1、分子动力学实验 SJTU.CMS. April 2012 1. 空位形成能 2. 表面、界面能 3. 层错能 4. 晶格常数与体弹模量 5. 熔化You and Your Computer你手机的计算能力，已经超越了 NASA 1969 年 拥有的计算能力的总和。NASA 用那些计算能力 发射人上了月球，而你用更强的计算能力发射 愤怒的小鸟去砸猪。Linux分子动力学五要素 1. 粒子间相互作用势 2. 初始条件 3. 边界条件 4. 求解牛顿运动方程 5. 粒子运动轨迹LAMMPS Molecular Dynamics Simulator AtomEye: atomistic configu
2、ration viewerpwd pwd print name of working directory mkdir mkdir haha make directory cd cd haha change directory cd upper directory cd back home gedit gedit a edit a file cat cat a concatenate files ls ls list cp cp a b copy file a to file b cp r AB copy a file folder rm rm b remove Tab * Basic Linu
3、x Commands NAME SYNOPSIS DESCRIPTION1. 空位形成能Point Defects: Vacancy Model system: Cu, fcc, a 0 = 3.61 Tasks: 1. generate a point defect within an equilibrium lattice 2. calculate the formation energy Model system Cu Initial conditions fcc lattice defect-free state, vacancy Supercell N, PBCs Interatom
4、ic potentials EAM (Cu) Ensembles Minimize(1) Copy the file folder to home and then get into it. $ cp -r share/md . $ cd md $ cd 1_vacancy $ ls (2) What is the setup in input file $ gedit in.vacancy (3) Run LAMMPS $ lmp -in in.vacancy (4) After running, view the configuration $ A.i686 a0.cfg (5) View
5、 the result data $ cat dataTa b 键 切换视角 k, Alt + H, Alt + +/- 改变颜色 Delete / Insert 下一帧/上一帧 PgUp / PgDn 原子变大/变小 滚轮 放大/缩小 方向键 旋转 q 关闭 Atomeye 命令units metal boundary p p p atom_style atomic lattice fcc 3.61 region box block 0 6 0 6 0 6 create_box 1 box create_atoms 1 box pair_style eam/alloy pair_coeff
6、* * jin_copper_lammps.setfl Cu timestep 0.005 variable E equal pe variable N equal atoms compute pe all pe/atom dump 1 all cfg 1 a*.cfg id type xs ys zs c_pe run 0 fix extra all print 1 “pefect lattice, 0K: atoms = $N, energy = $E“ region centerpoint block 3 3.05 3 3.05 1 1.05 delete_atoms region ce
7、nterpoint run 0 fix extra all print 1 “ an atom deleted, 0K: atoms = $N, energy = $E“ 周期边界条件 指定fcc晶体 box大小 Cu的EAM势 删除一个原子Vacancy formation energy： 1 pefect lattice, 0K: atoms = 864, energy = -3015.371512 2 an atom deleted, 0K: atoms = 863, energy = -3010.585469 3 after minimization: atoms = 863, ene
8、rgy = -3010.6240332. 表面、界面能Planar Defects: Surface and Grain Boundary Model system: Cu, fcc, a 0 = 3.610 Tasks: 1. Surface energies of (111) and (100); 2. Grain boundary energiesModel system Cu Initial conditions T, P Supercell N, PBCs Interatomic potentials EAM (Cu) Ensembles MinimizeSurface energy
9、: Method perfect region vacuum 2 surfaces N 0 atoms, E 0 N atoms, E S = (E E 0 *N/N 0 ) / (2*A) h 1 h 3 h 2 (111) Surface: h 1 = a 0 /211-2*L 1 ; h 2 = a 0 /2-110*L 2 ; h 3 = a 0 111*L 3 (100) Surface: h 1 = a 0 100*L 1 ; h 2 = a 0 010*L 2 ; h 3 = a 0 001*L 3Surface energy: Calculations perfect: N 0
