# Deep Generator auto_test tutorial.
[TOC]
## how to use auto_test
### configure and param.json
At this step, we assume that you have prepared some graph files like `graph.*.pb` and the particular pseudopotential `POTCAR`.
The main code of this step is
```
dpgen test PARAM MACHINE
```
where `PARAM` and `MACHINE` are both json files. `MACHINE` is the same as above.
The whole program contains a series of tasks shown as follows. In each task, there are three stages of work, generate, run and compute.
+ `00.equi`:(default task) the equilibrium state
+ `01.eos`: the equation of state
+ `02.elastic`: the elasticity like Young's module
+ `03.vacancy`: the vacancy formation energy
+ `04.interstitial`: the interstitial formation energy
+ `05.surf`: the surface formation energy
Dpgen auto_test will auto make dir for each task it tests, the dir name is the same as the dir name. And the test results will in a plain text file named result. For example `cat ./01.eos/Al/std-fcc/deepmd/result`
We take Al as an example to show the parameter settings of `param.json`.
The first part is the fundamental setting for particular alloy system.
```json
"_comment": "models",
"potcar_map" : {
"Al" : "/somewhere/POTCAR"
},
"conf_dir":"confs/Al/std-fcc",
"key_id":"API key of Material project",
"task_type":"deepmd",
"task":"eos",
```
You need to add the specified paths of necessary `POTCAR` files in "potcar_map". The different `POTCAR` paths are separated by commas.
Then you also need to add the folder path of particular configuration, which contains `POSCAR` file.
```
"confs/[element or alloy]/[std-* or mp-**]"
std-*: standard structures, * can be fcc, bcc, hcp and so on.
mp-**: ** means Material id from Material Project.
```
Usually, if you add the relative path of POSCAR as the above format,
`dpgen test` will check the existence of such file and automatically downloads the standard and existed configurations of the given element or alloy from Materials Project and stores them in **confs** folder, which needs the API key of Materials project.
+ `task_type` contains 3 optional types for testing, i.e. **vasp**, **deepmd** and **meam**.
+ `task` contains 7 options, **equi**, **eos**, **elastic**, **vacancy**, **interstitial**, **surf** and **all**. The option **all** can do all the tasks.
It is worth noting that the subsequent tasks need to rely on the calculation results of the equilibrium state, so it is necessary to give priority to the calculation of the equilibrium state while testing. And due to the stable consideration, we recommand you to test the equilibrium state of **vasp** before other tests.
The second part is the computational settings for vasp and lammps. According to your actual needs， you can choose to add the paths of specific INCAR or use the simplified INCAR by setting `vasp_params`. The priority of specified INCAR is higher than using `vasp_params`. The most important setting is to add the folder path `model_dir` of **deepmd** model and supply the corresponding element type map. Besides, `dpgen test` also is able to call common lammps packages, such as **meam**.
```json
"relax_incar":"somewhere/relax_incar",
"scf_incar":"somewhere/scf_incar",
"vasp_params": {
"ecut": 650,
"ediff": 1e-6,
"kspacing": 0.1,
"kgamma": false,
"npar": 1,
"kpar": 1,
"_comment": " that's all "
},
"lammps_params": {
"model_dir":"somewhere/example/Al_model",
"type_map":["Al"],
"model_name":false,
"model_param_type":false
},
```
The last part is the optional settings for various tasks mentioned above. You can change the parameters according to actual needs.
