LAMMPS Help3

From EVOCD
Revision as of 11:27, 30 April 2019 by 2nayeon (Talk | contribs)

Jump to: navigation, search

Contents

Questions / Comments

Please contact me if you have any questions or comments about this tutorial.

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

Abstract

Movie showing the minimization of the grain boundary structure for an aluminum Sigma5 (310) symmetric tilt grain boundary.

The objective of this tutorial is to generate a symmetric tilt grain boundary in LAMMPS. This tutorial can serve as a precursor to more advanced techniques, whereby in-plane translations and atom deletion criteria are used to sample a large number of potential structures to find the global minimum energy grain boundary structure[1][2].

Author(s): Mark A. Tschopp Nayeon Lee

Corresponding Author: Mark Tschopp

Methodology

The following input script shows how multiple translations and an atom deletion criteria are used to calculate the minimum energy structure. This input script for LAMMPS[3] can be called with a command of the form, "lmp_exe < input.script." This script contains loops over x-translations, z-translations, and atom overlap distances (an atom is deleted when an atom pair with a nearest neighbor distance is less than this distance). The unique minimum energy structures are saved as a dump file with the energy appended to the filename in a new folder specified by the 'gbname' variable. The dump files can then be easily scanned through for the global minimum energy structure. Simulations performed on Aug 2014 LAMMPS version.

LAMMPS Input file


# LAMMPS Input File for Grain Boundaries 
# Mark Tschopp, Dec2009 
# This file will generate a single Sigma5(310) STGB

# ---------- Initialize Simulation --------------------- 
clear 
units metal 
dimension 3 
boundary p p p 
atom_style atomic 

# ---------- Create Atomistic Structure --------------------- 
lattice fcc 4.05 
region whole block 0.000000 12.807225 -64.0361225 64.0361225 0.000000 4.050000 units box 
create_box 2 whole 
region upper block INF INF 0.000000 64.0361225 INF INF units box 
lattice fcc 4.05 orient x  0  3  1 orient y  0 -1  3 orient z  1  0  0 
create_atoms 1 region upper 
region lower block INF INF -64.0361225 0.000000 INF INF units box 
lattice fcc 4.05 orient x  0  3 -1 orient y  0  1  3 orient z  1  0  0 
create_atoms 2 region lower 
group upper type 1 
group lower type 2  

# ---------- Define Interatomic Potential --------------------- 
pair_style eam/alloy 
pair_coeff * * Al99.eam.alloy Al Al
neighbor 2.0 bin 
neigh_modify delay 10 check yes 
 
# ---------- Displace atoms and delete overlapping atoms --------------------- 
displace_atoms upper move 0 0 0 units lattice 
delete_atoms overlap 0.35 lower upper
 
# ---------- Define Settings --------------------- 
compute csym all centro/atom fcc
compute eng all pe/atom 
compute eatoms all reduce sum c_eng 

# ---------- Run Minimization --------------------- 
reset_timestep 0 
thermo 10 
thermo_style custom step pe lx ly lz press pxx pyy pzz c_eatoms 
dump 		1 all cfg 25 dump.sig5_minimization_*.cfg mass type xs ys zs c_csym c_eng fx fy fz
dump_modify     1 element Al Al
min_style cg 
minimize 1e-15 1e-15 5000 5000 
undump 1

# ---------- Run Minimization 2--------------------- 
# Now allow the box to expand/contract perpendicular to the grain boundary
reset_timestep 0 
thermo 10 
thermo_style custom step pe lx ly lz press pxx pyy pzz c_eatoms 
fix 1 all box/relax y 0 vmax 0.001
min_style cg 
minimize 1e-15 1e-15 5000 5000 

# ---------- Calculate GB Energy --------------------- 
variable minimumenergy equal -3.360000
variable esum equal "v_minimumenergy * count(all)" 
variable xseng equal "c_eatoms - (v_minimumenergy * count(all))" 
variable gbarea equal "lx * lz * 2" 
variable gbe equal "(c_eatoms - (v_minimumenergy * count(all)))/v_gbarea" 
variable gbemJm2 equal ${gbe}*16021.7733 
variable gbernd equal round(${gbemJm2}) 
print "GB energy is ${gbemJm2} mJ/m^2" 
 
# ---------- Dump data into Data file ------------- 
reset_timestep 0 
dump 		1 all cfg 10000 dump.al_sig5_310_*.cfg mass type xs ys zs c_csym c_eng fx fy fz
dump_modify     1 element Al Al
minimize 1e-15 1e-15 5000 5000
undump 1

write_restart restart.al_sig5_310_stgb

print "All done" 

LAMMPS Logfile

Here is an example logfile that is obtained after running this script.


