Simulation Of Crystal Growth Research Articles

Numerical simulation of polymer crystal growth under flow field using a coupled phase-field and lattice Boltzmann method

In the present study, the polymer crystal growth under the flow field is numerically simulated by using a coupled phase field (PF) and lattice Boltzmann (LB) method. Firstly, the phase field method is presented to capture the growth interface of polymer crystals, including the common morphologies of spherulite and shish-kebab crystallites. Then the lattice Boltzmann method is introduced to solve the viscous non-Newtonian flows of the polymer melt, where the half-way bounce back boundary condition is imposed with the aid of shape level-set (LS) function which is used to represent the crystal interface at each time. At last, the crystal growth for spherulites and shish-kebab crystallites under flow field is simulated by using the coupled PF–LB method, where the cross-WLF model is chosen to describe the melt viscosity. The effects of the flow velocity on the crystal morphologies, including single and multiple spherulite and shish-kebab crystallites, are analyzed in detail. The numerical results show that the flow velocity has an important impact on the crystal morphologies, and the crystals grow more faster towards the upstream direction, especially in the single and multi spherulites growth process.

Crystallization of cross-linked polyethylene by molecular dynamics simulation

The crystallization of polymers is not, despite its importance in science and engineering, entirely understood due to the challenge of tracking the behavior of individual polymer chains in the crystallizing melt. However, increasing computational resources have brought the crystallization process within reach of molecular simulations, and several groups have published simulations of crystal nucleation and growth in polymers. Yet, these studies have focused on linear polymer chains, and no results have been reported on cross-linked polymers, which are common in everyday applications. Here, we perform molecular dynamics simulations of the homogeneous crystallization of cross-linked polyethylene at high undercooling. Large cross-link densities cause the crystallization to slow down and reduce the final degree of crystallization. As expected, cross-links are rejected from the crystals into the amorphous phase. We observe that at all cross-link densities the intercrystalline amorphous phase is characterized by a single distribution of free segment lengths (amorphous segments with no cross-links). The findings provide a basis for detailed computational studies of semi-crystalline cross-linked polymer systems.

The Prediction Model of Crystal Growth Simulation Built by Machine Learning and Its Applications

The Prediction Model of Crystal Growth Simulation Built by Machine Learning and Its Applications

Numerical Simulation of Crystal Growth in Injection Molded Thermoplastics based on Monte Carlo Method with Shear Rate Tracking

Semi-crystalline thermoplastic polymer can have crystalline structure when it solidifies. The most commonly observed crystals in injection molded polymer are spherulites, which are usually observed throughout the thickness of the specimen. This work has aimed at building a numerical simulation model for nucleation and spherulite growth with shear rate tracking, which will enhance nuclei counting. A voxel method has been implemented for impingement while Hoffman-Laurent model is employed to calculate the growth rate. Filling flow and solidification process of injection molding have been numerically simulated to provide accurate shear rate and temperature to the spherulite growth simulation. The spherulitic development of an injection-molded polypropylene during the solidification have been simulated and quantitatively analyzed.

Simulations of crystal aggregation and growth: Towards correct crystal area

Simulating crystal growth and aggregation can provide insight into factors that control the final product properties. Classical models involve formation of a volume‐equivalent single crystal upon aggregation. This approach does not preserve particle area, resulting in an inadequate model of supersaturation depletion. Alternatively, crystal area can be computed accurately by a Monte Carlo method where each primary particle of an aggregate is described in its full geometric complexity. However, the drawback of this method is its computational cost. Thus, a third method is introduced as a compromise, describing particles by their volume and area and preserving both upon aggregation. The so‐obtained two‐dimensional model requires growth rate expressions in volume and area. We provide a method for parametrizing these expressions so that total volume and area closely match the values obtained with the method based on full geometric information. The parameters depend on primary particle geometry and the amount of growth. © 2019 American Institute of Chemical Engineers AIChE J, 65: e16525, 2019

Templated fabrication of hierarchically porous metal-organic frameworks and simulation of crystal growth.

