- Letter
- Open Access
Microscopic picture of paraelectric perovskites from structural prototypes
Phys. Rev. Research 4, L012042 – Published 29 March, 2022
DOI: https://doi.org/10.1103/PhysRevResearch.4.L012042
Abstract
We highlight with first-principles molecular dynamics the persistence of intrinsic Ti off-centerings for in its cubic paraelectric phase. Intriguingly, these are inconsistent with the space group often used to atomistically model this phase using density-functional theory or similar methods. Therefore, we deploy a systematic symmetry analysis to construct representative structural models in the form of supercells that satisfy a desired point symmetry but are built from the combination of lower-symmetry primitive cells. We define as structural prototypes the smallest of these that are both energetically and dynamically stable. Remarkably, two 40-atom prototypes can be identified for paraelectric ; these are also common to many other perovskites. These prototypes can offer structural models of paraelectric phases that can be used for the computational engineering of functional materials. Last, we show that the emergence of -cation off-centerings and the primitive-cell phonon instabilities is controlled by the equilibrium volume, in turn, dictated by the filler cation.
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Supplemental Material
References (67)
- J. G. Bednorz and K. A. Müller, Perovskite-type oxides—the new approach to high- superconductivity, Rev. Mod. Phys. 60, 585 (1988).
- J. Hwang, R. R. Rao, L. Giordano, Y. Katayama, Y. Yu, and Y. Shao-Horn, Perovskites in catalysis and electrocatalysis, Science 358, 751 (2017).
- A. K. Jena, A. Kulkarni, and T. Miyasaka, Halide perovskite photovoltaics: Background, status, and future prospects, Chem. Rev. 119, 3036 (2019).
- F. Jona and G. Shriane, Ferroelectric Crystals (Dover, New York, 1962)
- M. E. Lines and A. M. Glass, Principles and Applications of Ferroelectrics and Related Materials (Clarendon, Oxford, 1977).
- A. von Hippel, R. G. Breckenridge, F. G. Chesley, and L. Tisza, High dielectric constant ceramics, Ind. Eng. Chem. 38, 13 (1946).
- W. J. Merz, The electric and optical behavior of single-domain crystals, Phys. Rev. 76, 1221 (1949).
- R. Comès, M. Lambert, and A. Guinier, The chain structure of and , Solid State Commun. 6, 715 (1968).
- R. Comès, M. Lambert, and A. Guinier, Désordre linéaire dans les cristaux (cas du silicium, du quartz, et des pérovskites ferroélectriques), Acta Crystallogr., Section A: Cryst. Phys., Diffr. Theor. Gen. Crystallogr. 26, 244 (1970).
- I. B. Bersuker, On the origin of ferroelectricity in perovskite-type crystals, Phys. Lett. 20, 589 (1966).
- A. S. Chaves, F. C. S. Barreto, R. A. Nogueira, and B. Zẽks, Thermodynamics of an eight-site order-disorder model for ferroelectrics, Phys. Rev. B 13, 207 (1976).
- I. B. Bersuker, Pseudo-Jahn–Teller effect—A two-state paradigm in formation, deformation, and transformation of molecular systems and solids, Chem. Rev. 113, 1351 (2013).
- E. A. Stern, Character of Order-Disorder and Displacive Components in Barium Titanate, Phys. Rev. Lett. 93, 037601 (2004).
- B. Ravel, E. A. Stern, R. I. Vedrinskii, and V. Kraizman, Local structure and the phase transitions of , Ferroelectrics 206, 407 (1998).
- B. Zalar, V. V. Laguta, and R. Blinc, NMR Evidence for the Coexistence of Order-Disorder and Displacive Components in Barium Titanate, Phys. Rev. Lett. 90, 037601 (2003).
- I. Levin, V. Krayzman, and J. C. Woicik, Local structure in perovskite : Reverse Monte Carlo refinements from multiple measurement techniques, Phys. Rev. B 89, 024106 (2014).
