VASP Computing Elastic Constants of Au: Difference between revisions

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VASP: Computing Elastic Constants of Au</STRONG></font></P>
VASP: Computing Elastic Constants of Au</STRONG></font></P>
<DIV>
<DIV>
<P ALIGN="CENTER"><STRONG> </STRONG></P>
<P ALIGN="CENTER"><STRONG> Modified by Yanming Wang (Sep, 2015)</STRONG></P>
</DIV>
</DIV>


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===Input files===
===Input files===


Here we give an example of how to use VASP to compute the elastic constants C11, C12 and C44 of Au. We performed this calculation on <tt>MC2</tt> in PARALLEL mode in <tt>~/Codes/VASP/runs/Au_bulk_C11</tt> and <tt>~/Codes/VASP/runs/Au_bulk_C44</tt> two directories. Each directory contains the following files.
(Under construction!!!)

Here we give an example of how to use VASP to compute the elastic constants C11 and C44 of LDA-Au. We performed this calculation on <tt>MC-CC</tt> in PARALLEL model in the <tt>~/Codes/VASP/runs/Au/LDA/perfect.21x21x21</tt> directory. This directory contains the following files.


'''INCAR'''
'''INCAR'''


<pre>
<pre>
PREC = High
ENCUT = 400 or 500??

ISIF = 2 ! It relaxes atoms but keep cell volme fixed!
ISMEAR = 1
ISTART = 0
ICHARG = 2
ISMEAR = 1
SIGMA = 0.1
SIGMA = 0.1

EDIFF = 1E-09
NELM = 40
ENMAX = 500
ENCUT = 500

ISIF = 2
NSW = 100
IBRION = 2
</pre>
</pre>


Line 32: Line 41:
</pre>
</pre>


'''POSCAR'''
'''POSCAR '''

Here's an example for Au C11 and C12 calculation, which will be changed later in PBS script every iteration.


<pre>
<pre>
POSCAR for FCC Au (created manually)
POSCAR for FCC Au (created manually)
POSCAR for FCC Au
POSCAR for FCC Au
4.062241 from acurate VASP lattice calculation
4.067877 from acurate VASP lattice calculation
1.000 0.0 0.0 first Bravais lattice vector
1.000 0.0 0.0 first Bravais lattice vector
0.0 1.0 0.0 second Bravais lattice vector
0.0 1.0 0.0 second Bravais lattice vector
0.0 0.0 1.0 third Bravais lattice vector
0.0 0.0 1.0 third Bravais lattice vector
4 number of atoms per species
4 number of atoms per species
selective dynamics
selective dynamics
direct direct or cart (only first letter is significant)
direct direct or cart (only first letter is significant)
0.00000 0.00000 0.00000 T T T
0.0000 0.0000 0.0000 T T T
0.50000 0.50000 0.00000 T T T
0.5000 0.5000 0.0000 T T T
0.00000 0.50000 0.50000 T T T
0.0000 0.5000 0.5000 T T T
0.50000 0.00000 0.50000 T T T
0.5000 0.0000 0.5000 T T T
</pre>
</pre>


Here's an example for Si C44 calculation, which will be changed later in PBS script every iteration.
To do this calculation, you also need to put the LDA pseudopotential file as <tt>POTCAR</tt> in this directory.
<pre>
POSCAR for FCC Au
4.067877 universal scaling factor
1.000 1.000 0.0 first lattice vector
-1.0 1.0 0.0 second lattice vector
0.0 0.0 1.0 third lattice vector
8 number of atoms per species
selective dynamics
direct direct or cart (only first letter is significant)
0.0000 0.5000 0.0000 T T T
0.2500 0.7500 0.5000 T T T
0.0000 0.0000 0.0000 T T T
0.5000 0.0000 0.0000 T T T
0.2500 0.2500 0.5000 T T T
0.5000 0.5000 0.0000 T T T
0.7500 0.7500 0.5000 T T T
0.7500 0.2500 0.5000 T T T
</pre>


'''POTCAR'''
===Run VASP===


In this example, we currently choose the US-LDA PP of Au provided by VASP. We will provide results of simulations with Au PAW-LDA PP in the later section.
Now we are ready to run


