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Results are presented from numerical experiments aiming at the computation of stochastic phase-field models for phase transformations by coarse-graining molecular dynamics. The studied phase transformations occur between a solid crystal and…

Numerical Analysis · Mathematics 2009-08-11 Erik von Schwerin

In the manufacturing process of high-performance particulate materials, viscous sintering plays a crucial role, particularly in fields such as polymer processing and additive manufacturing. The interactions between microscopic particles,…

Computational Engineering, Finance, and Science · Computer Science 2024-12-06 Xiaoxu Dai , Bo Qian , Arkadz Kirshtein , Qingcheng Yang

The phase-field method has become in recent years the method of choice for simulating microstructural pattern formation during solidification. One of its main advantages is that time-dependent three-dimensional simulations become feasible.…

Materials Science · Physics 2007-05-23 M. Dejmek , R. Folch , A. Parisi , M. Plapp

The phase-change material antimony sulfide (Sb$_2$S$_3$) relies on rapid and reversible phase transitions between crystalline and amorphous states, which are critical for their performance in data storage and photonics applications. In this…

Materials Science · Physics 2026-05-21 Souvik Chakraborty , Wen-Qing Li , Yun Liu

In this work, we present a variational and quantitative phase-field model for non-isothermal sintering processes. The model is derived via an extended non-diagonal phase-field model. The model evolution equations have naturally…

Materials Science · Physics 2023-08-10 Timileyin David Oyedeji , Yangyiwei Yang , Herbert Egger , Bai-Xiang Xu

Grain growth fundamentally shapes the microstructure of crystalline materials upon annealing, affecting their overall mechanical and functional properties. Recently, it has been rationalized that grain growth in polycrystals does not result…

We consider the grain growth and stagnation in polycrystalline microstructures. From the phase field crystal modelling of the coarsening dynamics, we identify a transition from a grain-growth stagnation upon deep quenching below the melting…

Materials Science · Physics 2013-09-20 Mathias Bjerre , Jens Magelund Tarp , Luiza Angheluta , Joachim Mathiesen

Phase-Field Crystal (PFC) models are able to resolve atomic length scale features of materials during temporal evolution over diffusive time scales. Traditional PFC models contain solid and liquid phases, however many important materials…

Materials Science · Physics 2015-06-16 Edwin J. Schwalbach , James A. Warren , Kuo-An Wu , Peter W. Voorhees

Dopants can significantly affect the properties of oxide ceramics through their impact on the property-determined microstructure characteristics such as grain boundary (GB) segregation, space charge layer formation in the GB vicinity, and…

Atomically thin 2-dimensional heterostructures are a promising, novel class of materials with groundbreaking properties. The possiblity of choosing the many constituent components and their proportions allows optimizing these materials to…

Mesoscale and Nanoscale Physics · Physics 2019-10-23 Petri Hirvonen , Vili Heinonen , Haikuan Dong , Zheyong Fan , Ken R. Elder , Tapio Ala-Nissila

We study the evolution from a liquid to a crystal phase in two-dimensional curved space. At early times, while crystal seeds grow preferentially in regions of low curvature, the lattice frustration produced in regions with high curvature is…

Soft Condensed Matter · Physics 2015-06-16 Nicolas A. Garcia , Richard A. Register , Daniel A. Vega , Leopoldo R. Gomez

Strongly anisotropic geomaterials undergo fracture under compressive loading. This paper applies a phase-field fracture model to study this fracture process. While phase-field fracture models have several advantages, they provide unphysical…

This paper unravels micromechanical aspects of metallic materials whose microstructure comprises grains of two or more phases. The local plastic response is determined by (i) the relative misorientation of the slip systems of individual…

Materials Science · Physics 2016-12-06 T. W. J. de Geus , F. Maresca , R. H. J. Peerlings , M. G. D. Geers

We show that a minimal model for viscous fingering with a nematic liquid crystal in which anisotropy is considered to enter through two different viscosities in two perpendicular directions can be mapped to a two-fold anisotropy in the…

Soft Condensed Matter · Physics 2009-10-31 R. Folch , J. Casademunt , A. Hernandez-Machado

It is well documented in many experiments that crystallographic effects play an important role in the generation of two-phase patterns during the solidification of eutectic alloys. In particular, in lamellar composites, large patches of…

Materials Science · Physics 2015-07-01 Supriyo Ghosh , Mathis Plapp

Phase transition problems on curved surfaces can lead to a panopticon of fascinating patterns. In this paper we consider finite element approximations of phase field models with a spatially inhomogeneous and anisotropic surface energy…

Numerical Analysis · Mathematics 2025-06-09 Harald Garcke , Robert Nürnberg

We address a three-dimensional, coarse-grained description of dislocation networks at grain boundaries between rotated crystals. The so-called amplitude expansion of the phase-field crystal model is exploited with the aid of finite element…

Materials Science · Physics 2018-05-31 Marco Salvalaglio , Rainer Backofen , K. R. Elder , Axel Voigt

Bunching and meandering instability of steps at the 4H-SiC(0001) surface is studied by the kinetic Monte Carlo simulation method. Change in the character of step instability is analyzed for different rates of particle jumps towards step. In…

Materials Science · Physics 2015-06-19 Filip Krzyzewski , Magdalena A. Zaluska-Kotur

Directional solidification of water-based solutions has emerged as a versatile technique for templating hierarchical porous materials. However, the underlying mechanisms of pattern formation remain incompletely understood. In this work, we…

Materials Science · Physics 2026-03-20 Kaihua Ji , Alain Karma

Strain hardening is a key feature observed in many rocks deformed in the so-called ``semi-brittle'' regime, where both crystal plastic and brittle deformation mechanisms operate. Dislocation storage has long been recognised as a major…

Geophysics · Physics 2025-02-14 Nicolas Brantut