A dictionary
|Key | Type | Example | Discription |
| :---------------- | :--------------------- | :-------------------------------------- | :-------------------------------------------------------------|
| potcar_map | dict | {"Al": "example/POTCAR"} |a dict like { "element" : "position of POTCAR" } |
| conf_dir | path like string | "confs/Al/std-fcc" | the dir which contains vasp's POSCAR |
| key_id | string| "DZIwdXCXg1fiXXXXXX" |the API key of Material project|
| task_type | string | "vasp" | task type, one of deepmd vasp meam |
| task | string | "equi" | task, one of equi, eos, elastic, vacancy, interstitial, surf or all |
| vasp_params| dict | seeing below | params relating to vasp INCAR|
| lammps_params | dict| seeing below| params relating to lammps |
the keys in param["vasp_params"]
|Key | Type | Example | Discription |
| :---------------- | :--------------------- | :-------------------------------------- | :-------------------------------------------------------------|
| ecut | real number | 650 | the plane wave cutoff for grid. |
| ediff | real number | 1e-6 |Tolerance of Density Matrix |
| kspacing | real number | 0.1 | Sample factor in Brillouin zones |
| kgamma | boolen | false | whether generate a Gamma centered grid |
| npar | positive integer | 1 | the number of k-points that are to be treated in parallel |
| kpar | positive integer | 1 | the number of bands that are treated in parallel |
the keys in param["lammps_params"]
|Key | Type | Example | Discription |
| :---------------- | :--------------------- | :-------------------------------------- | :-------------------------------------------------------------|
| model_dir | path like string | "example/Al_model" | the model dir which contains .pb file |
| type_map | list of string | ["Al"] | a list contains the element, usually useful for multiple element situation |
| model_name | boolean | false | |
| model_param_type | boolean | false | |
### auto_test tasks
#### 00.equi
```json
"_comment":"00.equi",
"store_stable":true,
```
+ `store_stable`:(boolean) whether to store the stable energy and volume
param.json
| Field | Type | Example | Discription |
| :---------------- | :--------------------- | :-------------------------------------- | :-------------------------------------------------------------|
| EpA(eV) | real number | -3.7468 | the potential energy of a atom|
| VpA(A^3)| real number | 16.511| theEquilibrium volume of a atom |
test results
```
conf_dir: EpA(eV) VpA(A^3)
confs/Al/std-fcc -3.7468 16.511
```
| Field | Type | Example | Discription |
| :---------------- | :--------------------- | :-------------------------------------- | :-------------------------------------------------------------|
| EpA(eV) | real number | -3.7468 | the potential energy of a atom|
| VpA(A^3)| real number | 16.511| theEquilibrium volume of a atom |
#### 01.eos
```json
"_comment": "01.eos",
"vol_start": 12,
"vol_end": 22,
"vol_step": 0.5,
```
+ `vol_start`, `vol_end` and `vol_step` determine the volumetric range and accuracy of the **eos**.
test results
```
conf_dir:confs/Al/std-fcc
VpA(A^3) EpA(eV)
15.500 -3.7306
16.000 -3.7429
16.500 -3.7468
17.000 -3.7430
```
| Field | Type| Example| Discription |
| :---------------- | :--------------------- | :-------------------------------------- | :-------------------------------------------------------------|
| EpA(eV) | list of real number | [15.5,16.0,16.5,17.0] | the potential energy of a atom in quilibrium state|
| VpA(A^3)| list of real number |[-3.7306, -3.7429, -3.746762, -3.7430] | the equilibrium volume of a atom |
#### 02.elastic
```json
"_comment": "02.elastic",
"norm_deform": 2e-2,
"shear_deform": 5e-2,
```
+ `norm_deform` and `shear_deform` are the scales of material deformation.
This task uses the stress-strain relationship to calculate the elastic constant.
|Key | Type | Example | Discription |
| :---------------- | :--------------------- | :-------------------------------------- | :-------------------------------------------------------------|
| norm_deform | real number | 0.02 | uniaxial deformation range |
| shear_deform | real number | 0.05| shear deformation range |
test results
```
conf_dir:confs/Al/std-fcc
130.50 57.45 54.45 4.24 0.00 0.00
57.61 130.31 54.45 -4.29 -0.00 -0.00
54.48 54.48 133.32 -0.00 -0.00 -0.00
4.49 -4.02 -0.89 33.78 0.00 -0.00
-0.00 -0.00 -0.00 -0.00 33.77 4.29
0.00 -0.00 -0.00 -0.00 4.62 36.86
# Bulk Modulus BV = 80.78 GPa
# Shear Modulus GV = 36.07 GPa
# Youngs Modulus EV = 94.19 GPa
# Poission Ratio uV = 0.31
```
| Field | Type | Example | Discription |
| :---------------- | :--------------------- | :-------------------------------------- | :-------------------------------------------------------------|
| elastic module(GPa)| 6*6 matrix of real number| [[130.50 57.45 54.45 4.24 0.00 0.00] [57.61 130.31 54.45 -4.29 -0.00 -0.00] [54.48 54.48 133.32 -0.00 -0.00 -0.00] [4.49 -4.02 -0.89 33.78 0.00 -0.00] [-0.00 -0.00 -0.00 -0.00 33.77 4.29] [0.00 -0.00 -0.00 -0.00 4.62 36.86]]| Voigt-notation elastic module;sequence of row and column is (xx, yy, zz, yz, zx, xy)|
| bulk modulus(GPa) | real number | 80.78 | bulk modulus |
| shear modulus(GPa) | real number | 36.07 | shear modulus |
