# LAMMPS Extrinsic Stacking-Fault Energy

## Contents

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

## Abstract

This tutorial demonstrates how to create an extrinsic stacking-fault in FCC metals, taking Cu as an example, and how to estimate its energy (SFE) using molecular dynamics (MD). The stacking fault is created using two different processes. The first process is the shearing of the crystal on {111} slip plane along the <112> direction, as in the actual deformation process in metals. In the second, the stacking fault is created through the thought process whereby a layer one atom thick parallel to {111} plane is removed and the material put back together. LAMMPS is used to perform MD calculations while OVITO, visualization software for atomic structures is used to visualize the stacking fault using the energy per atom and centro-symmetry parameters generated by LAMMPS.

Author(s): Dennis Williams, Richard Glaze IV, Firas Akasheh*, Mark A. Tschopp**

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

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

(**) U.S. Army Research Laboratory

## Introduction

In general, metals have crystalline structures having long-range order consisting of a repetitive unit cell. Nevertheless, crystalline materials are never perfect and normally have defects. This tutorial focuses on a planar defect which is one of the three types of crystallographic defects: line and point. In this tutorial, the focus will be on the planar defect called extrinsic stacking fault. Defects form when the regular patterns are interrupted. Extrinsic stacking faults are interstitial agglomerate of atoms occupying a plane which does not imitate a systems original sequence such as ABCABCABC… and rather ABCACBCABC… It is as if one closed plane, C in this case, has been inserted, disrupting the otherwise perfect stacking. Such straying from perfect order increases the energy of the material. The stacking-fault energy (SFE) quantifies this additional energy and is measured in terms of energy per unit area of the stacking fault. The SFE has a significant effect on the deformation behavior of metals. Metals with low stacking fault energy tend to have more twinning, more extended (partial) dislocations which have less mobility and less inclination to cross slip. This affects ductility, climb, hardening, and texture development during deformation. Also, stacking faults provide a strong barrier to dislocation motion which becomes more notable in nanoscale metallic structures.

### Description of Simulation

Slips planes occur on the plane (111) in FCC crystals. So first LAMMPS generates a FCC copper (Cu) cell with a 44.2745 x 25.5619 x 62.6263 dimension and a xyz orientation [112], [-110], and [-1-11] respectively with a total of 6200 atoms created. The boundaries of the cell structure are periodic in the x and y and free surface in the z direction. The input script file is written to simulate the insertion of a plane of atoms and calculate the extrinsic stacking fault energy $E_s$. First the initial cohesive energy $E_c$ of the relaxed cell structure is calculated; then the top region will be shift to the right while the bottom to the left to simulate the extrinsic stacking fault and disruption of the sequence; the potential energy of that system is calculated, then the cohesive energy of the extrinsic stacking fault model $E_s$ is calculated. After both values are obtained the extrinsic stacking fault energy $E_s$ can be calculated using this equation. $Y$ will then be the extra energy gained by having created the extrinsic stacking-fault.

$Y=(N*(E_s-E_c))/A$,

## Input

### LAMMPS input script for FCC

This input script was run using the July 1 2014 version of LAMMPS. The input script files were created and named sCu_ext.txt and iCu_ext.txt. sCu_ext.txt represents the file where the atoms are only slid. iCu_ext.txt represents the file where the atoms are separated and a layer of atoms is manually inserted in the gap. To run this script the alloy file, LAMMPS executable file, and script file must all be in the same destination folder. Open the command prompt and run the "lmp_win_no-mpi.exe < sCu_ext.txt" or “lmp_win_no-mpi.exe<iCu_ext.txt” and "lmp_win_no-mpi.exe" refers to the LAMMPS executable.

