Competing Phases

To calculate the limiting chemical potentials of elements in the material (needed for calculating the defect formation energies) we need to consider the energies of all competing phases. doped does this by calling the CompetingPhases Class, which then queries Materials Project to obtain all the relevant competing phases to be calculated. In some cases the Materials Project may not have all known phases in a certain chemical space, so it’s a good idea to cross-check the generated competing phases with the ICSD in case you suspect any are missing.

For this functionality to work correctly, you must have POTCARs set up to work with pymatgen and you will also need an API key for the Materials Project (both of which are described on the Installation docs page).

• Note that at present this uses the ‘Legacy API’ from the Materials Project, and so the API key you use (either in ~/.pmgrc.yaml or supplied to CompetingPhases with the api_key parameter) should correspond to the Materials Project legacy API. This key can be found here.

Tip

You can run this notebook interactively through Google Colab or Binder – just click the links! If running on Colab, then you’ll need to run !pip install doped in a cell to install the package, and !git clone https://github.com/SMTG-Bham/doped to download the example data (and update paths in the code cells accordingly).

from doped.chemical_potentials import CompetingPhases

For example, if we want to calculate the chemical potentials with ZrO₂ as our host material, we would generate the relevant competing phases like so:

cp = CompetingPhases("ZrO2")  # default e_above_hull = 0.1 eV/atom
# if you don't have your MP API key set up in ~/.pmgrc.yaml, you can supply it as a parameter in this function

Note

Note: The current algorithm for how doped queries the Materials Project (MP) and determines relevant competing phases to be calculated, is that it first queries the MP for all phases with energies above hull less than e_above_hull eV/atom (optional parameter in CompetingPhases(); default is 0.05 eV/atom) in the chemical space of the host material. It then determines which of these phases border the host material in the phase diagram (i.e. which are competing phases and thus determine the chemical potentials), as well as which phases would border the host material if their energies were downshifted by e_above_hull. The latter are included as well, and so e_above_hull acts as an uncertainty range for the MP-calculated formation energies, which may not be accurate due to functional choice (GGA vs hybrid DFT / GGA+U / RPA etc.), lack of vdW corrections etc.

The default e_above_hull of 50 meV/atom works well in accounting for MP formation energy inaccuracies in most known cases. However, some critical thinking is key (as always!) and so if there are any obvious missing phases or known failures of the Materials Project energetics in your chemical space of interest, you should adjust this parameter to account for this (or alternatively manually include these known missing phases in your competing phase calculations, to be included in parsing and chemical potential analysis later on).

Particular attention should be paid for materials containing transition metals, (inter)metallic systems, mixed oxidation states, van der Waals (vdW) binding and/or large spin-orbit coupling (SOC) effects, for which the Materials Project energetics are typically less reliable.

Tip

Often e_above_hull can be lowered (e.g. to 0) to reduce the number of calculations while retaining good accuracy relative to the typical error of defect calculations.

cp.entries contains pymatgen ComputedStructureEntry objects for all the relevant competing phases, which includes useful data such as their structures, magnetic moment and (MP-calculated GGA) band gaps.

print(len(cp.entries))
print([entry.name for entry in cp.entries])

28
['O2', 'Zr', 'Zr3O', 'Zr4O', 'ZrO2', 'Zr3O', 'Zr3O', 'Zr2O', 'ZrO2', 'ZrO2', 'Zr', 'ZrO2', 'ZrO2', 'ZrO2', 'ZrO2', 'ZrO2', 'ZrO2', 'Zr', 'ZrO2', 'ZrO2', 'ZrO2', 'ZrO2', 'ZrO2', 'Zr', 'Zr6O11', 'ZrO2', 'ZrO2', 'ZrO2']

