摘要
凝聚态的微观结构历来就是物理学家、生物学家、化学家和材料科学家竭力探索的重要课题。而欲从凝聚态的无序的结构中归纳出有序的规律,定量描述就是一个必不可少的环节。但是,由于众所周知的难度,这种定量描述直到计算机模拟出现才有了可能,随着计算机和计算科学的发展,通过计算机模拟来揭示微观结构的奥秘已成为凝聚态研究的热点和前沿。本学位论文就是以分子动力学方法计算机模拟所得的系统的瞬态构型为原始数据,采用多种几何学的方法来对系统的微观结构进行定量描述研究的。论文工作旨在得到凝聚态微观结构的清晰的物理模型。
Voronoi-Delaunay(简称V-D)理论由于其概念简单和几何图像清晰,正受到人们越来越多的重视。V-D网络蕴涵着体系的极强大的信息,能够为体系的微观结构研究提供基本的几何数据。本文利用推广的V-D的几何模型,采用修正的Voronoi多面体构算方法和基于Voronoi S-网络的追踪法,对以LiCl晶体为代表的碱金属卤化物在熔化过程中的微观结构从度量特性和形状特性等方面进行了众多的几何参数的计算和统计分析,取得了颇为丰硕的成果。
本论文工作的主要贡献是:
1.系统地总结了离散点、球体和非球凸体等不同体系下的V-D方法,把经改进的方法应用于碱金属卤化物熔盐和熔盐溶液的研究;
2.修正了Voronoi多面体的逐次切割法,使之能应用于不同半径粒子和多粒子以及亚Voronoi多面体的场合;针对Voronoi多面体分析参数中键角的丰度叠加问题,提出了利用Delaunay单纯形(简称DS)面角代替键角的新的研究方法;
3.针对熔盐结构的特殊性,提出了度量DS的新参数-立方体程度和它的计算实现;针对离子系,提出了晶面DS和晶格DS的新概念,并综合单纯形体积、面积、球形度、四面体系数等参数丰度分析,提出了基于单纯形的熔融理论,使熔化理论更具一般性;
4针对离子系,提出了亚DS网络和“有心”、“无心”EDS等一系列新概念以及这些亚DS的计算实现方法;并在此基础上提出了利用基于阴阳离子大分类的亚DS网络和基于构成亚DS的四粒子组的阴阳离子小分类的亚DS网络的中程结构的新的研究方法;另外,针对Voronoi网络的特殊性,也提出了多元混合染色的研究方法;
5.由于空穴的存在和分布与体系的性质有着密切关系,我们利用V-D方法修正和补充了“嵌入法”,使其更有效地寻找体系中的微观空穴。同时,对系统的微观空穴结构也进行了相应的讨论。
虽然国外关于液体理论的研究成果众多,但是这种研究多以Lennard-Jones(LJ)模型液体为对象,利用V-D理论对熔盐和熔盐溶液作研究还很罕见。本论文研究方法的实施对象选择了熔盐和熔盐溶液。这样的选择不仅是因为熔盐系在冶金和新能源(熔盐燃料电池、熔盐核反应堆、太阳能发电储热介质等)等方面的应用价值,而且因为熔盐是由阴、阳两种离子组成,对它的V-D方法研究可以得到比单分子液体更多的结构信息,因而本文的研究对一般的液态结构理论会有所贡献。此外,通过分子动力学方法,容易实现熔盐急冷形成非晶态固体的计算机模拟,因此本论文的熔盐结构研究结果对开展非晶态离子固体的研究也会有所启发。
本文的结构安排如下:第一章前言;第二章阐述了V-D方法的几何知识及其在计算机上的实现;第三章叙述了LiCl熔化过程中局部结构的Voronoi域的参数分析;第四章叙述了LiCl熔化过程中局部结构的Delaunay S-单纯形的参数分析;第五章探究了碱金属卤化物的中程结构;第六章介绍了微观空穴的分析方法;第七章总结。
The microcosmic structure of the condensed state has always been an important topic which physicists, biologists, chemists and material scientists explore teeth and nail. To induce the law of order from the orderless structure of the condensed state, quantificational description is an absolutely necessary tache. However, because of the well-known difficulty, such quantificational description was not possible until the computer simulation came out. With the development of computer science and computational science, to open out the arcanum of the microcosmic structure by computer simulation has become the hotpot and the leading field of the research on the condensed state. Taking the instantaneous configurations of the system obtained by the computer simulation with molecular dynamics method as source data, this thesis conducts the quantificational description of the system's microcosmic structure by means of several geometrical methods, and it aims at obtaining a clear physical model of the microcosmic structure of the condensed state.