Input for sCu_ext.txt

 # Input file for Stack Fault Energy surface of Copper # Dennis Williams and Richard Glaze IV, 2014 # --------------- INITIALIZATION ------------------ units metal dimension 3 boundary p p s atom_style atomic variable latparam1 equal 3.615 variable x_displace1 equal \${latparam1}/sqrt(6) variable x_displace2 equal -\${latparam1}/sqrt(6) variable xdim equal \${latparam1}*sqrt(6)/2*10 variable ydim equal \${latparam1}*sqrt(2)/2*10 # ------------------ ATOM DEFINITION ------------------- lattice fcc \${latparam1} region 1 block -.001 \${xdim} -.001 \${ydim} -.001 28.875194 units box region 2 block -.001 \${xdim} -.001 \${ydim} 28.875194 30.68269 units box region 3 block -.001 \${xdim} -.001 \${ydim} 30.68269 63.17288 units box region whole block 0 \${xdim} 0 \${ydim} 0 63.17288 units box create_box 3 whole lattice fcc \${latparam1} orient x 1 1 2 orient y -1 1 0 orient z -1 -1 1 create_atoms 1 region 1 lattice fcc \${latparam1} orient x 1 1 2 orient y -1 1 0 orient z -1 -1 1 create_atoms 2 region 2 lattice fcc \${latparam1} orient x 1 1 2 orient y -1 1 0 orient z -1 -1 1 create_atoms 3 region 3 # ------------------------ FORCE FIELDS ----------------------- pair_style eam/alloy pair_coeff * * FeCuNi.eam.alloy Cu Cu Cu #---------------------------Settings---------------------------- compute csym all centro/atom fcc compute peratom all pe/atom compute eatoms all reduce sum c_peratom thermo 1 thermo_style custom step pe c_eatoms dump 1 all custom 1 dump.relax.1.* id type xs ys zs c_peratom c_csym run 0 #this command creates a model of the script before the displacement and minimization occur variable E equal "c_eatoms" variable Eo equal \$E #variable E equal "c_eatoms" computes the initial energy of the model before any sliding is done #E is necessary to store the initial energy in Eo group bot region 1 group mid region 2 group top region 3 displace_atoms bot move \${x_displace1} 0.0 0.0 units box displace_atoms top move \${x_displace2} 0.0 0.0 units box #displace_atoms command will displace the top layer in the positive x-direction and the bottom layer in the negative x-direction thus creating an extrinsic stacking-fault. fix 1 all setforce 0 0 NULL min_style cg minimize 1e-10 1e-10 1000 1000 variable Ef equal "c_eatoms" variable Cf equal 1.60217657e-16 variable A equal (\${xdim}*\${ydim})*1e-20 variable SFE equal ((\${Ef}-\${Eo})*\${Cf})/\${A} #variable Ef equal "c_eatoms" computes the final energy of the system after sliding is done #variable A is the area of the Stacking fault plane #variable Cf is the conversion factor of electro volts to millijoules #variable SFE is the stacking-fault energy of the system #--------------------------------------- #################################### # SIMULATION DONE print "All done" print "Initial energy of atoms = \${Eo} eV" print "Final energy of atoms = \${Ef} eV" print "Stacking-fault energy = \${SFE} mJ/m^2"

Input for iCu_ext.txt

 # Input file for Stack Fault Energy surface of Copper # Dennis Williams and Richard Glaze IV, 2014 # --------------- INITIALIZATION ------------------ units metal dimension 3 boundary p p s atom_style atomic variable latparam1 equal 3.615 variable z_displace equal 2.08712 variable x_displace equal \${latparam1}/sqrt(6) variable xdim equal \${latparam1}*sqrt(6)/2*10 variable ydim equal \${latparam1}*sqrt(2)/2*10 # ------------------ ATOM DEFINITION ------------------- lattice fcc \${latparam1} region 1 block -.001 \${xdim} -.001 \${ydim} -.001 28.875194 units box region 2 block -.001 \${xdim} -.001 \${ydim} 28.875194 30.68269 units box region 3 block -.001 \${xdim} -.001 \${ydim} 28.875194 63.17288 units box region whole block 0 \${xdim} 0 \${ydim} 0 63.17288 units box create_box 3 whole lattice fcc \${latparam1} orient x 1 1 2 orient y -1 1 0 orient z -1 -1 1 create_atoms 1 region 1 lattice fcc \${latparam1} orient x 1 1 2 orient y -1 1 0 orient z -1 -1 1 #create_atoms 2 region 2 lattice fcc \${latparam1} orient x 1 1 2 orient y -1 1 0 orient z -1 -1 1 create_atoms 3 region 3 # ------------------------ FORCE FIELDS ----------------------- pair_style eam/alloy pair_coeff * * FeCuNi.eam.alloy Cu Cu Cu #---------------------------Settings---------------------------- compute csym all centro/atom fcc compute peratom all pe/atom compute eatoms all reduce sum c_peratom thermo 1 thermo_style custom step pe c_eatoms dump 1 all custom 1 dump.relax.1.* id type xs ys zs c_peratom c_csym run 0 #this command creates a model of the script before the displacement and minimization occur variable E equal "c_eatoms" variable Eo equal \$E #variable E equal "c_eatoms" computes the initial energy of the model before any sliding is done #E is necessary to store the initial energy in Eo group bot region 1 group mid region 2 group top region 3 displace_atoms top move \${x_displace} 0.0 0.0 units box displace_atoms bot move \${x_displace} 0.0 0.0 units box displace_atoms top move 0.0 0.0 \${z_displace} units box create_atoms 2 region 2 #this create_atoms command will now create atoms in the gap formed when displacing the top region in the positive z-direction by one layer of atoms. fix 1 all setforce 0 0 NULL min_style cg minimize 1e-10 1e-10 1000 1000 variable Ei equal 200*-3.54022 variable Ef equal "c_eatoms" variable Cf equal 1.60217657e-16 variable A equal (\${xdim}*\${ydim})*1e-20 variable SFE equal ((\${Ef}-(\${Eo}+\${Ei}))*\${Cf})/\${A} #variable Ei is the energy of the inserted atoms #variable Ef equal "c_eatoms" computes the final energy of the system after sliding is done #variable A is the area of the Stacking fault plane #variable Cf is the conversion factor of electro volts to millijoules #variable SFE is the stacking-fault energy of the system #--------------------------------------- #################################### # SIMULATION DONE print "All done" print "Initial energy of atoms = \${Eo} eV" print "Final energy of atoms = \${Ef} eV" print "Stacking-fault energy = \${SFE} mJ/m^2"