| Youngs Modulus(GPa) | real number | 94.19 | Youngs Modulus|
| Poission Ratio | real number | 0.31 | Poission Ratio |
#### 03.vacancy
```json
"_comment":"03.vacancy",
"supercell":[3,3,3],
```
+ `supercell`:(list of integer) the supercell size used to generate vacancy defect and interstitial defect
|Key | Type | Example | Discription |
| :---------------- | :--------------------- | :-------------------------------------- | :-------------------------------------------------------------|
| supercell | list of integer | [3,3,3] | the supercell size used to generate vacancy defect and interstitial defect |
test result
```
conf_dir:confs/Al/std-fcc
Structure: Vac_E(eV) E(eV) equi_E(eV)
struct-3x3x3-000: 0.859 -96.557 -97.416
```
| Field | Type | Example | Discription |
| :---------------- | :--------------------- | :-------------------------------------- | :-------------------------------------------------------------|
|Structure| list of string |['struct-3x3x3-000'] | structure name|
| Vac_E(eV) | real number |0.723 | the vacancy formation energy |
| E(eV) | real number | -96.684 | potential energy of the vacancy configuration |
| equi_E(eV) | real number |-97.407 | potential energy of the equilibrium state|
#### 04.interstitial
```json
"_comment":"04.interstitial",
"insert_ele":["Al"],
"reprod-opt":false,
```
+ `insert_ele`:(list of string) the elements used to generate point interstitial defect
+ `repord-opt`:(boolean) whether to reproduce trajectories of interstitial defect
|Key | Type | Example | Discription |
| :---------------- | :--------------------- | :-------------------------------------- | :-------------------------------------------------------------|
| insert_ele | list of string | ["Al"] | the elements used to generate point interstitial defect |
| reprod-opt | boolean | false | whether to reproduce trajectories of interstitial defect|
test result
```
conf_dir:confs/Al/std-fcc
Insert_ele-Struct: Inter_E(eV) E(eV) equi_E(eV)
struct-Al-3x3x3-000: 3.919 -100.991 -104.909
struct-Al-3x3x3-001: 2.681 -102.229 -104.909
```
| Field | Type | Example | Discription |
| :---------------- | :--------------------- | :-------------------------------------- | :-------------------------------------------------------------|
|Structure| string |'struct-Al-3x3x3-000' | structure name|
| Inter_E(eV) | real number |0.723 | the interstitial formation energy |
| E(eV) | real number | -96.684 | potential energy of the interstitial configuration |
| equi_E(eV) | real number |-97.407 | potential energy of the equilibrium state|
#### 05.surface
```json
"_comment": "05.surface",
"min_slab_size": 10,
"min_vacuum_size": 11,
"_comment": "pert xz to work around vasp bug...",
"pert_xz": 0.01,
"max_miller": 2,
"static-opt":false,
"relax_box":false,
```
+ `min_slab_size` and `min_vacuum_size` are the minimum size of slab thickness and the vacuume width.
+ `pert_xz` is the perturbation through xz direction used to compute surface energy.
+ `max_miller` (integer) is the maximum miller index
+ `static-opt`:(boolean) whether to use atomic relaxation to compute surface energy. if false, the structure will be relaxed.
+ `relax_box`:(boolean) set true if the box is relaxed, otherwise only relax atom positions.
|Key | Type | Example | Discription |
| :---------------- | :--------------------- | :-------------------------------------- | :-------------------------------------------------------------|
| min_slab_size| real number| 10 | the minimum size of slab thickness |
|min_vacuum_size | real number| 11 | the minimum size of the vacuume width |
|pert_xz | real number| 0.01 | the perturbation through xz direction used to compute surface energy |
|max_miller | integer| 2 | the maximum miller index |
|static-opt|boolean| false | whether to use atomic relaxation to compute surface energy. if false, the structure will be relaxed. |
|relax_box | boolean | false | set true if the box is relaxed, otherwise only relax atom positions |
test result
```
conf_dir:confs/Al/std-fcc
Miller_Indices: Surf_E(J/m^2) EpA(eV) equi_EpA(eV)
struct-000-m1.1.1m: 0.673 -3.628 -3.747
struct-001-m2.2.1m: 0.917 -3.592 -3.747
```
| Field | Type | Example| Discription|
| :---------------- | :--------------------- | :-------------------------------------- | :-------------------------------------------------------------|
|Miller_Indices| string | struct-000-m1.1.1m | Miller Indices|
|Surf_E(J/m^2)| real number | 0.673 | the surface formation energy |
| EpA(eV) | real number | -3.628 | potential energy of the surface configuration |
| equi_EpA | real number | -3.747 | potential energy of the equilibrium state|
## The content of the auto_test
The atom configuration file to be testes.
### param.json
| Key | Type | Example | Discription |
| :---------------- | :--------------------- | :-------------------------------------- | :-------------------------------------------------------------|
| potcar_map | dict | {"Al": "example/POTCAR"} |a dict like { "element" : "position of POTCAR" } |
| conf_dir | path_like | confs/Al/std-fcc | the dir which contains vasp's POSCAR |
### 00.equi
equi will test the the equilibrium state and get the following results.
