VASP Computing Ideal Shear Strength of Au: Difference between revisions

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</pre>
</pre>


The <tt>shear_rlx.tcl</tt> script is listed below.
Here is the [[media:vasp_au_shear_rlx_tcl.txt‎ | shear_rlx.tcl]] script.


The results will be stored in the <tt>stress_rlx.dat</tt> file. The first column is proportional to the applied shear strain. The second column is the number of iterations for relaxing the normal stress components given this shear strain. In this test case, the maximum number of iteration at each shear strain is 20. Columns 3,4,5 are the normal stresses (in kB, 1kB = 100MPa). Column 6 is the desired shear stress.
<pre>
#####################################
# definition of functions
#####################################
proc write_POSCAR { posfile a0 ax ay az bx by bz cx cy cz } {


We can select the relaxed shear stress value by the following shell command.
#set posfile "POSCAR"
set fileID [open $posfile w ]


grep " 20 " stress_rlx.dat
puts $fileID "POSCAR for FCC Au (created by tcl)"
puts $fileID "$a0"
puts $fileID [format "%15.12f %15.12f %15.12f" $ax $ay $az]
puts $fileID [format "%15.12f %15.12f %15.12f" $bx $by $bz]
puts $fileID [format "%15.12f %15.12f %15.12f" $cx $cy $cz]
puts $fileID "1"
puts $fileID "Cartesian (real coordinates r)"
puts $fileID "0 0 0"


The data can be plotted by Matlab or Gnuplot to give the following curve. The maximum stress (i.e. the ideal shear strength) is ?? MPa. (To be completed. The data we get is consistent with Ogata et al. PRB 70, 104104, 2004.)
close $fileID
}

proc read_POSCAR { posfile } {

#set posfile "POSCAR"
set fileID [open $posfile r ]

# first line is comment
gets $fileID line

# second line is a0
gets $fileID line
scan $line "%f" a0

# now comes three lines specifying the cell
gets $fileID line
scan $line "%f %f %f" ax ay az

gets $fileID line
scan $line "%f %f %f" bx by bz

gets $fileID line
scan $line "%f %f %f" cx cy cz

# skip the rest of the file
close $fileID

# return cell geometry as a list
return [list $a0 $ax $ay $az $bx $by $bz $cx $cy $cz]
}

proc get_stress { } {

set fileID [open "get_stress" w ]
puts $fileID "grep \"in kB\" OUTCAR | sed \'s/in kB //\' "
close $fileID
file attributes get_stress -permissions u+x

exec ./get_stress

}

proc run_vasp { ncpu } {

#if { $ncpu == 1 } {
# exec ./vasp
#} else {
set fileID [open "run_vasp" w ]
puts $fileID "mpiexec --comm=ib -np $ncpu ../../../../bin/vasp.2008-11-15"
close $fileID
file attributes run_vasp -permissions u+x
exec ./run_vasp
#}

}

#####################################
# beginning of main program
#####################################

if { $argc == 0 } {
set ncpu 1
} elseif { $argc > 0 } {
set ncpu [lindex $argv 0]
}
puts "ncpu = $ncpu"

# modulus in kilobar (100 MPa)
set C11 2020
set C12 1690
set C44 450

if { 0 } {
# compute nu, E using isotropic approximation
set lambda $C12
set mu [expr ($C11-$C12)/2.0 ]
set nu [expr $lambda / (2.0*($lambda + $mu)) ]
# lambda = 2*mu*nu / (1-2*nu)
set YoungsModulus [expr 2*$mu*(1+$nu) ]
puts "mu = $nu nu = $nu E = $YoungsModulus"
} else {
# directly set nu, E
set YoungsModulus 780
set nu 0.44
puts "nu = $nu E = $YoungsModulus"
}

set S11 [expr 1/$YoungsModulus ]
set S12 [expr -$nu/$YoungsModulus ]

puts "S11 = $S11 S12 = $S12"

set factor 0.4
set sig_tol 0.1

set a0 4.0615
#set a0 4.062

set ax0 [expr sqrt(6)/4]
set ay0 0
set az0 [expr -sqrt(2)/4]

set bx0 [expr sqrt(6)/6]
set by0 [expr sqrt(3)/3]
set bz0 0

set cx0 [expr sqrt(6)/4]
set cy0 0
set cz0 [expr sqrt(2)/4]