We can plot our phase diagram like this, which can show why certain phases are included as competing phases:

import doped
import matplotlib.pyplot as plt

plt.rcdefaults()
plt.style.use(f"{doped.__path__[0]}/utils/doped.mplstyle")  # use doped style
from pymatgen.ext.matproj import MPRester
from pymatgen.analysis.phase_diagram import PhaseDiagram, PDPlotter

system = ["Zr", "O"]  # system we want to get phase diagram for
mpr = MPRester()  # object for connecting to MP Rest interface, may need to specify API key here
entries = mpr.get_entries_in_chemsys(system)  # get all entries in the chemical system
pd = PhaseDiagram(entries)  # create phase diagram object
plotter = PDPlotter(pd, show_unstable=0.1, backend="matplotlib")  # plot phase diagram
plot = plotter.get_plot()

In this case, we see that there are many low-energy polymorphs of ZrO₂ on the MP database. If for example we had already calculated the different polymorphs of ZrO₂ and knew the MP-predicted groundstate (i.e. with MP-calculated energy above hull of zero) was indeed the groundstate with our chosen DFT setup, we could then remove the extra ZrO₂ phases here like so:

cp.entries = [entry for entry in cp.entries if entry.name != "ZrO2" or entry.data["e_above_hull"] == 0]
print(len(cp.entries))
print([entry.name for entry in cp.entries])

12
['O2', 'Zr', 'Zr3O', 'Zr4O', 'ZrO2', 'Zr3O', 'Zr3O', 'Zr2O', 'Zr', 'Zr', 'Zr', 'Zr6O11']

Similarly, if we had prior knowledge that the Materials Project data was accurate for our chosen host material, or were doing a high-throughput investigation where we were happy to sacrifice some accuracy/completeness for efficiency, we could set e_above_hull to zero (i.e. total confidence in the MP data):

cp = CompetingPhases("ZrO2", e_above_hull=0)
print(len(cp.entries))
print([entry.name for entry in cp.entries])

4
['O2', 'Zr', 'Zr3O', 'ZrO2']

Indeed, if we plot our phase diagram again, only showing the stable MP entries, we see that only Zr₃O and O₂ border ZrO₂, and so these (plus any remaining elements; i.e. Zr here) are the only competing phases generated with e_above_hull = 0:

plotter = PDPlotter(pd, show_unstable=0, backend="matplotlib")  # plot phase diagram
plot = plotter.get_plot()

Just to illustrate, this is what our phase diagram would look like for a ternary system like Cu\(_2\)SiSe\(_3\) (a promising solar absorber):

system = ["Cu", "Si", "Se"]  # system we want to get phase diagram for
mpr = MPRester()  # object for connecting to MP Rest interface, may need to specify API key here
entries = mpr.get_entries_in_chemsys(system)  # get all entries in the chemical system
pd = PhaseDiagram(entries)  # create phase diagram object
plotter = PDPlotter(pd, show_unstable=0.01, backend="matplotlib")  # plot phase diagram
plot = plotter.get_plot()

Generating input files

We can then set up the competing phase calculations with doped as described below, or use the pymatgen ComputedStructureEntry objects in cp.entries to set these up in your desired format with python / atomate / AiiDA etc.

k-points convergence testing is done at GGA (PBEsol by default) and is set up to account for magnetic moment convergence as well. Here we interface with vaspup2.0 to make it easy to use on the HPCs (with the generate-converge command to run the calculations and data-converge to quickly parse and analyse the results).

You may want to change the default ENCUT (350 eV) or k-point densities that the convergence tests span (5 - 120 kpoints/ų for semiconductors & insulators and 40 - 1000 kpoints/ų for metals). Note that ISMEAR is set to 0 (gaussian smearing) for semiconductors & insulators and 2 (2nd order Methfessel-Paxton smearing) for metals by default, following the recommended choices in VASP, and k-point convergence testing is not required for molecules (Γ-point sampling is sufficient).

Note that doped generates “molecule in a box” structures for the gaseous elemental phases H₂, O₂, N₂, F₂ and Cl₂. The molecule is placed in a slightly-symmetry-broken (to avoid metastable electronic solutions) 30 Å cuboid box, and relaxed with Γ-point-only k-point sampling.

The kpoints convergence calculations are set up with:

cp.convergence_setup(
    user_incar_settings={"GGA": "PE"}
)  # For custom INCAR settings, any flags that aren't numbers or True/False need to be input as strings with quotation marks

O2 is a molecule in a box, does not need convergence testing

Note

You may need to increase the default range of k-points to test convergence for certain systems, which can be controlled with the kpoints_metals and kpoints_nonmetals parameters for cp.convergence_setup.

Tip

Usually we expect mostly equivalent energy convergence with respect to k-points / basis set for semi-local (GGA) and hybrid DFT. However, this may not be the case when there is a major qualitative change in behaviour between semi-local/hybrid DFT, such as going from metallic at the GGA level to semiconducting with hybrid DFT – which can occur for relatively low band gap systems. In these cases, it can be worth performing the convergence tests with hybrid DFT to see if convergence is reached at lower k-point densities / basis set sizes.

!ls competing_phases/Zr3O_EaH_0
!ls competing_phases/Zr3O_EaH_0/kpoint_converge

kpoint_converge
k3,3,3 k4,4,4 k5,5,5 k6,6,6 k7,7,7 k8,8,8 k9,9,9

This creates a folder called competing_phases with all the relevant competing phases and k-point convergence test calculation directories. The naming format is <Formula>_EaH_<MP Energy above Hull> (‘EaH’ stands for ‘Energy above Hull’). These can be quickly run on HPCs using vaspup2.0, by creating a job file for the HPC scheduler (vaspup2.0 example here), copying it into each directory and running the calculation with a bash loop like:

for i in *EaH*  # (in the competing_phases directory) – for each competing phase
do cp job $i/kpoint_converge
cd $i/kpoint_converge
for k in k*   # for each kpoint calculation directory
do cp job $k
cd $k
qsub job  # may need to change 'qsub' to 'sbatch' if the HPC scheduler is SLURM
cd ..
done
cd ../..
done

Within each competing phase directory in competing_phases, the vaspup2.0 data-converge command can be run to quickly parse the results and determine the converged k-mesh (see the vaspup2.0 homepage for examples).

Next, you want to relax each competing phase with the converged k-point mesh, and calculate the energy with the same DFT functional and settings as your defect supercell calculations. doped can generate these folders for the relaxations of the competing phases.

The k-point meshes are Γ-centred Monkhorst-Pack by default. By default doped will make the calculation inputs assuming a HSE06 INCAR (see HSESet.yaml for default values) and kpoint densities of 200 kpoints/ų for metals and 64 kpoints/ų for semiconductors/insulators. Assuming you’ve followed the k-point convergence testing workflow above, you should change the KPOINTS file to match the converged mesh in each case, however the default densities are good starting points. doped will automatically set SIGMA and ISMEAR accordingly depending on whether the phase is a semiconductor or metal, and will set NUPDOWN appropriately for molecules (i.e. O₂ has triplet spin).

These relaxations can be set up with:

cp.vasp_std_setup(
    user_incar_settings={"ENCUT": 600}
)  # For custom INCAR settings, any flags that aren't numbers or True/False need to be input as strings with quotation marks

If you make a dictionary, as shown below, of the converged k-points for each competing phase, you can quickly generate the corresponding KPOINTS files for the relaxations like this:

from pymatgen.io.vasp.inputs import Kpoints

converged_kpoints_dict = {
    "Zr3O_EaH_0": [2, 2, 2],
    "Zr_EaH_0": [11, 11, 11],
    "ZrO2_EaH_0": [8, 8, 8],
}  # etc...

for name, kpts in converged_kpoints_dict.items():
    kpoints = Kpoints.gamma_automatic(kpts=kpts)
    kpoints.write_file(f"competing_phases/{name}/vasp_std/KPOINTS")

!ls competing_phases/Zr3O_EaH_0
!ls competing_phases/Zr3O_EaH_0/vasp_std

kpoint_converge vasp_std
INCAR   KPOINTS POSCAR  POTCAR

Remember that the final ENCUT used for the energy calculations should be the same as for your host material & defects, and that you may still need to account for Pulay stress by increasing ENCUT for the geometry relaxations (a typical rule of thumb being 1.3*converged ENCUT) or re-relaxing each structure until the volume change is minimal (roughly <0.3%). This is not a concern for the molecule-in-a-box competing phases, due to the large simulation box size and fixed volume.

Tip

For hybrid DFT competing phase relaxations, it is often a good idea to use the NKRED(X,Y,Z) INCAR tag(s), which reduce the k-point grid used in the Fock exchange potential by the factor specified, to speed up the calculations while retaining good accuracy. Note that NKRED(X,Y,Z) needs to divide into the number of k-points in the corresponding direction. Typically NKRED(X,Y,Z) has a greater effect on energy rather than force accuracy, and so it is often useful to use NKRED(X,Y,Z) values of 2 – or possibly 3 for high k-point densities – to pre-converge the structure relaxation, before then continuing the calculations without NKRED(X,Y,Z) for the final energy; which often then only requires one or two ionic steps.

NKRED(X,Y,Z) is particularly useful for metals, where overall dense k-point grids are required, but the Fock exchange contribution typically converges at much lower k-point densities. In such cases, NKRED(X,Y,Z) can be used to greatly reduce the computational cost with minimal loss of accuracy. A further relaxation/energy calculation without NKRED(X,Y,Z) may not be required in these cases, but it is good practice to check the accuracy by comparing the energies of the same structure with and without NKRED(X,Y,Z).

Extrinsic Competing Phases

If you’re investigating extrinsic impurities/doping in your system, you also need to calculate the chemical potentials for these extrinsic species, which can be done using doped in a similar fashion as for the intrinsic species:

from doped.chemical_potentials import ExtrinsicCompetingPhases

ex_cp = ExtrinsicCompetingPhases(composition="ZrO2", extrinsic_species="La", e_above_hull=0.03)

len(ex_cp.entries)
print([entry.name for entry in ex_cp.entries])

['La', 'La2Zr2O7', 'La']

The same competing phase generation algorithm as described above is used for extrinsic competing phases, ensuring no unnecessary additional phases are generated.

The setup for convergence testing and relaxations is done in the exact same way as before:

ex_cp.convergence_setup(
    user_incar_settings={"ENCUT": 550}
)  # For custom INCAR settings, any flags that aren't numbers or True/False need to be input as strings with quotation marks

!ls competing_phases/La2Zr2O7_EaH_0
!ls competing_phases/La2Zr2O7_EaH_0/kpoint_converge

kpoint_converge
k1,1,1 k2,2,2 k3,3,3 k4,4,4

ex_cp.vasp_std_setup(
    user_incar_settings={"ENCUT": 550}
)  # For custom INCAR settings, any flags that aren't numbers or True/False need to be input as strings with quotation marks

!ls competing_phases/La2Zr2O7_EaH_0
!ls competing_phases/La2Zr2O7_EaH_0/vasp_std

kpoint_converge vasp_std
INCAR   KPOINTS POSCAR  POTCAR

Parsing Competing Phases

Read in data from vasprun.xml files

Once you’ve calculated your competing phases, you will want to parse the results to determine the chemical potential limits of your host material. To do this, we need to parse the vasprun.xml(.gz) files from your final production-run competing phase calculations. To download the vasprun.xml(.gz) files from the HPCs recursively, you can recursively rsync:

rsync -azvuR hpc:'path/to/the/base/folder/competing_phases/./*_EaH_*/vasp_std/vasprun.xml*' .

where the /./ indicates where you’d like to start the recurse from, so you only keep the folder structure from the formula_EaH_* point onwards. If you’ve done spin-orbit coupling (SOC) calculations with results in vasp_ncl folders, then you need to change vasp_std to vasp_ncl above, or to whatever name you’ve given the production-run folders. Note that you can compress the vasprun.xml files to save space (with e.g. find . -name vasprun.xml -exec gzip {} \;) and these will still be parsed fine by doped.

All analysis is performed with the CompetingPhasesAnalyzer class, and all you need to supply it is the formula of your host system and the path to the base folder in which you have all your formula_EaH_*/vasp_std/vasprun.xml(.gz) files.