- M. S. Senn, D. A. Keen, T. C. A. Lucas, J. A. Hriljac, and A. L. Goodwin, Emergence of Long-Range Order in from Local Symmetry-Breaking Distortions, Phys. Rev. Lett. 116, 207602 (2016).
- C. Shi, S. J. L. Billinge, E. Puma, S. H. Bang, N. J. H. Bean, J.-C. de Sugny, R. G. Gambee, R. C. Haskell, A. Hightower, and T. C. Monson, Barium titanate nanoparticles: Short-range lattice distortions with long-range cubic order, Phys. Rev. B 98, 085421 (2018).
- A. Bencan, E. Oveisi, S. Hashemizadeh, V. K. Veerapandiyan, T. Hoshina, T. Rojac, M. Deluca, G. Drazic, and D. Damjanovic, Atomic scale symmetry and polar nanoclusters in the paraelectric phase of ferroelectric materials, Nat. Commun. 12, 3509 (2021).
- W. Zhong, D. Vanderbilt, and K. M. Rabe, Phase Transitions in from First Principles, Phys. Rev. Lett. 73, 1861 (1994).
- W. Zhong, D. Vanderbilt, and K. M. Rabe, First-principles theory of ferroelectric phase transitions for perovskites: The case of , Phys. Rev. B 52, 6301 (1995).
- Y. Girshberg and Y. Yacoby, Ferroelectric phase transitions and off-centre displacements in systems with strong electron-phonon interaction, J. Phys.: Condens. Matter 11, 9807 (1999).
- H. Fu and L. Bellaiche, Ferroelectricity in Barium Titanate Quantum Dots and Wires, Phys. Rev. Lett. 91, 257601 (2003).
- R. Pirc and R. Blinc, Off-center Ti model of barium titanate, Phys. Rev. B 70, 134107 (2004).
- L. Walizer, S. Lisenkov, and L. Bellaiche, Finite-temperature properties of (Ba,Sr) systems from atomistic simulations, Phys. Rev. B 73, 144105 (2006).
- H. Krakauer, R. Yu, C.-Z. Wang, K. M. Rabe, and U. V. Waghmare, Dynamic local distortions in , J. Phys.: Condens. Matter 11, 3779 (1999).
- I. Ponomareva, L. Bellaiche, T. Ostapchuk, J. Hlinka, and J. Petzelt, Terahertz dielectric response of cubic , Phys. Rev. B 77, 012102 (2008).
- T. Nishimatsu, U. V. Waghmare, Y. Kawazoe, and D. Vanderbilt, Fast molecular-dynamics simulation for ferroelectric thin-film capacitors using a first-principles effective hamiltonian, Phys. Rev. B 78, 104104 (2008).
- Y. Qi, S. Liu, I. Grinberg, and A. M. Rappe, Atomistic description for temperature-driven phase transitions in , Phys. Rev. B 94, 134308 (2016).
- M. Paściak, T. R. Welberry, J. Kulda, S. Leoni, and J. Hlinka, Dynamic Displacement Disorder of Cubic , Phys. Rev. Lett. 120, 167601 (2018).
- L. Chen, B. Xu, Y. Yang, and L. Bellaiche, Macroscopic and microscopic structures of cesium lead iodide perovskite from atomistic simulations, Adv. Funct. Mater. 30, 1909496 (2020).
- Q. Zhang, T. Cagin, and W. A. Goddard, The ferroelectric and cubic phases in ferroelectrics are also antiferroelectric, Proc. Natl. Acad. Sci. USA 103, 14695 (2006).
- Z. Wang, O. I. Malyi, X. Zhao, and A. Zunger, Mass enhancement in and perovskites from symmetry breaking, Phys. Rev. B 103, 165110 (2021).
- X.-G. Zhao, O. I. Malyi, S. J. L. Billinge, and A. Zunger, Intrinsic local symmetry-breaking in nominally cubic paraelectric , arXiv:2106.05231.
- We stress here that as we refer to different supercell sizes throughout this paper, we use the term lattice parameter to indicate the average lattice parameter of an equivalent five-atom primitive cell, e.g., the actual supercell lattice parameter divided by 4 for a supercell.