write_POSCAR "POSCAR.0" $a0 $ax0 $ay0 $az0 $bx0 $by0 $bz0 $cx0 $cy0 $cz0
#run_vasp $ncpu

puts "bx0 = $bx0"

set datafile "stress_rlx.dat"
set rlxfileID [open $datafile w ]

set max_dx_iter 50
set stop_dx_iter 50
set start_dx_iter 1
set reset_poscar 1
set max_rlx_iter 20

for { set dx_iter $start_dx_iter } { $dx_iter <= $stop_dx_iter } { incr dx_iter 1 } {

# set cell dimension: bx
set dx [expr sqrt(6)/6 * $dx_iter/$max_dx_iter]
set bx [expr $bx0 + $dx]
puts "dx = $dx bx = $bx"

# set cell dimensions other than bx
if { $dx_iter == $start_dx_iter } {
if { $reset_poscar } {
# initialize cell value
set ax $ax0
set cx $cx0
set by $by0
set az $az0
set cz $cz0
write_POSCAR "POSCAR" $a0 $ax $ay0 $az $bx $by $bz0 $cx $cy0 $cz
write_POSCAR "POSCAR.$dx_iter" $a0 $ax $ay0 $az $bx $by $bz0 $cx $cy0 $cz

} else {
# read cell value from POSCAR
set cell [ read_POSCAR "POSCAR" ]
set a0 [lindex $cell 0 ]
set ax [lindex $cell 1 ]
set ay [lindex $cell 2 ]
set az [lindex $cell 3 ]
# set bx [lindex $cell 4 ]
set by [lindex $cell 5 ]
set bz [lindex $cell 6 ]
set cx [lindex $cell 7 ]
set cy [lindex $cell 8 ]
set cz [lindex $cell 9 ]

puts "read cell geometry:"
puts " $a0"
puts " $ax $ay $az"
puts " $bx $by $bz"
puts " $cx $cy $cz"
}
}

# adjusting box to relax normal stress components to zero
for { set rlx_iter 0 } { $rlx_iter <= $max_rlx_iter } { incr rlx_iter 1 } {

run_vasp $ncpu

set stress [ get_stress ]
scan $stress "%f %f %f %f %f %f" sig_xx sig_yy sig_zz sig_xy sig_yz sig_zx

puts $rlxfileID "$dx $rlx_iter $stress"
flush $rlxfileID

if { $rlx_iter < $max_rlx_iter } {

if { 0 } {
# account for Poisson's effect
set e_xx [expr $sig_xx * $S11 + $sig_yy * $S12 + $sig_zz * $S12]
set e_yy [expr $sig_xx * $S12 + $sig_yy * $S11 + $sig_zz * $S12]
set e_zz [expr $sig_xx * $S12 + $sig_yy * $S12 + $sig_zz * $S11]

set bx [expr $e_yy * ($bx0+$dx) * $factor + $bx ]
} else {
# do not account for Poisson's effect
set e_xx [expr $sig_xx / $C11 ]
set e_yy [expr $sig_yy / $C11 ]
set e_zz [expr $sig_zz / $C11 ]
}

puts "sig_xx = $sig_xx sig_yy = $sig_yy sig_zz = $sig_zz"
puts "e_xx = $e_xx e_yy = $e_yy e_zz = $e_zz"

set ax [expr $e_xx * $ax0 * $factor + $ax ]
set cx [expr $e_xx * $cx0 * $factor + $cx ]
set by [expr $e_yy * $by0 * $factor + $by ]
set az [expr $e_zz * $az0 * $factor + $az ]
set cz [expr $e_zz * $cz0 * $factor + $cz ]

write_POSCAR "POSCAR" $a0 $ax $ay0 $az $bx $by $bz0 $cx $cy0 $cz
write_POSCAR "POSCAR.$dx_iter.[expr $rlx_iter+1]" $a0 $ax $ay0 $az $bx $by $bz0 $cx $cy0 $cz
}
}
}
close $rlxfileID

# End of program
</pre>

The TCL script uses the <tt>run_vasp</tt> script, which is listed below.

