第一性原理方法研究PdSn2材料终端总能及占位分析并对比摘要：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 (C e) StructurePrimitive Vectors:A1 = a XA2 = ½ b Y - ½ c ZA3 = ½ b Y + ½ c Z•Basis Vectors:B1 = - z1A2 + z1A3 = + z1 c Z (Pd-I) (4a) B2 = + ½ A2 + (½ - z1) A2 + (½ + z1) A3 = + ½ a X + ½ b Y + z1 c Z (Pd-I) (4a) B3 = - z2A2 + z2A3 = + z2 c Z (Pd-II) (4a) B4 = + ½ A2 + (½ - z2) A2 + (½ + z2) A3 = + ½ a X + ½ b Y + z2 c Z (Pd-II) (4a) B5 = + x3A1 + (y3 - z3) A2 + (y3 + z3) A3 = + x3 a X + y3 b Y + z3 c Z (Sn-I) (8b) B6 = - x3A1 - (y3 + z3) A2 - (y3 - z3) A3 = - x3 a X - y3 b Y + z3 c Z (Sn-I) (8b)B7 = + (x3 - ½) A1 + (½ - y3 - z3) A2 + (½ - y3 + z3)A3 = + (x3 - ½) a X + (y3 + ½) b Y + z3c Z(Sn-I) (8b)B8 = + (½ - x3) A1 + (y3 - z3 - ½) A2 + (y3 + z3 +½) A3 = + (½ - x3) a X + (y3 - ½) b Y + z3 cZ(Sn-I) (8b)B9 = + x4A1 + (y4 - z4) A2 + (y4 + z4) A3 = + x4 a X + y4 b Y + z4 c Z (Sn-II) (8b) B10 = - x4A1 - (y4 + z4) A2 - (y4 - z4) A3 = - x4 a X - y4 b Y + z4 c Z (Sn-II) (8b)B11 = + (x4 - ½) A1 + (½ - y4 - z4) A2 + (½ - y4 + z4)A3 = + (x4 - ½) a X + (y4 + ½) b Y + z4c Z(Sn-II) (8b)B12 = + (½ - x4) A1 + (y4 - z4 - ½) A2 + (y4 + z4 +½) A3 = + (½ - x4) a X + (y4 - ½) b Y + z4 cZ(Sn-II) (8b)2 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m0、波尔兹曼常数kB)，原子序数，而不依赖任何经验参数即可合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，它使用赝势和平面波基组，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方法或超软赝势，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、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 vasp>r31& ,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”*-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“vasp>rf&,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vasp>LOG-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vasp>LOG-BAND&4.计算结果与讨论Primitive vectorsa(1) = 6.47800000 0.00000000 0.00000000a(2) = 0.00000000 3.23900000 -6.07750000a(3) = 0.00000000 3.23900000 6.07750000Volume = 255.03915151Basis Vectors:Atom Lattice Coordinates Cartesian CoordinatesPd 0.00000000 -0.01000000 0.01000000 0.00000000 0.00000000 0.12155000Pd 0.50000000 0.49000000 0.51000000 3.23900000 3.23900000 0.12155000Pd 0.00000000 -0.23800000 0.23800000 0.00000000 0.00000000 2.89289000Pd 0.50000000 0.26200000 0.73800000 3.23900000 3.23900000 2.89289000Sn 0.34200000 0.03300000 0.28300000 2.21547600 1.02352400 1.51937500Sn -0.34200000 -0.28300000 -0.03300000 -2.21547600 -1.02352400 1.51937500Sn -0.15800000 0.21700000 0.46700000 -1.02352400 2.21547600 1.51937500Sn 0.15800000 -0.46700000 -0.21700000 1.02352400 -2.21547600 1.51937500Sn 0.25000000 0.37500000 0.12500000 1.61950000 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 -0.37500000 1.61950000 -1.61950000 -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) in text, eV/atomS i t e o c c u p a n c y f r a c t i o nT/KT/KS i t e o c c u p a n c y f r a c t i o nS i t e o c c u p a n c y f r a c t i o nT/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+02Total Gibbs energy -7.07126E+03, Enthalpy -6.47479E+03, Volume 0.00000E+00 Component Moles W-Fraction Activity Potential Ref.StatePB 6.6700E-01 8.0131E-01 6.1632E-01 -6.0361E+03 SERRH 3.3300E-01 1.9869E-01 4.8036E-01 -9.1446E+03 SERPDSN2#1 STATUS ENTERED Driving force 0.0000E+00 Number 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 9.8697E-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 0Temperature 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+00 Component Moles W-Fraction Activity Potential Ref.StatePB 6.6700E-01 8.0131E-01 5.9447E-01 -6.0539E+03 SERRH 3.3300E-01 1.9869E-01 4.6134E-01 -9.0051E+03 SERPDSN2#1 STATUS ENTERED Driving force 0.0000E+00 Number 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 4.2077E-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 Component Moles W-Fraction Activity Potential Ref.StatePB 6.6700E-01 8.0131E-01 5.7127E-01 -6.0518E+03 SERRH 3.3300E-01 1.9869E-01 4.3759E-01 -8.9332E+03 SERPDSN2#1 STATUS ENTERED Driving force 0.0000E+00 Number 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 9.9361E-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 components 1.00000E+00, Mass 1.72470E+02Total Gibbs energy -6.99366E+03, Enthalpy -6.82206E+03, Volume 0.00000E+00 Component Moles W-Fraction Activity Potential Ref.StatePB 6.6700E-01 8.0131E-01 5.4781E-01 -6.0047E+03 SERRH 3.3300E-01 1.9869E-01 4.0678E-01 -8.9745E+03 SERPDSN2#1 STATUS ENTERED Driving force 0.0000E+00 Number 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, 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+00 Component Moles W-Fraction Activity Potential Ref.StatePB 6.6700E-01 8.0131E-01 5.2694E-01 -5.8595E+03 SERRH 3.3300E-01 1.9869E-01 3.6448E-01 -9.2309E+03 SERPDSN2#1 STATUS ENTERED Driving force 0.0000E+00 Number 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 Number 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 -6.92255E+03, Volume 0.00000E+00 Component 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 8.01313E-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, /aboutus/[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] 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