Because of simple conception and clear geometric pattern, V-D theory has been getting more and more recognition. V-D network contains powerful information of the system, and it can provide basic geometrical data for the research of the system's microcosmic structure. This thesis utilizes the extended V-D geometrical model, adopts the revised method of constructing and computing the Voronoi polyhedron and the tracing method based on Voronoi S-network, to conduct much calculation and statistical analysis for the geometric parameters from the aspects of the measurement characteristic and shape characteristic of the microcosmic structure in the melting process of alkali metals halide which is represented by LiCl crystal, and some plentiful and substantial results have been obtained.
The main contributions of this thesis include
1. Systematically summarizing the V-D method for different systems of discrete point set, spheroid and non-spherical convex body, and applying an improved method to studying the melting salt of alkali metals halide and the solution of the melting salt;
2. Revising the successive cutting method of constructing and computing the Voronoi polyhedron to make it applicable to the occasions of different radii particles, multiplicate particles and sub-Voronoi polyhedron; developing the new research method of replacing the bond-angle by the Delaunay simplex(DS) face angle for the problem of scale superposition of the bond-angle parameter in the analysis of the Voronoi polyhedron;
3. In allusion to the particularity of structure of melting salt, developing the cubic degree as a new parameter for measuring DS and its computer realization, developing the new idea of crystal surface DS and crystal lattice DS for ion systems, and integrating the scale analysis of volume, area, sphericity degree, tetrahedral coefficient of the simplex to develop the melting theory based on the parameter analysis of simplex and make it more general;
4. For ion systems, developing the new concepts of sub-DS network, centered sub-DS and centerless sub-DS and the computer realization method of these sub-DS; based on these concepts, developing the new research methods of intermediate range structure by using the sub-DS network based on classifying positive ion and negative ion and the sub-DS network based on classifying positive ion and negative ion in accordance with the four particles group constituting the sub-DS; for the particularity of Voronoi network, developing the research method of mixed multi-coloration;
5. Since the existence and distribution of the microcosmic hole are closely related to the system properties, by using the V-D method, we revise and complement the embedding technique to make it find the microcosmic holes of the system more effectively, in addition, we discuss the structure of microcosmic holes of the system accordingly.
Though there are many research results overseas on liquid theory, most of these studies take Lennard-Jones(L-J) model liquids as objects. Research on melting salt and the solution of melting salt using V-D theory is rare. The research method of this thesis chooses melting salt and the solution of melting salt as the implementary objects. These choices are not only because of the application value of melting salt system in the aspects of metallurgy and new energy sources (fuel batteries of melting salt, nuclear reactor of melting salt, solar dynamoelectric heat storage medium, etc.), but also due to that melting salt consists of both negative ion and positive ion, research on them using V-D theory can obtain much more structure information than the monoatomic molecule liquid, and thus the research of this thesis contributes to the structure theory of general liquid state. In addition, the computer simulation of melting salt forming non-crystal solid through quenching can be easily realized by means of molecular dynamic method, so the research results of the melting salt structure in this thesis may enlighten the research on non-crystal ion solid.
This thesis is organized as follows: Chapter 1 presents the introduction; Chapter 2 describes the geometrical knowledge of V-D method and the realization of V-D method on the computer; Chapter 3 presents the parameter analysis for the Voronoi field of local structure in LiCl melting process; Chapter 4 presents parameter analysis for the Delaunay S-simplex of local structure in LiCl melting process; Chapter 5 explores the intermediate range structure of alkali metals halide; Chapter 6 introduces the analysis method of microscopic hole; Chapter 7 summarizes the thesis.
