LAMMPS Relaxed Bi-layer

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Contents

Questions / Comments

Please contact me if you have any questions or comments about this tutorial. I'll try to add questions and answers to the bottom of the tutorial pages as they arise.

Email: Mark Tschopp, mark.tschopp@gatech.edu

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 *

Advisor(s): Firas Akasheh* and Mark A. Tschopp

(*) Mechanical Engineering Department, Tuskegee University, Tuskegee, AL 36088

Corresponding Author: Mark A. Tschopp

Relaxed-NiAl ending results colored by the c_csym showing full dislocation at 45 degree angle.

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].

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.

Energy.bmp


Figure 2.Misfit dislocation generated at interface colored by c_eng

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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

  1. 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)
  2. G.P. Purja Pun and Y. Mishin, "Development of an interatomic potential for the Ni-Al system," Phil. Mag. 89, 3245 (2009).
  3. 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/)
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