Traveling waves of the solidification and melting of cubic crystal lattices

Ankudinov, Vladimir; Elder, K. R.; Galenko, Peter

doi:10.1103/physreve.102.062802

Cited by 22 publications

(36 citation statements)

References 61 publications

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“…where is the driving force and is a field variable of Swift-Hohenberg free energy and ≠ 0 was considered in all cases designating the intermediate relaxation time for the atomic flux in this model. 31,36 The numerical simulations of two types of the PFC models Equations ( 6) and ( 15) for crystallization from the undercooled liquid to the BCC-crystal was performed for the three different domains of size…”

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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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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“…23,36 If one would like to include all these parameters in model and simultaneously take into account the second minimum and second peak of the correlation function C 2 (k m2 ), this expansion must be extended further. Thus, the 12-order (TwOF) fitting of correlation function as an expansion of nonlinear terms of free energy to the TwOF of wave vector in k-space could be used, 35 as follows:…”

Section: Correlation Function Fitting For the Two-mode Pfc Modelmentioning

confidence: 99%

“…Fitting at zero wave number C(k = 0) is performed in the approximation of compressibility of liquid. 35,39…”

Section: Correlation Function Fitting For the Two-mode Pfc Modelmentioning

confidence: 99%

“…Blue dashed line is eight-order (EOF) correlation function approximation Equation ( 12), 23 and red solid line is twelve12order (TwOF) fit Equation ( 13). 35 The input for an NN is the interatomic isotropic pair potential V(r), which is defined by the set of points with spatial resolution R. Typically, these potentials are represented as a sum of coefficients of splines at the prescribed knot positions; in present work, we interpolate them as a number of points R of the input layer size. Each point corresponds to the value of potential at the position r in real space.…”

Section: Figure 1 Correlation Function C(k)mentioning

confidence: 99%

“…The parameters predicted by ML approach is more physically reliable as soon as we trained the NN on the specific data with the correct values of C(k = 0) ≈ −45. 35,39 One can find that poor quality of the original MD data at low k (see red curve in Figure 4) leads to the loose quality of regular fitting. The ML approach in this case smooths the data and leads to the more precise result.…”

Section: Correlation Function Predictionmentioning

confidence: 99%

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Approximation of correlation functions in phase‐field crystal model by machine learning approach

Ankudinov

2020

Math Methods in App Sciences

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Two different phase-field crystal (PFC) free excess energy expansions have been analyzed with respect to the order of a truncation term and to the accuracy of a pair correlation functions fitting. The coefficients of the correlation function in PFC model was found for the aluminum crystal based on the molecular dynamics data. A machine learning (ML) approach has been utilized to construct a neural network (NN) for the PFC approximation of correlation functions. The effective iteratomic potentials of the embedded atom model were used as an input data for NN training. Obtained NN predicts the coefficients of the correlation functions with the potentials data as input. Predictions were studied and verified with respect to the properties of NN and parameters of ML.

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Velocity-Dependent Herring Equation

Galenko

2024

Phase Field Theory in Materials Physics

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Traveling waves of the solidification and melting of cubic crystal lattices

Cited by 22 publications

References 61 publications

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

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

Approximation of correlation functions in phase‐field crystal model by machine learning approach

Velocity-Dependent Herring Equation

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