Phase‐Field Crystal Modeling of Homogeneous and Heterogeneous Crystal Nucleation

Tóth, Gyula I.; Pusztai, Tamás; Tegze, György; Gránásy, László

doi:10.1002/9783527647903.ch6

Cited by 2 publications

(3 citation statements)

References 74 publications

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“…Such templates, depending on the mismatch to the crystalline structure evolving, may instigate the formation of single-crystal or polycrystalline structures [240]. Growth textures, obtained when supplementing the 1M-PFC model with a 5×5 flat square-lattice template (realized by a periodic potential term), show remarkable resemblance to the experiments (see figure 47) [241].…”

Section: Colloid Patterningmentioning

confidence: 74%

“…Other numerical methods (e. g., stable semi-implicit finite element discretisation combined with adaptive time stepping [165]) have also been used for PFC models, however, further investigations are needed to assess their numerical accuracy. In recent works (see, e. g., references [28,35]) the ELE has been solved using a semi-spectral successive approximation scheme combined with the operatorsplitting technique [166]. A different approach termed the fixed length simplified string method has been proposed to find the minimum energy path and the nucleation barrier in reference [32].…”

Section: Methodsmentioning

confidence: 99%

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Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview

Emmerich

Löwen

Wittkowski

et al. 2012

Advances in Physics

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342

417

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Here, we review the basic concepts and applications of the phase-field-crystal (PFC) method, which is one of the latest simulation methodologies in materials science for problems, where atomic-and microscales are tightly coupled. The PFC method operates on atomic length and diffusive time scales, and thus constitutes a computationally efficient alternative to molecular simulation methods. Its intense development in materials science started fairly recently following the work by Elder et al. [Phys. Rev. Lett. 88 (2002), p. 245701]. Since these initial studies, dynamical density functional theory and thermodynamic concepts have been linked to the PFC approach to serve as further theoretical fundaments for the latter. In this review, we summarize these methodological development steps as well as the most important applications of the PFC method with a special focus on the interaction of development steps taken in hard and soft matter physics, respectively. Doing so, we hope to present today's state of the art in PFC modelling as well as the potential, which might still arise from this method in physics and materials science in the nearby future.Keywords: phase-field-crystal (PFC) models, static and dynamical density functional theory (DFT and DDFT), condensed matter dynamics of liquid crystals and polymers, nucleation and pattern formation, simulations in materials science, colloidal crystal growth and growth anisotropy * Corresponding authors. Emails: heike.emmerich@uni-bayreuth. de, hlowen@thphy.uni-duesseldorf.de, and grana@szfki.hu

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Section: Colloid Patterningmentioning

confidence: 74%

Section: Methodsmentioning

confidence: 99%

Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview

Emmerich

Löwen

Wittkowski

et al. 2012

Advances in Physics

Self Cite

342

417

View full text Add to dashboard Cite

show abstract

“…[364,365,674,[1029][1030][1031][1032][1033][1034] for examples for and Refs. [1032,[1035][1036][1037][1038][1039] for an overview over the use of PFC models in nucleation theory). Although they involve more approximations than DDFT (and are thus quantitatively less accurate [407]), PFC models are very successful in this area.…”

Section: Nucleation and Solidificationmentioning

confidence: 99%

Classical dynamical density functional theory: from fundamentals to applications

Vrugt

Löwen

Wittkowski

2020

Advances in Physics

176

220

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Classical dynamical density functional theory (DDFT) is one of the cornerstones of modern statistical mechanics. It is an extension of the highly successful method of classical density functional theory (DFT) to nonequilibrium systems. Originally developed for the treatment of simple and complex fluids, DDFT is now applied in fields as diverse as hydrodynamics, materials science, chemistry, biology, and plasma physics. In this review, we give a broad overview over classical DDFT. We explain its theoretical foundations and the ways in which it can be derived. The relations between the different forms of deterministic and stochastic DDFT as well as between DDFT and related theories, such as quantum-mechanical time-dependent DFT, mode coupling theory, and phase field crystal models, are clarified. Moreover, we discuss the wide spectrum of extensions of DDFT, which covers methods with additional order parameters (like extended DDFT), exact approaches (like power functional theory), and systems with more complex dynamics (like active matter). Finally, the large variety of applications, ranging from fluid mechanics and polymer physics to solidification, pattern formation, biophysics, and electrochemistry, is presented.

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Phase‐Field Crystal Modeling of Homogeneous and Heterogeneous Crystal Nucleation

Cited by 2 publications

References 74 publications

Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview

Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview

Classical dynamical density functional theory: from fundamentals to applications

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