## Output for sCu_ext.txt

### LAMMPS logfile

The log file should look like the one shown below.

 LAMMPS (July 2014) # Input file for Stack Fault Energy surface of Copper # Dennis Williams and Richard Glaze IV, 2014 # --------------- INITIALIZATION ------------------ units metal dimension 3 boundary p p s atom_style atomic variable latparam1 equal 3.615 variable x_displace1 equal \${latparam1}/sqrt(6) variable x_displace1 equal 3.6150000000000002/sqrt(6) variable x_displace2 equal -\${latparam1}/sqrt(6) variable x_displace2 equal -3.6150000000000002/sqrt(6) variable xdim equal \${latparam1}*sqrt(6)/2*10 variable xdim equal 3.6150000000000002*sqrt(6)/2*10 variable ydim equal \${latparam1}*sqrt(2)/2*10 variable ydim equal 3.6150000000000002*sqrt(2)/2*10 # ------------------ ATOM DEFINITION ------------------- lattice fcc \${latparam1} lattice fcc 3.6150000000000002 Lattice spacing in x,y,z = 3.615 3.615 3.615 region 1 block -.001 \${xdim} -.001 \${ydim} -.001 28.875194 units box region 1 block -.001 44.27452710080594 -.001 \${ydim} -.001 28.875194 units box region 1 block -.001 44.27452710080594 -.001 25.561910139893698 -.001 28.875194 units box region 2 block -.001 \${xdim} -.001 \${ydim} 28.875194 30.68269 units box region 2 block -.001 44.27452710080594 -.001 \${ydim} 28.875194 30.68269 units box region 2 block -.001 44.27452710080594 -.001 25.561910139893698 28.875194 30.68269 units box region 3 block -.001 \${xdim} -.001 \${ydim} 30.68269 63.17288 units box region 3 block -.001 44.27452710080594 -.001 \${ydim} 30.68269 63.17288 units box region 3 block -.001 44.27452710080594 -.001 25.561910139893698 30.68269 63.17288 units box region whole block 0 \${xdim} 0 \${ydim} 0 63.17288 units box region whole block 0 44.27452710080594 0 \${ydim} 0 63.17288 units box region whole block 0 44.27452710080594 0 25.561910139893698 0 63.17288 units box create_box 3 whole Created orthogonal box = (0 0 0) to (44.2745 25.5619 63.1729) 1 by 1 by 1 MPI processor grid lattice fcc \${latparam1} orient x 1 1 2 orient y -1 1 0 orient z -1 -1 1 lattice fcc 3.6150000000000002 orient x 1 1 2 orient y -1 1 0 orient z -1 -1 1 Lattice spacing in x,y,z = 5.90327 5.11238 6.26136 create_atoms 1 region 1 Created 2800 atoms lattice fcc \${latparam1} orient x 1 1 2 orient y -1 1 0 orient z -1 -1 1 lattice fcc 3.6150000000000002 orient x 1 1 2 orient y -1 1 0 orient z -1 -1 1 Lattice spacing in x,y,z = 5.90327 5.11238 6.26136 create_atoms 2 region 2 Created 200 atoms lattice fcc \${latparam1} orient x 1 1 2 orient y -1 1 0 orient z -1 -1 1 lattice fcc 3.6150000000000002 orient x 1 1 2 orient y -1 1 0 orient z -1 -1 1 Lattice spacing in x,y,z = 5.90327 5.11238 6.26136 create_atoms 3 region 3 Created 3200 atoms # ------------------------ FORCE FIELDS ----------------------- pair_style eam/alloy pair_coeff * * FeCuNi.eam.alloy Cu Cu Cu #---------------------------Settings---------------------------- compute csym all centro/atom fcc compute peratom all pe/atom compute eatoms all reduce sum c_peratom thermo 1 thermo_style custom step pe c_eatoms dump 1 all custom 1 dump.relax.1.* id type xs ys zs c_peratom c_csym run 0 WARNING: No fixes defined, atoms won't move (../verlet.cpp:54) Memory usage per processor = 9.69936 Mbytes Step PotEng eatoms 0 -21773.224 -21773.224 Loop time of -2.45636e-008 on 1 procs for 0 steps with 6200 atoms Pair time (%) = 0 (-0) Neigh time (%) = 0 (-0) Comm time (%) = 0 (-0) Outpt time (%) = 0 (-0) Other time (%) = -2.45636e-008 (100) Nlocal: 6200 ave 6200 max 6200 min Histogram: 1 0 0 0 0 0 0 0 0 0 Nghost: 6769 ave 6769 max 6769 min Histogram: 1 0 0 0 0 0 0 0 0 0 Neighs: 416000 ave 416000 max 416000 min Histogram: 1 0 0 0 0 0 0 0 0 0 FullNghs: 832000 ave 832000 max 832000 min Histogram: 1 0 0 0 0 0 0 0 0 0 Total # of neighbors = 832000 Ave neighs/atom = 134.194 Neighbor list builds = 0 Dangerous builds = 0 #this command creates a model of the script before the displacement and minimization occur variable E equal "c_eatoms" variable Eo equal \$E variable Eo equal -21773.224253325923 #variable E equal "c_eatoms" computes the initial energy of the model before any sliding is done #E is necessary to store the initial energy in Eo group bot region 1 2800 atoms in group bot group mid region 2 200 atoms in group mid group top region 3 3200 atoms in group top