===Run VASP===
vasp


To compute the elastic constants we use the following script <tt>auto.B.serial</tt> to run <tt>vasp</tt> repeated with different values for the first C11 component of the first Bravais lattice vector. Make sure you have previously calculated the equilibrium lattice constant for
To compute the elastic constants, we prepared the following PBS scripts to submit the jobs to MC2 cluster. <tt>vasp.pbs.C11</tt> is used to to run <tt>vasp</tt> repeated with different values for the first component of the first Bravais lattice vector, '''$a'''. Here we put 4.067877 as the length of the lattice constant in the script, which is obtained from our previous VASP calculation. In generally, you are expected to put a reliable value from your lattice constant calculation with the same PP. The script automatically creates the POSCAR file for every '''a''' specified in the script in the range from 0.997 to 1.003. For C44 calculation, the PBS script <tt>vasp.pbs.C44</tt> changes the value of '''$a''' for the first and second component of the first Bravais lattice vector.

this supercell with 4 atoms, otherwise errors in the calculations could arise.
'''PBS Script for C11'''


<pre>
<pre>
#!/bin/bash
#!/bin/bash
#PBS -N vasp.Au.C11
#PBS -j oe
#PBS -l nodes=1:ppn=8,walltime=48:00:00
#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

cd $PBS_O_WORKDIR

module load vasp

rm WAVECAR
rm WAVECAR
for a in 0.997 0.998 0.999 1.000 1.001 1.002 1.003
for a in 0.997 0.998 0.999 1.000 1.001 1.002 1.003
Line 68: Line 125:
cat > POSCAR << FIN
cat > POSCAR << FIN
POSCAR for FCC Au
POSCAR for FCC Au
4.062241 from acurate VASP lattice calculation
4.067877 accurate equilibrium lattice constant
$a 0.0 0.0 first Bravais lattice vector
$a 0.0 0.0 first Bravais lattice vector
0.0 1.0 0.0 second Bravais lattice vector
0.0 1.0 0.0 second Bravais lattice vector
0.0 0.0 1.0 third Bravais lattice vector
0.0 0.0 1.0 third Bravais lattice vector
4 number of atoms per species
4 number of atoms per species
selective dynamics
selective dynamics
direct direct or cart (only first letter is significant)
direct direct or cart (only first letter is significant)
0.00000 0.00000 0.00000 T T T
0.0000 0.0000 0.0000 T T T
0.50000 0.50000 0.00000 T T T
0.5000 0.5000 0.0000 T T T
0.00000 0.50000 0.50000 T T T
0.0000 0.5000 0.5000 T T T
0.50000 0.00000 0.50000 T T T
0.5000 0.0000 0.5000 T T T
FIN
FIN


echo "a=$a"
echo "a=$a ncpu=$ncpu"

./vasp
cmd="mpiexec -np $ncpu vasp"
$cmd >& vasp.log


E=`tail -1 OSZICAR`
E=`tail -1 OSZICAR`
echo $a $E | sed -s 's/F=//; s/E0=//; s/d E =//;' >> Elatt.C11.dat
echo $a $E | sed -s 's/F=//; s/E0=//; s/d E =//;' >> Elatt.C11.dat


done
p=`grep pressure OUTCAR | cut -b 25-34`
</pre>
echo $a $p >> platt.C11.dat

'''PBS script for C44'''

<pre>
#!/bin/bash
#PBS -N vasp.Au.C44
#PBS -j oe
#PBS -l nodes=1:ppn=8,walltime=48:00:00
#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

cd $PBS_O_WORKDIR

module load vasp

rm WAVECAR
for a in 0.997 0.998 0.999 1.000 1.001 1.002 1.003
do
cat > POSCAR << FIN
POSCAR for FCC Au
4.067877 accurate equilibrium lattice constant
$a $a 0.0 first lattice vector
-1.0 1.0 0.0 second lattice vector
0.0 0.0 1.0 third lattice vector
8 number of atoms per species
selective dynamics
direct direct or cart (only first letter is significant)
0.0000 0.5000 0.0000 T T T
0.2500 0.7500 0.5000 T T T
0.0000 0.0000 0.0000 T T T
0.5000 0.0000 0.0000 T T T
0.2500 0.2500 0.5000 T T T
0.5000 0.5000 0.0000 T T T
0.7500 0.7500 0.5000 T T T
0.7500 0.2500 0.5000 T T T
FIN