引文
[1]M.Kimura,et al.,Nature of amorphous and liquid structure—computer simulation and statistical geometry[J],J.Non-Cryst.Solids,1984,Vol.61-62:535-540
[2]L.Oger,A.Gervois,et al.,Voronoi tessellation of packing of spheres:topological correlation and statistics[J],Philosophical Mag.B,1996,Ⅴ.74(2),177-197
[3]M.I.Aoki,K.Tzumuraya,Ab initio molecular dynamic studies of Volume stability of Voronoi polyhedra under pressure in metal glass[J],J.Chem.Phys.,1996,Vol.104(17):6719-6723
[4](a) G.F.Voronoi,J Reine Angew math 1908,Vo1.134:198-287;
(b) G.F.Voronoi,J Reine Angew math 1909,Vo1.136:67-181
[5]B.N.Delaunay,In Proceedings of the International Congress of Mathematicians[M],Toronto,August 11-16,1924;University of Toronto Press;Toronto,1928,695-700
[6]B.N.Delaunay,Sur la sphere vide.A la memoire de Georges Voronoi[J],Iav Akad Nauk SSSR Otd Mat Ⅰ Estestv nauk,1934,Vol.7:793-800
[7]J.D.Bernal,A Geometrical Approach to the Structure of Liquid[J],Nature,1959,Vo1.183:141-147
[8]J.D.Bernal,Liquids,Structure,Properties,Solid Interface[M],Edited by Hughel T J,Elsevier Publishing Company,Amsterdam,1965
[9]F.M.Richard,Areas,Volumes,paching,and protein structure[M],Ann.Rew.Biophys.,Bioneng,1977,Vol.6:151-176
[10]F.M.Richard,Calculation of molecular Volumes and areas for structures of known geometry[J],Methods in Enzymology,1985,Vo1.155:440-464
[11]B.J.Gelltly,J.L.Finney,Characterisation of models of multicomponent amorphous met-als:the radical alternative to the Voronoi polyhedron[J],J.Non-Cryst.Solids,1982,Vol.50:313-329
[12]W.Fisher,E.Koah,Geometrical packing analysis of molecular compounds[J],Z.Kristallogr,1979,Vo1.150:248-260
[13]N.N.Medvedev,Voronoi-Delaunay Method for Non-Crystalline Structures[M],SB Russian Academy of Science,Novosibirsk,2000(in Russian)
[14]汤正诠,邵俊,陈念怠,Voronoi多面体的构造方法及其实践[J],上海科技大学学报,1989,No.1:21
[15]邵俊,汤正诠,化学短程序和中程序的Voronoi多面分析[J],物理化学学报,1993, Vol.9(3)
[16]邵俊,汤正诠,LiCl急冷玻璃形成过程中局部结构的分子动力学模拟-基于周期性边界条件的Voronoi多面体计算[J],物理化学学报,1991.10;Vol.7(5)
[17]邵俊,汤正诠等,熔融LiCl中的Voronoi多面体[J],物理化学学报,1989,Vol.5(3)
[18]Tang Zhengquan,Shaojun,et al,A geometrical approach to the structure in LiCl quenching process[J],Acta Phys-Chim Sin,1990,Vol.6(1)
[19]汤正诠,邵俊,关于Voronoi多面体构算的一个标注[J],上海科技大学学报,1990,No.4
[20]汤正诠,邵俊,陈念贻,Voronoi多面体的计算[J],自然杂志,1989,Vol.9(9):719
[21]汤正诠,邵俊,简单液体中微观空洞的定量分析法[J],上海科技大学学报,1990,NO.2:29-35
[22]邵俊,汤正诠,陈念贻,熔融LiCl系中微观空洞的确定和分布[J],1990,Vol.6(2)
[23]汤正诠,邵俊,LiCl玻璃体中的微观空洞.分子动力学模拟的研究[J],科学通报,1991,No.1:38-40
[24]邵俊,汤正诠,LiCl急冷玻璃形成过程中微观空洞及其分布的分子动力学模拟[J],物理化学学报,1991,Vol.7(5):553-557
[25]A.H.Tissen,Precipitaiton average for large area[J],Monthly Weather Rev.,1911,Vol.39:1082-1084
[26]G.L.Dirichler,Uber die reduction der positiven quadraischen formen mit drei unbestimmten ganzen zalen[J],J.Reine u.Angew.Math,Vol.40:209-227
[27]A.Okabe,B.Boots,et al.,Spatial Tessellations:Concepts and Applications of Voronoi Diagrams[J],John Wiley Sons,Chicherster,West Sussex,England,1992
