Perovskite water-splitting

We perform computational screening of around 19 000 oxides, oxynitrides, oxysulfides, oxyfluorides, and oxyfluoronitrides in the cubic perovskite structure with photoelectrochemical cell applications in mind.

Castelli, I. E., Landis, D. D., Thygesen, K. S., Dahl, S., Chorkendorff, I., Jaramillo, T. F., and Jacobsen, K. W.

New cubic perovskites for one- and two-photon water splitting using the computational materials repository.

Energy Environ. Sci. 5, 9034.

Castelli, I. E., Olsen, T., Datta, S., Landis, D. D., Dahl, S., Thygesen, K. S., and Jacobsen, K. W.

Computational screening of perovskite metal oxides for optimal solar light capture.

Energy Environ. Sci. 5, 5814.

Castelli, I. E., Thygesen, K. S., and Jacobsen, K. W.

Calculated Pourbaix Diagrams of Cubic Perovskites for Water Splitting: Stability Against Corrosion.

Topics in Catalysis 57, 265.

Key-value pairs

key

description

unit

A_ion

A-ion in the cubic perovskite

B_ion

B-ion in the cubic perovskite

CB_dir

Direct position of the conduction band edge

CB_ind

Indirect position of the conduction band edge

VB_dir

Direct position of the valence band edge

VB_ind

Indirect position of the valence band edge

anion

Anion combination in the perovskite

combination

General formula

gllbsc_dir_gap

Direct bandgap calculated with GLLB-SC

eV

gllbsc_ind_gap

Indirect bandgap calculated with GLLB-SC

eV

heat_of_formation_all

Heat of formation calculated with respect to all the materials in the pool of references

eV

project

reference

standard (used to calculate the standard heat of formation) or pool (reference included in the calculation of the convex hull)

standard_energy

ABO3 candidates for water splitting

from __future__ import print_function
import ase.db
from ase.phasediagram import PhaseDiagram

con = ase.db.connect('cubic_perovskites.db')

references = [(row.formula, row.energy)
              for row in con.select('reference')]

with open('abo3.csv', 'w') as fd:
    print('# id, formula, heat of formation [eV/atom]', file=fd)
    for row in con.select(combination='ABO3'):
        pd = PhaseDiagram(references, filter=row.formula, verbose=False)
        energy = pd.decompose(row.formula)[0]
        heat = (row.energy - energy) / row.natoms
        if (heat < 0.21 and
            (3.1 > row.gllbsc_ind_gap > 1.4 or
             3.1 > row.gllbsc_dir_gap > 1.4) and
            (row.VB_ind - 4.5 > 1.23 and row.CB_ind - 4.5 < 0 or
             row.VB_dir - 4.5 > 1.23 and row.CB_dir - 4.5 < 0)):
            formula = row.A_ion + row.B_ion + row.anion
            print('{0}, {1}, {2:.3f}'.format(row.id, formula, heat), file=fd)

The 10 candidates are:

# id

formula

heat of formation [eV/atom]

14300

SrSnO3

0.020

14363

CaSnO3

0.164

14410

LiVO3

0.171

14425

CsNbO3

0.176

14688

BaSnO3

-0.084

14863

AgNbO3

0.207

14981

SnTiO3

0.103

15088

NaSbO3

0.205

15292

SrGeO3

0.157

15621

CaGeO3

0.158

Here are the band gaps:

../_images/abo3.svg
import matplotlib.pyplot as plt
import ase.db
con = ase.db.connect('cubic_perovskites.db')

rows = []
for i, line in enumerate(open('abo3.csv')):
    if line[0] == '#':
        continue
    id, formula = line.split(',')[:2]
    id = int(id)
    row = con.get(id)
    rows.append(row)
    plt.text(i - 1.25, -1.9, formula, rotation=60)

N = len(rows)
assert N == 10
x = range(N)
y = [(row.VB_ind + row.CB_ind) / 2 - 4.5 for row in rows]
dyd = [row.gllbsc_dir_gap / 2 for row in rows]
dyi = [row.gllbsc_ind_gap / 2 for row in rows]
plt.errorbar(x, y, dyd, color='k', lw=0, mew=2, elinewidth=2,
             label='Direct Gap')
plt.errorbar(x, y, dyi, color='r', lw=0, mew=2, elinewidth=2,
             label='Indirect Gap')
plt.xlim(-1, N)
plt.ylim(4.4, -2.2)
plt.axhline(y=0, xmin=-1, xmax=N, lw=2, color='b', ls='dashed')
plt.axhline(y=1.23, xmin=-1, xmax=N, lw=2, color='g', ls='dotted')
plt.text(N + 0.1, 0.2, 'H$^+$/H$_2$', color='b')
plt.text(N + 0.1, 1.43, 'O$_2$/H$_2$O', color='g')
plt.ylabel('Potential (V vs NHE) [eV]')
plt.xticks([-1], '')
plt.legend(loc=4)
plt.savefig('abo3.svg')

The stability of a material with respect to solid and dissolved phases can be evaluated using Pourbaix diagrams. Here how to generate the Pourbaix diagram for SrTiO3:

# creates: SrTiO3_pourbaix.png
import numpy as np
import matplotlib.pyplot as plt
import ase.db
from ase.phasediagram import Pourbaix, solvated

con = ase.db.connect('cubic_perovskites.db')

refs = []
for row in con.select('reference'):
    refs.append((row.formula, row.standard_energy))

# Add other solid/dissolved phases not included before:
refs += [('Ti6O', -5.443), ('Ti2O3', -13.907), ('Ti2O', -5.164),
         ('TiO', -4.838), ('SrO2', -5.356), ('Ti3O', -5.346),
         ('Ti3O5', -22.917), ('Sr4Ti3O10', -50.756), ('SrTi11O20', -93.313)]

# Extract the dissolved phases:
refs += solvated('SrTi')

pb = Pourbaix(refs, formula='SrTiO3')
U = np.linspace(-2, 2, 200)
pH = np.linspace(-2, 15, 300)
d, names, text = pb.diagram(U, pH, plot=True, show=False)

plt.savefig('SrTiO3_pourbaix.png')
../_images/SrTiO3_pourbaix.png

Here how to plot the energy differences for all (oxides: 10, oxynitrides: 7, oxyfluorides: 3) the candidate material and the most stable experimental known solid and dissolved phases at pH = 7 and for a potential between -1 and 2 V:

# creates: WS_pourbaix.png
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.cm as cm
from matplotlib.collections import PatchCollection
import matplotlib.patches as patches
import ase.db
from ase.phasediagram import Pourbaix, solvated

con = ase.db.connect('cubic_perovskites.db')

pH = 7.
Us = np.arange(-1, 2, 0.1)
E0 = -4.5
lb = -0.5  # lower bound for the energy scale
ub = 2.0  # upper bound for the energy scale

info = []
xs = []
ys = []
heats = []

for row in con.select('heat_of_formation_all<=0.21'):
    if (row.gllbsc_ind_gap >= 1.4 and row.gllbsc_ind_gap <= 3.1 and
        row.CB_ind <= 0 - E0 and row.VB_ind >= 1.23 - E0) or \
       (row.gllbsc_dir_gap >= 1.4 and row.gllbsc_dir_gap <= 3.1 and
        row.CB_dir <= 0 - E0 and row.VB_dir >= 1.23 - E0):
        name = row.A_ion + row.B_ion + row.anion
        energy = row.standard_energy

        info.append([name, row.gllbsc_ind_gap + E0, row.gllbsc_dir_gap + E0,
                     row.VB_ind + E0, row.CB_ind + E0,
                     row.VB_dir + E0, row.CB_dir + E0])

        refs = []
        for row_ref in con.select('reference'):
            refs.append((row_ref.formula, row_ref.standard_energy))