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.4.L012042 for additional details regarding the methodology, subgroups, NEB calculations, phonons, and template stability.
- M. Kotiuga, S. Halilov, B. Kozinsky, M. Fornari, N. Marzari, and G. Pizzi, A microscopic picture of paraelectric perovskites from structural prototypes, Materials Cloud Archive 2022.32 (2022), doi: 10.24435/materialscloud:jc-ky.
- L. Talirz, S. Kumbhar, E. Passaro, A. R. V. Yakutovich, V. Granata, G. Fernando, M. Borelli, M. N. Uhrin, S. P. Huber, Z. Spyros et al., Materials cloud, a platform for open computational science, Sci. Data 7, 299 (2020).
- D. L. Decker and Y. X. Zhao, Dielectric and polarization measurements on at high pressures to the tricritical point, Phys. Rev. B 39, 2432 (1989).
- J. P. Itié, B. Couzinet, A. Polian, A. M. Flank, and P. Lagarde, Pressure-induced disappearance of the local rhombohedral distortion in , Europhys. Lett. 74, 706 (2006).
- X. Zhang, Q. Liu, J.-W. Luo, A. J. Freeman, and A. Zunger, Hidden spin polarization in inversion-symmetric bulk crystals, Nat. Phys. 10, 387 (2014).
- L. Yuan, Q. Liu, X. Zhang J.-W. Luo, S.-S. Li, and A. Zunger, Uncovering and tailoring hidden rashba spin–orbit splitting in centrosymmetric crystals, Nat. Commun. 10, 906 (2019).
- R. Zhang, A. Marrazzo, N. Verstraete, N. Marzari, and T. Sohier, Gate control of spin-layer-locking FETs and application to monolayer LuIO, Nano Letters 21, 7631 (2021).
- G. Aeppli, A. V. Balatsky, H. M. Rønnow, and N. A. Spaldin, Hidden, entangled and resonating order, Nat. Rev. Mater. 5, 477 (2020).
- A. Zunger, S.-H. Wei, L. G. Ferreira, and J. E. Bernard, Special Quasirandom Structures, Phys. Rev. Lett. 65, 353 (1990).
- A. van de Walle, P. Tiwary, M. de Jong, D. L. Olmsted, M. Asta, A. Dick, D. Shin, Y. Wang, L. Q. Chen, and Z. K. Liu, Efficient stochastic generation of special quasirandom structures, Calphad: Comput. Coupling Phase Diagrams Thermochem. 42, 13 (2013).
- F. Körmann, A. Dick, B. Grabowski, T. Hickel, and J. Neugebauer, Atomic forces at finite magnetic temperatures: Phonons in paramagnetic iron, Phys. Rev. B 85, 125104 (2012).
- G. Trimarchi, Z. Wang, and A. Zunger, Polymorphous band structure model of gapping in the antiferromagnetic and paramagnetic phases of the Mott insulators MnO, FeO, CoO, and NiO, Phys. Rev. B 97, 035107 (2018).
- A. I. Lebedev, Ab initio studies of dielectric, piezoelectric, and elastic properties of ferroelectric superlattices, Phys. Solid State 51, 2324 (2009).
- B. K. Voas, T.-M. Usher, X. Liu, S. Li, J. L. Jones, X. Tan, V. R. Cooper, and S. P. Beckman, Special quasirandom structures to study the random alloy, Phys. Rev. B 90, 024105 (2014).
- J. Varignon, M. Bibes, and A. Zunger, Origin of band gaps in perovskite oxides, Nat. Commun. 10, 1658 (2019).
- X.-G. Zhao, G. M. Dalpian, Z. Wang, and A. Zunger, Polymorphous nature of cubic halide perovskites, Phys. Rev. B 101, 155137 (2020).
- B. Kozinsky, S. A. Akhade, P. Hirel, A. Hashibon, C. Elsässer, P. Mehta, A. Logeat, and U. Eisele, Effects of Sublattice Symmetry and Frustration on Ionic Transport in Garnet Solid Electrolytes, Phys. