Integrated Computational Materials Engineering (ICME)
LAMMPS Relaxed Bi-layer
Abstract
This example shows how to build a periodic stack of Al-Ni nanoscale laminates and to run an atomistic simulation to obtain the relaxed structure. Both Al and Ni are fcc metals. The global coordinated of the simulation box are aligned with the <100> crystallographic directions for both layers (x: [100], y: [010], and z:[001]). This example uses a parallel molecular dynamics code, LAMMPS[1].
Author(s): Tikelia Wright *
Author(s): Firas Akasheh* and Mark A. Tschopp
(*) Mechanical Engineering Department, Tuskegee University, Tuskegee, AL 36088
Corresponding Author: Mark A. Tschopp
INPUT
Description of Simulation
This molecular dynamics simulation first generates a bi-layered simulation cell. The [100], [010], and [001] crystal directions in both layers are aligned with the x, y, z- directions of the simulation box. For this example, the simulation box size is 54 lattice units for nickel and 47 lattice units for aluminum in the x and y direction and 7 lattice unit for nickel and 6 lattice unit for aluminum in the z direction. The keyword origin in the lattice command was used to eliminate gap at interface causing lattice to be shifted by a fraction preventing upper region from overlapping with atoms from lower region. The potential used here is the Mishin-Al-Ni-2009.eam.alloy[2] based on the embedded atom method. The upper region is made of nickel while the lower region is made of aluminum. The minimize command based on the conjugate gradient method (hence the min_style cg command) is used to bring each atom to its lowest energy causing the atoms to relax into a lower energy configuration. The custom dump file includes the x, y, and z coordinates the centrosymmetry parameter values, the potential energy, and the stress tensor per atom. This can directly be visualized using Ovito[3].
Relaxed-NiAl ending results colored by the c_csym showing full dislocation at 45 degree angle.
Lattice units vs. Box units
For this example, the use of lattice units rather than box units is more convenient. In box units the geometry is defined in simulation box units (ex. Angstrom, based on command unit).In units lattice (which is the default), the geometry is define in terms of units each representing the lattice parameter, ao, of the specific materials used. (A lattice consists of a unit cell, a set of basis atoms within that cell, and a set of transformation parameters (scale, origin, orient) that map the unit cell into the simulation box). Because the lattice parameters of Al and Ni are different, this example uses different number of the lattice units to minimize the accumulated mismatch over the size of the simulation box. The choice of 47 units and 54 units for Al and Ni, respectively, is based on this approach (better matches with larger number of units cells is possible but then the computational effort become high; a compromise should be made based on the specific circumstances and accuracy required by the user). If the match is poor, then non physical artifacts are introduced in the model in the form of higher energy and stresses at the edges of box making atoms have higher energy.
LAMMPS input script
This input script was run using the December 2011 version of Lammps. Changes in some commands in more recent versions may require revision of the input script. To run this script, store it in "relaxed.AlNi.txt" and then use "lmp_win_no-mpi.exe < relaxed.NiAl.txt
# Input file for bi-layered crystal, Nickle and Aluminum, relaxed # Tikelia Wright, July 2012 # ------------------------ INITIALIZATION ---------------------- clear units metal dimension 3 boundary p p p atom_style atomic # ----------------------- ATOM DEFINITION ----------------------- lattice fcc 3.52 region upper block 0 54 0 54 0 7 lattice fcc 4.05 region lower block 0 47 0 47 6.5 13 region whole union 2 upper lower create_box 2 whole lattice fcc 3.52 orient x 1 0 0 orient y 0 1 0 orient z 0 0 1 create_atoms 1 region upper lattice fcc 4.05 origin 0 0 .247 orient x 1 0 0 orient y 0 1 0 orient z 0 0 1 create_atoms 2 region lower # ------------------------ FORCE FIELDS ----------------------- pair_style eam/alloy pair_coeff * * Mishin-Ni-Al-2009.eam.alloy Ni Al #---------------------------Settings---------------------------- compute csym all centro/atom fcc compute eng all pe/atom compute eatoms all reduce sum c_eng compute strs all stress/atom #----------------------Run Minimization------------------------- reset_timestep 0 thermo 10 thermo_style custom step pe lx ly lz press pxx pyy pzz c_eatoms dump 1 all custom 10 dump.comp.* id type xs ys zs c_csym c_eng c_strs[1] c_strs[2] c_strs[3] min_style cg minimize 1e-15 1e-15 5000 5000 ###################################### # SIMULATION DONE print "All done"
Output
LAMMPS logfile
The log.lammps file should look like this below.
