Phase-field crystal modelling of crystal nucleation, heteroepitaxy and patterning

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

doi:10.1080/14786435.2010.487476

Cited by 60 publications

(57 citation statements)

References 115 publications

(124 reference statements)

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“…However, experiments on hard sphere colloidal systems [48,49,52] differ from the predictions of critical nucleation theory and the CNT calculation underestimates the nucleation rate by many orders of magnitude [57]. In computer simulation in 3D [58] and for phase-field-crystal calculations in 2D [59], a precursor-mediated two-step crystallization was observed. In experiments in 2D with attractive particle interactions [60,61] such precursors are found, too, but might be explained with sublimation rather than nucleation.…”

Section: Introductionmentioning

confidence: 97%

Two-dimensional colloidal systems in time-dependent magnetic fields

Dillmann

Maret

Keim

2013

Eur. Phys. J. Spec. Top.

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Abstract. We use super-paramagnetic colloidal particles confined by gravitation to a flat water-air interface as a model system to study the non-equilibrium liquid-solid phase transition in two dimensions. The system temperature is adjustable by changing the strength of an external magnetic field perpendicular to the water-air interface. Increasing the magnetic field on a timescale of milliseconds quenches the liquid to a strongly super-cooled state. If the system is cooled down out of equilibrium the solidification differs drastically from the equilibrium melting and freezing scenario as no hexatic phase is observable. The system solidifies to a polycrystalline structure with many grains of different orientations. Since the local closed packed order in two dimensions is sixfold, in both the fluid and the crystalline state, sensitive measures have to be developed. In the present manuscript we compare different methods to identify crystalline cluster locally and motivate the threshold values. Those are chosen in comparison with the isotropic fluid on one hand and large mono-crystals in thermal equilibrium on the other hand. With the given criteria for crystalline cluster the cluster are found not to be circular and fractal dimensions of the grains are given.

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Section: Introductionmentioning

confidence: 97%

Two-dimensional colloidal systems in time-dependent magnetic fields

Dillmann

Maret

Keim

2013

Eur. Phys. J. Spec. Top.

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“…These and other PFC results are reviewed in Ref. 12. Several studies suggest that nucleation is affected by the presence of a nearby (pseudo) spinodal [27][28][29].…”

Section: Introductionmentioning

confidence: 99%

“…Examples include cholesteric liquid crystals [1], hydronamic instabilities [2], superconducting vortices [3], block copolymers [4], as well as many others [5]. In recent years, there has been considerable renewed interest is the dynamical process of a first-order phase transition from a uniform (liquid) phase to a modulated (solid) phase following a quench [6][7][8][9][10][11][12]. If the supercooled liquid phase is long-lived, rare metastable equilibrium fluctuations locally initiate the phase transformation dynamics.…”

Section: Introductionmentioning

confidence: 99%

Liquid to solid nucleation via onion structure droplets

Barros

Klein

2013

The Journal of Chemical Physics

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We study homogeneous nucleation from a deeply quenched metastable liquid to a spatially modulated phase. We find, for a general class of density functional theories, that the universally favored nucleating droplet in dimensions d ≥ 3 is spherically symmetric with radial modulations resembling the layers of an onion. The existence of this droplet has important implications for systems with effective long-range interactions, and potentially applies to polymers, plasmas, and metals.

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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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Phase-field crystal modelling of crystal nucleation, heteroepitaxy and patterning

Cited by 60 publications

References 115 publications

Two-dimensional colloidal systems in time-dependent magnetic fields

Two-dimensional colloidal systems in time-dependent magnetic fields

Liquid to solid nucleation via onion structure droplets

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

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