材料计算与设计结业论文

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1、第一性原理方法研究PdSn材料终端总能及占位分析并对比2摘要：综合运用所学材料科学与工程知识，通过vasp软件对二元合金进行结构优 化，求出基态下的平衡晶胞参数，如晶格常数，晶轴间夹角，材料的能态密度等等， 并与参考文献进行对比。1 PdSn2(Ce )结构参数The PdSn2 (Ce)StructurePrimitive Vectors:A1 = a XA2 = % b Y - % c ZA3 = % b Y + % c ZBasis Vectors:B1=- z1A2 +z1A3=+z1 c Z(Pd-I)(4a)B2=+ % A2+ (% -z1)A2 +(%+ z1) A3=+ %

2、a X + % b Y +z1 cZ(Pd-I)(4a)B3=- z2A2 +z2A3=+z2 c Z(Pd-ll)(4a)B4=+ % A2+ (% -z2)A2 +(%+ z2) A3=+ % a X + % b Y +z2 cZ(Pd-ll)(4a)B5=+ x3 A1+ (y3 -z3)A2 +(y3+ z3) A3=+ x3 a X + y3 b Y +z3 cZ(Sn-I)(8b)B6=- x3A1-(y3+ z3) A2- (y3 -z3)A3=- x3a X - y3 b Y +z3c Z (Sn-I)(8b)B7= +(x3 -%) A1+ (% -y3 - z3) A2+

3、(% -y3 + z3)= + (x3 - %) a X +(y3+ %) b Y + z3(Sn-I) (8b)A3c ZB8= + (%- x3) A1+ (y3 - z3 - %)A2 +(y3+ z3 += + (%- x3)a X + (y3 - %) b Y + z3c (Sn-I) (8b)%) A3ZB9=+ x4 A1+ (y4 -z4)A2 +(y4+ z4) A3=+ x4a X + y4 b Y +z4c Z (Sn-II) (8b)Bio=- X4Al-(Y4+ zj A2-(Y4 - zjA3=- X4a X -庆 b Y +z4c Z (Sn-II) (8b)B1

4、1 = + (x4 - %) A1 + (% - y4 - z4) A2 + (% - y4 + z4) = + (x4 - %) a X + (y4 + %) b Y + z4 (Sn-II) (8b)A3C ZB12 = + (% - x4) A1 + (y4 - z4 - %) A2 + (y4 + z4 + = + (% - x4) a X + (y4 - %) b Y + z4 c (Sn-ll) (8b)%) A3Z2 第一性原理计算方法第一性原理就是从头计算，不需要任何参数，只需要一些基本的物理常量，就 可以得到体系基态的基本性质的原理。第一性原理通常是跟计算联系在一起的，是 指

5、在进行计算的时候除了告诉程序你所使用的原子和他们的位置外，没有其他的实 验的，经验的或者半经验的参量，且具有很好的移植性。从头算(ab initio)是狭 义的第一性原理计算，它是指不使用经验参数，只用电子质量，光速，质子中子质 量等少数实验数据去做量子计算。第一性原理方法(First-principle calculations) 或者叫从头算起法(ab initio)仅需采用五个基本物理常数(普朗克常数h、电荷e、 光速c、电子质量mO、波尔兹曼常数k)，原子序数，而不依赖任何经验参数即可合B 理预测微观体系的状态和性质，比如总能、晶体结构和电子结构等，进而计算构型 能、生成热和相变热等热

6、力学性质。本实验的计算都是通过计算材料学软件VASP运算完成，它使用贋势和平面波基 组，进行从头量子力学分子动力学计算，基于有限温度下的局域密度近似(用自由能 作为变量)以及对每一 MD步骤用有效矩阵对角方案和有效Pulay混合求解瞬时电子 基态。使用PAW方法或超软贋势，因此基组尺寸非常小，描述体材料一般需要每原子 不超过100个平面波，大多数情况下甚至每原子50个平面波就能得到可靠结果。它 采用周期性边界条件处理原子、分子、团簇、薄膜、晶体、准晶和无定性材料，以及 表面体系和固体，可以计算材料的结构参数(键长,键角,晶格常数，原子位置等)和构 型以及材料的电子结构(能级、电荷密度分布、能带

