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Deformation study of bicrystalline and nano-polycrystalline structures using phase field crystal method

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Science China(Physics,Mechanics & Astronomy) 2014年第6期57卷 1046-1056页

作者： LONG Jian ZHANG Shuai ZHAO YuLong LONG QingHua YANG Tao CHEN Zheng State Key Laboratory of Solidification Processing Northwestern Polytechnical University

Deformation behaviors of bicrystalline and nano-polycrystalline structures of various tilt angles and inclination angles in two dimensions are investigated in detail using a two-mode phase field crystal *** interaction between grain boundary(GB)and dislocation is also examined in bicrystals and nano-polycrystals that both contain asymmetric and symmetric tilt GBs,with energy analysis being carried out to analyze these *** deformation simulations,we assume the volume of each simulation cell at every time step is coincident with that of the initial state just before *** simulation results show that the behaviors of symmetric and asymmetric GBs in bicrystals and nano-polycrystals differ from each other depending on tilt angle and inclination angle.A new dislocation emission mechanism of interest is observed in bicrystals which contain low angle symmetric tilt *** angle GB has a higher mobility relative to high angle GB in both bicrystalline and nano-polycrystalline structures,as does asymmetric GB to symmetric *** generation,motion,pileup and annihilation of dislocations,grain rotation and grain coalescence are observed,which is consistent with the simulation results obtained by molecular *** simulation results can provide strong guidelines for experimentation.

关键词： phase field crystal grain boundary dislocation deformation mechanism

Benchmark Computations of the phase field crystal and Functionalized Cahn-Hilliard Equations via Fully Implicit,Nesterov Accelerated Schemes

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Communications in Computational Physics 2023年第2期33卷 367-398页

作者： Jea-Hyun Park Abner J.Salgado Steven M.Wise Department of Mathematics University of California Santa BarbaraCA 93106USA Department of Mathematics University of Tennessee KnoxvilleTN 37996USA.

We introduce a fast solver for the phase field crystal(PFC)and functionalized Cahn-Hilliard(FCH)equations with periodic boundary conditions on a rectangular domain that features the preconditioned Nesterov’s accelerated gradient descent(PAGD)*** discretize these problems with a Fourier collocation method in space,and employ various second-order schemes in *** observe a significant speedup with this solver when compared to the preconditioned gradient descent(PGD)*** the PAGD solver,fully implicit,second-order-in-time schemes are not only feasible to solve the PFC and FCH equations,but also do so more efficiently than some semi-implicit schemes in some cases where accuracy issues are taken into *** computations of four different schemes for the PFC and FCH equations are conducted and the results indicate that,for the FCH experiments,the fully implicit schemes(midpoint rule and BDF2 equipped with the PAGD as a nonlinear time marching solver)perform better than their IMEX versions in terms of computational cost needed to achieve a certain *** the PFC,the results are not as conclusive as in the FCH experiments,which,we believe,is due to the fact that the nonlinearity in the PFC is milder nature compared to the FCH *** also discuss some practical matters in applying the *** introduce an averaged Newton preconditioner and a sweeping-friction strategy as heuristic ways to choose good preconditioner *** sweeping-friction strategy exhibits almost as good a performance as the case of the best manually tuned parameters.

关键词： phase field crystal functionalized Cahn-Hilliard preconditioning Nesterov acceleration nonlinear solver.

Faceting transitions in crystal growth and heteroepitaxial growth in the anisotropic phase-field crystal model

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Chinese Physics B 2012年第11期21卷 500-506页

作者：陈成陈铮张静杨涛杜秀娟 State Key Laboratory of Solidification Processing Northwestern Polytechnical University

We modify the anisotropic phase-field crystal model （APFC）, and present a semi-implicit spectral method to numerically solve the dynamic equation of the APFC model. The process results in the acceleration of computations by orders of magnitude relative to the conventional explicit finite-difference scheme, thereby, allowing us to work on a large system and for a long time. The faceting transitions introduced by the increasing anisotropy in crystal growth are then discussed. In particular, we investigate the morphological evolution in heteroepitaxial growth of our model. A new formation mechanism of misfit dislocations caused by vacancy trapping is found. The regular array of misfit dislocations produces a small-angle grain boundary under the right conditions, and it could significantly change the growth orientation of epitaxial layers.

关键词： phase field crystal misfit dislocations heteroepitaxial growth

phase-field crystal modeling of shape transition of strained islands in heteroepitaxy

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Science China(Physics,Mechanics & Astronomy) 2012年第11期55卷 2042-2048页

作者： CHEN Cheng CHEN Zheng ZHANG Jing DU XiuJuan State Key Laboratory of Solidification Processing Northwestern Polytechnical UniversityXi'an 710072China

The phase-field crystal(PFC) model is employed to study the shape transition of strained islands in heteroepitaxy on vicinal *** influences of both substrate vicinal angles β and the lattice mismatch ξ are *** increase of substrate vicinal angles is found to be capable of significantly changing the surface nanostructures of epitaxial *** surface morphology of films undergoes a series of transitions that include Stranski-Krastonov(SK) islands,the couple growth of islands and the step flow as well as the formation of step *** addition,the larger ξ indicates an increased strained island density after coarsening,and results in the incoherent growth of strained islands with the creation of misfit ***,coalescence and faceting of strained islands are also *** facets in the shape transition of strained islands are found to be stable and can be determined by β and crystal symmetry of the film.

关键词： heteroepitaxy strained islands phase field crystal