[28]J.D.Boissonnat,M.Yvinee,Algorithmic Geometry[M],Cambridge University Press,Cambridge,U.K,1998
[29]F.Preparata,M.Shamos,Computational Geometry:An Introduction[M],SpringerVerlag,USA,1985
[30]V.Klee,On the complexity of d-dimensional Voronoi diagram[J],Archiv der mathematic,1980,Vol.34:75-80
[31]周培德,计算几何—算法设计与分析(第2版)[M],清华大学出版社,北京,2005
[32]C.Lawson,Software for surface interpolation,Mathematical software Ⅲ[M],Academic Press,New York,NY,USA,1977
[33]V.Rijan,Optimality of the Delaunay trigulation in,in proceedings of the 7th Annual ACM Symposium on Computaional Geometry,1991,357-372
[34]D.Schmitte,J.Sphner,On equiangularity of Delaunay diagrams in every dimention,in pro- ceedings of the 5th Canandian Conference on Computational Geometry,Waterloo,Cannada,346-351
[35]S.V.Anishchik,N.N.Mdvedev,Three-Dimensional Apollonian Packing as a Model for Dense Granular Systems[J],Phys Rev Lett,1995,Vol.75(23):4314-4317
[36]N.N.Medvedev,V.P.Voloshin,et al.,An Algorithm for Three-Dimensional Voronoi S-Network[J],Wiley Periodicals,Inc,2006
[37]V.A.Luchnikov,N.N.Medvedev et al.,Voronoi-Delaunay analysis of voids in systems of nonspherical particles[J],Phys Rev E,1999,Vol.59(6):7205-7212
[38]B.N.Delaunay,Peterburgskaja Shkola Teorii Chisel(Academy of Sciences of USSR,Moscow,1947)
[39](a)F.G.Fumi,M.P.Tosi,Ionic sizes and born repulsive parameters in the Nacl-Type alkalihalide-Ⅰ[J],J.Phys.Chem.Solids,1964,Vol.25:31-34
(b)M.P.Tosi,F.G.Fumi,Ionic sizes and born repulsive parameters in the Nacl-Type alkalihalide-Ⅱ[J],J.Phys.Chem.Solids,1964,Vol.25:45-52
[40]M.Hemmati,C.A.Angell,J.Non-Cryst.Solids,1997,Vol.217:236-249
[41]M.P.Allen,D.J.Tildesley,Computer Simulation of Liquids[M],Oxford:Oxford Univ.Press,1986:80
[42]F.Aurenhammer,R.Klein,In Handbook of computational Geometry[M];J.Sack,G.Urrutia,Eds,Elseier:Amsterdam,2000;Ch.5:201-290
[43]M.Gavrilova,J.Rokne,Swap conditions for dynamic Voronoi diagram for circles and segments.J Comput Aided Geom Des,1998,Vo1.16:89
[44](a) M.I.Karavelas,I.Z.Emiris,Prototype implementation for the planar additively weighted voronoi diagrams;Technical Report ECGTR-122201-01,INRIA Sophia-Antipolis,2002
(b) M.I.Karavelas,I.Z.Emiris,Project PRISME 2004
[45]F.Anton,D.Kirkpatrick,et al,The fourteenth Canadian Conference on Computational Geometry,Lethbrdge,AB,Canada,August 2002,72-76
[46](a) D.S.Kim,D.Kim,et al.,J Comput Aided Geom Des 2001,Vo1.18:541
(b) D.S.Kim,D.Kim,et al.,J Comput Aided Geom Des 2001,Vo1.18:563
[47]N.N.Medvedev,The Algorithm for Three-Dimensinal Vorooi Polyhedra[J],J Compu Phys,1986,Vol.67:223-229
[48]M.Gavrilova,J.Rokne,J Comput Aided Geom Des,2003,Vol.20:231
[49]M.Gavrilova,Ph.D.Thesis,Department of Computer Science,The University of Calgary,Calgary,AB,Canada,1999
[50]M.Gavrilova,Proceedings of the fourteenth Canadian Conference on Computational Geometry,Lethbrdge,AB,Canada,August 2002,82-87
[51]D.S.Kim,Y.Cho,et al.,J Comput Aided Geom Des 2005,Vol.37:1412
