A phase field crystal theory of the kinematics of dislocation lines

Skogvoll, Vidar; Angheluta, Luiza; Skaugen, Audun; Salvalaglio, Marco; Viñals, Jorge

doi:10.1016/j.jmps.2022.104932

Cited by 15 publications

(24 citation statements)

References 101 publications

(176 reference statements)

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“…The derivation of kinematic equations similar to equation (3.6) may yield fruitful analogies between otherwise physically dissimilar systems. For example, an equivalent to equation (3.6) was recently derived for dislocations in solids using a phase field approach [43]. Topological defects are also important in high energy physics and cosmology [17,95].…”

Section: Discussionmentioning

confidence: 99%

“…This formalism has been widely used to describe defects in superfluids, superconductors, XY models and classical ferromagnets, to name a few. A similar approach has been used to study dislocations in solids using a phase field model of the lattice displacement [22,43].…”

Section: Disclination Kinematicsmentioning

confidence: 99%

“…Such a transformation relating the location of the line to the field equations governing the evolution of the nematic tensor order parameter allows for an exact kinematic law of motion for the disclination, independent of the microscopic model governing the evolution of nematic order. The type of particle-field transformation that we introduce has been successfully used to analyse and track vortex motion in superfluids [38], the motion of point defects in n-vector models [39–41], and, more recently, the motion of dislocations in solids in both two [22,42] and three dimensions [43]. The method has also been used to describe disclination motion in nematic active matter, albeit in two spatial dimensions [44].…”

Section: Introductionmentioning

confidence: 99%

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Kinematics and dynamics of disclination lines in three-dimensional nematics

Schimming

Viñals

2023

Proc. R. Soc. A.

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An exact kinematic law for the motion of disclination lines in nematic liquid crystals as a function of the tensor order parameter Q is derived. Unlike other order parameter fields that become singular at their respective defect cores, the tensor order parameter remains regular. Following earlier experimental and theoretical work, the disclination core is defined to be the line where the uniaxial and biaxial order parameters are equal, or equivalently, where the two largest eigenvalues of Q cross. This allows an exact expression relating the velocity of the line to spatial and temporal derivatives of Q on the line, to be specified by a dynamical model for the evolution of the nematic. By introducing a linear core approximation for Q , analytical results are given for several prototypical configurations, including line interactions and motion, loop annihilation, and the response to external fields and shear flows. Behaviour that follows from topological constraints or defect geometry is highlighted. The analytic results are shown to be in agreement with three-dimensional numerical calculations based on a singular Maier–Saupe free energy that allows for anisotropic elasticity.

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Section: Discussionmentioning

confidence: 99%

Section: Disclination Kinematicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Kinematics and dynamics of disclination lines in three-dimensional nematics

Schimming

Viñals

2023

Proc. R. Soc. A.

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“…Recent studies of PFC models have focused on active matter with [212][213][214] and without [215][216][217][218][219][220][221] inertia, amorphous solids [222], bifurcation diagrams [219,220,[223][224][225], colored noise [226], cubic terms [227], crystals [228], dislocation lines [229], electromigration [230], grain boundaries [231,232], mixtures [200,220,[233][234][235], nucleation [236], solidification [237,238], and stress tensors [239].…”

Section: Related Theories: Pfc Models and Pftmentioning

confidence: 99%

Perspective: New directions in dynamical density functional theory

Vrugt

Wittkowski

2022

J. Phys.: Condens. Matter

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Classical dynamical density functional theory (DDFT) has become one of the central modeling approaches in nonequilibrium soft matter physics. Recent years have seen the emergence of novel and interesting fields of application for DDFT. In particular, there has been a remarkable growth in the amount of work related to chemistry. Moreover, DDFT has stimulated research on other theories such as phase field crystal models and power functional theory. In this perspective, we summarize the latest developments in the field of DDFT and discuss a variety of possible directions for future research.

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“…( 13) can be evaluated explicitly from the phase field as follows. We begin by using the result [19] n q (n)…”

Section: The Phase Field As a Configuration Tensormentioning

confidence: 99%

Elasticity versus phase field driven motion in the phase field crystal model

Acharya,

Angheluta,

Vinals

2022

Preprint

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The inherent inconsistency in identifying the phase field in the phase field crystal Theory with the material mass and, simultaneously, with material distortion is discussed. In its current implementation, elastic relaxation in the phase field crystal occurs on a diffusive time scale through a dissipative permeation mode. The very same phase field distortion that is included in solid elasticity drives diffusive motion, resulting in a non physical relaxation of the phase field crystal. We present two alternative theories to remedy this shortcoming. In the first case, it is assumed that the phase field only determines the incompatible part of the elastic distortion, and therefore one is free to specify an additional compatible distortion so as to satisfy mechanical equilibrium at all times (in the quasi static limit). A numerical solution of the new model for the case of a dislocation dipole shows that, unlike the classical phase field crystal model, it can account for the known law of relative motion of the two dislocations in the dipole. The physical origin of the compatible strain in this new theory remains to be specified. Therefore, a second theory is presented in which an explicit coupling between independent distortion and phase field accounts for the time dependence of the relaxation of fluctuations in both. Preliminary details of its implementation are also given.

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A phase field crystal theory of the kinematics of dislocation lines

Cited by 15 publications

References 101 publications

Kinematics and dynamics of disclination lines in three-dimensional nematics

Kinematics and dynamics of disclination lines in three-dimensional nematics

Perspective: New directions in dynamical density functional theory

Elasticity versus phase field driven motion in the phase field crystal model

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