echo "a=$a ncpu=$ncpu"

cmd="mpiexec -np $ncpu vasp"
$cmd >& vasp.log

E=`tail -1 OSZICAR`
echo $a $E | sed -s 's/F=//; s/E0=//; s/d E =//;' >> Elatt.C44.dat


done
done
Line 95: Line 215:
===Analyze data===
===Analyze data===


After running it as <tt>./auto.B.serial</tt>, it will create data files <tt>Elatt.C11.dat</tt> and <tt>platt.C11.dat</tt>.
After running the two scripts above for C11 and C44, the data files: <tt>Elatt.C11.dat</tt> and <tt>Elatt.C44.dat</tt> will be created.


If you choose your POTCAR for US-LDA PP, the date should be similar to
Launch <tt>octave</tt> and run the following functions [[media:fit_a0EB.m.txt | fit_a0EB.m]] and [[media:fit_a0B.m.txt | fit_a0B.m]],


fit_a0EB('Elatt.B.dat');
<tt>Elatt.C11.dat</tt>
<pre>
fit_a0B ('platt.B.dat');
0.997 1 -.17546258E+02 -.17546235E+02 -.175463E+02
0.998 1 -.17546476E+02 -.17546452E+02 -.175465E+02
0.999 1 -.17546606E+02 -.17546580E+02 -.175466E+02
1.000 1 -.17546649E+02 -.17546622E+02 -.175466E+02
1.001 1 -.17546605E+02 -.17546577E+02 -.175466E+02
1.002 1 -.17546476E+02 -.17546446E+02 -.175465E+02
1.003 1 -.17546261E+02 -.17546229E+02 -.175463E+02
</pre>


<tt>Elatt.C44.dat</tt>
The first line fits the energy data to a quadratic curve and computes the equilibrium lattice constant, cohesive energy and bulk modulus. (Refer to previous calculation?!)
<pre>
The second and third lines compute the elastic constants C11 and C44 which the results 214 GPa and 42 GPa respectively.
0.997 1 -.35092701E+02 -.35092739E+02 -.350927E+02
0.998 1 -.35093172E+02 -.35093210E+02 -.350932E+02
0.999 1 -.35093440E+02 -.35093474E+02 -.350934E+02
1.000 1 -.35093511E+02 -.35093539E+02 -.350935E+02
1.001 1 -.35093392E+02 -.35093411E+02 -.350934E+02
1.002 1 -.35093087E+02 -.35093098E+02 -.350931E+02
1.003 1 -.35092601E+02 -.35092607E+02 -.350926E+02
</pre>


Download the following Matlab functions.
===Parallel computation===
[[media:fit_a0EB.m.txt | fit_a0EB.m]],
[[media:fit_C11EB.m.txt | fit_C11EB.m]],
[[media:fit_C44EB.m.txt | fit_C44EB.m]],


Place the data files of <tt>Elatt.C11.dat</tt>, <tt>Elatt.C44.dat</tt>, <tt>Elatt.B.dat</tt> from [[VASP_Computing_Bulk_Modulus_of_Au | Bulk modulus calculation of Au]]
To run <tt>vasp</tt> in parallel, you need to submit [[media:vasp.pbs.txt | vasp.pbs]] as


Launch <tt>Matlab</tt>, and type the following commands.
qsub vasp.pbs
[a0, Ecoh, B] = fit_a0EB('Elatt.B.dat',4,4);
[C11,C12] = fit_C11EB('Elatt.C11.dat',a0,B);
C44 = fit_C44EB('Elatt.C44.dat',a0,C11,C12);


The first line fits the energy data to a quadratic curve and computes the equilibrium lattice constant, cohesive energy and bulk modulus(['''a0, Ecoh, B]''') respectively. The first '''4''' specifies the number of atoms in the computation cell and the second '''4''' is the number of atoms in a conventional unit cell.
The second lines computes the C11 and C12 elastic constants and the third line calculates C44. Suggested results are C11 = 206 GPa, C12 = 176 GPa and C44 = 36 GPa for calculations with US-LDA PP.