LAMMPS (21 Dec 2011)
# Input file for bi-layered crystal, Nickle and Aluminum, relaxed
# Tikelia Wright, July 2012
# ------------------------ INITIALIZATION ----------------------
clear
units metal
dimension 3
boundary p p p
atom_style atomic
# ----------------------- ATOM DEFINITION -----------------------
lattice fcc 3.52
Lattice spacing in x,y,z = 3.52 3.52 3.52
region upper block 0 54 0 54 0 7
lattice fcc 4.05
Lattice spacing in x,y,z = 4.05 4.05 4.05
region lower block 0 47 0 47 6.5 13
region whole union 2 upper lower
create_box 2 whole
Created orthogonal box = (0 0 0) to (190.35 190.35 52.65)
1 by 1 by 1 MPI processor grid
lattice fcc 3.52 orient x 1 0 0 orient y 0 1 0 orient z 0 0 1
Lattice spacing in x,y,z = 3.52 3.52 3.52
create_atoms 1 region upper
Created 89108 atoms
lattice fcc 4.05 origin 0 0 .247 orient x 1 0 0 orient y 0 1 0 orient z 0 0 1
Lattice spacing in x,y,z = 4.05 4.05 4.05
create_atoms 2 region lower
Created 57434 atoms
# ------------------------ FORCE FIELDS -----------------------
pair_style eam/alloy
pair_coeff * * Mishin-Ni-Al-2009.eam.alloy Ni Al
#---------------------------Settings----------------------------
compute csym all centro/atom fcc
compute eng all pe/atom
compute eatoms all reduce sum c_eng
compute strs all stress/atom
#----------------------Run Minimization-------------------------
reset_timestep 0
thermo 10
thermo_style custom step pe lx ly lz press pxx pyy pzz c_eatoms
dump 1 all custom 10 dump.comp.* id type xs ys zs c_csym c_eng c_strs[1] c_strs[2] c_strs[3]
min_style cg
minimize 1e-15 1e-15 5000 5000
WARNING: Resetting reneighboring criteria during minimization (min.cpp:167)
Memory usage per processor = 249.071 Mbytes
Step PotEng Lx Ly Lz Press Pxx Pyy Pzz eatoms
0 -235412.15 190.35 190.35 52.65 763559.25 285788.93 285788.93 1719099.9 -235412.15
10 -582697.15 190.35 190.35 52.65 18664.768 18208.125 18208.125 19578.053 -582697.15
20 -583722.84 190.35 190.35 52.65 17924.296 17446.186 17446.186 18880.516 -583722.84
30 -586145.83 190.35 190.35 52.65 14899.408 15205.587 15205.587 14287.049 -586145.83
40 -586299.13 190.35 190.35 52.65 14803.212 15125.676 15125.676 14158.284 -586299.13
50 -586345.93 190.35 190.35 52.65 14685.315 15001.672 15001.672 14052.6 -586345.93
60 -586379.46 190.35 190.35 52.65 14609.568 14923.005 14923.005 13982.693 -586379.46
70 -586437.21 190.35 190.35 52.65 14407.029 14710.173 14710.176 13800.739 -586437.21
80 -586497.64 190.35 190.35 52.65 14284.654 14586.239 14586.238 13681.485 -586497.64
90 -587371.65 190.35 190.35 52.65 11373.847 11750.217 11750.224 10621.099 -587371.65
100 -587448.48 190.35 190.35 52.65 11332.529 11723.811 11723.799 10549.977 -587448.48
110 -587489.71 190.35 190.35 52.65 11286.552 11688.166 11688.165 10483.325 -587489.71
120 -587511.42 190.35 190.35 52.65 11244.342 11652.703 11652.7 10427.622 -587511.42
130 -587614.11 190.35 190.35 52.65 10868.998 11323.633 11323.449 9959.9125 -587614.11
140 -587704.85 190.35 190.35 52.65 10674.95 11160.366 11160.372 9704.1122 -587704.85