displace_atoms bot move \${x_displace1} 0.0 0.0 units box displace_atoms bot move 1.475817570026865 0.0 0.0 units box displace_atoms top move \${x_displace2} 0.0 0.0 units box displace_atoms top move -1.475817570026865 0.0 0.0 units box #displace_atoms command will displace the top layer in the positive x-direction and the bottom layer in the negative x-direction thus creating an extrinsic stacking-fault. fix 1 all setforce 0 0 NULL min_style cg minimize 1e-10 1e-10 1000 1000 WARNING: Resetting reneighboring criteria during minimization (../min.cpp:173) Memory usage per processor = 11.0727 Mbytes Step PotEng eatoms 0 -21770.07 -21770.07 1 -21770.859 -21770.859 2 -21770.998 -21770.998 3 -21771.036 -21771.036 4 -21771.058 -21771.058 5 -21771.072 -21771.072 6 -21771.081 -21771.081 7 -21771.085 -21771.085 8 -21771.087 -21771.087 9 -21771.088 -21771.088 10 -21771.089 -21771.089 11 -21771.089 -21771.089 12 -21771.09 -21771.09 13 -21771.091 -21771.091 14 -21771.091 -21771.091 15 -21771.092 -21771.092 16 -21771.092 -21771.092 17 -21771.092 -21771.092 18 -21771.093 -21771.093 19 -21771.093 -21771.093 20 -21771.093 -21771.093 21 -21771.093 -21771.093 22 -21771.094 -21771.094 23 -21771.094 -21771.094 24 -21771.094 -21771.094 25 -21771.095 -21771.095 26 -21771.095 -21771.095 27 -21771.095 -21771.095 28 -21771.095 -21771.095 29 -21771.096 -21771.096 30 -21771.096 -21771.096 31 -21771.096 -21771.096 32 -21771.096 -21771.096 33 -21771.096 -21771.096 34 -21771.096 -21771.096 35 -21771.096 -21771.096 36 -21771.096 -21771.096 37 -21771.097 -21771.097 38 -21771.097 -21771.097 39 -21771.097 -21771.097 40 -21771.097 -21771.097 41 -21771.097 -21771.097 42 -21771.097 -21771.097 43 -21771.097 -21771.097 44 -21771.097 -21771.097 45 -21771.097 -21771.097 46 -21771.097 -21771.097 47 -21771.097 -21771.097 48 -21771.097 -21771.097 49 -21771.097 -21771.097 50 -21771.097 -21771.097 51 -21771.097 -21771.097 52 -21771.098 -21771.098 53 -21771.098 -21771.098 54 -21771.098 -21771.098 55 -21771.098 -21771.098 56 -21771.098 -21771.098 57 -21771.098 -21771.098 58 -21771.098 -21771.098 Loop time of 11.958 on 1 procs for 58 steps with 6200 atoms Minimization stats: Stopping criterion = energy tolerance Energy initial, next-to-last, final = -21770.0696963 -21771.0979782 -21771.0979797 Force two-norm initial, final = 3.99107 0.00243331 Force max component initial, final = 0.146198 7.82345e-005 Final line search alpha, max atom move = 0.125 9.77932e-006 Iterations, force evaluations = 58 191 Pair time (%) = 5.59371 (46.778) Neigh time (%) = 0 (0) Comm time (%) = 0.0180192 (0.150687) Outpt time (%) = 6.17811 (51.6652) Other time (%) = 0.168138 (1.40608) Nlocal: 6200 ave 6200 max 6200 min Histogram: 1 0 0 0 0 0 0 0 0 0 Nghost: 6768 ave 6768 max 6768 min Histogram: 1 0 0 0 0 0 0 0 0 0 Neighs: 419200 ave 419200 max 419200 min Histogram: 1 0 0 0 0 0 0 0 0 0 FullNghs: 838400 ave 838400 max 838400 min Histogram: 1 0 0 0 0 0 0 0 0 0 Total # of neighbors = 838400 Ave neighs/atom = 135.226 Neighbor list builds = 0 Dangerous builds = 0 variable Ef equal "c_eatoms" variable Cf equal 1.60217657e-16 variable A equal (\${xdim}*\${ydim})*1e-20 variable A equal (44.27452710080594*\${ydim})*1e-20 variable A equal (44.27452710080594*25.561910139893698)*1e-20 variable SFE equal ((\${Ef}-\${Eo})*\${Cf})/\${A} variable SFE equal ((-21771.097979613118-\${Eo})*\${Cf})/\${A} variable SFE equal ((-21771.097979613118--21773.224253325923)*\${Cf})/\${A} variable SFE equal ((-21771.097979613118--21773.224253325923)*1.6021765700000001e-016)/\${A} variable SFE equal ((-21771.097979613118--21773.224253325923)*1.6021765700000001e-016)/1.1317414832370896e-017 #variable Ef equal "c_eatoms" computes the final energy of the system after sliding is done #variable A is the area of the Stacking fault plane #variable Cf is the conversion factor of electro volts to millijoules #variable SFE is the stacking-fault energy of the system #--------------------------------------- #################################### # SIMULATION DONE print "All done" All done print "Initial energy of atoms = \${Eo} eV" Initial energy of atoms = -21773.224253325923 eV print "Final energy of atoms = \${Ef} eV" Final energy of atoms = -21771.097979613118 eV print "Stacking-fault energy = \${SFE} mJ/m^2" Stacking-fault energy = 30.101096182493457 mJ/m^2