#### 1.test results
| Field | Type | Example | Discription |
| :---------------- | :--------------------- | :-------------------------------------- | :-------------------------------------------------------------|
| EpA(eV) | real number | -3.7468 | the potential energy of a atom|
| VpA(A^3)| real number | 16.511| theEquilibrium volume of a atom |
#### 2.param.json
vasp
lammps
|key | Type | Example| Discription|
| :---------------- | :--------------------- | :-------------------------------------- | :-------------------------------------------------------------|
| store_stable | boolean | true |whether to store the stable energy and volume|
#### 3.atom configuration
The atom configuration is specified by param['conf_dir']/POSCAR
The box is periodic, so that particles interact across the boundary, and they can exit one end of the box and re-enter the other end
Here are the configuration file used by lammps and vasp , note that the following 2 configuration are **equal**.
lammps atom configuration example
```
# Al/std-fcc/conf.lmp
1 atoms
1 atom types
0.0000000000 2.8637824638 xlo xhi
0.0000000000 2.4801083646 ylo yhi
0.0000000000 2.3382685902 zlo zhi
1.4318912319 1.4318912319 0.8267027882 xy xz yz
Atoms # atomic
1 1 0.0000000000 0.0000000000 0.0000000000
```
vasp Al/std-fcc/POSCAR
```
Al1
1.0
0.000000 2.025000 2.025000
2.025000 0.000000 2.025000
2.025000 2.025000 0.000000
Al
1
direct
0.000000 0.000000 0.000000 Al
```
vasp atom configuration example
#### 4.lammps
##### 4.1 input file
lammps perform energy minimizations of the system,and use the results of energy minimizations as the test result.
```
# lammps.in
dimension 3
boundary p p p
atom_style atomic
box tilt large
read_data conf.lmp
......
min_style cg
fix 1 all box/relax iso 0.0 #
minimize 1.000000e-12 1.000000e-06 5000 500000
fix 1 all box/relax aniso 0.0
minimize 1.000000e-12 1.000000e-06 5000 500000
......
```
`minimize` perform an energy minimization of the system, by iteratively adjusting atom coordinates. Iterations are terminated when one of the stopping criteria is satisfied.
`fix` Apply an external pressure or stress tensor to the simulation box during an energy minimization. This allows the box size and shape to vary during the iterations of the minimizer so that the final configuration will be both an energy minimum for the potential energy of the atoms, and the system pressure tensor will be close to the specified external tensor.
`iso/aniso` The keyword iso means couple all 3 diagonal components together when pressure is computed (hydrostatic pressure), and dilate/contract the dimensions together.
The keyword aniso means x, y, and z dimensions are controlled independently using the Pxx, Pyy, and Pzz components of the stress tensor as the driving forces
#### 4.2 output file
after energy minimization,
dpgen will use the PotEng of the last step -3.7467628 as `EpA(eV)`
dpgen will use the Volume of the last step 16.510567as `VpA(A^3)`
```
Step PotEng Pxx Pyy Pzz Pxy Pxz Pyz Lx Ly Lz Volume c_mype
0 -3.7465689 -5490.0435 -5489.99 -5489.9875 8.0059506e-05 -0.00015863904 0.00072809883 2.8637825 2.4801084 2.3382686 16.607531 -3.7465689
21 -3.7467629 -829.55143 -829.56516 -829.55757 -1.7925939e-05 -9.5713646e-05 0.0038858896 2.8581981 2.4752722 2.333709 16.510567 -3.7467629
22 -3.7467628 -829.56697 -829.63547 -829.55631 0.00051858009 1.8511104e-07 -0.0017081319 2.8581981 2.4752722 2.333709 16.510567 -3.7467628
```
#### 5 vasp
##### 5.1 INCAR
some field of the INCAR will be changed according to
```
PREC=A
ENCUT=650 # will use param.json's
# ISYM=0
ALGO=fast
EDIFF=1.000000e-06 # will use param.json's
EDIFFG=-0.01
LREAL=A
NPAR=1 # will use param.json's
KPAR=1 # will use param.json's
ISMEAR=1
SIGMA=0.220000
ISTART=0
ICHARG=2
NELM=100
NELMIN=6
ISIF=6
IBRION=2
NSW=50
LWAVE=F
LCHARG=F
PSTRESS=0
KSPACING=0.100000 # will use param.json's
KGAMMA=F # will use param.json's
```
### 01.eos
eos will calculate the equation of state and get the following results.
Auto_test 01.eos will calculate the potential energy of single atom in a range of volumes.
You may then use the test results to draw the equation of state curve.