If you did not generate your competing phases with doped, you can still parse them with doped by providing a list of paths to the vasprun.xml(.gz) files using pathlib or os, as shown below.

from doped.chemical_potentials import CompetingPhasesAnalyzer

cpa = CompetingPhasesAnalyzer("ZrO2")

# in this case we have our competing phases in the ZrO2 subfolder of the competing_phases folder,
# with 'relax' subfolders in each <formula>_EaH_<energy above hull> folder
cpa.from_vaspruns(path="./competing_phases/ZrO2/", folder="relax")

Parsing 8 vaspruns and pruning to include only lowest-energy polymorphs...

If we want to save the parsed formation energies to a csv file, we can do so by providing a filename to the csv_path argument:

cpa.from_vaspruns(
    path="./competing_phases/ZrO2/",
    folder="relax",
    csv_path="competing_phases/zro2_competing_phase_energies.csv",
)

Parsing 8 vaspruns and pruning to include only lowest-energy polymorphs...
Competing phase formation energies have been saved to competing_phases/zro2_competing_phase_energies.csv

If you haven’t used doped to generate your competing phase calculations, you can parse the data from a list of vasprun.xml files using pathlib or os like so:

from pathlib import Path

path = "path/to/base"
all_paths = []
for p in Path(path).iterdir():
    if not p.name.startswith("."):
        pp = p / "relax" / "vasprun.xml"
        if pp.is_file():
            all_paths.append(pp)

cpa.from_vaspruns(all_paths)

Print Formation Energies as a LaTeX Table

You may want to print out the parsed calculation results for your competing phases as a LaTeX table, to be included in supplementary information of journal articles or in theses, to aid open-science and reproducibility. The formation energies are automatically saved to a csv file, which can be converted to LaTeX (see www.tablesgenerator.com/latex_tables) or Word formats, but you can also print out a nicely-formatted LaTeX table using the to_LaTeX_table() method as shown belo – either as a one- or two-column table; ordered alphabetially or in descending order of energies.

table = cpa.to_LaTeX_table()
print(table)

\begin{table}[h]
\centering
\caption{Formation energies per formula unit ($\Delta E_f$) of \ce{ZrO2} and all competing phases, with k-meshes used in calculations. Only the lowest energy polymorphs are included}
\label{tab:competing_phase_formation_energies}
\begin{tabular}{ccc}
\hline
Formula & k-mesh & $\Delta E_f$ (eV/fu) \\ \hline 
\ce{ZrO2} & 3$\times$3$\times$3 & -10.975 \\ 
\ce{O2} & 2$\times$2$\times$2 & 0.000 \\ 
\ce{Zr} & 9$\times$9$\times$5 & 0.000 \\ 
\ce{Zr2O} & 5$\times$5$\times$2 & -5.729 \\ 
\ce{Zr3O} & 5$\times$5$\times$5 & -5.987 \\ 
\hline
\end{tabular}
\end{table}

Note

The table does not use booktabs by default but you can change the horizontal lines (hline) to toprule, midrule and bottomrule to get the desired style effect. The output also relies on using the \ce{} command from the mhchem LaTeX package to get the correct formatting for the chemical formulae.

As a sidenote, you can also read in the data from a previously parsed csv file:

cpa.from_csv(csv_path="competing_phases/zro2_competing_phase_energies.csv")

Calculate the chemical potential limits

We can then calculate the chemical potential limits for our host material using the cpa.calculate_chempots() method. This will print out the chemical potential limits for each element in the host material, and also return a pandas dataframe containing the chemical potential limits for each element in the host material.

cpa.calculate_chempots()

Calculated chemical potential limits (in eV wrt elemental reference phases): 

                Zr       O
Limit                     
ZrO2-O2   -10.9754  0.0000
Zr3O-ZrO2  -0.1995 -5.3879

	Zr	O
Limit
ZrO2-O2	-10.9754	0.0000
Zr3O-ZrO2	-0.1995	-5.3879

Here, the compositions listed under Limit are the competing phases which are in equilibrium with the host/bulk material at the given point in the phase diagram, which corresponds to a vertex on the chemical stability region of the host – i.e. corresponding to a chemical potential limit for the host material. In other words, it represents an extremal point in the hyperplane of chemical potentials in which the host compound is stable. Thus in this case the “ZrO2-O2” limit corresponds to the oxygen-rich chemical potential limit, corresponding to the maximum oxygen chemical potential at which the host (ZrO2) is stable – in this case being in equilibrium with elemental \(O_2\). Likewise “Zr3O-ZrO2” represents the Zr-rich limit, where the Zr chemical potential is maximised (under the constraint of the host material being stable with respect to decomposition).