Hierarchically porous metal–organic frameworks (MOFs) have recently emerged as a novel crystalline hybrid material with tunable porosity. Many efforts have been made to develop hierarchically porous MOFs, yet their low-energy fabrication remains a challenge and the underlying mechanism is still unknown. In this study, the rapid fabrication of two hierarchically porous MOFs (Cu-BTC and ZIF-8) was carried out at room temperature and ambient pressure for 10 min using a novel surfactant as the template in a (Cu, Zn) hydroxy double salt (HDS) solution, where the (Cu, Zn) HDS accelerated the nucleation of crystals and the anionic surfactants served as templates to fabricate mesopores and macropores. The growth mechanism of hierarchically porous MOFs was analyzed via mesodynamics (MesoDyn) simulation, and then the synthetic mechanism of hierarchically porous MOFs at the molecular level was obtained. The as-synthesized hierarchically porous Cu-BTC showed a high uptake capacity of 646 mg g−1, which is about 25% higher as compared with microporous Cu-BTC (516 mg g−1) for the capture of toluene. This study provides a theoretical basis for the large-scale fabrication of hierarchically porous MOFs and offers a reference for the understanding of their synthetic mechanism.

Axisymmetric lattice Boltzmann simulation of the heat-exchanger method-based sapphire crystal growth

The crystal-growth process in a heat-exchanger method (HEM)-based system was simulated using the lattice Boltzmann technique. The two-dimensional enthalpy-based lattice Boltzmann model was extended to treat the axisymmetric solid-liquid phase change problems. The proposed model demonstrates high accuracy over a large range of Biot and Stefan numbers and exhibits superiority over the first-order perturbation method, especially, in cases involving large Stefan numbers. Macroscopic crystal-growth simulations primarily focus on flow patterns in the melt and heat-transfer processes inside the crucible. Effects of dimensionless convective boundaries and Rayleigh numbers (Ra) on transport phenomena and the crystal/melt interface have also been discussed. It was observed that a decrease in the superheating temperature causes an increase in crystal fraction and decline in convection intensity. The area of the cooling zone mainly influences crystal growth rate during the initial stages of the process. In the later stages, however, the Biot number corresponding to the heating boundary assumes a more significant role. At low Rayleigh numbers, heat transfer via conduction is dominant in the melt. With increase in Ra values, melt convection tends to strengthen, thereby tending to deform the isothermal lines and phase interface.

Numerical Simulation of Crystal Growth in Two Transport Fields Using a Coupled Map Lattice

A new coupled map lattice model is proposed for crystal growth in two transport fields. Three types of numerical simulation are performed with the coupled map lattice, which are directional solidif...

Epitaxial Growth of Well-Aligned Single-Crystalline VO2 Micro/Nanowires Assisted by Substrate Facet Confinement

Vanadium dioxide (VO2) nanowires/microbeams have attracted great interest recently because of their pronounced single-domain metal–insulator phase transition (MIT) behavior, which is promising for various device applications and deeper mechanism investigation. It is known that monoclinic VO2 nanostructures can be effectively prepared by a simple thermal evaporation method, while the growth of dense and ordered VO2 micro/nanowires with controlled cross sections is still a challenge. In the current study, we have selected different crystal facets as the growth template and achieved controllable growth of well-aligned VO2 micro/nanowire arrays. Combined with the crystal growth simulations, it is clarified that the epitaxial growth of VO2 micro/nanowires on TiO2 substrates is mainly dominated by both the initial crystallization mechanism and confinement of the crystal facets. The current studies not only show the potentials of fabricating VO2 micro/nanowire array-based devices but also demonstrate a facile st...

Anisotropic Three-Dimensional Thermal Stress Modeling and Simulation of Homoepitaxial AlN Single Crystal Growth by the Physical Vapor Transport Method

We develop a thermal-elastic stress model using the finite element method to predict three-dimensional anisotropic stress in AlN single crystals homoepitaxially grown by the physical vapor transport process; we also perform numerical experiments for a 1-in. AlN crystal surrounded by different cone-tube designs and grown along various orientations. The influences of the cone-tube shape and the growth orientation on the stresses inside the AlN crystal are investigated in detail. The simulation results show that the von Mises stress exceeds 1.11 GPa under all specified growth conditions, while the anisotropy is negligible. The resolved shear stresses are strongly dependent on the thermal gradient inside the growing crystal and the growth orientation. Strong anisotropy of the resolved shear stress is observed upon tilting of the growth orientation. The resolved shear stress along {0001}⟨112̅0⟩ primary slip system reveals that the c-axis growing crystal is under tensile stress along all three primary slip directions. Nevertheless, an inversion of the resolved shear stress from tensile to compressive along the −a3 slip direction is observed when changing the growth orientation. The total resolved shear stress shows 6-fold symmetry, reflection symmetry and 2-fold symmetry along [001], [10√3], and [100] growth orientations, respectively.