7、、电子态密度和ELF)等。3 第一性原理计算步骤A、进入系统，将模版文件夹解压到桌面。建立自己的文件目录，将模板中文件夹内容 拷到自己的文件夹，将化合物修改成MnP,然后进入-R31,在相应的势函数库中 寻找元素的POTCAR，将计算文件夹-R31中的POTCAR中内容换成自己的化合物元 素的POTCAR内容之和。按下面的步骤进行计算。B、先打开*-r31文件夹，点击右键，打开“终端”运行界面，输入vaspr31 & , 然后回车，计算开始执行。(进行晶胞参数优化)C、3-5分钟后敲击回车键，等待运行完毕，出现“ * done “。将R32或r31文 件夹中除INCAR外的所有文件拷贝到”*-

8、rf “文件夹中，右键点击出现”终端“， 然后输入” cp CONTCAR POSCAR，回车，输入“y”确认。(即将CONTCAR中内 容拷贝到POSCAR中，使得本次计算的初始晶胞参数是在前一次r31或R32计算 结果的基础上进行。)然后输入“ vasprf&,等待完成。D、将*-rf文件夹中所有内容(除 INCAR )拷贝到*-DOS文件夹，终端运行 vaspLOG-DOS&,E、将*-rf文件夹中所有内容（除INCAR, KPOINTS）拷贝到*-BAND文件夹，终端 运行 vaspLOG-BAND&4. 计算结果与讨论Primitive vectorsa(1) =6.47800000

9、0.00000000 0.00000000a(2) = 0.00000000a(3) = 0.000000003.23900000 -6.077500003.23900000 6.07750000Volume = 255.03915151Basis Vectors:Cartesian CoordinatesAtom Lattice CoordinatesSn -0.15800000 0.21700000 0.46700000-1.02352400 2.21547600 1.51937500Sn 0.15800000 -0.46700000 -0.217000001.02352400 -2.21

10、547600 1.51937500Sn 0.25000000 0.37500000 0.125000001.61950000 1.61950000 -1.51937500Sn -0.25000000 -0.12500000 -0.37500000-1.61950000 -1.61950000 -1.51937500Sn -0.25000000 0.37500000 0.12500000-1.61950000 1.61950000 -1.51937500Sn 0.25000000 -0.12500000 -0.375000001.61950000 -1.61950000 -1.51937500P

11、d0.00000000 -0.010000000.010000000.000000000.000000000.12155000Pd0.500000000.490000000.510000003.239000003.239000000.12155000Pd0.00000000 -0.238000000.238000000.000000000.000000002.89289000Pd0.500000000.262000000.738000003.239000003.239000002.89289000Sn0.342000000.033000000.283000002.215476001.02352

12、4001.51937500Sn -0.34200000 -0.28300000 -0.03300000-2.21547600 -1.02352400 1.519375005. The total energies of the stable elements and the end-member compounds of the O phase based on Ti2AlNb with the sublattice model described in Formula (1) intext, eV/atomElementEtotElementEtotElementEtot(a) Pure e

13、lementsCo-6.8886Cu-3.7179Ni-5.5143Pb-3.5733Rh-7.2694(b) End-member compoundsEnd-memberEtotEnd-memberEtotEnd-memberEtotCo:Co-19.369Ni:Co-18.4471Rh:Co-20.2193Co:Cu-12.8351Ni:Cu-11.9812Rh:Cu-13.3822Co:Ni-16.7227Ni:Ni-15.3607Rh:Ni-16.9011Co:Pb-13.3157Ni:Pb-12.4051Rh:Pb-14.6327Co:Rh-20.4498Ni:Rh-18.933Rh

14、:Rh-20.7571Cu:Co-16.7069Pb:Co-15.991Cu:Cu-10.5729Pb:Cu-10.2548Cu:Ni-13.4544Pb:Ni-14.0112Cu:Pb-10.4188Pb:b-10.3386Cu:Rh-17.347Pb:Rh-17.5235noitcarfycnapuccoeti1.0noitcarfycnapuccoetiSRh0.3Pb0.6Co0.1 yCo4ayPb4a电 yRh4ayCo8bT yPb8byRh8bnoitcarfycnapuccoetiS864000200 400 600 800 1000 1200 1400 1600T/KY T

15、Rh0.3Pb0.6Cu0.1yCu4al yPb4a yRh4a yCu8b yPb8b yRh8b020040060080010001200T/K6. TCW 计算：Output from POLY-3Database: USER CMCConditions:T=1500, P=100000, N=1, X(RH)=3.33E-1DEGREES OF FREEDOM 0Temperature 1500K (1227C, 2240F), Pressure 1.000000E+05Number of moles of components 1.00000E+00, Mass 1.72470E+

16、02Total Gibbs energy -7.07126E+03, Enthalpy -6.47479E+03, Volume 0.00000E+00Component Moles W-Fraction Activity Potential Ref.StatePB6.6700E-01 8.0131E-01 6.1632E-01 -6.0361E+03 SERRH3.3300E-01 1.9869E-01 4.8036E-01 -9.1446E+03 SERPDSN2#1 STATUS ENTEREDDriving force 0.0000E+00Number of moles 1.0000E

17、+00, Mass 1.7247E+02Mass fractions:PB 8.01313E-01 RH 1.98687E-01Constitution:Sublattice 1 Number of sites 0.33RH 9.8697E-01 PB 1.3027E-02Sublattice 2 Number of sites 0.67PB 9.9394E-01 RH 6.0623E-03Output from POLY-3Database: USER CMCConditions:T=1400, P=100000, N=1, X(RH)=3.33E-1DEGREES OF FREEDOM 0

18、Temperature 1400K (1127C, 2060F), Pressure 1.000000E+05Number of moles of components 1.00000E+00, Mass 1.72470E+02Total Gibbs energy -7.03664E+03, Enthalpy -6.62041E+03, Volume 0.00000E+00Component Moles W-Fraction Activity Potential Ref.StatePB6.6700E-01 8.0131E-01 5.9447E-01 -6.0539E+03 SERRH3.330

19、0E-01 1.9869E-01 4.6134E-01 -9.0051E+03 SERPDSN2#1 STATUS ENTEREDDriving force 0.0000E+00Number of moles 1.0000E+00, Mass 1.7247E+02Mass fractions:PB 8.01313E-01 RH 1.98687E-01Constitution:Sublattice 1 Number of sites 0.33RH 9.9068E-01 PB 9.3167E-03Sublattice 2 Number of sites 0.67PB 9.9579E-01 RH 4

20、.2077E-03Output from POLY-3Database: USER CMCConditions:T=1300, P=100000, N=1, X(RH)=3.33E-1DEGREES OF FREEDOM 0Temperature 1300K (1027C, 1880F), Pressure 1.000000E+05Number of moles of components 1.00000E+00, Mass 1.72470E+02Total Gibbs energy -7.01129E+03, Enthalpy -6.73543E+03, Volume 0.00000E+00

21、Component Moles W-Fraction Activity Potential Ref.StatePB6.6700E-01 8.0131E-01 5.7127E-01 -6.0518E+03 SERRH3.3300E-01 1.9869E-01 4.3759E-01 -8.9332E+03 SERPDSN2#1 STATUS ENTEREDDriving force 0.0000E+00Number of moles 1.0000E+00, Mass 1.7247E+02Mass fractions:PB 8.01313E-01 RH 1.98687E-01Constitution

22、:Sublattice 1 Number of sites 0.33RH 9.9361E-01 PB 6.3949E-03Sublattice 2 Number of sites 0.67PB 9.9725E-01 RH 2.7470E-03Output from POLY-3Database: USER CMCConditions:T=1200, P=100000, N=1, X(RH)=3.33E-1DEGREES OF FREEDOM 0Temperature 1200K (927C, 1700F), Pressure 1.000000E+05Number of moles of com