[52]P.Richard,L.Oger,et al.,Gervois,A.Eur Phys J E,2001,Vol.6:295
[53]P.L.Spedding,R.M.Spencer.Simulation of packing density and liquid flow of mixed beds,Ⅱ Voronoi polyhedra studies[J],Comput.Chem.Eng.,1998,Vol.22(1-2):247-257
[54]K.Tsumuraya,Voronoi polyhedron analyses in metal liquids and glasses,Voronoi's impact on modern scene[M].Book 2/Ed.P.Engl,H.Syta/Inst.of Math.Kiev,1998,176-185
[55]M.Liska,P.Perrichta,et al.,The structure of molecular dynamics simulated oxide glasses viewed through Voronoi polyhedron tessellation[J],J.Non-Cryst.Solid,1995,Vo1.193:249-252
[56]B.Vessal,M.Amini,et al.,Simulaiton and characterization of the structure of vitreous silica[J],Mol.Simulation,1995,Vo1.15(2):123-127
[57]E.E.David,C.W.David,Voronoi polyhedron as a tool for studying salvation structure[J],J.Chem.Phys,1982,Vol.76(9):123-127
[58]N.W.Thomas,An extantion of the Voronoi analysis of crystal structures[J],Acta Crys.B.Structure Sci.1996.Vol.52(6):939-953
[59]M.I.Mendelv,et al.,Partial structure correlations in amorphous NiS3LalT[J],Non-Cryst.Solids,1998,Vol.240(1-3):35-42
[60]A.E.Galasyev,Molecular dynamics study of FCC-BCC transition by the crystallization of liquid sodium[J],Kristallographia,1998,Vol.43(4):739-744
[61]J.L.Meijering,Interface area,edge length,and number of vertices in crystal aggregates with random sodium[J],Phillips Res.Rep,1953,Vol.8:270-290
[62]N.L.Lavnik,et al.,On the probability density distribution of the nearest neighbors of molecules,Russian Journal of physical chemistry,1996,Vol.70(6):1140-1142
[63]J.L Finney,Random pckings and the structure of simple liquids,Ⅰ.The geometry of random close packing[J],Roy.Soc.London,1970,Vol.319:479-494
[64]V.A.Luchinikov,N.N.Medvedev,et al.,Medium-range order of amorphous silicon studied by the V-D method[J],Mol.Phys,1996,Vol.88:1337-1348
[65]J.P.Troadec,A.Gervois,et al.,Statistic of Voronoi cells of slightly perturbed face centered cubic and hexagonal close-packed lattices[J],Europhys.Lett.1998,Vol.42(2):167-172
[66]江泽涵,多面体的欧拉定理和闭曲面的拓扑分类[M],人民教育出版社,1979
[67]S.Kumar,S.K.Kurta,et al.,Properties of a three-dimenstional Possion -Voronoi tessella-tion:A Monte Carlo Study[J].J.State.Phys,1992,Vol.67(3/4):523-551
[68]M.Kimura,et al.,Nature of amorphous and liquid structure computer simulation and statistical geometry[J].Journal of Non-Crystalline Solids,1984,v.61-62,p.535-540
[69]N.N.Medvedev,et al.,Analusis of perturbated crystal packing[J],Russian Journal of structural chemistry,1985,Vol.26(3):59-67
[70]A.Gaiger,et al.,Structure of stable and metastable water[J],Russian Journal of structural chemistry,1992,T.33(2):79-87
[71]W.Brostow,W.Chybicki,et al.,Voronoi polyhedra and Delaunay simplexes in the structure analysis of molecular-dynamics-simulated materials[J],Phys.Rev.B.,1998,Vol.57(21):13448-13452
[72]G.B.Bokii,Crystal Chemistry[M],Moscow University Press,1960
[73]B.K.Bernstain,Morden Crystaalography[M],Science Press,1979
