ELASTIC3rd: 3rd ELASTIC constants calculator¶
Introduction¶
Elastic3rd is an open source code to calculate the higher order elastic constants(HOECs) of materials from first principles.
Features¶
- Support strain-energy method for calculating TOECs, FOECs for all symmetry and FFOECs for cubic
- Support post processing by considering higher order effect
- Support CASTEP(in Materials Studio, both under Windows and Linux) and VASP
- Support python 2.7.x and pyython 3.5 +
Features under developing¶
- Strain-stress method
- Separate elastic constants method (ref. PRL. 121, 216001, 2018)
Installation¶
Requirements¶
python, numpy, scipy, matplotlib
Installation¶
by pip
pip install elastic3rdby setup.py
Download the code and entre the folder ELASTIC3rd/src, and then run
python setup.py install
Get Started¶
Simplest way to run¶
- Prepare the INPUT file and the input file for first principlec code
- Enter the folder
- Simply run
elastic3rd run
Inputs¶
The inputs for Elastic3rd can be divided into two parts. The first one is the INPUT file, and the second is the input files for first princples code.
INPUT¶
| Parameters | Default | Comments |
|---|---|---|
| BaseName | Si |
|
| CrystalType | Cubic1 |
|
| Ord | 3 | The order of elastic constants |
| EnergyCode | CASTEP | The first principles code, currently support CASTEP and VASP |
| EnergyRun | 1 |
|
| MaxStrain | 5 | The maximum strain, in unit of %. e.g. 5 means the strain range is -5% to 5% |
| STEPS | 5 | The number of points in each strain mode |
| NP | 1 | The number of cores used in the first principles codes |
First principles inputs¶
- CASTEP For CASTEP, two files are required for calculating, BaseName.cell and BaseName.param. For details, ref. CASTEP files .
- VASP To run VASP, four files are required: INCAR, POSCAR, KPOINTS and POTCAR. For details, ref. VASP files .
Calculation¶
Using CASTEP or VASP¶
Currently, Elastic3rd support CASTEP and VASP to calculate the energy or stress. Hence, the user can call vasp or castep by setting the INPUT file.
Note: The CASTEP is tested using the CASTEP module in Materials Studio. By default, the user should provide RunCASTEP.bat (windows) or RunCASTEP.sh (linux) in current folder. Usually, this file loacted in Materials_Studio_ install_pathetcCASTEPbin
For VASP, it runs vasp by mpirun -np NP vasp_std. So, please ensure that mpirun and vasp_std can be found in yout PATH.
Using other first principles code¶
If the user want to use other first principles code to calculate the energy of stress, the user only need to prepare the following thing:
write a python file named with the code’s name(e.g. qe.py, lower required) under elastic3rd/energy/
In this file, the user need to write the following functions
- get_base_vec(BaseName): this function get the lattice vector from the code’s input file
- write_base_vec(BaseName, BaseVec): this function write out the lattice vector to the code’s input file
- run(NP, BaseName): this function return the string to run the code
- get_energy(BaseName): this function get the energy from the code’s output file
- copy_files(BaseName, Path): this function copy the required files of the code
Then in the INPUT file, the file can call the code by specify “EnergyCode QE”
Post¶
The SOECs and TOECs (only taking second and third order effect into consideration) are printed in the log file on the screen.
If the author want to taken higher-order effect into consideration, the user can run elastic3rd post command in the folder where the job submitted or use Elastic3rdPost.py script in the example folder
For elastic3rd post command, please use -h for detail help.
For test, the user can run elastic3rd post in the example/Si/CASTEP folder directly.
Outputs¶
The structure of outputs¶
All the output are stored in the folder named BaseName, of which the value is set in INPUT file. The following is the structure of the results.
Output files¶
This section gives an explanation for each file generated by Elastic3rd.
| File name | Comments |
|---|---|
| INPUT | A backup of INPUT file |
| EEnergy.txt | The energy of each strain mode(each column) and each strain(each row) |
| Energy_Strain.txt | The energy of single strain, in which there are several values in different unit |
| Energy_Mode.txt | The eneargy of single strain mode. In unit of eV |
| Folders | Comments |
|---|---|
| Mode0 | This folder contains the result of undeformed structure |
| ModeN | This folder contains the result of differen strain modes |
| StrainN | This folder contains the result of different strains |
Note: here N is integer and N>0
Log file¶
By default, the log file is not saved, but print in the screen. And it can be saved by re-direction.