LAMMPS (13 Jul 2010)
# LAMMPS Input File for Grain Boundaries 
# Mark Tschopp, Dec2009 
# This file will generate a single Sigma5(310) STGB

# ---------- Initialize Simulation --------------------- 
clear 
units metal 
dimension 3 
boundary p p p 
atom_style atomic 

# ---------- Create Atomistic Structure --------------------- 
lattice fcc 4.05 
Lattice spacing in x,y,z = 4.05 4.05 4.05
region whole block 0.000000 12.807225 -64.0361225 64.0361225 0.000000 4.050000 units box 
create_box 2 whole 
Created orthogonal box = (0 -64.0361 0) to (12.8072 64.0361 4.05)
  1 by 1 by 1 processor grid
region upper block INF INF 0.000000 64.0361225 INF INF units box 
lattice fcc 4.05 orient x  0  3  1 orient y  0 -1  3 orient z  1  0  0 
Lattice spacing in x,y,z = 5.12289 5.12289 4.05
create_atoms 1 region upper 
Created 200 atoms
region lower block INF INF -64.0361225 0.000000 INF INF units box 
lattice fcc 4.05 orient x  0  3 -1 orient y  0  1  3 orient z  1  0  0 
Lattice spacing in x,y,z = 5.12289 5.12289 4.05
create_atoms 2 region lower 
Created 200 atoms
group upper type 1 
200 atoms in group upper
group lower type 2  
200 atoms in group lower

# ---------- Define Interatomic Potential --------------------- 
pair_style eam/alloy 
pair_coeff * * Al99.eam.alloy Al Al
neighbor 2.0 bin 
neigh_modify delay 10 check yes 
 
# ---------- Displace atoms and delete overlapping atoms --------------------- 
displace_atoms upper move 0 0 0 units lattice 
delete_atoms overlap 0.35 lower upper
Deleted 2 atoms, new total = 398
 
# ---------- Define Settings --------------------- 
compute csym all centro/atom fcc
compute eng all pe/atom 
compute eatoms all reduce sum c_eng 

# ---------- Run Minimization --------------------- 
reset_timestep 0 
thermo 10 
thermo_style custom step pe lx ly lz press pxx pyy pzz c_eatoms 
dump 		1 all cfg 25 dump.sig5_minimization_*.cfg id type xs ys zs c_csym c_eng fx fy fz
dump_modify     1 element Al Al
min_style cg 
minimize 1e-15 1e-15 5000 5000 
Memory usage per processor = 3.58369 Mbytes
Step PotEng Lx Ly Lz Press Pxx Pyy Pzz eatoms 
       0   -1318.9843    12.807225    128.07225         4.05    875.32429   -2675.7752    7333.2608   -2031.5128   -1318.9843 
      10   -1329.7948    12.807225    128.07225         4.05    4786.2646    2230.1043    9306.1111    2822.5783   -1329.7948 
      20    -1330.138    12.807225    128.07225         4.05    5741.5477    3251.6199    10395.111    3577.9118    -1330.138 
      30   -1330.2064    12.807225    128.07225         4.05    5762.2257    3246.6439    10519.567    3520.4656   -1330.2064 
      40   -1330.2128    12.807225    128.07225         4.05    5812.6504    3332.1043    10542.913    3562.9335   -1330.2128 
      50   -1330.2136    12.807225    128.07225         4.05    5811.3217    3335.8029    10533.825    3564.3374   -1330.2136 
     766   -1333.6024    12.807225    128.07225         4.05   -6.3617301    -262.3388     1197.774    -954.5204   -1333.6024 
Loop time of 5.19081 on 1 procs for 766 steps with 398 atoms

Minimization stats:
  Stopping criterion = linesearch alpha is zero
  Energy initial, next-to-last, final = 
        -1318.98429985     -1333.60243356     -1333.60243356
  Force two-norm initial, final = 17.5886 0.000221422
  Force max component initial, final = 6.25036 3.74708e-05
  Final line search alpha, max atom move = 0.25 9.36769e-06
  Iterations, force evaluations = 766 2310

Pair  time (%) = 4.35802 (83.9565)
Neigh time (%) = 0.00490403 (0.0944753)
Comm  time (%) = 0.297343 (5.72827)
Outpt time (%) = 0.391773 (7.54745)
Other time (%) = 0.138767 (2.67332)

