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

Emmerich, Heike; Löwen, Hartmut; Wittkowski, Raphael; Gruhn, Thomas; Tóth, Gyula I.; Tegze, György; Gránásy, László

doi:10.1080/00018732.2012.737555

Cited by 344 publications

(425 citation statements)

References 300 publications

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“…However, as can be seen from Eqs. (18), (19) and (20), v = 0 at T = T sp since ω m = 0 at T sp . As the temperature is decreased below T sp , v increases but remains less than v nl for small |T − T sp |.…”

Section: Model Fluidmentioning

confidence: 99%

“…[8,15,16] within the so-called phase-field crystal description in one spatial dimension and in Ref. [17][18][19] in two spatial dimensions, in both cases focusing on the properties of pulled fronts. The more accurate DDFT approach used here extends and generalises these results to both types of crystallisation fronts and to two spatial dimensions.…”

Section: Introductionmentioning

confidence: 99%

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Generation of Defects and Disorder from Deeply Quenching a Liquid to Form a Solid

Archer

Walters

Thiele

et al. 2016

Springer Proceedings in Mathematics &Amp; Statistics

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We show how deeply quenching a liquid to temperatures where it is linearly unstable and the crystal is the equilibrium phase often produces crystalline structures with defects and disorder. As the solid phase advances into the liquid phase, the modulations in the density distribution created behind the advancing solidification front do not necessarily have a wavelength that is the same as the equilibrium crystal lattice spacing. This is because in a deep enough quench the front propagation is governed by linear processes, but the crystal lattice spacing is determined by nonlinear terms. The wavelength mismatch can result in significant disorder behind the front that may or may not persist in the latter stage dynamics. We support these observations by presenting results from dynamical density functional theory calculations for simple one-and two-component two-dimensional systems of soft core particles.

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Section: Model Fluidmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generation of Defects and Disorder from Deeply Quenching a Liquid to Form a Solid

Archer

Walters

Thiele

et al. 2016

Springer Proceedings in Mathematics &Amp; Statistics

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show abstract

“…Previous studies of Langevin noise in PFC have used such a cutoff to carry out simulations [74][75][76][77] . The issue of whether introducing noise may lead to a double counting of fluctuations has often been discussed.…”

Section: B Short-wavelength Noise Cutoffmentioning

confidence: 99%

Phase-field-crystal study of grain boundary premelting and shearing in bcc iron

et al. 2013

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We use the phase-field-crystal (PFC) method to investigate the equilibrium premelting and nonequilibrium shearing behaviors of [001] symmetric tilt grain boundaries (GBs) at high homologous temperature over the complete range of misorientation 0 < θ < 90 • in classical models of bcc Fe. We characterize the dependence of the premelted layer width W as a function of temperature and misorientation. In addition, we compute the thermodynamic disjoining potential whose derivative with respect to W represents the structural force between crystal-melt interfaces due to the spatial overlap of density waves. The disjoining potential is also computed by molecular dynamics (MD) simulations, for quantitative comparison with PFC simulations, and coarse-grained amplitude equations (AE) derived from PFC that provide additional analytical insights. We find that, for GBs over an intermediate range of misorientation (θmin < θ < θmax), W diverges as the melting temperature is approached from below, corresponding to a purely repulsive disjoining potential, while for GBs outside this range (θ < θmin or θmax < θ < 90 • ), W remains finite at the melting point. In the latter case, W corresponds to a shallow attractive minimum of the disjoining potential. The misorientation range where W diverges predicted by PFC simulations is much smaller than the range predicted by MD simulations when the small dimensionless parameter ǫ of the PFC model is matched to liquid structure factor properties. However it agrees well with MD simulations with a lower ǫ value chosen to match the ratio of bulk modulus and solid-liquid interfacial free-energy, consistent with the amplitude-equation prediction that θmin and 90 • − θmax scale as ∼ ǫ 1/2 . The incorporation of thermal fluctuations in PFC is found to have a negligible effect on this range. In response to a shear stress parallel to the GB plane, GBs in PFC simulations exhibit coupled motion normal to this plane or sliding. Furthermore, the coupling factor exhibits a discontinuous change as a function of θ that reflects a transition between two coupling modes. Sliding is only observed over a range of misorientation that is a strongly increasing function of temperature for T /TM ≥ 0.8 and matches roughly the range where W diverges at the melting point. The coupling factor for the two coupling modes is in excellent quantitative agreement with previous theoretical predictions [J. W. Cahn, Y. Mishin, and A. Suzuki, Acta Mater. 54, 4953 (2006)].

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“…It is worth mentioning that phase-field continuum approaches do not necessarily work only at large scales. For instance, the Phase-Field-Crystal method [248][249][250], allows one to directly trace the crystal structure and its evolution. This approach offers several advantages over typical atomistic simulations as it filters out all vibrational dynamics while retaining atomic scale interactions yielding both elastic and even plastic deformations.…”

Section: Discussionmentioning

confidence: 99%

Continuum modelling of semiconductor heteroepitaxy: an applied perspective

Bergamaschini

Salvalaglio

Backofen

et al. 2016

Advances in Physics: X

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Semiconductor heteroepitaxy involves a wealth of qualitatively different, competing phenomena. Examples include threedimensional island formation, injection of dislocations, mixing between film and substrate atoms. Their relative importance depends on the specific growth conditions, giving rise to a very complex scenario. The need for an optimal control over heteroepitaxial films and/or nanostructures is widespread: semiconductor epitaxy by molecular beam epitaxy or chemical vapour deposition is nowadays exploited also in industrial environments. Simulation models can be precious in limiting the parameter space to be sampled while aiming at films/nanostructures with the desired properties. In order to be appealing (and useful) to an applied audience, such models must yield predictions directly comparable with experimental data. This implies matching typical time scales and sizes, while offering a satisfactory description of the main physical driving forces. It is the aim of the present review to show that continuum models of semiconductor heteroepitaxy evolved significantly, providing a promising tool (even a working tool, in some cases) to comply with the above requirements. Several examples, spanning from the nanometre to the micron scale, are illustrated. Current limitations and future research directions are also discussed.

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

Cited by 344 publications

References 300 publications

Generation of Defects and Disorder from Deeply Quenching a Liquid to Form a Solid

Generation of Defects and Disorder from Deeply Quenching a Liquid to Form a Solid

Phase-field-crystal study of grain boundary premelting and shearing in bcc iron

Continuum modelling of semiconductor heteroepitaxy: an applied perspective

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