## Output for iCu_ext.txt

### LAMMPS logfile

The log file for second script should look like this:

 LAMMPS (July 2014) # Input file for Stack Fault Energy surface of Copper # Dennis Williams and Richard Glaze IV, 2014 # --------------- INITIALIZATION ------------------ units metal dimension 3 boundary p p s atom_style atomic variable latparam1 equal 3.615 variable z_displace equal 2.08712 variable x_displace equal \${latparam1}/sqrt(6) variable x_displace equal 3.6150000000000002/sqrt(6) variable xdim equal \${latparam1}*sqrt(6)/2*10 variable xdim equal 3.6150000000000002*sqrt(6)/2*10 variable ydim equal \${latparam1}*sqrt(2)/2*10 variable ydim equal 3.6150000000000002*sqrt(2)/2*10 # ------------------ ATOM DEFINITION ------------------- lattice fcc \${latparam1} lattice fcc 3.6150000000000002 Lattice spacing in x,y,z = 3.615 3.615 3.615 region 1 block -.001 \${xdim} -.001 \${ydim} -.001 28.875194 units box region 1 block -.001 44.27452710080594 -.001 \${ydim} -.001 28.875194 units box region 1 block -.001 44.27452710080594 -.001 25.561910139893698 -.001 28.875194 units box region 2 block -.001 \${xdim} -.001 \${ydim} 28.875194 30.68269 units box region 2 block -.001 44.27452710080594 -.001 \${ydim} 28.875194 30.68269 units box region 2 block -.001 44.27452710080594 -.001 25.561910139893698 28.875194 30.68269 units box region 3 block -.001 \${xdim} -.001 \${ydim} 28.875194 63.17288 units box region 3 block -.001 44.27452710080594 -.001 \${ydim} 28.875194 63.17288 units box region 3 block -.001 44.27452710080594 -.001 25.561910139893698 28.875194 63.17288 units box region whole block 0 \${xdim} 0 \${ydim} 0 63.17288 units box region whole block 0 44.27452710080594 0 \${ydim} 0 63.17288 units box region whole block 0 44.27452710080594 0 25.561910139893698 0 63.17288 units box create_box 3 whole Created orthogonal box = (0 0 0) to (44.2745 25.5619 63.1729) 1 by 1 by 1 MPI processor grid lattice fcc \${latparam1} orient x 1 1 2 orient y -1 1 0 orient z -1 -1 1 lattice fcc 3.6150000000000002 orient x 1 1 2 orient y -1 1 0 orient z -1 -1 1 Lattice spacing in x,y,z = 5.90327 5.11238 6.26136 create_atoms 1 region 1 Created 2800 atoms lattice fcc \${latparam1} orient x 1 1 2 orient y -1 1 0 orient z -1 -1 1 lattice fcc 3.6150000000000002 orient x 1 1 2 orient y -1 1 0 orient z -1 -1 1 Lattice spacing in x,y,z = 5.90327 5.11238 6.26136 #create_atoms 2 region 2 lattice fcc \${latparam1} orient x 1 1 2 orient y -1 1 0 orient z -1 -1 1 lattice fcc 3.6150000000000002 orient x 1 1 2 orient y -1 1 0 orient z -1 -1 1 Lattice spacing in x,y,z = 5.90327 5.11238 6.26136 create_atoms 3 region 3 Created 3400 atoms # ------------------------ FORCE FIELDS ----------------------- pair_style eam/alloy pair_coeff * * FeCuNi.eam.alloy Cu Cu Cu #---------------------------Settings---------------------------- compute csym all centro/atom fcc compute peratom all pe/atom compute eatoms all reduce sum c_peratom thermo 1 thermo_style custom step pe c_eatoms dump 1 all custom 1 dump.relax.1.