Nlocal:    398 ave 398 max 398 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Nghost:    5281 ave 5281 max 5281 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Neighs:    27704 ave 27704 max 27704 min
Histogram: 1 0 0 0 0 0 0 0 0 0
FullNghs: 55442 ave 55442 max 55442 min
Histogram: 1 0 0 0 0 0 0 0 0 0

Total # of neighbors = 55442
Ave neighs/atom = 139.302
Neighbor list builds = 3
Dangerous builds = 0
undump 1

# ---------- Run Minimization 2--------------------- 
# Now allow the box to expand/contract perpendicular to the grain boundary
reset_timestep 0 
thermo 10 
thermo_style custom step pe lx ly lz press pxx pyy pzz c_eatoms 
fix 1 all box/relax y 0 vmax 0.001
min_style cg 
minimize 1e-15 1e-15 5000 5000 
Memory usage per processor = 3.43888 Mbytes
Step PotEng Lx Ly Lz Press Pxx Pyy Pzz eatoms 
       0   -1333.6024    12.807225    128.07225         4.05   -6.3617301    -262.3388     1197.774    -954.5204   -1333.6024 
      10    -1333.605    12.807225    128.20832         4.05   -841.94577   -891.13967   -20.783769   -1613.9139    -1333.605 
      20    -1333.605    12.807225    128.20608         4.05   -826.51441   -879.30405    3.3043329   -1603.5435    -1333.605 
      30    -1333.605    12.807225    128.20654         4.05   -828.43998   -880.95627     2.999739   -1607.3634    -1333.605 
      40    -1333.605    12.807225    128.20729         4.05   -832.39474   -884.11935  -0.96690522    -1612.098    -1333.605 
      42    -1333.605    12.807225    128.20679         4.05   -829.31937   -881.81499    3.5751362   -1609.7182    -1333.605 
Loop time of 0.797956 on 1 procs for 42 steps with 398 atoms

Minimization stats:
  Stopping criterion = linesearch alpha is zero
  Energy initial, next-to-last, final = 
        -1333.60243356     -1333.60504971     -1333.60504971
  Force two-norm initial, final = 4.96626 0.0149609
  Force max component initial, final = 4.96626 0.0148234
  Final line search alpha, max atom move = 6.91964e-05 1.02572e-06
  Iterations, force evaluations = 42 331

Pair  time (%) = 0.674209 (84.492)
Neigh time (%) = 0 (0)
Comm  time (%) = 0.0393722 (4.93413)
Outpt time (%) = 0.000830889 (0.104127)
Other time (%) = 0.0835438 (10.4697)

Nlocal:    398 ave 398 max 398 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Nghost:    5233 ave 5233 max 5233 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Neighs:    27721 ave 27721 max 27721 min
Histogram: 1 0 0 0 0 0 0 0 0 0
FullNghs: 55442 ave 55442 max 55442 min
Histogram: 1 0 0 0 0 0 0 0 0 0

Total # of neighbors = 55442
Ave neighs/atom = 139.302
Neighbor list builds = 0
Dangerous builds = 0

# ---------- Calculate GB Energy --------------------- 
variable minimumenergy equal -3.360000
variable esum equal "v_minimumenergy * count(all)" 
variable xseng equal "c_eatoms - (v_minimumenergy * count(all))" 
variable gbarea equal "lx * lz * 2" 
variable gbe equal "(c_eatoms - (v_minimumenergy * count(all)))/v_gbarea" 
variable gbemJm2 equal ${gbe}*16021.7733 
variable gbemJm2 equal 0.03542512656*16021.7733 
variable gbernd equal round(${gbemJm2}) 
variable gbernd equal round(567.5733469) 
print "GB energy is ${gbemJm2} mJ/m^2" 
GB energy is 567.5733469 mJ/m^2 
 
# ---------- Dump data into Data file ------------- 
reset_timestep 0 
dump 		1 all cfg 10000 dump.al_sig5_310_*.cfg id type xs ys zs c_csym c_eng fx fy fz
dump_modify     1 element Al Al
minimize 1e-15 1e-15 5000 5000
Memory usage per processor = 3.58369 Mbytes
Step PotEng Lx Ly Lz Press Pxx Pyy Pzz eatoms 
       0    -1333.605    12.807225    128.20679         4.05   -829.31937   -881.81499    3.5751362   -1609.7182    -1333.605 
       2    -1333.605    12.807225    128.20704         4.05   -830.86046   -882.97143    1.3125102   -1610.9225    -1333.605 
Loop time of 0.0632482 on 1 procs for 2 steps with 398 atoms