A Cannibalistic Approach to Grand Canonical Crystal Growth.

Canonical molecular dynamics simulations of crystal growth from solution suffer from severe finite-size effects. As the crystal grows, the solute molecules are drawn from the solution to the crystal, leading to a continuous drop in the solution concentration. This is in contrast to experiments in which the crystal grows at an approximately constant supersaturation of a bulk solution. Recently, Perego et al. [ J. Chem. Phys. 2015, 142, 144113] showed that in a periodic setup in which the crystal is represented as a slab, the concentration in the vicinity of the two surfaces can be kept constant while the molecules are drawn from a part of the solution that acts as a molecular reservoir. This method is quite effective in studying crystallization under controlled supersaturation conditions. However, once the reservoir is depleted, the constant supersaturation conditions cannot be maintained. We propose a variant of this method to tackle this depletion problem by simultaneously dissolving one side of the crystal while letting the other side grow. A continuous supply of particles to the solution due to the crystal dissolution maintains a steady solution concentration and avoids reservoir depletion. In this way, a constant supersaturation condition can be maintained for as long as necessary. We have applied this method to study the growth and dissolution of urea crystal from water solution under constant supersaturation and undersaturation conditions, respectively. The computed growth and dissolution rates are in good agreement with those obtained in previous studies.

Adsorption of Kinetic Hydrate Inhibitors on Growing Surfaces: A Molecular Dynamics Study.

We investigate the mechanism of a typical kinetic hydrate inhibitor (KHI), polyvinylcaprolactam (PVCap), which has been applied to prevent hydrate plugs from forming in gas pipe lines, using molecular dynamics simulations of crystal growth of ethylene oxide hydrate. Water-soluble ethylene oxide is chosen as a guest species to avoid problems associated with the presence of the gas phase in the simulation cell such as slow crystal growth. A PVCap dodecamer adsorbs irreversibly on the hydrate surface which grows at supercooling of 3 K when the hydrophobic part of two pendent groups are trapped in open cages at the surface. The amide hydrogen bonds make no contribution to the adsorption. PVCap can adsorb on various crystallographic planes of sI hydrate. This is in contrast to antifreeze proteins, each of which prefers a specific plane of ice. The trapped PVCap gives rise to necessarily the concave surface of the hydrate. The crystal growth rate decreases with increasing surface curvature, indicating that the inhibition by PVCap is explained by the Gibbs-Thomson effect.

Tetrahedron-tiling method for crystal structure prediction

Reliable and robust methods of predicting the crystal structure of a compound, based only on its chemical composition, is crucial to the study of materials and their applications. Despite considerable ongoing research efforts, crystal structure prediction remains a challenging problem that demands large computational resources. Here we propose an efficient approach for first-principles crystal structure prediction. The new method explores and finds crystal structures by tiling together elementary tetrahedra that are energetically favorable and geometrically matching each other. This approach has three distinguishing features: a favorable building unit, an efficient calculation of local energy, and a stochastic Monte Carlo simulation of crystal growth. By applying the method to the crystal structure prediction of various materials, we demonstrate its validity and potential as a promising alternative to current methods.

『改造された桜井プログラム』による結晶成長形のComputer Simulation

『改造された桜井プログラム』による結晶成長形のComputer Simulation

Remote control system for high-perfomance computer simulation of crystal growth by the PFC method

Modeling of crystallization process by the phase field crystal method (PFC) - one of the important directions of modern computational materials science. In this paper, the practical side of the computer simulation of the crystallization process by the PFC method is investigated. To solve problems using this method, it is necessary to use high-performance computing clusters, data storage systems and other often expensive complex computer systems. Access to such resources is often limited, unstable and accompanied by various administrative problems. In addition, the variety of software and settings of different computing clusters sometimes does not allow researchers to use unified program code. There is a need to adapt the program code for each configuration of the computer complex. The practical experience of the authors has shown that the creation of a special control system for computing with the possibility of remote use can greatly simplify the implementation of simulations and increase the performance of scientific research. In current paper we show the principal idea of such a system and justify its efficiency.

