Rotation-limited growth of three-dimensional body-centered-cubic crystals

Tarp, Jens M.; Mathiesen, Joachim

doi:10.1103/physreve.92.012409

Cited by 5 publications

(2 citation statements)

References 24 publications

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“…The Asaro-Tiller-Grinfeld instability was studied using the PFC model, and the results were in quantitative agreement with continuum theory [26,27]. The PFC model has also been used to study coupling during grain growth [16,17,[28][29][30], and the results match well with molecular dynamics simulations [9].…”

Section: Introductionsupporting

confidence: 53%

Grain growth and grain translation in crystals

McReynolds

Voorhees

2016

Acta Materialia

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Grain growth is generally driven to minimize the overall grain boundary energy. However, for low-angle grain boundaries the requirement that lattice planes be continuous across the boundary gives rise to a coupling between the normal motion of the grain boundary and the tangential motion of the lattice. We show through phase-field crystal simulations this coupling in polycrystalline systems can give rise to a rigid body translation of the lattice as a grain shrinks. The process is mediated by significant climb of the dislocations in the boundary and dislocation reactions at the trijunctions. Thus the grain growth process is coupled to vacancy diffusion processes as well as the dynamics of grain trijunctions. Moreover, grain shrinkage can cease because of dislocation behavior near the trijunction, illustrating that this coupling can have an influence on the grain growth process in polycrystals.

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Section: Introductionsupporting

confidence: 53%

Grain growth and grain translation in crystals

McReynolds

Voorhees

2016

Acta Materialia

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“…The Brazovskii model 32 and closely related Phase Field Crystal models 33,34 have been applied to a broad range of systems undergoing pattern formation and selection of a specific length scale. These Brazovskii-type models have previously been employed to describe block copolymers 26,29,[35][36][37] but the approach is very general and also nucleation and pattern formation processes [38][39][40] , crystal defect dynamics 33,[41][42][43] , grain boundary melting [44][45][46] and liquid crystals 47,48 have been studied. A Brazovskii-type model was also famously shown by Swift and Hohenberg 49 to describe Rayleigh-BÃl'nard convection.…”

Section: The Free Energymentioning

confidence: 99%

Substrate curvature governs texture orientation in thin films of smectic block copolymers

et al. 2020

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Self-assembly of ordered nanometer-scale patterns is interesting in itself, but its practical value depends on the ability to predict and control pattern formation. In this paper we demonstrate theoretically and numerically that engineering of extrinsic as well as intrinsic substrate geometry may provide such a controllable ordering mechanism for block copolymers films. We develop an effective two-dimensional model of thin films of striped-phase diblock copolymers on general curved substrates. The model is obtained as an expansion in the film thickness and thus takes the third dimension into account, which crucially allows us to predict the preferred orientations even in the absence of intrinsic curvature. We determine the minimum-energy textures on several curved surfaces and arrive at a general principle for using substrate curvature as an ordering field, namely that the stripes will tend to align along directions of maximal curvature.

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