#### 1.test results
Field | Type | Example | Discription |
| :---------------- | :--------------------- | :-------------------------------------- | :-------------------------------------------------------------|
| EpA(eV) | list of real number | [15.5,16.0,16.5,17.0] | the potential energy of a atom in quilibrium state|
| VpA(A^3)| list of real number |[-3.7306, -3.7429, -3.746762, -3.7430] | the equilibrium volume of a atom |
#### 2.param.json
vol_start, vol_end and vol_step determine the volumetric range and accuracy of the eos.
|Key | Type | Example | Discription |
| :---------------- | :--------------------- | :-------------------------------------- | :-------------------------------------------------------------|
| vol_start |real number | 12 | the start volume |
| vol_end | real number | 22 | the end volume |
| vol_step | real number | 0.5 | the intervel to change volume |
The param.json above will become a list below.
each volume in volume_list will become the target
```python
volume_list = list(range(vol_start,vol_end,vol_step))
```
#### 3.atom configuration
The initial atom configuration will be the equilibrium state atom configuration(configuration of the last step of 00.equi)
The box will contain only one atom.
The box is periodic, so that particles interact across the boundary, and they can exit one end of the box and re-enter the other end.
And the box and atom position will deform proportionally in x,y,z direction to reach the target volume.
For, examle, the file below will generate a box with single atom.
the box volume is 2.857588\*2.474744\*2.333211==16.50 A^(3)
```
# vol-16.50/conf.lmp
1 atoms
1 atom types
0.0000000000 2.8575880000 xlo xhi
0.0000000000 2.4747440000 ylo yhi
0.0000000000 2.3332110000 zlo zhi
1.4287940000 1.4287940000 0.8249150000 xy xz yz
Atoms # atomic
1 1 2.8547961365 3.2972419997 2.3309314529
```
the images below are atom configuration of volume 12.0, 16.5, 21.5
#### 4.lammps
Lammps will create a serials of folders and each of the folder will contain different a conf.lmp file.
All of the conf.lmp will contain only one atom, the box size of these conf.lmp will be different
##### 4.1 input file
lammps perform an energy minimizations of the system,and use the results of energy minimizations as the test result.
notice that lammps will not fix all box/relax 0.0, that means lammps will **not** try to keep the stress of box to 0.0 (this is different from 00.equi)
```
# vol-16.50 lammps.in
units metal
dimension 3
boundary p p p
atom_style atomic
box tilt large
read_data conf.lmp
......
min_style cg
minimize 1.000000e-12 1.000000e-06 5000 500000
......
```
##### 4.2 output file
After the energy minimization(in this example, the energy minimization had run only one step before it stopped).
dpgen will use the PotEng of the last step -3.7467628 as `EpA(eV)` where `VpA(A^3)==16.50`
```
# vol-16.50/log.lammps
Step PotEng Pxx Pyy Pzz Pxy Pxz Pyz Lx Ly Lz Volume c_mype
0 -3.7467629 -315.56544 -315.60474 -315.65689 -0.00081929052 -0.0015852434 -0.038537753 2.857588 2.474744 2.333211 16.499999 -3.7467629
1 -3.7467629 -315.56544 -315.60474 -315.65689 -0.00081929052 -0.0015852434 -0.038537753 2.857588 2.474744 2.333211 16.499999 -3.746762
```
#### 5.VASP
VASP will calculate the potential energy of the atom configuration. The VASP INCAR is the same as 00.equi's.
### 02.elasitc
Calculate the elastic module, bulk modulus, shear modulus, Youngs Modulus, Poission Ratio.
#### 1.test results
| Field | Type | Example | Discription |
| :---------------- | :--------------------- | :-------------------------------------- | :-------------------------------------------------------------|
| elastic module(GPa)| 6*6 matrix of real number| [[130.50 57.45 54.45 4.24 0.00 0.00] [57.61 130.31 54.45 -4.29 -0.00 -0.00] [54.48 54.48 133.32 -0.00 -0.00 -0.00] [4.49 -4.02 -0.89 33.78 0.00 -0.00] [-0.00 -0.00 -0.00 -0.00 33.77 4.29] [0.00 -0.00 -0.00 -0.00 4.62 36.86]]| Voigt-notation elastic module;sequence of row and column is (xx, yy, zz, yz, zx, xy)|
| bulk modulus(GPa) | real number | 80.78 | bulk modulus |
| shear modulus(GPa) | real number | 36.07 | shear modulus |
| Youngs Modulus(GPa) | real number | 94.19 | Youngs Modulus|
| Poission Ratio | real number | 0.31 | Poission Ratio |
#### 2.param.json
norm_deform and shear_deform are the scales of material deformation. This task uses the stress-strain relationship to calculate the elastic constant.
|Key | Type | Example | Discription |
| :---------------- | :--------------------- | :-------------------------------------- | :-------------------------------------------------------------|
| norm_deform | real number | 0.02 | uniaxial deformation range |
| shear_deform | real number | 0.05| shear deformation range |
#### 3.atom configuration
##### 3.1 uniaxial deformation
norm_deform=0.02 will become a list ,and then this list will become a list of 3*3 matrix,which will change the configuration of the simulation box.
