Exploring the Nitride Perovskites Composition Space with Chemical Heuristics and First-Principles Calculations Dr Daniel Davies [email protected] Live session: EL03.06.03: Theory and Design of Ionic Semiconductors April 23 2021 - 2:15 – 4:15 pm EDT Department of Chemistry A B

The search for nitride perovskites 1. K. R. Talley et al., Synthesis of Ferroelectric LaWN3 – The First Nitride Perovskite, arXiv (2020) 2. R. Sarimento-Pérez et al., Prediction of Stable Nitride Perovskites, Chem. Mater. (2015) • Oxide and halide perovskites (inorganic and mixed organic-inorganic) are an exciting research area owing to their optoelectronic properties. • Recently, there has been growing interest in nitride perovskites.1,2 • Thermodynamic stability screening of 3,906 cubic ABN3 perovskites à 22 within 200 meV/atom of convex hull.2 Key questions: • Can we rule out specific ABN3 compositions from chemical considerations before running first-principles calculations? • To what extent does octahedral tilting affect thermodynamic stability in nitride perovskites?

Using oxidation states data to filter out unlikely compounds [A+B2+] [A+B5+] [A2+B4+] [A3+B3+] [A+B8+] [A2+B7+] [A3+B6+] [A4+B5+] Total X- 2,535 2,535 O2- 856 2,365 2,550 5,771 N3- 90 275 700 799 1,864 1. D. W. Davies et al., SMACT: Semiconducting Materials by Analogy and Chemical Theory, JOSS (2018) 2. Y. Ding et al., Data Mining Element Charges in Inorganic Materials, JPCL (2020) [A+B2+] [A+B5+] [A2+B4+] [A3+B3+] [A+B8+] [A2+B7+] [A3+B6+] [A4+B5+] Total X- 321 321 O2- 116 442 1,332 1,890 N3- 12 25 182 155 374 • Including 61 metals (up to Bi) = 3660 A-B-anion chemical systems. • Charge neutrality Σq = 0 & electrostatic qA ≤ qB limits are applied in SMACT1 All-inclusive oxidation states set Data-driven oxidation states set: tolerance of 5% ICSD occurrence2 374 326 remove duplicates 279 rA shannon ≥ rB shannon Reduced search space for nitride perovskites

A reduced nitride perovskite search space [A+B8+] [A2+B7+] [A3+B6+] [A4+B5+] • B site limited to 11 elements stable in (V) to (VIII) oxidation states: Ta, Nb, V, W, Mo, Cr, Re, Ru, Os, Ir, Sb • Most metals are A site candidates in at least one chemical system • Large space of potential A4+B5+N3 and A3+B6+N3 perovskites to explore How might structural distortions stabilise these hypothetical nitride perovskites?

Applying octahedral tilts systematically 1. A.M. Glazer, The Classification of Tilted Octahedra in Perovskites, Acta Cryst. B (1972) Computational details • DFT using VASP • PBEsol +U (MP set) GGA XC functional 550 eV plane-wave cutoff • 0.01 eVÅ-1 atomic force convergence 1. volume only 2. lattice parameters and ionic positions • G-centred k-point mesh, density > 90 Å-3 • Calculations automated using Pymatgen and Fireworks Glazer tilt Space group a0a0a0 Pm3m a-a-a- R3c a0a0c- I4/mcm a0a0c+ P4/mbm a0b-b- Imma a-b+a- Pnma a+a+a+ Im3 a0b-c+ Cmcm a0b+b+ I4/mmm a+a+c- P42/nmc a-a-c- C2/c a0b-c- C2/m a-b-c- P1 a+b-c- P21/m a+b+c+ Immm a0a0c- a+b+c+ • BN6 octahedral tilting reduce the symmetry of the cubic perovskite structure • 15 tilt systems can occur in real crystals, each leading to a different space group1 • Each tilt system is imposed on each cubic perovskite, which is then relaxed fully

Increased stability from octahedral tilts High symmetry Multiple A-site Low symmetry Lowest energy structure Energy of cubic structure meV/atom • Scenario 1: All tilts relax to cubic structure (rA >>rB ) • Scenario 2: Significant stability gain in lower symmetry perovskite space group • Scenario 3: Significant stability gain accompanied by transition to non-perovskite phase Short (1.4 Å) N-N distances

Increased stability from octahedral tilts High symmetry Multiple A-site Low symmetry Lowest energy structure Energy of cubic structure meV/atom Short (1.4 Å) N-N distances Ehull • Scenario 1: All tilts relax to cubic structure (rA >>rB ) • Scenario 2: Significant stability gain in lower symmetry perovskite space group • Scenario 3: Significant stability gain accompanied by transition to non-perovskite phase

Increased stability from octahedral tilts High symmetry Multiple A-site Low symmetry Lowest energy structure Energy of cubic structure meV/atom Ehull • Scenario 1: All tilts relax to cubic structure (rA >>rB ) • Scenario 2: Significant stability gain in lower symmetry perovskite space group • Scenario 3: Significant stability gain accompanied by transition to non-perovskite phase Ehull

Overall trends in DFT total energy reduction [A+B8+] [A2+B7+] [A3+B6+] [A4+B5+] • Large thermodynamic stability gain when octahedral tilting is possible • Majority of resultant compounds adopt a low-symmetry hettotype of the perovskite structure • See expected Goldschmidt tolerance factor trends with respect to relative ionic radii rA & rB rA = 1.01 Å rA = 1.30 Å

Hypothetical electronic structures  Z T Y 6 R U X  Y −6 −4 −2 0 2 4 6 (neUgy (eV) TRtDO D26 N (S) NE (V) NE (S) NE (d) ZU (d) ZrNbN3  Z T Y 6 R U X  Y −6 −4 −2 0 2 4 6 (neUgy (eV) TRWDO D26 N (S) W (S) W (d) Y (S) Y (d) If synthesis is possible: • many of the compounds are likely to have desirable electronic properties • From hybrid DFT band structures: ✅ Band gaps suitable for PV ✅ Highly dispersive VB & CB However, nitride perovskites remain elusive. We must consider: • Correction schemes for accurate decomposition energies • Dynamic stability and mapping of phonon modes to lower symmetry structures • Unknown competing phases to populate otherwise sparse nitride phase diagrams YWN3 Hybrid DFT (HSE06 functional)

Acknowledgements & Software Thanks to • Prof. David Scanlon • Prof. Aron Walsh • Dr. Christopher Savory Electronic structure calculations • VASP (www.vasp.at) Everything else is open-source Python • SMACT: smact.readthedocs.io • PyTilting: gitlab.com/pyseries/pytilting • Sumo: smtg-ucl.github.io/sumo • Pymatgen: pymatgen.org • Fireworks: materialsproject.github.io/fireworks Contact • @danwdavies • [email protected] • EL03.06.03 ✉ 💬