It can be divided into five parts
- Part1: the logo part
+=============================================================+
| EEEEE L A SSSSS TTTTT IIIII CCCCC 33333 RRRRR DDD |
| E L A A S T I C 3 R R D D |
| EEEE L A A SSSSS T I C 3333 RRRRR D D |
| E L AAAAA S T I C 3 R R D D |
| EEEEE LLLLL A A SSSSS T IIIII CCCCC 33333 R R DDD |
+-------------------------------------------------------------+
| Version: ELASTIC3PY version 2.0 |
| Date: 2019-01-27 |
| Author: Liao Mingqing |
| E_mail: liaomq1900127@163.com |
| FGMS @ Harbin Institute of Technology(HIT) |
| URL:https://github.com/hitliaomq/ELASTIC3rd |
|Please Cite: |
| Mingqing Liao,ELASTIC3rd,(2018).doi:10.5281/zenodo.2525580 |
+=============================================================+
- Part2: The summary of the calculation
===================The input parameters===================
The Runing mode is : NEW
The BaseName is : Si
The crystal symmetry is : c1
The order of elastic is : 3.0
The code for calculating the energy : CASTEP
The maximum of the strain : 8.0
The steps run in every mode : 9.0
The core used in energy calculate : 8.0
- Part3: the result of intial structure
====================Crystal Structure====================
BaseVec:
5.4647128853 0.0000000210 -0.0000000454
-0.0000000000 5.4647128382 -0.0000000222
0.0000000000 0.0000000000 5.4647129020
Lattice Parameter:
a b c alpha beta gamma
5.464713 5.464713 5.464713 90.000 90.000 90.000
Volume : 163.193194972
Energy of undeformed structure:
eV Hartree kJ/mol kcal/mol
-858.6574758785 -31.5550611783 -82847.8330874176 -19801.1085892908
- Part4: the result of different strains and strain modes
==================Deformed Crystal========================
----------------------------------------------------------
Start calculating Mode 1
Start calculating Strain -8.0 in Mode 1
[[0.84 0. 0. ]
[0. 1. 0. ]
[0. 0. 1. ]]
BaseVec:
5.0084920896 0.0000000210 -0.0000000454
0.0000000000 5.4647128382 -0.0000000222
0.0000000000 0.0000000000 5.4647129020
Lattice Parameter:
a b c alpha beta gamma
5.008492 5.464713 5.464713 90.000 90.000 90.000
Volume : 149.569033772
Energy:
eV Hartree kJ/mol kcal/mol
-858.0935122952 -31.5343359114 -82793.4188860286 -19788.1032822074
End of Strain -8.0 in Mode 1
Start calculating Strain -6.0 in Mode 1
[[0.88 0. 0. ]
[0. 1. 0. ]
[0. 0. 1. ]]
BaseVec:
5.1263550880 0.0000000210 -0.0000000454
0.0000000000 5.4647128382 -0.0000000222
0.0000000000 0.0000000000 5.4647129020
Lattice Parameter:
a b c alpha beta gamma
5.126355 5.464713 5.464713 90.000 90.000 90.000
Volume : 153.088786718
Energy:
eV Hartree kJ/mol kcal/mol
-858.3477769585 -31.5436799598 -82817.9516909908 -19793.9667636885
End of Strain -6.0 in Mode 1
...
- Part5: the post process part
==================Post Processing========================
[[ 77.22101104 -117.3314942 ]
[ 217.27559666 -670.1092832 ]
[ 218.38708611 26.16025079]
[ 227.66199634 -632.04346098]
[ 424.89246809 -1747.12822498]
[ 439.3186686 -408.3765645 ]]
[11 12 44]
[153.05111127 65.0171889 73.22518077]
[111 112 123 144 155 456]
[-703.9889652 -435.4462948 -88.79485798 71.7458725 -257.35598339
-51.04707056]
========================!!!END!!!=========================
Theory Background¶
The strain-energy method to calculate TOECs is based on the conituumn elasticity theory. The base equation is as follows (note: the Einstein summation notation is used in the following equations):
Where
- \(E\) is the energy of the deformed structure
- \(E_0\) is the energy of the initial structure
- \(V_0\) is the volume of the initial structure
- \(C_{ijkl}\) is SOECs
- \(C_{ijklmn}\) is TOECs
- \(\eta_{ij}\) is the Lagrangian strain
And the Lagrangian strain can be written as follows:
The F is the deformation gradient, and can be expressed by the lattic vector of deformed structure(r’) and intial structure (r).
when using symmetrical strain, the deformation gradient can be expressed by the Lagrangian strain.
where \(y_i\) and \(\lambda_i\) are the eigenvector and eigenvalue of Y, I is the identity matrix.
For each strain mode, we only adjust the amplitude. Hence, we can express the strain as a function of strain amplitude \(\eta\), then we have
Finally, we can choose different strain modes, then get different equations about TOECs and SOECs. By solving the equations, we can get the value of SOECs and TOECs.
Examples¶
Help on the elastic3rd command¶
There are two command to submit jobs or do post process.