```python
norm_deform=0.02
norm_strains = [-norm_def, -0.5*norm_deform, 0.5*norm_deform, norm_def]
# the result of the command above
norm_strains = [-0.02, -0.01, 0.01, 0.02]
```
#For X-axis uniaxial deformation, the list above will become the matrix list below.
$norm\_x\_matrix\_list=
[\begin{pmatrix}
0.98 & 0 & 0\\
0 & 1 & 0\\
0 & 0 & 1
\end{pmatrix} , \begin{pmatrix}
0.99 & 0 & 0\\
0 & 1 & 0\\
0 & 0 & 1
\end{pmatrix},
\begin{pmatrix}
1.01 & 0 & 0\\
0 & 1 & 0\\
0 & 0 & 1
\end{pmatrix}, \begin{pmatrix}
1.02 & 0 & 0\\
0 & 1 & 0\\
0 & 0 & 1
\end{pmatrix}]$
The initial atom configuration will be the equilibrium state atom configuration(configuration of the last step of 00.equi)
for each matrix in norm_matrix_list, the atom position and box size of the initial atom configuration will deform accordingly.
For example, the initial box size will be a Lower triangular matrix
$box\_size=\begin{pmatrix}
xx & & \\
xy & yy & \\
xz & yz & zz
\end{pmatrix} =\begin{pmatrix}
2.858198 & 0.0 & 0.0\\
1.429099 & 2.475272 & 0\\
1.429099 & 0.825091 & 2.333709
\end{pmatrix}$
The atom position in the box is
(note that the atom may be out of the simulation box, but the box is periodic, the atom will be move into the box automatically)
$atom\_position = \begin{pmatrix}
x & y & z
\end{pmatrix} = \begin{pmatrix}
2.855406 & 3.297945 & 2.331429
\end{pmatrix}$
The box_size and atom_position will according to the matrix in norm_matrix_list.
for example,
$box\_size\_x\_axis\_0.98=\begin{pmatrix}
2.858198 & 0.0 & 0.0\\
1.429099 & 2.475272 & 0\\
1.429099 & 0.825091 & 2.333709
\end{pmatrix} \begin{pmatrix}
0.98 & 0 & 0\\
0 & 1 & 0\\
0 & 0 & 1
\end{pmatrix}=\begin{pmatrix}
2.800451 & 0 & 0\\
1.400225 & 2.475272 & 0\\
1.400225 & 0.825091 & 2.333709
\end{pmatrix}$
$atom\_position\_x\_axis\_0.98 = \begin{pmatrix}
2.855406 & 3.297945 & 2.331429
\end{pmatrix} \begin{pmatrix}
0.98 & 0 & 0\\
0 & 1 & 0\\
0 & 0 & 1
\end{pmatrix}$
##### 3.2 shear deform
shear_deform=0.05 will become a list ,and then this list will become a list of 3*3 matrix,which will change the configuration of the simulation box.
```python
shear_deform=0.05
shear_strains = [-shear_deform, -0.5*shear_deform, 0.5*shear_deform, shear_deform]
# the result of the command above
shear_strains = [-0.05, -0.025, 0.025, 0.05]
```
#For yz shear deformation, the list above will become the matrix list below.
$shear\_yz\_matrix\_list=
[\begin{pmatrix}
1 & 0 & 0\\
0 & 1 & -0.05\\
0 & -0.05 & 1
\end{pmatrix} , \begin{pmatrix}
1 & 0 & 0\\
0 & 1 & -0.025\\
0 & -0.025 & 1
\end{pmatrix},
\begin{pmatrix}
1 & 0 & 0\\
0 & 1 & 0.025\\
0 & 0.025 & 1
\end{pmatrix}, \begin{pmatrix}
1 & 0 & 0\\
0 & 1 & 0.05\\
0 & 0.05 & 1
\end{pmatrix}]$
and then box_size matrix and atom_position vector will change according to the matrix above
#### 4.lammps
##### 4.1 input file
lammps perform an energy minimizations of the system,and use the results of energy minimizations as the test result.
notice that lammps will not fix all box/relax 0.0, that means lammps will **not** try to keep the stress of box to 0.0 (this is different from 00.equi)
```
# dfm-000/lammps , x-axis deform -0.02
min_style cg
minimize 1.000000e-12 1.000000e-06 5000 500000
```
##### 4.2 output file
After the energy minimization(in this example, the energy minimization had run only one step before it stopped).