<span style="background:yellow"> '''C44 of 36 GPa is a bit lower than the paper's result of 47 GPa (The experimental value is 45 GPa).''' </span>
You will need the following two files to do this calculation in parallel on SU-AHPCRC:
[[media:auto.B.par.Au.txt | auto.B.par]] and
[[media:B.pbs.Au.txt | B.pbs]].

Latest revision as of 05:42, 6 September 2015

VASP: Computing Elastic Constants of Au

Modified by Yanming Wang (Sep, 2015)


Input files

Here we give an example of how to use VASP to compute the elastic constants C11, C12 and C44 of Au. We performed this calculation on MC2 in PARALLEL mode in ~/Codes/VASP/runs/Au_bulk_C11 and ~/Codes/VASP/runs/Au_bulk_C44 two directories. Each directory contains the following files.

INCAR 

PREC = High

ISTART = 0 
ICHARG = 2  
ISMEAR = 1
SIGMA = 0.1

EDIFF  = 1E-09  
NELM = 40      
ENMAX = 500     
ENCUT = 500    

ISIF = 2 
NSW = 100  
IBRION = 2

KPOINTS 

21x21x21
0        0 = automatic generation of k-points
Monkhorst
21 21 21
0 0 0

POSCAR

Here's an example for Au C11 and C12 calculation, which will be changed later in PBS script every iteration. 

POSCAR for FCC Au (created manually)
POSCAR for FCC Au
4.067877         from acurate VASP lattice calculation
1.000  0.0 0.0     first  Bravais lattice vector
0.0 1.0 0.0     second Bravais lattice vector
0.0 0.0 1.0     third  Bravais lattice vector
4               number of atoms per species
selective dynamics
direct           direct or cart (only first letter is significant)
0.0000  0.0000  0.0000 T T T
0.5000  0.5000  0.0000 T T T
0.0000  0.5000  0.5000 T T T
0.5000  0.0000  0.5000 T T T

Here's an example for Si C44 calculation, which will be changed later in PBS script every iteration. 

POSCAR for FCC Au
4.067877         universal scaling factor
1.000  1.000  0.0     first  lattice vector
-1.0 1.0 0.0     second lattice vector
0.0 0.0 1.0     third  lattice vector
8               number of atoms per species
selective dynamics
direct           direct or cart (only first letter is significant)
0.0000    0.5000    0.0000  T T T
0.2500    0.7500    0.5000  T T T
0.0000    0.0000    0.0000  T T T
0.5000    0.0000    0.0000  T T T
0.2500    0.2500    0.5000  T T T
0.5000    0.5000    0.0000  T T T
0.7500    0.7500    0.5000  T T T
0.7500    0.2500    0.5000  T T T

POTCAR

In this example, we currently choose the US-LDA PP of Au provided by VASP. We will provide results of simulations with Au PAW-LDA PP in the later section.

Run VASP

To compute the elastic constants, we prepared the following PBS scripts to submit the jobs to MC2 cluster. vasp.pbs.C11 is used to to run vasp repeated with different values for the first component of the first Bravais lattice vector, $a. Here we put 4.067877 as the length of the lattice constant in the script, which is obtained from our previous VASP calculation. In generally, you are expected to put a reliable value from your lattice constant calculation with the same PP. The script automatically creates the POSCAR file for every a specified in the script in the range from 0.997 to 1.003. For C44 calculation, the PBS script vasp.pbs.C44 changes the value of $a for the first and second component of the first Bravais lattice vector.

PBS Script for C11 

#!/bin/bash
#PBS -N vasp.Au.C11
#PBS -j oe
#PBS -l nodes=1:ppn=8,walltime=48:00:00
#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

cd $PBS_O_WORKDIR

module load vasp

rm WAVECAR 
for a in 0.997 0.998 0.999 1.000 1.001 1.002 1.003
do
cat > POSCAR << FIN
POSCAR for FCC Au
4.067877        accurate equilibrium lattice constant
$a  0.0 0.0     first  Bravais lattice vector
0.0 1.0 0.0     second Bravais lattice vector
0.0 0.0 1.0     third  Bravais lattice vector
4               number of atoms per species
selective dynamics
direct           direct or cart (only first letter is significant)
0.0000  0.0000  0.0000 T T T
0.5000  0.5000  0.0000 T T T
0.0000  0.5000  0.5000 T T T
0.5000  0.0000  0.5000 T T T
FIN

