Simulating complex crystal structures using the phase-field crystal model

Alster, Eli; Montiel, David; Thornton, Katsuyo; Voorhees, Peter W.

doi:10.1103/physrevmaterials.1.060801

Cited by 19 publications

(13 citation statements)

References 41 publications

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“…Finally, to model the hexagonal structures in three dimensions one should use the more complex form of the excessive energy term and also introduce higher modes to the pair-correlation functions of eight-order or 12-order approximations [16]. The general question here: is it enough to have a higher-order expansion pair-correlation function to describe hexagonal symmetries, or it is necessary to introduce three-point correlations even approximated as combinations of pair-correlation functions [47][48][49][50][51]?…”

Section: Results and Discussion (A) Dynamical Distributionmentioning

confidence: 99%

Structure diagram and dynamics of formation of hexagonal boron nitride in phase-field crystal model

Ankudinov

Galenko

2022

Phil. Trans. R. Soc. A.

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The phase-field crystal (PFC-model) is a powerful tool for modelling of the crystallization in colloidal and metallic systems. In the present work, the modified hyperbolic phase-field crystal model for binary systems is presented. This model takes into account slow and fast dynamics of moving interfaces for both concentration and relative atomic number density (which were taken as order parameters). The model also includes specific mobilities for each dynamical field and correlated noise terms. The dynamics of chemical segregation with origination of mixed pseudo-hexagonal binary phase (the so-called ‘triangle phase’) is used as a benchmark in two spatial dimensions for the developing model. Using the free energy functional and specific lattice vectors for hexagonal crystal, the structure diagram of co-existence of liquid and three-dimensional hexagonal phase for the binary PFC-model was carried out. Parameters of the crystal lattice correspond to the hexagonal boron nitride (BN) crystal, the values of which have been taken from the literature. The paper shows the qualitative agreement between the developed structure diagram of the PFC model and the previously known equilibrium diagram for BN constructed using thermodynamic functions. This article is part of the theme issue ‘Transport phenomena in complex systems (part 2)’.

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Section: Results and Discussion (A) Dynamical Distributionmentioning

confidence: 99%

Structure diagram and dynamics of formation of hexagonal boron nitride in phase-field crystal model

Ankudinov

Galenko

2022

Phil. Trans. R. Soc. A.

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“…Formally, there is one peak representing the main Bragg reflection peak from a set of crystal planes; in practice, only the first few [smallest] kpeaks are retained (e.g., one for 2D HCP and 3D BCC, two for 2D squares and 3D FCC, three for 3D HPC 3D [37], etc). We can also expand to 3-point correlations following the recent work of Seymour et al [38][39][40] in order to extend the range of crystalline structures to non-metallic materials. It is noted that the use of higher order correlations typically requires that we go beyond 1-mode analysis of the free energy in order to retain the accuracy of simpler 1-mode approximations used for simpler structures.…”

Section: A a New Density Functional Approach: Expanding Around The Vmentioning

confidence: 99%

Thermodensity coupling in phase-field-crystal-type models for the study of rapid crystallization

Kocher

Provatas

2019

Phys. Rev. Materials

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We self-consistently derive a formalism that couples a Phase Field Crystal (PFC) density field to thermal transport. It yields a theory for non-uniform transient temperature and density evolution, and includes local latent heat release during atomic rearrangements of the PFC density field. The basic formalism is applied to the original PFC model, demonstrating its capacity to capture heat transfer and recalescence in solidification. With an aim towards consistently incorporating temperature and other thermodynamic variables into PFC modelling, a new classical density field theory for solid/liquid/vapor systems is then derived. It presents a different approach to those used in the PFC literature while retaining the major advantages that have become the hallmark of PFC modelling; the new model is also based entirely on physical density, temperature and pressure scales. We end the paper by applying the thermal-density coupling formalism to this new multi-phase density functional theory/PFC model.

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“…More importantly, the incorporation of multi-point correlations can enable the study of broader material systems and enrich the properties of the PFC modeling. Limited attempts have been made to explore the influence of multipoint correlations in PFC [35,[39][40][41][42]. For example, Seymour and Provatas [39] approximated the three-point direct correlation function as the product of two-point direct correlations to model structures with a specific bond angle, such as triangular, honeycomb, or square, and Kocher and Provatas [40] used both three-and four-point direct correlations to model vapor-liquid-solid transitions.…”

Section: Introductionmentioning

confidence: 99%

“…For example, Seymour and Provatas [39] approximated the three-point direct correlation function as the product of two-point direct correlations to model structures with a specific bond angle, such as triangular, honeycomb, or square, and Kocher and Provatas [40] used both three-and four-point direct correlations to model vapor-liquid-solid transitions. Alternatively, Alster et al [41] expanded the three-point correlation function in terms of Legen-dre polynomials in Fourier space and constructed various crystalline phases (including the ABX 3 perovskite structure) from their PFC model. Recently, we developed a general PFC formulation to incorporate any multipoint direct correlations satisfying the condition of rotational invariance [35], from which effects of bond-angle dependency and adjustment can be achieved through the four-point correlation, and a variety of 2D and 3D crystal structures, such as 3D diamond cubic phase and 2D rhombic or 3D simple monoclinic structure with tunable bond angles, can be stabilized.…”

Section: Introductionmentioning

confidence: 99%

Control of phase ordering and elastic properties in phase field crystals through three-point direct correlation

Wang,

Liu,

Duan

et al. 2022

Preprint

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Effects of three-point direct correlation on properties of the phase field crystal (PFC) modeling are examined, for the control of various ordered and disordered phases and their coexistence in both three-dimensional and two-dimensional systems. Such effects are manifested via the corresponding gradient nonlinearity in the PFC free energy functional that is derived from classical density functional theory. Their significant impacts on the stability regimes of ordered phases, phase diagrams, and elastic properties of the system, as compared to those of the original PFC model, are revealed through systematic analyses and simulations. The nontrivial contribution from three-point direct correlation leads to the variation of the critical point of order-disorder transition to which all the phase boundaries in the temperature-density phase diagram converge. It also enables the variation and control of system elastic constants over a substantial range as needed in modeling different types of materials with the same crystalline structure but different elastic properties. The capability of this PFC approach in modeling both solid and soft matter systems is further demonstrated through the effect of three-point correlation on controlling the vapor-liquid-solid coexistence and transitions for body-centered cubic (bcc) phase and on achieving the liquid-stripe or liquid-lamellar phase coexistence. All these provide a valuable and efficient method for the study of structural ordering and evolution in various types of material systems.

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Simulating complex crystal structures using the phase-field crystal model

Cited by 19 publications

References 41 publications

Structure diagram and dynamics of formation of hexagonal boron nitride in phase-field crystal model

Structure diagram and dynamics of formation of hexagonal boron nitride in phase-field crystal model

Thermodensity coupling in phase-field-crystal-type models for the study of rapid crystallization

Control of phase ordering and elastic properties in phase field crystals through three-point direct correlation

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