分子动力学实验分子动力学实验 SJTU.CMS. April 2012 1. 空位形成能空位形成能 2. 表面、界面能表面、界面能 3. 层错能层错能 4. 晶格常数与体弹模量晶格常数与体弹模量 5. 熔化熔化 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。 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 configuration viewer pwdpwdprint name of working directory mkdirmkdirhahamake directory cdcdhahachange directory cdupper directory cdback home geditgeditaedit a file catcataconcatenate files lslslist cpcpabcopy file a to file b cprABcopy a file folder rmrmbremove Tab * Basic Linux Commands NAMESYNOPSISDESCRIPTION 1. 空位形成能空位形成能 Point Defects: Vacancy Model system: Cu, fcc, a0= 3.61 Tasks: 1. generate a point defect within an equilibrium lattice 2. calculate the formation energy Model systemCu Initial conditions fcc lattice defect-free state, vacancy SupercellN, PBCs Interatomic potentialsEAM (Cu) EnsemblesMinimize (1) Copy the file folder to home and then get into it. $ cp-rshare/md. $ cdmd $ cd1_vacancy $ ls (2) What is the setup in input file $geditin.vacancy (3) Run LAMMPS $ lmp-inin.vacancy (4) After running, view the configuration $ A.i686a0.cfg (5) View the result data $ catdata Tab 键键切换视角切换视角 k, Alt + H, Alt + +/-改变颜色改变颜色 Delete / Insert下一帧下一帧/上一帧上一帧 PgUp / PgDn原子变大原子变大/变小变小 滚轮滚轮放大放大/缩小缩小 方向键 方向键旋转旋转 q关闭关闭 Atomeye 命令命令 units metal boundary p p p atom_styleatomic lattice fcc 3.61 region box block 0 6 0 6 0 6 create_box1 box create_atoms1 box pair_styleeam/alloy pair_coeff* * jin_copper_lammps.setfl Cu timestep0.005 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_atomsregion centerpoint run 0 fix extra all print 1 “ an atom deleted, 0K: atoms = $N, energy = $E“ 周期边界条件周期边界条件 指定指定fcc晶体晶体 box大小大小 Cu的的EAM势 删除一个原子 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, energy = -3010.624033 2. 表面、界面能表面、界面能 Planar Defects: Surface and Grain Boundary Model system: Cu, fcc, a0= 3.610 Tasks: 1.Surface energies of (111) and (100); 2.Grain boundary energies Model systemCu Initial conditionsT, P SupercellN, PBCs Interatomic potentialsEAM (Cu) EnsemblesMinimize Surface energy: Method perfect regionvacuum 2 surfaces N0atoms, E0 N atoms, E S= (E E0*N/N0) / (2*A) h1 h3 h2 (111) Surface: h1= a0/211-2*L1; h2= a0/2-110*L2; h3= a0111*L3 (100) Surface: h1= a0100*L1; h2= a0010*L2; h3= a0001*L3 Surface energy: Calculations perfect: N0= 123772, E0= 431965.9291 eV (111): NS1= 124722, ES1= 434642.1217 eV, AS1= 39.792*104.659 2 (100): NS2= 123772, ES2= 431275.1878 eV, AS2= 39.71*104.69 2 S1= (ES1 E0*NS1/N0)*16020 / (2*AS1) = 1230 mJ/m2 S2= (ES2 E0*NS2/N0)*16020 / (2*AS2) = 1331 mJ/m2 Grain boundary energy S1:(111) GB= (E E0*N/N0) / A S1 S2 h3 region2vacuum h1 h2 region1 S2:(100)GB GB+S1+S2: N = 248494, E = 866449.3465 eV, A = 39.755*104.677 2 GB= (E E0*N/N0)*16020 / A S1 S2= 512 mJ/m2 a1 a2 a3 a1 a2 a3 region 1: a1= a0/211-2; a2= a0/2-110; a3= a0111 region 2: a1= a0100; a2= a0010; a3= a0001 (1) Change into the 2nddirectory $ cd/2_surface_boundary $ ls (2) What is the commands in bash file $catrun.sh (3) Run bash file $ ./run.sh (4) After running, view the configuration $ A.i686a0.cfg #!/bin/bash lmp p data u 1:2 w lp p data u 2:3 w lp unitsmetal boundaryp p p atom_styleatomic latticefcc 3.61 region box block 0 4 0 4 0 4 create_box1 box create_atoms1 box pair_styleeam/alloy pair_coeff* * jin_copper_lammps.setfl Cu timestep0.01 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 xs ys zs dump_modify1 element Cu fix1 all npt temp 10 2000 1 iso 0 0 10 run 120000 Tab 键键切换视角切换视角 k, Alt + H, Alt + +/-改变颜色改变颜色 Delete / Insert下一帧下一帧/上一帧上一帧 PgUp / PgDn原子变大原子变大/变小变小 滚轮滚轮放大放大/缩小缩小 方向键 方向键旋转旋转 q关闭关闭 Atomeye 命令命令 10K500K1000K2000K The MSD contains information on the atomic diffusivity. If the system is solid, MSD 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. 均方根位移（均方根位移（MSD) Temperature VS timeVolume VS. Temperature Solidification crystal glass