* id type xs ys zs c_peratom c_csym run 0 WARNING: No fixes defined, atoms won't move (../verlet.cpp:54) Memory usage per processor = 9.69936 Mbytes Step PotEng eatoms 0 -21773.224 -21773.224 Loop time of 1.12923e-007 on 1 procs for 0 steps with 6200 atoms Pair time (%) = 0 (0) Neigh time (%) = 0 (0) Comm time (%) = 0 (0) Outpt time (%) = 0 (0) Other time (%) = 1.12923e-007 (100) Nlocal: 6200 ave 6200 max 6200 min Histogram: 1 0 0 0 0 0 0 0 0 0 Nghost: 6769 ave 6769 max 6769 min Histogram: 1 0 0 0 0 0 0 0 0 0 Neighs: 416000 ave 416000 max 416000 min Histogram: 1 0 0 0 0 0 0 0 0 0 FullNghs: 832000 ave 832000 max 832000 min Histogram: 1 0 0 0 0 0 0 0 0 0 Total # of neighbors = 832000 Ave neighs/atom = 134.194 Neighbor list builds = 0 Dangerous builds = 0 #this command creates a model of the script before the displacement and minimization occur variable E equal "c_eatoms" variable Eo equal \$E variable Eo equal -21773.224253325923 #variable E equal "c_eatoms" computes the initial energy of the model before any sliding is done #E is necessary to store the initial energy in Eo group bot region 1 2800 atoms in group bot group mid region 2 200 atoms in group mid group top region 3 3400 atoms in group top displace_atoms top move \${x_displace} 0.0 0.0 units box displace_atoms top move 1.475817570026865 0.0 0.0 units box displace_atoms bot move \${x_displace} 0.0 0.0 units box displace_atoms bot move 1.475817570026865 0.0 0.0 units box displace_atoms top move 0.0 0.0 \${z_displace} units box displace_atoms top move 0.0 0.0 2.0871200000000001 units box create_atoms 2 region 2 Created 200 atoms #this create_atoms command will now create atoms in the gap formed when displacing the top region in the positive z-direction by one layer of atoms. fix 1 all setforce 0 0 NULL min_style cg minimize 1e-10 1e-10 1000 1000 WARNING: Resetting reneighboring criteria during minimization (../min.cpp:173) Memory usage per processor = 11.0735 Mbytes Step PotEng eatoms 0 -22478.113 -22478.113 1 -22478.903 -22478.903 2 -22479.042 -22479.042 3 -22479.079 -22479.079 4 -22479.101 -22479.101 5 -22479.115 -22479.115 6 -22479.125 -22479.125 7 -22479.129 -22479.129 8 -22479.131 -22479.131 9 -22479.132 -22479.132 10 -22479.133 -22479.133 11 -22479.133 -22479.133 12 -22479.133 -22479.133 13 -22479.134 -22479.134 14 -22479.135 -22479.135 15 -22479.135 -22479.135 16 -22479.136 -22479.136 17 -22479.136 -22479.136 18 -22479.136 -22479.136 19 -22479.137 -22479.137 20 -22479.137 -22479.137 21 -22479.137 -22479.137 22 -22479.138 -22479.138 23 -22479.138 -22479.138 24 -22479.138 -22479.138 25 -22479.138 -22479.138 26 -22479.138 -22479.138 27 -22479.138 -22479.138 28 -22479.139 -22479.139 29 -22479.139 -22479.139 30 -22479.139 -22479.139 31 -22479.139 -22479.139 32 -22479.139 -22479.139 33 -22479.139 -22479.139 34 -22479.14 -22479.14 35 -22479.14 -22479.14 36 -22479.141 -22479.141 37 -22479.141 -22479.141 38 -22479.141 -22479.141 39 -22479.141 -22479.141 40 -22479.141 -22479.141 41 -22479.141 -22479.141 42 -22479.141 -22479.141 43 -22479.141 -22479.141 44 -22479.141 -22479.141 45 -22479.141 -22479.141 46 -22479.141 -22479.141 47 -22479.141 -22479.141 48 -22479.142 -22479.142 49 -22479.142 -22479.142 50 -22479.142 -22479.142 51 -22479.142 -22479.142 52 -22479.142 -22479.142 53 -22479.142 -22479.142 54 -22479.142 -22479.142 55 -22479.142 -22479.142 56 -22479.142 -22479.142 57 -22479.142 -22479.142 58 -22479.142 -22479.142 59 -22479.142 -22479.142 60 -22479.142 -22479.142 61 -22479.142 -22479.142 62 -22479.142 -22479.142 63 -22479.142 -22479.142 64 -22479.142 -22479.142 65 -22479.142 -22479.142 66 -22479.142 -22479.142 67 -22479.142 -22479.142 Loop time of 14.3226 on 1 procs for 67 steps with 6400 atoms Minimization stats: Stopping criterion = energy tolerance Energy initial, next-to-last, final = -22478.1133611 -22479.1416331 -22479.1416339 Force two-norm initial, final = 3.99107 0.00214074 Force max component initial, final = 0.146198 6.12736e-005 Final line search alpha, max atom move = 0.125 7.6592e-006 Iterations, force evaluations = 67 221 Pair time (%) = 6.31521 (44.0928) Neigh time (%) = 0 (0) Comm time (%) = 0.024026 (0.167749) Outpt time (%) = 7.8152 (54.5657) Other time (%) = 0.168119 (1.1738) Nlocal: 6400 ave 6400 max 6400 min Histogram: 1 0 0 0 0 0 0 0 0 0 Nghost: 6986 ave 6986 max 6986 min Histogram: 1 0 0 0 0 0 0 0 0 0 Neighs: 433200 ave 433200 max 433200 min Histogram: 1 0 0 0 0 0 0 0 0 0 FullNghs: 866400 ave 866400 max 866400 min Histogram: 1 0 0 0 0 0 0 0 0 0 Total # of neighbors = 866400 Ave neighs/atom = 135.375 Neighbor list builds = 0 Dangerous builds = 0 variable Ei equal 200*-3.54022 variable Ef equal "c_eatoms" variable Cf equal 1.60217657e-16 variable A equal (\${xdim}*\${ydim})*1e-20 variable A equal (44.27452710080594*\${ydim})*1e-20 variable A equal (44.27452710080594*25.561910139893698)*1e-20 variable SFE equal ((\${Ef}-(\${Eo}+\${Ei}))*\${Cf})/\${A} variable SFE equal ((-22479.141633815099-(\${Eo}+\${Ei}))*\${Cf})/\${A} variable SFE equal ((-22479.141633815099-(-21773.224253325923+\${Ei}))*\${Cf})/\${A} variable SFE equal ((-22479.141633815099-(-21773.224253325923+-708.04399999999998))*\${Cf})/\${A} variable SFE equal ((-22479.141633815099-(-21773.224253325923+-708.04399999999998))*1.6021765700000001e-016)/\${A} variable SFE equal ((-22479.141633815099-(-21773.224253325923+-708.04399999999998))*1.6021765700000001e-016)/1.1317414832370896e-017 #variable Ei is the energy of the inserted atoms #variable Ef equal "c_eatoms" computes the final energy of the system after sliding is done #variable A is the area of the Stacking fault plane #variable Cf is the conversion factor of electro volts to millijoules #variable SFE is the stacking-fault energy of the system #--------------------------------------- #################################### # SIMULATION DONE print "All done" All done print "Initial energy of atoms = \${Eo} eV" Initial energy of atoms = -21773.224253325923 eV print "Final energy of atoms = \${Ef} eV" Final energy of atoms = -22479.141633815099 eV print "Stacking-fault energy = \${SFE} mJ/m^2" Stacking-fault energy = 30.105991553865966 mJ/m^2

