A modified two-mode phase-field crystal model applied to face-centered cubic and body-centered cubic orderings

Asadi, Ebrahim; Zaeem, Mohsen Asle

doi:10.1016/j.commatsci.2015.04.004

Cited by 27 publications

(19 citation statements)

References 24 publications

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“…The necessary data my be provided by the X-Ray diffraction measurements which gives us the reference parameters of the liquid state (density), equilibrium wave number and structure factor for both phases. The perspective system for the calculation of the nature of transition may be the pure Iron with the Homogeneous-BCC-FCC-BCC phase transformations [18][19][20][21]. Moreover there is an attempt to use the molecular dynamics data for such calculations [13,21].…”

Section: Resultsmentioning

confidence: 99%

“…The structure selection is based on the thermodynamic rule of the minimal energy for a virtually existed structure. The structure diagram is constructed in coordinates "dimensionless undercooling -relative atomic density" with the amplitude expansion of the free energy (2) for a given crystalline phase [18][19][20].…”

Section: The Diagram Of Structures and Analytical Solutionsmentioning

confidence: 99%

“…With this aim, we write the Maxwell area rule [13,14,[18][19][20][21] and solve the equations for the entire range of control parameter values 0 ≤ ε ≤ 1. The example of the system of equations showed below representing the conditions for the coexistence of the homogeneous and BCC phases: Fig.…”

Section: Construction Of Structure Diagrammentioning

confidence: 99%

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Simulation of crystalline pattern formation by the MPFC method

2017

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Abstract.The Phase Field Crystal model in hyperbolic formulation (modified PFC or MPFC), is investigated as one of the most promising techniques for modeling the formation of crystal patterns. MPFC is a convenient and fundamentally based description linking nano-and meso-scale processes in the evolution of crystal structures. The presented model is a powerful tool for mathematical modeling of the various operations in manufacturing. Among them is the definition of process conditions for the production of metal castings with predetermined properties, the prediction of defects in the crystal structure during casting, the evaluation of quality of special coatings, and others. Our paper presents the structure diagram which was calculated for the one-mode MPFC model and compared to the results of numerical simulation for the fast phase transitions. The diagram is verified by the numerical simulation and also strongly correlates to the previously calculated diagrams. The computations have been performed using software based on the effective parallel computational algorithm.

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Section: Resultsmentioning

confidence: 99%

Section: The Diagram Of Structures and Analytical Solutionsmentioning

confidence: 99%

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Simulation of crystalline pattern formation by the MPFC method

2017

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“…This model incorporates the first two density wave vectors in its formulation and damps out the dynamics of the system except near the first two density wave lengths, q 0 and q 1 ; the Helmholtz free energy of this two-mode PFC model is [19,25] …”

Section: Introductionmentioning

confidence: 99%

Quantifying a two-mode phase-field crystal model for BCC metals at melting point

Asadi

Zaeem

2015

Computational Materials Science

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“…Asadi and M. Asle Zaeem [22], which has the same DOFs as Wu et al two-mode PFC model [20], but it has a dependent parameter that enable exact minimization of the free energy in different phases. This model and the method to determine its phase diagrams will be explained in the next section.…”

Section: Introductionmentioning

confidence: 99%

Revisiting phase diagrams of two-mode phase-field crystal models

Emdadi

Zaeem

Asadi

2016

Computational Materials Science

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In this work, phase diagrams of a modified two-mode phase-field crystal (PFC) that show two-dimensional (2D) and three-dimensional (3D) crystallographic structures were determined by utilizing a free energy minimization method. In this study the modified two-mode PFC model (presented by E. Asadi and M. Asle Zaeem, Comput. Mater. Sci. 2015) was used, in which the free energy can be exactly minimized in each stable crystal structure allowing calculation of accurate phase diagrams for two-mode PFC models. Different crystal structures, such as square, triangle, body-centered cubic (bcc), face-centered cubic (fcc), and stripe lattice structures as well as their coexistence regions were considered in the calculations. The model parameters were discussed to calculate phase diagrams that can be used as a guideline by other researchers for studying solidification and solid state phase transformation using two-mode PFC model.

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A modified two-mode phase-field crystal model applied to face-centered cubic and body-centered cubic orderings

Cited by 27 publications

References 24 publications

Simulation of crystalline pattern formation by the MPFC method

Simulation of crystalline pattern formation by the MPFC method

Quantifying a two-mode phase-field crystal model for BCC metals at melting point

Revisiting phase diagrams of two-mode phase-field crystal models

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