```
Step PotEng Pxx Pyy Pzz Pxy Pxz Pyz Lx Ly Lz Volume c_mype
0 -3.7440621 27804.084 11040.856 10437.716 0.082776521 0.063238993 852.90808 2.800451 2.475272 2.333709 16.176986 -3.7440621
1 -3.7440621 27804.102 11040.877 10437.739 0.081399331 0.061721109 852.90771 2.800451 2.475272 2.333709 16.176986 -3.7440621
```
will use the result Pxx Pyy Pzz Pxy Pxz Pyz of the last MD step as the stress tensor.
that is,
$stress\_x\_axis\_0.98=\begin{pmatrix}
Pxx & Pxy & Pxz\\
Pyx & Pyy & Pyz\\
Pzx & Pzy & Pzz
\end{pmatrix}=\begin{pmatrix}
27804.1 & 0.0813993 & 0.0617211\\
0.0813993 & 11040.9 & 852.908\\
0.0617211 & 852.908 & 10437.7
\end{pmatrix}$
#### 5.vasp
The atom configuration is the same as lammps's.
VASP will calculate the potential energy of the atom configuration. The VASP INCAR is the same as 00.equi's.
#### 6.data analyze
the strain_matrix and corresponding stress_matrix will be used to calculate the elastic tensor using least-squares fit.
```python3
# lst_strains: list of strain objects to fit
# lst_stresses: list of stress objects to use in fit
# eq_stress: the stress of equilibrium state
pymatgen.analysis.elasticity.elastic.from_independent_strains(lst_strain,
lst_stress,
eq_stress = equi_stress)
```
This will return elastic module, bulk modulus, shear modulus, Youngs modulus and Poission ratio.
### 03.vacancy
Calculate the vacancy formation energy
#### 1.test results
the results will be a table,here only show one row of the table.
| Field | Type | Example | Discription |
| :---------------- | :--------------------- | :-------------------------------------- | :-------------------------------------------------------------|
|Structure| list of string |['struct-3x3x3-000'] | structure name|
| Vac_E(eV) | real number |0.723 | the vacancy formation energy |
| E(eV) | real number | -96.684 | potential energy of the vacancy configuration |
| equi_E(eV) | real number |-97.407 | potential energy of the equilibrium state|
#### 2.param.json
norm_deform and shear_deform are the scales of material deformation. This task uses the stress-strain relationship to calculate the elastic constant.
|Key | Type | Example | Discription |
| :---------------- | :--------------------- | :-------------------------------------- | :-------------------------------------------------------------|
| supercell | list of integer | [3,3,3] | the supercell size used to generate vacancy defect and interstitial defect |
#### 3.atom configuration
Auto_test will use the 00.equi result atom configuration CONTCAR.
and create a supercell with param.json's supercell.
The atom configuration will be auto generated by pymatgen's module
Class pymatgen.analysis.defects.generators.VacancyGenerator.
Atom configuration for vacancies will be based on periodically equivalent sites.
```python3
pymatgen.analysis.defects.generators.VacancyGenerator(Structure.from_file(task_poscar))
```
VASP CONTCAR of 00.equi
```
Al1
1.00000000000000
0.0000000000000000 2.0213150252059031 2.0213150252059031
2.0213150252059031 0.0000000000000000 2.0213150252059031
2.0213150252059031 2.0213150252059031 -0.0000000000000000
Al
1
Direct
0.0000000000000000 0.0000000000000000 0.0000000000000000
0.00000000E+00 0.00000000E+00 0.00000000E+00
```
vasp POSCAR to test vacancy formation energy
```
Al26
1.0
0.000000 6.063945 6.063945
6.063945 0.000000 6.063945
6.063945 6.063945 0.000000
Al
26
direct
0.000000 0.000000 0.333333 Al
0.000000 0.000000 0.666667 Al
0.000000 0.333333 0.000000 Al
0.000000 0.333333 0.333333 Al
1.000000 0.333333 0.666667 Al
0.000000 0.666667 0.000000 Al
1.000000 0.666667 0.333333 Al
0.000000 0.666667 0.666667 Al
0.333333 0.000000 0.000000 Al
0.333333 0.000000 0.333333 Al
0.333333 1.000000 0.666667 Al
0.333333 0.333333 0.000000 Al
0.333333 0.333333 0.333333 Al
0.333333 0.333333 0.666667 Al
0.333333 0.666667 0.000000 Al
0.333333 0.666667 0.333333 Al
0.333333 0.666667 0.666667 Al
0.666667 0.000000 0.000000 Al
0.666667 1.000000 0.333333 Al
0.666667 0.000000 0.666667 Al
0.666667 0.333333 0.000000 Al
0.666667 0.333333 0.333333 Al
0.666667 0.333333 0.666667 Al
0.666667 0.666667 0.000000 Al
0.666667 0.666667 0.333333 Al
0.666667 0.666667 0.666667 Al
```
#### 4.lammps
lammps perform energy minimizations of the system,a nd use the potential energy results of energy minimizations as the vacancy formation atom configuration result.
