and also, if it is needed, long-range dipole-dipole interactions, by accounting for the interaction with elastic deformations.…”

Section: Introductionmentioning

confidence: 99%

THE PHASE TRANSITIONS CHARACTER AND MICROSCOPIC MODELS FOR Sn_2P_2S(Se)_6 FERROELECTRICS

Vysochanskii¹,

Drobnich²

2002

Condens. Matter Phys.

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The paper considers an example of concrete objects, i.e. ferroelectrics of Sn 2 P 2 S 6 family, for which, according to general estimations, a correlation between the shape of a phase diagram (the presence of a Lifshitz point and of a tricritical point) and a crossover "displacive to order/disorder" is observed. Simulations by means of microscopic models, which most adequately represent a dipole ordering in these crystals, are analyzed. A dimension dependence of a ferroelectric phase transition temperature for microcrystals of Sn 2 P 2 S 6 compound is considered.

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What do Landau free energies really look like for structural phase transitions?

Cited by 38 publications

References 19 publications

Phase transition in Sr₈[Al₁₂O₂₄](MoO₄)₂ aluminate sodalite (SAM)

Phase transition in Sr₈[Al₁₂O₂₄](MoO₄)₂ aluminate sodalite (SAM)

Coarse graining from variationally enhanced sampling applied to the Ginzburg–Landau model

THE PHASE TRANSITIONS CHARACTER AND MICROSCOPIC MODELS FOR Sn_2P_2S(Se)_6 FERROELECTRICS

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What do Landau free energies really look like for structural phase transitions?

Cited by 38 publications

References 19 publications

Phase transition in Sr8[Al12O24](MoO4)2 aluminate sodalite (SAM)

Phase transition in Sr8[Al12O24](MoO4)2 aluminate sodalite (SAM)

Coarse graining from variationally enhanced sampling applied to the Ginzburg–Landau model

THE PHASE TRANSITIONS CHARACTER AND MICROSCOPIC MODELS FOR Sn_2P_2S(Se)_6 FERROELECTRICS

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Phase transition in Sr₈[Al₁₂O₂₄](MoO₄)₂ aluminate sodalite (SAM)

Phase transition in Sr₈[Al₁₂O₂₄](MoO₄)₂ aluminate sodalite (SAM)