23、ponents 1.00000E+00, Mass 1.72470E+02Total Gibbs energy -6.99366E+03, Enthalpy -6.82206E+03, Volume 0.00000E+00Component Moles W-Fraction Activity Potential Ref.StatePB6.6700E-01 8.0131E-01 5.4781E-01 -6.0047E+03 SERRH3.3300E-01 1.9869E-01 4.0678E-01 -8.9745E+03 SERPDSN2#1 STATUS ENTEREDDriving forc

24、e 0.0000E+00Number of moles 1.0000E+00, Mass 1.7247E+02Mass fractions:PB 8.01313E-01 RH 1.98687E-01Constitution:Sublattice 1 Number of sites 0.33RH 9.9580E-01 PB 4.1989E-03Sublattice 2 Number of sites 0.67PB 9.9835E-01 RH 1.6492E-03Output from POLY-3Database: USER CMCConditions:T=1100, P=100000, N=1

25、, X(RH)=3.33E-1DEGREES OF FREEDOM 0Temperature 1100K (827C, 1520F), Pressure 1.000000E+05Number of moles of components 1.00000E+00, Mass 1.72470E+02Total Gibbs energy -6.98215E+03, Enthalpy -6.88327E+03, Volume 0.00000E+00Component Moles W-Fraction Activity Potential Ref.StatePB6.6700E-01 8.0131E-01

26、 5.2694E-01 -5.8595E+03 SERRH3.3300E-01 1.9869E-01 3.6448E-01 -9.2309E+03 SERPDSN2#1 STATUS ENTEREDDriving force 0.0000E+00Number of moles 1.0000E+00, Mass 1.7247E+02Mass fractions:PB 8.01313E-01 RH 1.98687E-01Constitution:Sublattice 1 Number of sites 0.33RH 9.9735E-01 PB 2.6497E-03Sublattice 2 Numb

27、er of sites 0.67PB 9.9913E-01 RH 8.7470E-04Output from POLY-3Database: USER CMCConditions:T=1000, P=100000, N=1, X(RH)=3.33E-1DEGREES OF FREEDOM 0Temperature 1000K (727C, 1340F), Pressure 1.000000E+05Number of moles of components 1.00000E+00, Mass 1.72470E+02Total Gibbs energy -6.97516E+03, Enthalpy

28、 -6.92255E+03, Volume 0.00000E+00Component Moles W-Fraction Activity Potential Ref.StatePB 6.6700E-01 8.0131E-01 5.1630E-01 -5.4965E+03 SERRH 3.3300E-01 1.9869E-01 3.0266E-01 -9.9369E+03 SERPDSN2#1 STATUS ENTERED Driving force 0.0000E+00Number of moles 1.0000E+00, Mass 1.7247E+02Mass fractions:PB 8.

29、01313E-01 RH 1.98687E-01Constitution:Sublattice 1 Number of sites 0.33RH 9.9834E-01 PB 1.6568E-03Sublattice 2 Number of sites 0.67PB 9.9962E-01 RH 3.7827E-04参考书目：1 张朝晖，吴波.计算机在材料科学与工程中的应用M.长沙：中南大学出版社, 2008:130-135.2 福州大学材料学院多尺度材料设计与应用实验室, 3 无机材料晶体结构数据库, http:/icsd.ill.eu/icsd/index.php.4 韦丹，固体物理M.北京：清华大学出版社，2007.5 刘静安.挤压模具技术的理论与实践M.重庆：科学技术文献出版社重庆分社.1989.6 谷兰成.陈学同.我国铝型材挤压业的现状及未来J.山东冶金，1998, 20(4)： 1620.7 刘汉武，丁桦，崔建忠.铝型材挤压分流组合模型有限元分析与计算J.模具工 业.1999(4)：911.8 孟凡中.弹塑性有限变形理论和有限元法M.北京：清华大学出版社，1985.9 周飞，彭颖红.阮学榆.铝型材挤压过程有限元数值模拟J.中国有色金属学报，1998, 8(4)：637643.