Again, if we set csv_path, it will save the calculated chemical potential limits to a csv file:

cpa.calculate_chempots(csv_path="competing_phases/zro2_chempots.csv")

Saved chemical potential limits to csv file:  competing_phases/zro2_chempots.csv
Calculated chemical potential limits (in eV wrt elemental reference phases): 

                Zr       O
Limit                     
ZrO2-O2   -10.9754  0.0000
Zr3O-ZrO2  -0.1995 -5.3879

	Zr	O
Limit
ZrO2-O2	-10.9754	0.0000
Zr3O-ZrO2	-0.1995	-5.3879

To use these parsed chemical potential limits for computing the defect formation energies with doped (i.e. with the DefectThermodynamics plotting & analysis methods) we can use the cpa.chempots attribute, which is a dictionary of the chemical potential limits for each element in the host material:

cpa.chempots

{'limits': {'ZrO2-O2': {'Zr': -20.81910468, 'O': -7.006602065},
  'Zr3O-ZrO2': {'Zr': -10.04321996, 'O': -12.394544425}},
 'elemental_refs': {'O': -7.006602065, 'Zr': -9.84367624},
 'limits_wrt_el_refs': {'ZrO2-O2': {'Zr': -10.975428439999998, 'O': 0.0},
  'Zr3O-ZrO2': {'Zr': -0.19954371999999942, 'O': -5.387942359999999}}}

The keys in the 'limits' and 'limits_wrt_el_refs' sub-dictionaries list the competing phases at the given chemical potential limit, as explained above, while 'elemental_refs' gives the computed reference energies per atom of the elemental phases (used to obtain the formal chemical potentials, which are referenced to the energies of the elements in their standard states).

As shown in the defect thermodynamics and plotting customisation tutorials, we can specify the chemical potential limit at which to obtain the defect formation energies using the limit parameter, which we can set to either "X-rich"/"X-poor" where X is an element in the system, in which case the most X-rich/poor limit will be used (e.g. “O-rich”), or a key in the chempots["limits"] dictionary.

If you want to save it to use at a later date / in a different notebook/environment without having to re-parse your results, you can dump it to a json file with dumpfn and then load it again with loadfn:

from monty.serialization import dumpfn, loadfn

dumpfn(cpa.chempots, fn="competing_phases/zro2_chempots.json")
zro2_chempots = loadfn("competing_phases/zro2_chempots.json")

Analysing and visualising the chemical potential limits

Once you’ve parsed your competing phase calculations and calculated the chemical potential limits (with cpa.calculate_chempots()) you can also visualize your calculated chemical potential limits as shown:

from pymatgen.analysis.chempot_diagram import ChemicalPotentialDiagram

cpd = ChemicalPotentialDiagram(cpa.intrinsic_phase_diagram.entries)
plot = cpd.get_plot()
plot.show("png", dpi=400)

Because cpd.get_plot() returns a plotly object, it’s almost infinitely customisable using plot.update_scenes() - you can change colours, fonts, axes and even data after it’s been plotted. See the docs for more info.

Beware that because we only generated the relevant competing phases on the Zr-O phase diagram for our ZrO₂ host material, we have not calculated all phase in the Zr-O chemical space (just those that are necessary to determine the chemical potential limits of ZrO₂), and so these chemical potential diagram plots are only accurate in the vicinity of our host material.