        # Extract the dissolved phases:
        refs += solvated(row.A_ion + row.B_ion)

        for U in Us:
            pb = Pourbaix(refs, name)
            results, refs_energy = pb.decompose(U, pH, verbose=False)
            Ediff = (energy - refs_energy) / 5
            Ediff = min(Ediff, ub)
            Ediff = max(Ediff, lb)
            xs.append(len(info) - 1)
            ys.append(U)
            heats.append(Ediff)

fig = plt.figure(figsize=(20, 16))
ax = fig.add_subplot(111)

cx = 0.3
cy = 0.05
rects = []
for i in range(len(heats)):
    rect = patches.Rectangle((xs[i] - cx, ys[i] - cy), 2 * cx, 2 * cy)
    rects.append(rect)
p = PatchCollection(rects, edgecolors=None, linewidths=0, cmap=cm.RdYlGn_r)
p.set_array(np.array(heats))
ax.add_collection(p)

for i in range(len(info)):
    plt.plot([i - cx, i + cx], [info[i][3], info[i][3]], '-',
             color='k', linewidth=3)
    plt.plot([i - cx, i + cx], [info[i][4], info[i][4]], '-',
             color='k', linewidth=3)
    plt.plot([i - cx, i + cx], [info[i][5], info[i][5]], '-',
             color='r', linewidth=3)
    plt.plot([i - cx, i + cx], [info[i][6], info[i][6]], '-',
             color='r', linewidth=3)
    plt.text(i, 2.5, round(info[i][1], 1), color='k', fontsize=17.5,
             verticalalignment='top', horizontalalignment='center')
    plt.text(i, 2.75, round(info[i][2], 1), color='r', fontsize=17.5,
             verticalalignment='top', horizontalalignment='center')
plt.plot([cx, cx], [info[0][3], info[0][3]], '-', color='k', linewidth=3,
         label='Indirect BE')
plt.plot([cx, cx], [info[0][5], info[0][5]], '-', color='r', linewidth=3,
         label='Direct BE')
plt.text(len(info) + 1.5, 2.5, 'Indirect BG', color='k', fontsize=17.5,
         verticalalignment='top', horizontalalignment='left')
plt.text(len(info) + 1.5, 2.75, 'Direct BG', color='r', fontsize=17.5,
         verticalalignment='top', horizontalalignment='left')

for i in range(len(info)):
    formula = info[i][0]
    for j in range(10):
        if str(j) in formula:
            formula = formula.replace(str(j), "$_" + str(j) + "$")
    plt.text(i - cx, -1.25, formula, rotation=60, va='bottom', ha='left',
             fontsize=20.5, color='k')

xmax = len(info) + 4
plt.text(xmax + 0.05, -1, 'pH$=' + str(pH) + '$', color='black', fontsize=20.5,
         verticalalignment='center')
plt.axhline(1.23, xmin=0, xmax=xmax, color='g', ls='dotted', lw=3.5)
plt.text(xmax + 0.05, 1.23, 'O$_2$/H$_2$O', color='g', fontsize=16.5)
plt.axhline(0, xmin=0, xmax=xmax, color='b', ls='dashed', lw=3.5)
plt.text(xmax + 0.05, 0, 'H$^+$/H$_2$', color='b', fontsize=16.5)

cbar = plt.colorbar(p, orientation='horizontal', shrink=0.5)
cbar.set_label(r'$\Delta E$ [eV/atom]', fontsize=24.5)

plt.ylabel('$E$ [V vs NHE]', fontsize=26.5)
plt.yticks([-1, -0.5, 0, 0.5, 1, 1.5, 2],
           ['-1.0', '-0.5', '0.0', '0.5', '1.0', '1.5', '2.0'],
           fontsize=18.5)
plt.xticks([])
plt.legend()
plt.xlim(xmin=-0.5, xmax=xmax)
plt.ylim(ymin=-2.3, ymax=2.9)
plt.gca().invert_yaxis()

plt.savefig('WS_pourbaix.png')
../_images/WS_pourbaix.png