空位晶体相场模型模拟二维晶体相形貌图
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摘要
[目的]揭示空位晶体相场模型(VPFC)中二维周期性晶体相空位缺陷结构形貌。[方法]对标准晶体相场模型的自由能函数进行修正得到空位晶体相场模型,再利用空位晶体相场方程,研究二维相图中不同相晶体结构形貌图,以及晶体结构中出现空位的条件。[结果]当平均原子密度数值位于不同晶体相时,呈现出不同的二维周期性晶体结构形貌图。[结论]将晶体结构形貌图与其原子密度曲线对照,可见该模型中晶体相结构主要有六角"凸起"相、条状相和六角"凹坑"相。当平均原子密度数值位于相图中局部粒子相和六角"凸起"相之间时,二维周期性晶体结构中将出现空位,并且晶粒内部空位随机分布,空位数目与原子密度值有关。
[Objective]The vacancy morphology of two-dimensional periodic crystal structure was estimated through the vacancy phase field crystal(VPFC)model.[Methods]The free energy function of VPFC model was obtained by modifying simple phase field crystal model.The VPFC model was used to study the different periodic crystal profiles in the two-dimensional phases diagram and explore the condition of vacancy presenting.[Results]Different kinds of the two-dimensional periodic crystal structure patterns were obtained by selecting the average atomic density values in different phases.[Conclusion]Combining topography of crystal structure with atomic density curve reveals that hexagonal bumps,stripes and hexagonal holes are main structures in the crystal sample.When the average atomic density value is located in the phase diagram of the coexistence zone of the local particles and hexagonal bumps phase,vacancy structures appear in the crystal.Moreover,the vacancies are randomly distributed and their number are related to the atomic density values.
[Objective]The vacancy morphology of two-dimensional periodic crystal structure was estimated through the vacancy phase field crystal(VPFC)model.[Methods]The free energy function of VPFC model was obtained by modifying simple phase field crystal model.The VPFC model was used to study the different periodic crystal profiles in the two-dimensional phases diagram and explore the condition of vacancy presenting.[Results]Different kinds of the two-dimensional periodic crystal structure patterns were obtained by selecting the average atomic density values in different phases.[Conclusion]Combining topography of crystal structure with atomic density curve reveals that hexagonal bumps,stripes and hexagonal holes are main structures in the crystal sample.When the average atomic density value is located in the phase diagram of the coexistence zone of the local particles and hexagonal bumps phase,vacancy structures appear in the crystal.Moreover,the vacancies are randomly distributed and their number are related to the atomic density values.
引文
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[19]Chan P Y,Goldenfeld N,Dantzig J.Molecular dynamics on diffusive time scales from the phase-field-crystal equation[J].Phys Rev E Stat Nonlin Soft Matter Phys,2009,79(32):35701.
[20]Silván M M,Hernández M A,Costa V T,et al.Structured porous silicon sub-micrometer wells grown by colloidal lithography[J].Epl,2006,76(4):690-695.
[21]Huang Z.Metal-assisted chemical etching of silicon:A review[J].Advanced Materials,2011,23(2):285-308.
[22]M M S,M A H,V T C.Structured porous silicon submicrometer wells grown by colloidal lithography[J].EPL(Europhysics Letters),2006,76(4):690-695.
[23]Faustini M,Sko G L,Boissiere C,et al.Liquid deposition approaches to self-assembled periodic nanomasks[J].Scripta Materialia,2014,74(2):13-18.
[24]Sousa C T,Leitao D,Proenca M P,et al.Nanoporous alumina as templates for multifunctional application[J].Appl Phys Rev,2014,1:031102.
[25]Vohra V,Yunus S,Attout A,et al.Bifunctional microstructured films and surfaces obtained by soft lithography from breath figure arrays[J].Soft Matter,2009,5(8):1656-1661.
[26]刘培生.晶体点缺陷基础[M].北京:科学出版社,2010.Liu P S.Crystal Point Defect Foundation[M].Beijing:Science Press,2010.
[2]Keblinski P,Phillpot S R,Wolf D A N L,et al.Amorphous structure of grain boundaries and grain junctions in nanocrystalline silicon by molecular-dynamics simulations[J].Acta Materialia,1997,45(3):987-998.
[3]Elder K R,Grant M.Modeling elastic and plastic deformations in nonequilibrium processing using phase field crystals[J].Phys Rev E Stat Nonlin Soft Matter Phys,2004,70(5):1605-1618.
[4]Elder K R,Rossi G,Kanerva P,et al.Patterning of heteroepitaxial over layers from nano to micron scales[J].Phys Rev Lett,2012,108:6102-6106.
[5]Elder K R,Katakowski M,Haataja M,et al.Modeling elasticity in crystal growth[J].Physical Review Letters,2002,88(24):930-933.