This is an example of what this looks like for a higher-dimensional quaternary system:

from monty.serialization import loadfn

cpd = ChemicalPotentialDiagram(loadfn("competing_phases/ytos_phase_diagram.json").entries)
plot = cpd.get_plot(formulas_to_draw=["Y2Ti2S2O5"])
plot.show("png", dpi=400)

Parsing Extrinsic Species

Likewise if you’ve generated and calculated the competing phases for extrinsic species (i.e. to obtain the chemical potential limits for dopants/extrinsic impurities in your host system), you can easily parse them using the same CompetingPhaseAnalyzer class.

la_cpa = CompetingPhasesAnalyzer("ZrO2", extrinsic_species="La")
la_cpa.from_vaspruns(
    path="./competing_phases/La_ZrO2/",
    folder="relax",
    csv_path="./competing_phases/zro2_la_competing_phase_energies.csv",
)
df = la_cpa.calculate_chempots(csv_path="./competing_phases/zro2_la_chempots.csv")

Parsing 11 vaspruns and pruning to include only lowest-energy polymorphs...
Competing phase formation energies have been saved to ./competing_phases/zro2_la_competing_phase_energies.csv
Calculating chempots for La
Saved chemical potential limits to csv file:  ./competing_phases/zro2_la_chempots.csv
Calculated chemical potential limits (in eV wrt elemental reference phases): 

                Zr       O        La La-Limiting Phase
Limit                                                 
ZrO2-O2   -10.9754  0.0000 -9.463016          La2Zr2O7
Zr3O-ZrO2  -0.1995 -5.3879 -1.381266          La2Zr2O7

As before, we can get the chemical potential limits in the format required for the DefectThermodynamics plotting and analysis methods using cpa.chempots, which can be easily dumped to a reusable json file for later use:

from monty.serialization import dumpfn, loadfn

dumpfn(la_cpa.chempots, fn="competing_phases/zro2_la_chempots.json")
la_chemlims = loadfn("competing_phases/zro2_la_chempots.json")

Combining multiple extrinsic chemical potentials

If for example you were interested in simulating defect complexes where you introduce more than one extrinsic defect at a time, or if you wanted to plot all the possible dopant species in one transition level diagram, you will need to combine your chemical potential limits for these extrinsic species.

To combine several extrinsic chemical potential limits, you will need to save the different sets of parsed chemical potentials with CompetingPhaseAnalyzer to chempots.json files as shown above. You can then combine these chemical potential limits with:

from doped.chemical_potentials import combine_extrinsic
from monty.serialization import loadfn

first = loadfn("competing_phases/zro2_la_chempots.json")
second = loadfn("competing_phases/zro2_y_chempots.json")
extrinsic_species = "Y"  # this should be set to whatever is the extrinsic species in the second dictionary
d = combine_extrinsic(first=first, second=second, extrinsic_species=extrinsic_species)
print(d)

{'elemental_refs': {'O': -7.006602065, 'Zr': -9.84367624, 'La': -5.00458616, 'Y': -5.50458616}, 'limits': {'ZrO2-O2-La2Zr2O7-Y2Zr2O7': {'Zr': -20.81910468, 'O': -7.006602065, 'La': -14.467573640000001, 'Y': -14.967573640000001}, 'Zr3O-ZrO2-La2Zr2O7-Y2Zr2O7': {'Zr': -10.04321996, 'O': -12.394544425, 'La': -6.3856601000000035, 'Y': -6.8856601000000035}}, 'limits_wrt_el_refs': {'ZrO2-O2-La2Zr2O7-Y2Zr2O7': {'Zr': -10.975428439999998, 'O': 0.0, 'La': -9.462987480000002, 'Y': -9.962987480000002}, 'Zr3O-ZrO2-La2Zr2O7-Y2Zr2O7': {'Zr': -0.19954371999999942, 'O': -5.387942359999999, 'La': -1.3810739400000038, 'Y': -1.8810739400000038}}}

As the output of combine_extrinsic() is a dictionary, it can either be dumped to a new json file with dumpfn or you can keep adding new chemical potential limits to it.

NB: the limits must be in the same order in all dictionaries you’re combining. Make sure to double check all energies have been combined correctly.