## Post-Processing

### Visualization

The atomic structure during the simulation can be visualized using specialized software, in our case OVITO (www.ovito.org; developer: Alexander Stukowski). First, open Ovito. Then, select File, then Open Local Files. Then, navigate to the directory of the dump files LAMMPS created. The first dump file, dump.relax.1.0 should be the visualization of the model before sliding. An image of what you should see is located in Figure 1. Different colors are used to distinguish the two halves of the crystal which will be displaced with respect to each other. Now, if you would like the view the model after the sliding or the removal of a layer is done, go back to File and Open Local Files. Then, locate the last dump file created and double click it or single click it and press Open. The image that should appear can be seen in Figure 2. Notice how the stacking order is disrupted at the mid plane in comparison to the perfect stacking shown in Figure 1. To visually see the stacking fault you have two options. In both options, you use the Color coding option under the “Add modification…” drop box in Ovito. The first option is by Color coding by the property titled “c_peratom”. This option shows you the energy per atom. The other option is to color code the model by “c_csym”. This means they are color coded by their center of symmetry. For both of these options you are required to create a Slice which would get rid of the surface atoms as their center of symmetry and energy are too high. To do this you have to choose the “Slice” option under the “Add modification…” drop box. Set the normal to x and y to be 0 while the normal to the z direction is set to 1. Then, set the slice width high enough that it includes all but 6 layers. Finally, adjust the distance until it only excludes the 6 outer layers. After this step, you can resume to Color coding by “c_peratom” or “c_csym”. Make sure the Color coding option is above the Slice option in the area marked “Modifications”, then press “Adjust range”. Figure 3 shows the model color coded by the energy per atom. Figure 4 has the model color coded by the atoms’ center of symmetry. A close up of the normal stacking arrangement (B-C-A) can be found in Figure 5. Figure 6 has a close up of the stacking fault. This figure shows proof that the stacking-fault has been correctly created.

Figure 1: Model before slipping or deleting with 3600 atoms created by two layers of 1800 atoms.
Figure 2: Model after the sliding or deleting (depending on which script you chose to run) is complete.
Figure 3: (a) side (b) top view of the perfect stacking arrangement A-C-B before slipping or deleting.
Figure 4: (a) side (b) top view of the stacking arrangement after sliding/deleting. Notice the gap in between atoms in the top view because the first and third layer are aligned proving it’s an B-C-B arrangement.
Figure. 5: Visualization of the intrinsic stacking fault, (a) color coded by the centrosymmetry parameter, and (b) color coded by energy per atom. The layers in the middle where the stacking fault was created have higher energies than surrounding layers

## Acknowledgments

We 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 gratefully acknowledged.