The formation energy will be the different between vacancy configuration and equilibrium configuration.
```
min_style cg
fix 1 all box/relax iso ${Px}
minimize 1.000000e-12 1.000000e-06 5000 500000
fix 1 all box/relax aniso ${Px}
minimize 1.000000e-12 1.000000e-06 5000 500000
```
#### 5.vasp
VASP will calculate the potential energy of vacancy configuration and equilibrium configuration. The formation energy will be the different between them.
### 04.interstitial
Calculate the interstitial formation energy.
#### 1.test results
the results will be in a table, here only show one row of the table.
| Field | Type | Example | Discription |
| :---------------- | :--------------------- | :-------------------------------------- | :-------------------------------------------------------------|
|Structure| string |'struct-Al-3x3x3-000' | structure name|
| Inter_E(eV) | real number |0.723 | the interstitial formation energy |
| E(eV) | real number | -96.684 | potential energy of the interstitial configuration |
| equi_E(eV) | real number |-97.407 | potential energy of the equilibrium state|
#### 2.param.json
|Key | Type | Example | Discription |
| :---------------- | :--------------------- | :-------------------------------------- | :-------------------------------------------------------------|
| insert_ele | list of string | ["Al"] | the elements used to generate point interstitial defect |
| reprod-opt | boolean | false | whether to reproduce trajectories of interstitial defect|
#### 3.atom configuration
Auto_test will use the 00.equi result atom configuration CONTCAR.
and create a supercell with param.json's supercell.
The atom configuration will be auto generated by pymatgen's module
Class pymatgen.analysis.defects.generators.VacancyGenerator.
Atom configuration for interstitials will be based on a simple Voronoi analysis
```python3
pymatgen.analysis.defects.generators.InterstitialGenerator(Structure.from_file(task_poscar), insert_ele)
```
#### 4.lammps
##### 4.1 input file
lammps perform energy minimizations of the system,a nd use the potential energy results of energy minimizations as the interstitials formation atom configuration result.
The formation energy will be the different between interstitials configuration and equilibrium configuration.
```
min_style cg
fix 1 all box/relax iso 0.0
minimize 1.000000e-12 1.000000e-06 5000 500000
fix 1 all box/relax aniso 0.0
minimize 1.000000e-12 1.000000e-06 5000 500000
```
#### 5.VASP
will calculate the potential energy of interstitials configuration and equilibrium configuration. The formation energy will be the different between them.
### 05.surface
Calculate the surface formation energy
#### 1.test results
the results will be in a table, here only show one row of the table.
| Field | Type | Example| Discription|
| :---------------- | :--------------------- | :-------------------------------------- | :-------------------------------------------------------------|
|Miller_Indices| string | struct-000-m1.1.1m | Miller Indices|
|Surf_E(J/m^2)| real number | 0.673 | the surface formation energy |
| EpA(eV) | real number | -3.628 | potential energy of the surface configuration |
| equi_EpA | real number | -3.747 | potential energy of the equilibrium state|
#### 2.param.json
norm_deform and shear_deform are the scales of material deformation. This task uses the stress-strain relationship to calculate the elastic constant.
|Key | Type | Example | Discription |
| :---------------- | :--------------------- | :-------------------------------------- | :-------------------------------------------------------------|
| min_slab_size| real number| 10 | the minimum size of slab thickness |
|min_vacuum_size | real number| 11 | the minimum size of the vacuume width |
|pert_xz | real number| 0.01 | the perturbation through xz direction used to compute surface energy |
|max_miller | integer| 2 | the maximum miller index |
|static-opt|boolean| false | whether to use atomic relaxation to compute surface energy. if false, the structure will be relaxed. |
|relax_box | boolean | false | set true if the box is relaxed, otherwise only relax atom positions |
#### 3.atom configuration
The atom configuration will be auto generated by pymatgen's module
`pymatgen.core.surface.Structure` and `pymatgen.core.surface.generate_all_slabs` with `equilibrium state atom structure, max_miller, min_slab_size, min_vacuum_size`
```python
all_slabs = generate_all_slabs(Structure.from_file(poscar), max_miller, min_slab_size, min_vacuum_size)
```
the images are slab configuration.
#### 4.lammps
lammps will calculate the potential energy of the configuration.and divide the atom numbers as the surface formation energy.
the surface energy will be the difference between surface formation energy and the potential energy of a atom in equilibrium configuration.
#####4.1 input file
```
min_style cg
minimize 1.000000e-12 1.000000e-06 5000 500000
```
#### 5.VASP
VASP will calculate the potential energy of the configuration.and divide the atom numbers as energy of one atom. The VASP INCAR is the same as 00.equi's
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