- elastic3rd run command
ELASTIC3RD version: 2.5.1
Copyright © FGMS @ HIT
usage: elastic3rd run [-h] [-i INPUT]
optional arguments:
-h, --help show this help message and exit
-i INPUT, --input INPUT
The input file for Elastic3rd. Default: 'INPUT'
- elastic3rd post command
ELASTIC3RD version: 2.5.1
Copyright © FGMS @ HIT
usage: elastic3rd post [-h] [-n N] [-i INPUT] [-sm STRAINMODE] [-fig FIG] [-v VOLUME] [-e ENERGY]
optional arguments:
-h, --help show this help message and exit
-n N, --n N The order of elastic constant taken into consideration in the post process. Default: 3
-i INPUT, --input INPUT
The input file for Elastic3rd. Default: 'INPUT'
-sm STRAINMODE, --strainmode STRAINMODE
The strainmode file for Elastic3rd, None means using the code to generate it. Default: None
-fig FIG, --fig FIG Show the fitting fig. Default: 0
-v VOLUME, --volume VOLUME
The volume of initial structure. Default: None
-e ENERGY, --energy ENERGY
The file of the energy result. If None, it will try to find in current folder or in the
BaseName folder. Default: None
Submit jobs¶
There are several examples in example folder.
For Si and C, both VASP and CASTEP input files are prepared in the folder, and for Mg, only CASTEP input file is prepared.
The user can run these examples by following steps
- For copy right, the author can’t provide the RunCASTEP.bat or RunCASTEP.sh (for CASTEP) and POTCAR (for VASP) files. The user should provide these file in the current folder.
- For CASTEP, the user should copy RunCASTEP.bat or RunCASTEP.sh in their Materils Studio installation folder.
- For VASP, the user should provide the POTCAR file
- Submit the job
There are several ways to submit the job.
- Using elastic3rd run command.
- Using the runElastic3rd.py (in example folder) script by running python runElastic3rd.py. If the user want to save the log into file, please run python runElastic3rd.py >> Result.txt
- Submit jobs in queue system. If the user want to run Elastic3rd in queue system, the following is an example. Please note that it assume the python and vasp is exists in the PATH
#PBS -l nodes=1:ppn=24
#PBS -l walltime=48:00:00
#PBS -l pmem=8gb
#PBS -A open
#PBS -j oe
cd $PBS_O_WORKDIR
python runElastic3rd.py
Post¶
There are several ways to do the post processing.
- Using elastic3rd post command
Assumpt that the current folder is the folder where the job has been submitted. When enter the current folder, the user can do the post process by elastic3rd post to get the SOECs and TOECs. For more options, please run elastic3rd post -h.
For test, the user can run elastic3rd post in the example/Si/CASTEP folder directly. It should print the following lines in the screen.
ELASTIC3RD version: 2.5.1
Copyright © FGMS @ HIT
BaseVec:
5.4647128853 0.0000000210 -0.0000000454
-0.0000000000 5.4647128382 -0.0000000222
0.0000000000 0.0000000000 5.4647129020
Lattice Parameter:
a b c alpha beta gamma
5.464713 5.464713 5.464713 90.000 90.000 90.000
Volume : 163.1931949715094
[11 12 44]
[153.05111127 65.0171889 73.22518077]
[111 112 123 144 155 456]
[-703.9889652 -435.4462948 -88.79485798 71.7458725 -257.35598339
-51.04707056]
- Using Elastic3rdPost.py script
Change some parameters (e.g. Flag_Ord) by the user, then run python Elastic3rdPost.py
By running this script, it will print the following thing in the screen and show some figures of fitting result (here only show 1 figure)
BaseVec:
5.4647128853 0.0000000210 -0.0000000454
-0.0000000000 5.4647128382 -0.0000000222
0.0000000000 0.0000000000 5.4647129020
Lattice Parameter:
a b c alpha beta gamma
5.464713 5.464713 5.464713 90.000 90.000 90.000
Volume : 163.1931949715094
[ 77.22101104 -117.33149423]
[ 217.27559666 -670.10928332]
[218.3870861 26.16025386]
[ 227.66199634 -632.04346107]
[ 424.89246807 -1747.1282253 ]
[ 439.3186686 -408.37656319]
[153.05111127 65.01718889 73.22518077]
[-703.98896537 -435.44629486 -88.79485803 71.74587404 -257.35598342
-51.0470704 ]
- By calling the post or post_single or post_mode from elastic3rd.post.post
Ref Elastic3rdPost.py.
Citing¶
Mingqing Liao, Yong Liu, Shun-li Shang e.t. al. Elastic3rd: A tool for calculating third-order elastic constants from first principles submitted to computer physics communication (2020)
and give the following link: Elastic3rd