150 -587772.64 190.35 190.35 52.65 10417.311 10929.712 10929.116 9393.1072 -587772.64
160 -587798.94 190.35 190.35 52.65 10394.426 10912.077 10911.451 9359.7501 -587798.94
170 -587814.18 190.35 190.35 52.65 10374.478 10895.28 10894.828 9333.3262 -587814.18
180 -587860.82 190.35 190.35 52.65 10242.392 10778.627 10778.077 9170.471 -587860.82
190 -587874.2 190.35 190.35 52.65 10214.369 10753.964 10753.776 9135.367 -587874.2
200 -587905.02 190.35 190.35 52.65 10126.41 10676.015 10675.658 9027.5561 -587905.02
210 -587929.13 190.35 190.35 52.65 10055.924 10613.062 10612.938 8941.7733 -587929.13
220 -587941.62 190.35 190.35 52.65 10028.754 10589.387 10589.275 8907.6007 -587941.62
230 -587959.35 190.35 190.35 52.65 9970.4501 10537.131 10536.975 8837.2443 -587959.35
240 -587969.87 190.35 190.35 52.65 9934.1734 10504.434 10504.624 8793.4622 -587969.87
250 -588557.67 190.35 190.35 52.65 7695.282 8459.2628 8469.8335 6156.7498 -588557.67
260 -588595.22 190.35 190.35 52.65 7689.1285 8459.1714 8467.7467 6140.4673 -588595.22
270 -588612.91 190.35 190.35 52.65 7679.7949 8453.3072 8458.9039 6127.1737 -588612.91
280 -588630.19 190.35 190.35 52.65 7658.9062 8435.5576 8438.2346 6102.9264 -588630.19
290 -588646.55 190.35 190.35 52.65 7637.4002 8416.3747 8417.955 6077.8711 -588646.55
300 -588652.55 190.35 190.35 52.65 7626.59 8406.6737 8407.4982 6065.598 -588652.55
310 -588660.19 190.35 190.35 52.65 7606.0644 8387.1089 8387.5956 6043.4887 -588660.19
320 -588667.42 190.35 190.35 52.65 7578.9255 8360.9013 8361.1099 6014.7655 -588667.42
330 -588675.69 190.35 190.35 52.65 7556.7506 8339.6121 8339.7179 5990.9218 -588675.69
340 -588807.56 190.35 190.35 52.65 6907.0488 7706.7941 7696.0167 5318.3357 -588807.56
350 -588864.81 190.35 190.35 52.65 6838.7066 7644.7747 7635.0943 5236.2508 -588864.81
360 -588874.65 190.35 190.35 52.65 6832.4928 7639.4064 7630.4715 5227.6006 -588874.65
370 -588890.22 190.35 190.35 52.65 6788.6742 7595.7119 7590.3337 5179.977 -588890.22
380 -588897.83 190.35 190.35 52.65 6785.9049 7594.1235 7588.4386 5175.1524 -588897.83
390 -588910.46 190.35 190.35 52.65 6742.6824 7552.2819 7546.8944 5128.871 -588910.46
400 -588917.55 190.35 190.35 52.65 6733.2489 7543.7487 7538.5925 5117.4055 -588917.55
410 -588930.39 190.35 190.35 52.65 6680.0399 7492.4767 7486.8712 5060.7719 -588930.39
420 -588941.75 190.35 190.35 52.65 6647.038 7460.7873 7455.4542 5024.8726 -588941.75
430 -588951.98 190.35 190.35 52.65 6622.3444 7437.1009 7432.3123 4997.6199 -588951.98
440 -588956.08 190.35 190.35 52.65 6615.5124 7430.7404 7426.1958 4989.6011 -588956.08
450 -588960.52 190.35 190.35 52.65 6603.3729 7419.0904 7414.74 4976.2882 -588960.52
460 -589093.55 190.35 190.35 52.65 5791.4221 6623.6537 6618.7808 4131.8317 -589093.55
470 -589683.91 190.35 190.35 52.65 4083.2708 4974.8329 4986.2067 2288.7729 -589683.91
480 -589709.29 190.35 190.35 52.65 4083.8257 4979.4192 4990.6199 2281.438 -589709.29
490 -589714.79 190.35 190.35 52.65 4081.7822 4978.2733 4989.2807 2277.7927 -589714.79
