Deep Generator auto_test tutorial.

• Deep Generator auto_test tutorial.
  • how to use auto_test
    • configure and param.json
    • auto_test tasks
  • The content of the auto_test
    • param.json
    • 00.equi
    • 01.eos
    • 02.elasitc
    • 03.vacancy
    • 04.interstitial
    • 05.surface

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.

    "_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.

"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

    "_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

    "_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

    "_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

    "_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

    "_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

    "_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

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.

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.

$norm\mathrm{\_}x\mathrm{\_}matrix\mathrm{\_}list=[\left(\begin{array}{ccc}0.98& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right),\left(\begin{array}{ccc}0.99& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right),\left(\begin{array}{ccc}1.01& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right),\left(\begin{array}{ccc}1.02& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right)]$

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

$box\mathrm{\_}size=\left(\begin{array}{ccc}xx& & \\ xy& yy& \\ xz& yz& zz\end{array}\right)=\left(\begin{array}{ccc}2.858198& 0.0& 0.0\\ 1.429099& 2.475272& 0\\ 1.429099& 0.825091& 2.333709\end{array}\right)$

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)

$atom\mathrm{\_}position=\left(\begin{array}{ccc}x& y& z\end{array}\right)=\left(\begin{array}{ccc}2.855406& 3.297945& 2.331429\end{array}\right)$

The box_size and atom_position will according to the matrix in norm_matrix_list.
for example,

$box\mathrm{\_}size\mathrm{\_}x\mathrm{\_}axis\mathrm{\_}0.98=\left(\begin{array}{ccc}2.858198& 0.0& 0.0\\ 1.429099& 2.475272& 0\\ 1.429099& 0.825091& 2.333709\end{array}\right)\left(\begin{array}{ccc}0.98& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right)=\left(\begin{array}{ccc}2.800451& 0& 0\\ 1.400225& 2.475272& 0\\ 1.400225& 0.825091& 2.333709\end{array}\right)$

$atom\mathrm{\_}position\mathrm{\_}x\mathrm{\_}axis\mathrm{\_}0.98=\left(\begin{array}{ccc}2.855406& 3.297945& 2.331429\end{array}\right)\left(\begin{array}{ccc}0.98& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right)$

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.

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.

$shear\mathrm{\_}yz\mathrm{\_}matrix\mathrm{\_}list=[\left(\begin{array}{ccc}1& 0& 0\\ 0& 1& -0.05\\ 0& -0.05& 1\end{array}\right),\left(\begin{array}{ccc}1& 0& 0\\ 0& 1& -0.025\\ 0& -0.025& 1\end{array}\right),\left(\begin{array}{ccc}1& 0& 0\\ 0& 1& 0.025\\ 0& 0.025& 1\end{array}\right),\left(\begin{array}{ccc}1& 0& 0\\ 0& 1& 0.05\\ 0& 0.05& 1\end{array}\right)]$

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,

$stress\mathrm{\_}x\mathrm{\_}axis\mathrm{\_}0.98=\left(\begin{array}{ccc}Pxx& Pxy& Pxz\\ Pyx& Pyy& Pyz\\ Pzx& Pzy& Pzz\end{array}\right)=\left(\begin{array}{ccc}27804.1& 0.0813993& 0.0617211\\ 0.0813993& 11040.9& 852.908\\ 0.0617211& 852.908& 10437.7\end{array}\right)$

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.

# 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.

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

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

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