10、 = 123772, E 0 = 431965.9291 eV (111): N S1 = 124722, E S1 = 434642.1217 eV , A S1 = 39.792*104.659 2 (100): N S2 = 123772, E S2 = 431275.1878 eV , A S2 = 39.71*104.69 2 S1 = (E S1 E 0 *N S1 /N 0 )*16020 / (2*A S1 ) = 1230 mJ/m 2 S2 = (E S2 E 0 *N S2 /N 0 )*16020 / (2*A S2 ) = 1331 mJ/m 2Grain bound
11、ary energy S1:(111) GB = (E E 0 *N/N 0 ) / A S1 S2 h 3 region2 vacuum h 1 h 2 region1 S2:(100) GB GB+S1+S2: N = 248494, E = 866449.3465 eV , A = 39.755*104.677 2 GB = (E E 0 *N/N 0 )*16020 / A S1 S2 = 512 mJ/m 2a 1 a 2 a 3 a 1 a 2 a 3 region 1: a 1 = a 0 /211-2; a 2 = a 0 /2-110; a 3 = a 0 111 regio
12、n 2: a 1 = a 0 100; a 2 = a 0 010; a 3 = a 0 001(1) Change into the 2 nd directory $ cd /2_surface_boundary $ ls (2) What is the commands in bash file $ cat run.sh (3) Run bash file $ ./run.sh (4) After running, view the configuration $ A.i686 a0.cfg#!/bin/bash lmp in.100 log log.100 lmp in.111 log
13、log.111 lmp in.GB log log.GB echo “%“ echo “ “ echo “(100) “ grep log.100 echo “ “ echo “(111) “ grep log.111 echo “ “ echo “ GB “ grep log.GB echo “ “ echo “%“ run.sh% (100) Number of Particles = 11520, Energy = 40204.95349 Number of Particles = 8640, Energy = 30075.76547 Size of (100): A = 469.155
14、6 (111) Number of Particles = 46080, Energy = 160819.814 Number of Particles = 34560, Energy = 120448.5379 Size of (111): A = 1083.468448 GB Number of Particles = 248494, Energy = 866449.3465 Size of GB x*y: A = 4161.446533 % S = (E E 0 *N/N 0 ) / (2*A) Surface energy：(111) surface (100) surfaceTa b
15、 键 切换视角 k, Alt + H, Alt + +/- 改变颜色 Delete / Insert 下一帧/上一帧 PgUp / PgDn 原子变大/变小 滚轮 放大/缩小 方向键 旋转 q 关闭 Atomeye 命令h 1 h 2 h 3 region 1 region 2 vacuum 56 units 56 units box 150 units 4 Grain boundary 4.1 Model a 1 a 2 a 3 Unit cell region 1: a 1 = a 0 /211-2; a 2 = a 0 /2-110; a 3 = a 0 111 h 1 = 9*a 1
16、; h 2 = 41*a 2 ; h 3 = 56*a 3 region 2: a 1 = a 0 100; a 2 = a 0 010; a 3 = a 0 001 h 1 = 11*a 1 ; h 2 = 29*a 2 ; h 3 = 97*a 3 S1 S2 GBGrain boundary3. 层错能2 High Tensile Strength and Ductility of Cu with NanoSized Twins Lu et al., Science 287 (2000) 1463; 304 (2004) 422. dislocation fluxtwin in expe
17、rimentstwin boundary 89 118 77 56,400 atoms twin in CuTwin faults intrinsic stacking fault Extrinsic stacking fault ISF ESF TSF planar fault in FCCfree surface ESF Extrinsic stacking fault (ESF) free surfacePlanar Defects: Stacking Fault Energy Model system: Cu, Al, fcc Tasks: (1) clarify three type