echo "a=$a  ncpu=$ncpu"

cmd="mpiexec -np $ncpu vasp"
$cmd >& vasp.log

E=`tail -1 OSZICAR`
echo $a $E | sed -s 's/F=//; s/E0=//; s/d E =//;' >> Elatt.C11.dat

done

PBS script for C44 

#!/bin/bash
#PBS -N vasp.Au.C44
#PBS -j oe
#PBS -l nodes=1:ppn=8,walltime=48:00:00
#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

cd $PBS_O_WORKDIR

module load vasp

rm WAVECAR 
for a in 0.997 0.998 0.999 1.000 1.001 1.002 1.003
do
cat > POSCAR << FIN
POSCAR for FCC Au
4.067877        accurate equilibrium lattice constant 
$a  $a  0.0     first  lattice vector
-1.0 1.0 0.0    second lattice vector
0.0 0.0 1.0     third  lattice vector
8               number of atoms per species
selective dynamics
direct          direct or cart (only first letter is significant)
0.0000    0.5000    0.0000  T T T
0.2500    0.7500    0.5000  T T T
0.0000    0.0000    0.0000  T T T
0.5000    0.0000    0.0000  T T T
0.2500    0.2500    0.5000  T T T
0.5000    0.5000    0.0000  T T T
0.7500    0.7500    0.5000  T T T
0.7500    0.2500    0.5000  T T T
FIN

echo "a=$a  ncpu=$ncpu"

cmd="mpiexec -np $ncpu vasp"
$cmd >& vasp.log

E=`tail -1 OSZICAR`
echo $a $E | sed -s 's/F=//; s/E0=//; s/d E =//;' >> Elatt.C44.dat

done

Analyze data

After running the two scripts above for C11 and C44, the data files: Elatt.C11.dat and Elatt.C44.dat will be created.

If you choose your POTCAR for US-LDA PP, the date should be similar to

Elatt.C11.dat 

0.997 1  -.17546258E+02  -.17546235E+02 -.175463E+02
0.998 1  -.17546476E+02  -.17546452E+02 -.175465E+02
0.999 1  -.17546606E+02  -.17546580E+02 -.175466E+02
1.000 1  -.17546649E+02  -.17546622E+02 -.175466E+02
1.001 1  -.17546605E+02  -.17546577E+02 -.175466E+02
1.002 1  -.17546476E+02  -.17546446E+02 -.175465E+02
1.003 1  -.17546261E+02  -.17546229E+02 -.175463E+02

Elatt.C44.dat 

0.997 1  -.35092701E+02  -.35092739E+02 -.350927E+02
0.998 1  -.35093172E+02  -.35093210E+02 -.350932E+02
0.999 1  -.35093440E+02  -.35093474E+02 -.350934E+02
1.000 1  -.35093511E+02  -.35093539E+02 -.350935E+02
1.001 1  -.35093392E+02  -.35093411E+02 -.350934E+02
1.002 1  -.35093087E+02  -.35093098E+02 -.350931E+02
1.003 1  -.35092601E+02  -.35092607E+02 -.350926E+02

Download the following Matlab functions. fit_a0EB.m, fit_C11EB.m, fit_C44EB.m,

Place the data files of Elatt.C11.dat, Elatt.C44.dat, Elatt.B.dat from Bulk modulus calculation of Au

Launch Matlab, and type the following commands. 

[a0, Ecoh, B] = fit_a0EB('Elatt.B.dat',4,4);
[C11,C12] = fit_C11EB('Elatt.C11.dat',a0,B);
C44 = fit_C44EB('Elatt.C44.dat',a0,C11,C12);

The first line fits the energy data to a quadratic curve and computes the equilibrium lattice constant, cohesive energy and bulk modulus([a0, Ecoh, B]) respectively. The first 4 specifies the number of atoms in the computation cell and the second 4 is the number of atoms in a conventional unit cell. The second lines computes the C11 and C12 elastic constants and the third line calculates C44. Suggested results are C11 = 206 GPa, C12 = 176 GPa and C44 = 36 GPa for calculations with US-LDA PP.

C44 of 36 GPa is a bit lower than the paper's result of 47 GPa (The experimental value is 45 GPa).

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