500 -589719.45 190.35 190.35 52.65 4071.5886 4968.6414 4980.4759 2265.6487 -589719.45
510 -589723.08 190.35 190.35 52.65 4065.6121 4963.3566 4975.2353 2258.2443 -589723.08
520 -589726.59 190.35 190.35 52.65 4052.2244 4950.7279 4963.1382 2242.8071 -589726.59
530 -589824.57 190.35 190.35 52.65 3702.368 4632.0229 4649.5845 1825.4967 -589824.57
540 -589843.27 190.35 190.35 52.65 3702.8556 4635.7072 4651.2379 1821.6218 -589843.27
550 -589853.36 190.35 190.35 52.65 3700.1072 4634.2185 4648.3774 1817.7257 -589853.36
560 -589857.47 190.35 190.35 52.65 3695.567 4630.5934 4644.492 1811.6155 -589857.47
570 -589868.55 190.35 190.35 52.65 3675.4941 4612.3628 4627.6842 1786.4355 -589868.55
580 -589871.35 190.35 190.35 52.65 3672.7959 4610.3064 4625.3956 1782.6858 -589871.35
590 -589877.36 190.35 190.35 52.65 3665.3898 4604.2961 4619.0118 1772.8614 -589877.36
600 -589879.36 190.35 190.35 52.65 3662.5557 4602.0557 4616.4541 1769.1573 -589879.36
610 -589880.34 190.35 190.35 52.65 3660.6072 4600.3153 4614.7525 1766.7539 -589880.34
620 -589884.73 190.35 190.35 52.65 3643.5132 4584.6829 4599.5629 1746.2938 -589884.73
630 -589990.35 190.35 190.35 52.65 3315.619 4295.958 4309.2387 1341.6602 -589990.35
640 -590002.53 190.35 190.35 52.65 3315.1535 4297.6457 4309.9352 1337.8795 -590002.53
650 -590005.11 190.35 190.35 52.65 3313.4225 4296.49 4308.3326 1335.4448 -590005.11
660 -590008.89 190.35 190.35 52.65 3308.5921 4291.8204 4304.0972 1329.8587 -590008.89
670 -590010.19 190.35 190.35 52.65 3306.7197 4289.9928 4302.4637 1327.7025 -590010.19
680 -590016.47 190.35 190.35 52.65 3284.6813 4268.3176 4281.4768 1304.2495 -590016.47
690 -590021.31 190.35 190.35 52.65 3274.3174 4258.6563 4271.2514 1293.0445 -590021.31
700 -590022.38 190.35 190.35 52.65 3272.554 4257.0373 4269.6173 1291.0072 -590022.38
710 -590044.25 190.35 190.35 52.65 3190.8629 4179.0547 4190.8401 1202.6938 -590044.25
720 -590049.24 190.35 190.35 52.65 3186.3464 4175.3215 4187.0618 1196.6559 -590049.24
730 -590051.22 190.35 190.35 52.65 3181.1112 4170.4659 4182.0941 1190.7735 -590051.22
740 -590056.67 190.35 190.35 52.65 3163.0556 4153.5648 4164.997 1170.6051 -590056.67
750 -590131.43 190.35 190.35 52.65 2892.3705 3905.6495 3912.1162 859.34572 -590131.43
760 -590139.1 190.35 190.35 52.65 2891.6678 3905.0666 3912.757 857.17976 -590139.1
770 -590150 190.35 190.35 52.65 2886.9084 3899.9272 3910.8518 849.94626 -590150
780 -590152.97 190.35 190.35 52.65 2881.6614 3894.8561 3906.676 843.45206 -590152.97
790 -590155.38 190.35 190.35 52.65 2874.565 3888.2414 3900.2709 835.18279 -590155.38
800 -590158.93 190.35 190.35 52.65 2866.9762 3881.3595 3893.6324 825.93682 -590158.93
803 -590159.2 190.35 190.35 52.65 2866.62 3881.1088 3893.2999 825.45129 -590159.2
Loop time of 6982.33 on 1 procs for 803 steps with 146542 atoms
Minimization stats:
Stopping criterion = max force evaluations
Energy initial, next-to-last, final =
-235412.147027 -590159.101512 -590159.204125
