Crystal structures predicted by the PFC method with atomic density fluctuations

Starodumov, Ilya; Ankudinov, Vladimir; Galenko, Peter

doi:10.1016/j.matpr.2018.12.117

Cited by 2 publications

(2 citation statements)

References 30 publications

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“…To study the noise influence on crystal structure, we consider the formation of metastable structure in three-dimensional case of stochastic MPFC equation. The formation of such metastable structures was discussed in Starodumov et al 58,59 With this aim, we choose the initial parameters as for an equilibrium periodic Body Centered Cubic (BCC) structure (see structure diagram in Galenko et al 25 ): 0 = 0.06, ΔB 0 = 0.1, functional parameters a = v = B x 0 = 1, = 0.1, noise amplitude A = 1. Numeric simulations for crystallization from the undercooled liquid to the periodic solution was FIGURE 1 Effect of noise on the structure factor S(k) evolution of two-dimensional stochastic MPFC equation (12).…”

Section: Metastable Structure Formationmentioning

confidence: 99%

Correlated noise effect on the structure formation in the phase‐field crystal model

Ankudinov

Starodumov

Kryuchkov

et al. 2020

Math Methods in App Sciences

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A phase-field crystal model (PFC model) which takes into account exponential relaxation of the atomic flux and its fluctuations is developed. The model corresponds to a system undergoing phase transformation described with a partial differential equation of hyperbolic type. Such a model covers slow and rapid regimes of interface propagation at small and large driving forces during melting and solidification. The analysis is done for the evolution of atomic crystal lattices appearing from a metastable homogeneous liquid for the chemically pure system supercooled below its critical temperature. Numerical simulation of the system "Liquid -Body Centered Cubic (BCC) crystal lattice" allows us to formulate the hypothesis about the formation of metastable periodic solutions (atomic configurations which are not in the thermodynamic equilibrium) during the relaxation of atomic configurations to the stable equilibrium. These metastable states may be destroyed (or even avoided) due to the action of colored noise. Namely, considering spatiotemporal correlations of the atomic flux fluctuations, we have found that the temporal correlations promote selecting long-range atomic lattices, whereas the spatial correlations corresponding to the periodic structure scales decelerate such processes.

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Section: Metastable Structure Formationmentioning

confidence: 99%

Correlated noise effect on the structure formation in the phase‐field crystal model

Ankudinov

Starodumov

Kryuchkov

et al. 2020

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

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“…However, for the symmetrical domains such structures can be generated by the confinement-induced standing waves. [37][38][39] This problem can be obeyed by the addition of noise specified using the fluctuation-dissipation theorem. 6 One should note that for the given point, we have obtained different spatial symmetry positions of atomic density.…”

Section: Bcc Structure Formationmentioning

confidence: 99%

About one unified description of the first‐ and second‐order phase transitions in the phase‐field crystal model

Ankudinov

Starodumov

Galenko

2020

Math Methods in App Sciences

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Modeling of crystal micro-structures and their dynamics during fast phase transitions can be performed by the phase-field crystal (PFC) model in the hyperbolic formulation (Modified Phase Field Crystal [MPFC] model). This method is suitable for a continual modeling of the atomic density field at diffusion time intervals (slow diffusion dynamics) and short intervals of atomic flux relaxation (fast structural relaxation). Since the PFC model describes transitions of the first and second order, we present a description of both transitions in a unified manner. We show how phase transitions of each order can be treated using specific analytical transformations. To justify the unified approach to description of the first-and second-order transformations, we provide results of numerical simulation of phase changes between homogeneous structure and Body Centered Cubic (BCC) crystal lattice. The set of benchmarks for different domains shows coincidence of instantaneous atomic distributions and free energies in both forms.

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Crystal structures predicted by the PFC method with atomic density fluctuations

Cited by 2 publications

References 30 publications

Correlated noise effect on the structure formation in the phase‐field crystal model

Correlated noise effect on the structure formation in the phase‐field crystal model

About one unified description of the first‐ and second‐order phase transitions in the phase‐field crystal model

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