Phase-field simulations of crystal growth in a two-dimensional cavity flow

In this paper, we consider a phase-field model for dendritic growth in a two-dimensional cavity flow and propose a computationally efficient numerical method for solving the model. The crystal is fixed in the space and cannot be convected in most of the previous studies, instead the supercooled melt flows around the crystal, which is hard to be realized in the real world experimental setting. Applying advection to the crystal equation, we have problems such as deformation of crystal shape and ambiguity of the crystal orientation for the anisotropy. To resolve these difficulties, we present a phase-field method by using a moving overset grid for the dendritic growth in a cavity flow. Numerical results show that the proposed method can predict the crystal growth under flow.

Analyzing and Driving Cluster Formation in Atomistic Simulations.

In this paper a set of computational tools for identifying the phases contained in a system composed of atoms or molecules is introduced. The method is rooted in graph theory and combines atom centered symmetry functions, adjacency matrices, and clustering algorithms to identify regions of space where the properties of the system constituents can be considered uniform. We show how this method can be used to define collective variables and how these collective variables can be used to enhance the sampling of nucleation events. We then show how this method can be used to analyze simulations of crystal nucleation and growth by using it to analyze simulations of the nucleation of the molecular crystal urea and simulations of nucleation in a semiconducting alloy. The semiconducting alloy example we discuss is particular challenging as multiple nucleation centers are formed. We show, however, that our algorithm is able to detect the grain boundaries in the resulting polycrystal.

A framework for multi-scale simulation of crystal growth in the presence of polymers.

We present a multi-scale simulation method for modeling crystal growth in the presence of polymer excipients. The method includes a coarse-grained (CG) model for small molecules of known crystal structure whose force field is obtained using structural properties from atomistic simulations. This CG model is capable of stabilizing the molecular crystal structure and capturing the crystal growth from the melt for a wide range of small organic molecules, as demonstrated by application of our method to the molecules isoniazid, urea, sulfamethoxazole, prilocaine, oxcarbazepine, and phenytoin. This CG model can also be used to study the effect of additives, such as polymers, on the inhibition of crystal growth by polymers, as exemplified by our simulation of suppression of the rate of crystal growth of phenytoin, an active pharmaceutical ingredient (API), by a cellulose excipient, functionalized with acetate (Ac), hydroxy-propyl (Hp) and succinate (Su) groups. We show that the efficacy of the cellulosic polymers in slowing crystal growth of small molecules strongly depends on the functional group substitution on the cellulose backbone, with the acetate substituent group slowing crystal growth more than does the deprotonated succinate group, which we confirm by experimental drug supersaturation studies.

Numerical Simulation of Multi-Crystalline Silicon Crystal Growth Using a Macro–Micro Coupled Method during the Directional Solidification Process

In this work, the crystal growth of multi-crystalline silicon (mc-Si) during the directional solidification process was studied using the cellular automaton method. The boundary heat transfer coefficient was adjusted to get a suitable temperature field and a high-quality mc-Si ingot. Under the conditions of top adiabatic and bottom constant heat flux, the shape of the crystal-melt interface changes from concave to convex with the decrease of the heat transfer coefficient on the side boundaries. In addition, the nuclei form at the bottom boundary while columnar crystals develop into silicon melt with amzigzag-faceted interface. The higher-energy silicon grains were merged into lower energy ones. In the end, the number of silicon grains decreases with the increase of crystal length.

Validation, verification, and benchmarking of crystal growth simulations

The variety of physical phenomena in crystal growth processes requires diverse software tools for the numerical simulations. Both, dedicated 2D or 3D ready-to-use software for coupled simulations of a crystallization furnace and general-purpose 3D simulation packages have been used in the literature. This work proposes a general strategy for model development: validation of the physical model using model experiments; verification of the numerical model using analytical or high-accuracy solutions; testing of the computational efficiency using complex benchmark cases. The application of these steps is demonstrated for various models in directional solidification of silicon showing the capabilities of various open source or commercial software packages.