Transition Metal Dicalcogenite, Alloys, Density functional theory, GQCA
- Colab notebook for data visualization
.
This notebook is used to compute the thermodynamic properties and statistical attributes from the ab initio calculations executed from the TMD-Alloy Workflow. Below, we describe the functions covered by the actual version.
def root_lagrange_multiplier(x, T):
"""
Parameters:
x (float): The composition of alloy, such as 0<=x<=1.
T (float): Temperature in Kelvin.
Returns:
eta (float): The value of Lagrange multiplier.
"""'This function calculate the value of Lagrange multiplier η, which is related to the average composition constrain evaluated as x at temperature T.
def xj(self, j, T, eta):
"""
Calculates the Cluster probabilities for each class in GQCA.
Parameters:
j (int): number of class, in the same order of the input file gqca_inputs.yml.
T (float): Temperature in Kelvin.
eta (float): The value of Lagrange multiplier within GQCA.
Returns:
xj (float): The value of cluster probability for the j-th class of alloy.
"""The function xj compute the cluster probabilities associated with the class j, at temperature T, in which the η value calculated by the function root_lagrange_multiplier(x, T) enters as a parameter to ensure the composition constrain.
def xj0(j, x):
"""
Calculates the Cluster probabilities associated with a regular solution.
Parameters:
j (int): number of class, in the same order of the input file gqca_inputs.yml.
x (float): The composition of alloy, such as 0<=x<=1.
Returns:
xj0 (float): The value of cluster probability in the limit of a regular solution for the j-th class of alloy.
"""This function returns the cluster probabilities associated with a regular solution xj0 for class j, when the alloy has composition fixed at x.
def emix(x, T):
"""
Calculates the mixing energy for the alloy at a given composition and temperature.
Parameters:
x (float): The composition of alloy, such as 0<=x<=1.
T (float): Temperature in Kelvin.
Returns:
emix (float): The value of mixing energy for the alloy at composition x and temperature T.
"""The function emix is used to calculate the mixing energy of the alloy with average compostion x at temperature T.
def smix(x, T):
"""
Calculates the mixing entropy for the alloy at a given composition and temperature.
Parameters:
x (float): The composition of alloy, such as 0<=x<=1.
T (float): Temperature in Kelvin.
Returns:
smix (float): The value of mixing entropy for the alloy at composition x and temperature T.
"""The function smix(x, T) is used to calculate the the mixing entropy, according to the GQCA expression. Its input arguments are the average composition x and the temperature T (in Kelvin).
def fmix(x, T):
"""
Calculates the mixing Helmholtz free energy for the alloy at a given composition and temperature.
Parameters:
x (float): The composition of alloy, such as 0<=x<=1.
T (float): Temperature in Kelvin.
Returns:
fmix (float): The value of mixing Helmholtz free energy for the alloy at composition x and temperature T.
"""This function sum the contributions from emix and smix to return the mixing free energy of alloy, calculated at average composition x and temperature T.
def kld(x, T):
"""
Calculates the Kullback-Leibler Divergence D_{KL}(xj||xj0) between the xj and xj0 probability distributions.
Parameters:
x (float): The composition of alloy, such as 0<=x<=1.
T (float): Temperature in Kelvin.
Returns:
dkl (float): The value of Kullback-Leibler Divergence at composition x and temperature T.
"""The function kld returns the Kullback-Leibler divergence between the probabilities distributions computed from xj and xj0 functions explained above. It uses both functions, employing as input parameters the average compostion of alloy and its temperature T in Kelvin.
def second_derivative(self, x, T):
"""
Calculates the second derivative of the Helmholtz free energy using finite differences
Parameters:
x (float): The composition of alloy, such as 0<=x<=1.
T (float): Temperature in Kelvin.
Returns:
d2fmix/dx2 (float): The second derivative at composition x and temperature T.
"""In this workflow, the SimStack framework generates configurations to analyze the thermodynamic properties of binary alloys within the Generalized Quasichemical Approximation (GQCA). For this, five different WaNos are combined: SOD-2022, Mult-It, UnpackMol, DFT-VASP, Wannier90, WanTIBEXOS, FHI-Aims, and Table-Generator. A table containing the clusters' total energies, degeneracy factors, and several site substitutions is the expected output of this protocol.
To create the workflow depicted in Figure 1, you must use the drag-and-drop standard procedure of Simstack in eight steps.
Figure 1. This workflow aims to perform several calculations of cluster configurations within the GQCA framework. It is made from SOD-2022, Mult-It, UnpackMol, DFT-VASP, Wannier90, WanTIBEXOS, FHI-Aims, and DB-Generator WaNos connected by the AdvancedFor loop control.
To get this workflow up and running on your available computational resources, install the below libraries on Python 3.6 or newer.
1. Atomic Simulation Environment (ASE).
2. Python Materials Genomics (Pymatgen).
3. Numpy, os, sys, re, yaml, subprocess.
4. json, csv, shutil, tarfile. - INSOD file, containing system definition, supercell size, number of substitutions, and specie replacements, as explained in Site Occupation Disorder (SOD) software manual.
- SGO file containing the matrix-vector representations of the symmetry operators associated with the space group of the parent structure associated with the alloy. You can create this file using the Bilbao Crystallographic Server. As explained in SOD manual, the first three numbers in each line are one row of the operator matrix, and the fourth number is the component of the operator translation vector.
- All information to the next WaNo will be contained in the
calcs.tarfile.
- You need to check the box Structures.
- In the tarfile field, configure the path
SOD-2022/outputs/calcs.tarif it is not properly configured.
- Configure the
filename from the file command on the top of the AdvancedFor loop, as indicated in Figure 1. - From the in command on the top of the loop, configure
list(range(Mult-It.struct_len)).
- Check the box Multivariable-mode.
- The input-file variable should be set as
Mult-It/outputs/structure_output_dict.yml. - Structures-int variable should be set as
${file}. - Structures variable should be set as
Mult-It/outputs/Structures.tar.
POSCAR files (named as Mol_geom.xyz) should be passed to DFT-VASP WaNo.
- INCAR tab: as an option, we can set all INCAR flags available within VASP. However, we expose only a few of them, which is essential for the problem. See the GUI of this WaNo. A brief description of each flag pops up when we hover the mouse over the inputs.
- KPOINTS tab: Here, the user can define two types of KPOINTS,
Kpoints_lengthandKpoints_Monkhorst. - Analysis tab: Aimed to compute Bader charge analysis and DOS.
- Files_Run tab: Mandatory loads the POSCAR file, and as an option, can load INCAR, POTCAR, KPOINTS, and KORINGA files. The KORINGA file can be any file. In the case of this problem, it loads the Input_data.yml file. Poscar_file variable should be set as
AdvancedForEach/${file_ITER}/UnpackMol/outputs/Mol_geom.xyz.
- OUTCAR file.
- control.in file.
- geometry.in file.
- bands.out file.
- wannier90.win file.
- wannier90.wout file.
- input.dat file.
- kpoint.dat file.
- tb_hr.dat file.
- output file.
-
OUTCAR file.
-
Imports tab: Search_in_File variable should be set as vasp_results.yml and import this file using
AdvancedForEach/*/DFT-VASP/outputs/vasp_results.ymlcommand. -
Search_Parameters: Set the variables
total_energyandtitle.
- Table-dict.yml containing the variables defined in the Search_Parameters field above, as shown in Figure 1.
Developer: Celso Ricardo C. Rêgo, Multiscale Materials Modelling and Virtual Design, Institute of Nanotechnology, Karlsruhe Institute of Technology https://www.int.kit.edu/wenzel.php.