18、s of planar faults in fcc metals (2) calculate stacking fault energies (3) compare: Al and CuModel system Cu, Al Initial conditions T, P Supercell N, PBCs Interatomic potentials EAM Ensembles Minimizeunits metal boundary p p p atom_style atomic read_data isf-Cu # 读取其他文件中的构型 pair_style eam/alloy pair
19、_coeff * * jin_copper_lammps.setfl Cu timestep 0.005 minimize 1.0e-8 1.0e-8 1000 1000 compute pe all pe/atom dump 1 all cfg 1 a.isf.*.cfg id type xs ys zs c_pe dump_modify 1 element Cu run 0 variable E equal pe variable N equal atoms print “- isf in Cu, E = $E -“ input file: in.isfCu#!/bin/bash lmp
20、in.isfCu lmp in.esfCu lmp in.twinCu lmp in.refCu lmp in.isfAl lmp in.esfAl lmp in.twinAl lmp in.refAl run.sh(1) Change into the 3 rd directory $ cd /3_stacking_fault $ ls (2) What is the commands in bash file $ gedit run.sh (3) Run bash file $ ./run.sh (4) After running, view the configuration $ cd
21、cfg $ ls $ A.i686 esf-Cu.a4.cfg (5) View the result data $ cat dataTa b 键 切换视角 k, Alt + H, Alt + +/- 改变颜色 Delete / Insert 下一帧/上一帧 PgUp / PgDn 原子变大/变小 滚轮 放大/缩小 方向键 旋转 q 关闭 Atomeye 命令- isf in Cu, E = -40119.62288 - - esf in Cu, E = -40119.56232 - - Twin in Cu, E = -40120.10708 - - ref of Cu, E = -4012
22、0.50995 - - - - isf in Al, E = -38615.90978 - - esf in Al, E = -38615.22202 - - Twin in Al, E = -38618.18627 - - ref of Al, E = -38621.04416 - orthogonal box = (0 0 0) to (15.3371 35.4196 269.239) orthogonal box = (0 0 0) to (17.1827 39.6817 301.637) for Cu: area (A) = 15.3371 35.4196 for Al: area (
23、A) = 17.1827 39.6817 Stacking fault energy:results usf isf 1 utf 2 utf 3 utf Displacement (b p ) 012 3 4 (mJ m -2 )4.晶格常数与体弹模量Model system Cu, Al, Si Initial conditions perfect lattice Supercell N, PBCs Interatomic potentials EAM (Cu, Al), Stilling-Weber (Si) Ensembles None (we calculate ground stat
24、e properties, 0 K)(1) Copy the file folder to home and then get into it. $ cp -r share/md2 . $ cd md2 $ cd 4_lattice (2) What is the setup in input file $ gedit in.diamond (3) Run LAMMPS $ lmp -i in.diamond (4) Plot $ gnuplot p data.d u 1:2 w lp# bulk Silicon lattice # 注释行，随便给 units metal # 单位，指定为la
25、mmps里的金属类的单位，长度为，能量为eV。 atom_style atomic # 原子模式 variable x index 5.4305 5.4306 5.4307 5.4308 5.4309 5.4310 5.4311 5.4312 5.4313 5.4314 # 定义变量x，在运行中x逐一取这些值。本例中为各个晶格常数 lattice diamond $x # 晶格，指定金刚石结构的晶格，晶格常数为x的值 #lattice diamond 5.431 #lattice fcc 3.615 # 如果计算fcc结构的晶格，则将晶格常数取在3.615附近 #lattice bcc 3.2
26、8 # 同上 #lattice sc 2.60 # 同上 region box block 0 3 0 3 0 3 # 划定区域，x 0,3, y 0,3 z 0,3，单位为晶胞 create_box 1 box # 在上面这个区域里创建一个模拟的盒子 create_atoms 1 box # 将这个盒子按晶格填满一种原子 pair_style sw # 选取 sw 势 pair_coeff * * Si.sw Si # 势文件名为 Si.sw mass 1 28 # 给定硅的质量，此处与势对应 variable P equal pe # 定义 P 为体系总势能 timestep 0.005
