Derivation of the phase-field-crystal model for colloidal solidification

Teeffelen, Sven van; Backofen, Rainer; Voigt, Axel; Löwen, Hartmut

doi:10.1103/physreve.79.051404

Cited by 206 publications

(297 citation statements)

References 62 publications

(142 reference statements)

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“…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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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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“…[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%

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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“…It can be related to other continuum fields theories such as classical density-functional theory 8,9 and the atomic density function theory 10 . The PFC-model may also be considered as a conserved version of the Swift-Hohenberg equation and provides an efficient method for simulating liquid-solid transitions 11,12 , colloidal solidification 13 , dislocation motion and plasticity 14,15 , glass formation 16 , epitaxial growth 6,17 , grain boundary premelting 18 , surface reconstructions 19 , and grain boundary energies 20 .…”

Section: Introductionmentioning

confidence: 99%

Marginal stability analysis of the phase field crystal model in one spatial dimension

Galenko

Elder

2011

Phys. Rev. B

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The problem of wave-length k f and velocity V selection for a solid front invading an unstable homogeneous phase is considered. A marginal stability analysis is used to predict k f and V for the parabolic and hyperbolic (or modified) phase-field crystal models in one-dimension. It is shown that the marginally selected wave-number of the periodic crystal monotonically increases with increasing undercooling and relaxation times. At high undercooling and relaxation times it is found that the system can select a k f that is unstable to an Eckhaus instability in the bulk phase. This may imply a transition to highly defected or glassy states in higher dimensions.

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Derivation of the phase-field-crystal model for colloidal solidification

Cited by 206 publications

References 62 publications

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

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

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

Marginal stability analysis of the phase field crystal model in one spatial dimension

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