[6]高英俊,罗志荣,黄礼琳,等.韧性材料的微裂纹扩展和连通的晶体相场模拟[J].中国有色金属学报,2013,20(4):316-320.Gao Y J,Luo Z R,Huang L L,et al.Phase-field-crystal modeling for microcrack propagation and connecting of ductile materials[J].The Chinese Jounal of Nonferrous Metals,2013,20(4):316-320.
[7]Berry J,Grant M,Elder K R.Diffusive atomistic dynamics of edge dislocations in two dimensions[J].Physical Review E,2006,73(3):80-98.
[8]Hm S I S.Analysis and visualization of multiply oriented lattice structures by a two-dimensional continuous wavelet transform[J].Phys Rev E Stat Nonlin Soft Matter Phys,2006,74(3):236-243.
[9]Chan P.Scaling and pattern formation in condensed matter systems[J].Pro Quest Dissertations and Theses;Thesis—University of Illinois at Urbana-Champaign,2007(1):21-25.
[10]高英俊,黄礼琳,周文权,等.高温应变作用下的亚晶界湮没与位错旋转机制的晶体相场模拟[J].中国科学-技术科学,2015,45(3):306-321.Gao Y J,Huang L L,Zhou W Q,et al.Phase field crystal simulation of subgrain boundary annihilation and dislocation rotation mechanism under strain at high temperature[J].Science in China E,2015,45(3):306-321.
[11]高英俊,全四龙,邓芊芊,等.剪切应变下刃型位错的滑移机制的晶体相场模拟[J].物理学报,2015,64(10):106105.Gao Y J,Quan S L,Deng Q Q,et al.Phase field crystal simulation of grain boundary annihilation under strain strain at high temperature[J].Acta Phys Sin,2015,64(10):106105.
[12]Gao Y J,Deng Q Q,Quan S L,et al.Phase field crystal simulation of grain boundary movement and dislocation reaction[J].Frontiers of Materials Science,2014(8):176-184.
[13]罗志荣,黄世叶,茹谢辛,等.晶体相场法模拟大角度晶界的变形过程[J].广西科学,2013,20(4):311-315.Luo Z R,Huang S Y,Ru X X,et al.Phase-field-crystal modeling for deformation process of high-angle grain boundary[J].Guangxi Sciences,2013,20(4):311-315.
[14]卢成健,蒋丽婷,王玉玲,等.晶体相场法模拟小角度晶界的位错结构及其演化[J].广西科学,2013,20(4):316-320.Lu C J,Jiang L T,Wang Y L,et al.Dislocation structure evolution in low angle grain boundary[J].Guangxi Sciences,2013,20(4):316-320.
[15]Elder K R,Provatas N,Berry J,et al.Phase-field crystal modeling and classical density functional theory of freezing[J].Physical Review B,2007,75(6):794-802.
[16]Faghihi N,Provatas N,Elder K R,et al.Phase field crystal model for magneto-elasticity in isotropic ferromagnetic solids[J].Physical Review E,2013,88(3):29-44.
[17]Berry J.Simulation of an atomistic dynamic field theory for monatomic liquids:Freezing and glass formation[J].Physical Review E,2008,77(6):601-611.
[18]Robbins M J,Archer A J,Thiele U,et al.Modeling the structure of liquids and crystals using one-and twocomponent modified phase-field crystal models[J].Phys Rev E Stat Nonlin Soft Matter Phys,2012,85(61):61408.
[19]Chan P Y,Goldenfeld N,Dantzig J.Molecular dynamics on diffusive time scales from the phase-field-crystal equation[J].Phys Rev E Stat Nonlin Soft Matter Phys,2009,79(32):35701.
[20]Silván M M,Hernández M A,Costa V T,et al.Structured porous silicon sub-micrometer wells grown by colloidal lithography[J].Epl,2006,76(4):690-695.
[21]Huang Z.Metal-assisted chemical etching of silicon:A review[J].Advanced Materials,2011,23(2):285-308.
[22]M M S,M A H,V T C.Structured porous silicon submicrometer wells grown by colloidal lithography[J].EPL(Europhysics Letters),2006,76(4):690-695.
[23]Faustini M,Sko G L,Boissiere C,et al.Liquid deposition approaches to self-assembled periodic nanomasks[J].Scripta Materialia,2014,74(2):13-18.
[24]Sousa C T,Leitao D,Proenca M P,et al.Nanoporous alumina as templates for multifunctional application[J].Appl Phys Rev,2014,1:031102.
[25]Vohra V,Yunus S,Attout A,et al.Bifunctional microstructured films and surfaces obtained by soft lithography from breath figure arrays[J].Soft Matter,2009,5(8):1656-1661.
[26]刘培生.晶体点缺陷基础[M].北京:科学出版社,2010.Liu P S.Crystal Point Defect Foundation[M].Beijing:Science Press,2010.