<pre>
/opt/mpiexec/bin/mpiexec --comm=pmi -np 8 ../../../../bin/vasp.caiwei.mva2
</pre>

Latest revision as of 19:52, 28 December 2010

VASP: Ideal Shear Strength of Au


Input files

Here are the basic input files required for VASP calculation. Some of the files need to be changed since we need to perform a large number of calculations.

INCAR

System = fcc Au
LWAVE = .FALSE.
ENCUT  =  400
ISMEAR  = 1
SIGMA = 0.2
ISIF = 2

To increase plane wave cutoff, we manually put PREC = HIGH or PREC = Accurate. Default value is PREC = Medium

KPOINTS

43x43x43
0        0 = automatic generation of k-points
Monkhorst
43 43 43
0 0 0

POSCAR

POSCAR for FCC Au (created by tcl)
4.0615
 0.612372435696  0.000000000000 -0.353553390593
 0.408248290464  0.577350269190  0.000000000000
 0.612372435696  0.000000000000  0.353553390593
1
Cartesian  (real coordinates r)
0    0    0

You also need to put the LDA pseudopotential file as POTCAR in this directory.

Results

Perfect crystal

First, we perform a test simulation in which we relax the electrons in a gold perfect crystal. 

 qsub vasp.pbs

The vasp.pbs script is listed below. 

#!/bin/bash
#PBS -N Au_perf.43.E4.8
#PBS -j oe
#PBS -l nodes=1:ppn=8,walltime=24:00:00
#PBS -V

### ---------------------------------------
### BEGINNING OF EXECUTION
### ---------------------------------------

echo The master node of this job is `hostname`
echo The working directory is `echo $PBS_O_WORKDIR`
echo This job runs on the following nodes:
echo `cat $PBS_NODEFILE`

ncpu=`cat $PBS_NODEFILE | wc -w`
echo "Number of processors = $ncpu "

### end of information preamble

cd $PBS_O_WORKDIR
echo $PWD
/opt/mpiexec/bin/mpiexec --comm=pmi -np $ncpu ../../../../bin/vasp.caiwei.mva2 >& $PBS_O_WORKDIR/vasp.log

We run this test case on SU-AHPCRC. The calculation takes 160 seconds (on 8 CPUs) to finish. The ground state energy is E = -4.3951 eV.

Shear deformation

Next, we apply shear strain on (111) plane along the [1 -1 0] direction. This coresponds to in our coordinate system. Due to elastic anisotropy, we need to adjust other strain components, so that the only non-zero stress component is . Due to the symmetry of this problem, it turns out that we only need to adjust normal strain components.

For each applied strain , we need to run a series of VASP calculations to find the strain components that relax all other stress components except . After that, is increased a little further and the relaxation is repeated. For each , the shear stress at the end of the relaxation is recorded. The ideal shear stress is the maximum recorded value for .

The entire calculation is submitted by the following command. 

 qsub tcl.pbs

The tcl.pbs script is listed below. 

#!/bin/bash
#PBS -N Au_shear.43.E4.rlx
#PBS -j oe
#PBS -l nodes=1:ppn=8,walltime=96:00:00
#PBS -V

### ---------------------------------------
### BEGINNING OF EXECUTION
### ---------------------------------------

echo The master node of this job is `hostname`
echo The working directory is `echo $PBS_O_WORKDIR`
echo This job runs on the following nodes:
echo `cat $PBS_NODEFILE`

ncpu=`cat $PBS_NODEFILE | wc -w`
echo "Number of processors = $ncpu "

### end of information preamble

cd $PBS_O_WORKDIR

echo $PWD

/usr/bin/tclsh shear_rlx.tcl $ncpu

Here is the shear_rlx.tcl script.

The results will be stored in the stress_rlx.dat file. The first column is proportional to the applied shear strain. The second column is the number of iterations for relaxing the normal stress components given this shear strain. In this test case, the maximum number of iteration at each shear strain is 20. Columns 3,4,5 are the normal stresses (in kB, 1kB = 100MPa). Column 6 is the desired shear stress.

We can select the relaxed shear stress value by the following shell command. 

grep " 20  " stress_rlx.dat

The data can be plotted by Matlab or Gnuplot to give the following curve. The maximum stress (i.e. the ideal shear strength) is ?? MPa. (To be completed. The data we get is consistent with Ogata et al. PRB 70, 104104, 2004.)

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