[74]V.P.Voloshim,Y.I.Naberukhin,et al.,Can varois classes of atomic configuration(Delaunay Simplices) be distinguished in random dense packing of spherical particles?[J],Molecular Sire,1989,Vol.4:209-227
[75]N.N.Medvedev,Y.I Naberukhin,Shape of the Delaunay simplices in dense random packings of hard and soft spheres[J].J.Non-Cryst.Solids,1987,Vol.94:402-406
[76]V.A.Luchnicov,N.N.Medvedev,et al.,Inhomogeneity of the spatial distribution of vibrational modes in a computer model of amorphous argon[J].,Phys.Rev.E.,1995,Vol.51(21):15569-15572
[77]N.N.Medvedev,et al.,On the problem of isohedral coordination of simple liquids[J],Melts,1986,Vol.27(4):91-97
[78]S.R.Broadbent,J.M.Hammersley,Percolation process,Ⅰ.Crysals and mazes;Ⅱ.The connective constant[J],Cambridge Phil Soc,1957,Vol.53:629-645
[79]N.N.Medvedev,V.P.Volshin,et al.,Structure of simple liquids as percolation problem on Voronoi networks[J],J.Phys.A:Math.Gen.21,1988,L247-L252
[80]Y.I.Naberukhin,V.P.Volshin,et al.,Geometrical analysis of the structure of simple liquids:Percolation approach[J],Molec.Phys,1991,Vol.73(4):917-936
[81]钟正,樊启斌,张也挺,3维离散数据四面体快速生成算法研究[J],测绘学院学报,2004,Vol.21(4):286-288
[82]K.Ridgwaw,K.J.Turbuk,The random packing of spheres[J],British Chem.Eng.,1967,Vol 12(3):384-388
[83]J.Dodds,M.Leitzelement,The relation of the structure of packing of particles and their properties[J],Proc.Of winter school,Les Houches,France,1985/Eds.N.Boccara,Berlin, Spring-Verlag,1985
[84]G.Mason,Mobilization of oil bolbs in the pore space of a random sphere pcking[J],Chem.Eng.Sci.,1983,Vol38(9):1455-1460
[85]S.Bryant,M.Blunt,Phys Rev.A,1992,Vol.46:2004
[86]S.Bryant,G.Mason,et al.,J.Colloid Interface Sci,1996,Vol.177:88
[87]K.E.Thompson,H.S.Fogler,AIChE.J,1997,Vol.43:1377
[88]P.Richard,L.Oger,et al.,Grannular Matter[J],Springer-Verlag,Berlin,1999,Vol.1:203-211
[89]R.Bieshaar,A.Geiger,et al.,Calculation of chemical potential by a novel Delaunay-Simplex-Sampling technique for particle insertion[J],Mol.Simul,1995,Vol.15:189-196
[90]N.N.Medvedev,Y.I.Naberukhin,et al.,Geometry of empty space inside of granular system,Proc.of Ⅵth IEP conf,"Physical chemistry of collids and interfaces in oil prduction",Eds H.Toulhoat,J.Lecourtier.Paris,1992,355-356
[91]丘曹勇,GeO_2玻璃体中微观空洞和Delaunay单纯形的计算和研究—瞬时构型的数据挖掘,上海大学硕士学位论文,2005
[92]S.Sastry,S.C.David,et al.,Statisical geometry of particle packing.Ⅰ.Algorithm for exact determination of connectivity,Volume and surface of void space in monodisnerse and polydispers sphere packings[J],Physsical Review E,1997,Vol.56(3):5524-5532
[93]S.Sastry,M.T.Thomas,et al.,Free Volume in the hard sphere liquid[J].Mol.Phy.,1998,Vol.95(2):289-297
[94]A.Vishnyakov,V.N.Alexander,et al.,Statistical geometry of cavities in a metastable confined fluid[J],Phy.Rev.E.,2000,Vol.62(1):538-544
[95]M.G.Alincheneko,et al.,Effect of Cholesteral on the Properties of Phospholispid Membranes.4.Interatomic Voids[J].J.Phys.Chem.B,2005,Vol.109:16490-16502