27、# 步长为5飞秒 thermo 10 # 每10步在屏幕上输出一次热力学状态信息 dump 1 all cfg 1 a*.cfg id type xs ys zs # 输出构型文件 .cfg print “$x $P“ # 输出到屏幕 clear # 清除该次循环里的数据信息 next x # 跳转到下一个 x jump in.Silicon # 跳到 in.Silicon 文件头读起，完成循环。 输入文件 in.Silicon0 0 a dE da 平衡晶格常数 a 0 = 5.43094 五次多项式拟合结果 多项式拟合， 0 2 2 3.86504 a dE da eV 2 1. a 0
28、的计算 2. B 的计算 0 2 2 0 9 a M dE B ad a Si : M = 8 1 eV 2 = 160.22 GPa 最后得到： 弹性模量B= 101.305 Gpa （实验值：99 GPa） 其中，晶体结构（fcc、bcc、sc）5. 熔化 Melting Point: Cu 1357.77 K. Al 933.477 K.Cu (melting point = 1357.77 K) .model system Cu, Al Initial conditions T, P supercell number of atoms, PBCs Interatomic potenti
29、als EAM, Lennard-Jones ensembles NPT (Nos-Hoover thermostat) task 1) Observe Cu atom movement at different temperature 2) Compare MSD of Cu at different T 3) understand NPT, solid and liquid, phase transitions, diffusion, correlation functions (1) Change to the directory. $ cd 5_melting (2) What is
30、the setup in input file $ gedit in.melting (3) Run LAMMPS $ lmp -i in.melting (4) Plot $ gnuplot p data u 1:2 w lp p data u 2:3 w lpunits metal boundary p p p atom_style atomic lattice fcc 3.61 region box block 0 4 0 4 0 4 create_box 1 box create_atoms 1 box pair_style eam/alloy pair_coeff * * jin_c
31、opper_lammps.setfl Cu timestep 0.01 thermo 1000 variable N equal step variable pote equal pe variable T equal temp variable Press equal press variable V equal vol velocity all create 10 825577 dist gaussian fix extra all print 100 “$N $T $V $pote $Press“ file data dump 1 all cfg 10000 a*.cfg id type
32、 xs ys zs dump_modify 1 element Cu fix 1 all npt temp 10 2000 1 iso 0 0 10 run 120000Ta b 键 切换视角 k, Alt + H, Alt + +/- 改变颜色 Delete / Insert 下一帧/上一帧 PgUp / PgDn 原子变大/变小 滚轮 放大/缩小 方向键 旋转 q 关闭 Atomeye 命令10K 500K 1000K 2000KThe MSD contains information on the atomic diffusivity. If the system is solid, M
33、SD saturates to a finite value, while if the system is liquid, MSD grows linearly with time. In this case it is useful to characterize the system behavior in terms of the slope, which is the diffusion coefficient D: The 6 in the above formula must be replaced with 4 in two- dimensional systems. 均方根位
34、移（MSD)Temperature VS time Volume VS. Temperature Solidificationcrystal glass径向分布函数 rdf Crystal 熔化时 Glass1. 在一次研究Al原子运动过程的分子动力学实验中，得到如图 所示的原子均方位移（MSD ）随时间变化趋势。有图可知该 实验模拟的可 能是（ ）过程。 （a）单向拉伸 ； （b）单向压缩；（c）凝固；（d）熔化 2. 如图所示为一次分子动力学模拟中所采用的构型。该构型在 三个方向上均采用周期性边界条件，且在某一方向上加入真空 层。该构型最适用于研究（）。 （a）晶体材料内部的均匀熔化行为；（b ）纳米颗粒的塑性变 形 （c）单晶纳米线的单向拉伸过程；（d）纳米薄膜表面的纳米 压痕实验 3. 如图所示为某种材料的径向分布函数（RDF）。请问该材料 最有可能是（）。 （提示：Cu单晶中Cu原子最近邻距离约为2.56 ，石墨烯中C 原子最近邻距 离约为1.42 ） （a）Cu单晶纳米线；（b ）Cu单晶块体；（c）石墨烯；（d ）液氩
