王家毅,吴钦杰,廖彬,吴红凯,韩志洋,陈浩基

• 1:哈尔滨工业大学(深圳)材料科学与工程学院
• 2:哈尔滨工业大学(深圳)计算机科学与工程学院
• 3:哈尔滨工业大学(深圳)理学院

摘要(Abstract)：

等积球体在无限长圆管中的周期性最密堆积结构,可称之为柱状晶体。这类系统的最密结构种类繁多,并随着圆管与球体的直径比D连续变化。在一些较大D值的情况下,晶胞的颗粒数较多,晶胞结构在空间限制的影响下也变得异常复杂。要理解晶胞中每一个球体的排布和它怎样受到其他球体与圆管壁的影响,是一大挑战。本文提出,我们可以通过打印三维实物模型,去窥探复杂晶体结构中球体的空间排布以及球与球之间的接触网络。本文展示,这类柱状晶体结构可以通过熔融沉积成型、光固化快速成型、粉末烧结这三种不同的技术进行三维打印,并仔细讨论每种技术的流程、注意事项、利弊。

关键词(KeyWords)： 晶体;结构;三维打印;数字模型

Abstract:

Keywords:

基金项目(Foundation): 国家级大学生创新创业训练计划项目(201810213124);; 深圳市基础研究项目(JCYJ20160531193515801);; 深圳市引进人才启动经费(ED11409002)