Minimization stats:
  Stopping criterion = linesearch alpha is zero
  Energy initial, next-to-last, final = 
        -1333.60504971     -1333.60504973     -1333.60504973
  Force two-norm initial, final = 0.0149764 0.00581102
  Force max component initial, final = 0.014839 0.0054477
  Final line search alpha, max atom move = 0.000358523 1.95313e-06
  Iterations, force evaluations = 2 20

Pair  time (%) = 0.0428157 (67.6948)
Neigh time (%) = 0 (0)
Comm  time (%) = 0.00247025 (3.90566)
Outpt time (%) = 0 (0)
Other time (%) = 0.0179622 (28.3996)

Nlocal:    398 ave 398 max 398 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Nghost:    5233 ave 5233 max 5233 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Neighs:    27721 ave 27721 max 27721 min
Histogram: 1 0 0 0 0 0 0 0 0 0
FullNghs: 55442 ave 55442 max 55442 min
Histogram: 1 0 0 0 0 0 0 0 0 0

Total # of neighbors = 55442
Ave neighs/atom = 139.302
Neighbor list builds = 0
Dangerous builds = 0
undump 1

write_restart restart.al_sig5_310_stgb

print "All done" 
All done 

The grain boundary energy is calculated as 567.57 mJ/m^2. The final configuration is stored in a restart file for future use in predicting properties of grain boundaries. Additionally, files with atomic coordinates, energies, and centrosymmetry values are dumped for post-processing.

Images and movies

Figure 1 shows a movie of minimization of the grain boundary structure for the input script show above. Figure 2 shows a movie of minimization of the grain boundary structure for a modification of the input script above. Here, the "delete_atoms overlap 0.35 lower upper" command has been modified to "delete_atoms overlap 1.5 lower upper". This eliminates two atoms that are too close to each other near the grain boundary interface.

Figure 1. Movie showing the minimization of the grain boundary structure for an aluminum Sigma5 (310) symmetric tilt grain boundary.
Figure 2. Movie showing the minimization of the grain boundary structure for an aluminum Sigma5 (310) symmetric tilt grain boundary.

Figure 3 shows the image corresponding to the input script shown above. Notice how there are two atoms that are very close to each other at the boundary in Figure 3 (shown in red, colored by potential energy, i.e., high energy atoms). The final structures are shown in Figures 4 and 5 for the input script above and the modified input script, respectively. Interestingly, with this potential, the structure in Figure 4 is actually the lower energy grain boundary structure. The different structures for this one simple grain boundary may impart slightly different properties as well. Often, the convention is to use the minimum energy grain boundary structure for properties. However, some recent research has also explored metastable higher energy grain boundary structures and their impact on properties as well.

Figure 3. Image showing the grain boundary structure prior to minimization.
Figure 4. Image showing the grain boundary structure after minimization (overlap distance equals 0.35).
Figure 5. Image showing the grain boundary structure after minimization (overlap distance equals 1.50).

Miscellaneous

Sigma5 (210)<001> and Sigma5 (310)<001> have the same configuration.

Image showing the structure of Sigma 5.

Go Back

Acknowledgments

M.A. Tschopp would like to acknowledge funding provided under an NSF graduate fellowship for the initial work. Continued funding for investigating structure-property relationships in grain boundaries under the NEAMS (Nuclear Energy Advanced Modeling and Simulation) program is also acknowledged.

References

The initial methodology was used in the following papers:

  1. Tschopp, M. A., & McDowell, D.L. (2007). Structures and energies of Sigma3 asymmetric tilt grain boundaries in Cu and Al. Philosophical Magazine, 87, 3147-3173 (http://dx.doi.org/10.1080/14786430701455321).
  2. Tschopp, M. A., & McDowell, D.L. (2007). Asymmetric tilt grain boundary structure and energy in copper and aluminum. Philosophical Magazine, 87, 3871-3892 (http://dx.doi.org/10.1016/j.commatsci.2010.02.003).
  3. S. Plimpton, "Fast Parallel Algorithms for Short-Range Molecular Dynamics," J. Comp. Phys., 117, 1-19 (1995).
Personal tools
Namespaces

Variants
Actions
home
Materials
Material Models
Design
Resources
Projects
Education
Toolbox