Force two-norm initial, final = 76863.2 97.4051
Force max component initial, final = 4220.21 31.4348
Final line search alpha, max atom move = 2.50166e-005 0.000786391
Iterations, force evaluations = 803 5001
Pair time (%) = 6612.97 (94.7101)
Neigh time (%) = 2.0748 (0.0297151)
Comm time (%) = 13.0194 (0.186463)
Outpt time (%) = 300.838 (4.30856)
Other time (%) = 53.4293 (0.765208)
Nlocal: 146542 ave 146542 max 146542 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Nghost: 85077 ave 85077 max 85077 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Neighs: 1.37664e+007 ave 1.37664e+007 max 1.37664e+007 min
Histogram: 1 0 0 0 0 0 0 0 0 0
FullNghs: 2.74792e+007 ave 2.74792e+007 max 2.74792e+007 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Total # of neighbors = 27479226
Ave neighs/atom = 187.518
Neighbor list builds = 3
Dangerous builds = 0
######################################
# SIMULATION DONE
print "All done"All done
LAMMPS dumpfile
The following dump file in custom format was also generated during this simulation.
ITEM: TIMESTEP 0 ITEM: NUMBER OF ATOMS 146542 ITEM: BOX BOUNDS pp pp pp 0 190.35 0 190.35 0 52.65 ITEM: ATOMS id type xs ys zs c_csym c_eng c_strs[1] c_strs[2] c_strs[3] 1 1 0 0 0 2.78059 3.73195 -4.84256e+006 -4.84256e+006 -8.01071e+006 2 1 0.00924613 0.00924613 0 3.00566 -4.20457 -6.20038e+006 -6.20038e+006 -2.96094e+006 3 1 0.00924613 0 0.0334283 0.5103 -2.28028 -9.0751e+006 -1.19079e+006 -7.63674e+006 4 1 0 0.00924613 0.0334283 0.5103 -2.28028 -1.19079e+006 -9.0751e+006 -7.63674e+006 5 1 0.0184923 0 0 8.99922 -1.45256 -8.28824e+006 -1.10841e+006 -4.27007e+006 8 1 0.0184923 0.00924613 0.0334283 1.97215e-031 -4.94048 -811059 -1.12058e+006 -395017 219 1 0 0.0184923 0 8.99922 -1.45256 -1.10841e+006 -8.28824e+006 -4.27007e+006 221 1 0.00924613 0.0184923 0.0334283 1.97215e-031 -4.94048 -1.12058e+006 -811059 -395017
POST-PROCESSING
Energy Plot
This energy curve can be generated using Microsoft Excel.
Figure 2.Misfit dislocation generated at interface colored by c_eng
Acknowledgments
The author and first advisor would like to acknowledge the support to this work by the National Science Foundation, HBCUUP-RIA program, Program Manager Dr. Claudia Rankins, Award No. HRD-1137587. Additionally, the technical and logistical support of CAVS and HPC2 of Mississippi State University is acknowledged
The corresponding author author would like to acknowledge funding for the overarching EVOWiki project through the Department of Energy.
References
- ↑ S. Plimpton, "Fast Parallel Algorithms for Short-Range Molecular Dynamics," J. Comp. Phys., 117, 1-19 (1995). (http://www.sciencedirect.com/science/article/pii/S002199918571039X)
- ↑ G.P. Purja Pun and Y. Mishin, "Development of an interatomic potential for the Ni-Al system," Phil. Mag. 89, 3245 (2009).
- ↑ A.Stukowski, "Visualization and analysis of atomistic simulation data with OVITO - the Open Visualization Tool," Modelling Simul. Mater. Sci. Eng. 18 (2010), 015012.(http://ovito.org/)