作者(Author): 王家毅,吴钦杰,廖彬,吴红凯,韩志洋,陈浩基

参考文献(References)：

• [1] ASTE T,WEAIRE D.The pursuit of perfect packing[M].2nd ed.London:Taylor and Francis,2008.
• [2] 钱逸泰.结晶化学导论[M].合肥：中国科学技术大学出版社，2008.
• [3] PICKETT G T,GROSS M,OKUYAMA H.Spontaneous chirality in simple systems[J].Physical Review Letters,2000,85:3652-3655.
• [4] KOGA K,TANAKA H.Close-packed structures and phase diagram of soft spheres in cylindrical pores[J].Journal of Chemical Physics,2006,124:131103.
• [5] GORDILLO M C,MARTíNEZ-HAYA B,ROMERO-ENRIQUE J M.Freezing of hard spheres confined in narrow cylindrical pores[J].Journal of Chemical Physics,2006,125:144702.
• [6] DURáN-OLIVENCIA F J,Gordillo M C.Ordering of hard spheres inside hard cylindrical pores[J].Physical Review E,2009,79:061111.
• [7] MUGHAL A,CHAN H-K,WEAIRE D.Phyllotactic description of hard sphere packing in cylindrical channels[J].Physical Review Letters,2011,106:115704.
• [8] CHAN H K.Densest columnar structures of hard spheres from sequential deposition[J].Physical Review E,2011,84:050302(R).
• [9] MUGHAL A,CHAN H K,Weaire D,Hutzler S.Dense packings of spheres in cylinders:Simulations[J].Physical Review E,2012,85:051305.
• [10] CHAN H K.A hybrid helical structure of hard sphere packing from sequential deposition[J].Philosophical Magazine,2013,93:4057-4069.
• [11] MUGHAL A.Screw symmetry in columnar crystals[J].Philosophical Magazine,2013,93:4070-4077.
• [12] MUGHAL A,WEAIRE D.Theory of cylindrical dense packings of disks[J].Physical Review E,2014,89:042307.
• [13] YAMCHI M Z,BOWLES R K.Helical defect packings in a quasi-one-dimensional system of cylindrically confined hard spheres[J].Physical Review Letters,2015,115:025702.
• [14] FU L,STEINHARDT W,ZHAO H,et al.Hard sphere packings within cylinders[J].Soft Matter,2016,12:2505-2514.
• [15] FU L,BIAN C,SHIELDS IV C W,et al.Assembly of hard spheres in a cylinder:a computational and experimental study[J].Soft Matter,2017,13:3296-3306.
• [16] WINKELMANN J,HAFFNER B,WEAIRE D,ET Al.Corrected Article:Simulation and observation of line-slip structures in columnar structures of soft spheres[Phys.Rev.E 96,012610 (2017)][J].Physical Review E,2018,97:059902.
• [17] CHAN H K,WANG Y,HAN H.Densest helical structures of hard spheres in narrow confinement:An analytic derivation[J].AIP Advances,2019,9:125118.
• [18] HODAK M,GIRIFALCO L A.Ordered phases of fullerene molecules formed inside carbon nanotubes[J].Physical Review B,2003,67:075419.
• [19] KHLOBYSTOV A N,BRITZ D A,ARDAVAN A,et al.Observation of ordered phases of fullerenes in carbon nanotubes[J].Physical Review Letters,2004,92:245507.
• [20] TROCHE K S,COLUCI V R,BRAGA S F,et al.Prediction of ordered phases of encapsulated C60,C70,and C78 inside carbon nanotubes[J].Nano Letters,5:349-355.
• [21] PICHLER T.Molecular Nanostructures:Carbon Ahead[J].Nature Materials,2007,6:332-333.
• [22] LEGOAS S B,DOS SANTOS R P B,TROCHE K S,et al.Ordered phases of encapsulated diamondoids into carbon nanotubes[J].Nanotechnology,2011,22:315708.
• [23] WU Y,CHENG G,KATSOV K,et al.Composite mesostructures by nanoconfinement[J].Nature Materials,2004,3:816.
• [24] SANWARIA S,HORECHYY A,WOLF D,et al.Helical packing of nanoparticles confined in cylindrical domains of a self-assembled block copolymer structure[J].Angewandte Chemie International Edition,2014,53:9090.
• [25] TYMCZENKO M,MARSAL L F,TRIFONOV T,et al.Colloidal crystal wires[J].Advanced Materials,2008,20:2315-2318.
• [26] LOHR M A,ALSAYED A M,CHEN B G,et al.Helical packings and phase transformations of soft spheres in cylinders[J].Physical Review E,2010,81:040401(R).
• [27] MEAGHER A J,GARCíA-MORENO F,BANHART J,et al.An experimental study of columnar crystals using monodisperse microbubbles[J].Colloids and Surfaces A:Physicochemical and Engineering Aspects,2015,473:55-59.
• [28] JUNG Y,HA B Y.Confinement induces helical organization of chromosome-like polymers[J].Scientific Reports,2019,9:869.
• [29] LEE T,GIZYNSKI K,GRZYBOWSKI B A.Non-equilibrium self-assembly of monocomponent and multicomponent tubular structures in rotating fluids[J].Advanced Materials,2017,29:1704274.
• [30] 马盼盼.圆管中球体最密堆积晶体结构电阻率的理论研究[D].深圳：哈尔滨工业大学(深圳),2021.
• [31] BERMAN B.3-D printing:The new industrial revolution[J].Business Horizons,2012,55:155-162.
• [32] 梁应广，田长留，苏文瑛，等.逆向工程及3D打印技术的应用与精度分析[J].模具工业，2018,6,1001-2168(2018)06-0022-05.LIANG Y G,TIAN C L,SU W Y,et al..Application of reverse engineering and 3D printing technology and the precision analysis[J].Die & Mould Industry,2018,6,1001-2168(2018)06-0022-05.(in Chinese)
• [33] 陈志茹，夏承东，李龙，等.3D打印材料[J].金属世界，2018,5:15-18.CHEN Z R,XIA C D,LI L,et al..3D Printing Materials[J].Metal World 2018,5:15-18.(in Chinese)
• [34] Conner B P,Manogharan G P,Martof A N,et al.Making sense of 3-D printing:Creating a map of additive manufacturing products and services[J].Additive Manufacturing,2014,1-4:64-76.
• [35] 赵松.激光能量密度對高分子粉末材料SLS成型質量的影響[J].塑料工业，2019,12:53-57.ZHAO S.Effect of laser energy density on Selective Laser Sintering molding quality of polymer powder materials[J].China Plastics Industry,2019,12:53-57.(in Chinese)
• [36] 黄忠，韩江.金属3D打印技术的发展现状及制约因素[J].山东农业工程学院学报，2018,3:40-43.HUANG Z,HAN J.Development status and constraints of metal 3D printing technology[J].The Journal of Shandong Agriculture and Engineering University,2018,3:40-43.(in Chinese)
• [37] JIN W,CHAN H K,ZHONG Z.Shape-anisotropy-induced ordered packings in cylindrical confinement[J].Physical Review Letters,2020,124:248002.
• [38] JIN W,WANG Y,CHAN H K,et al.Confinement-induced columnar crystals of ellipses[J].Physical Review Research,2021,3:013053.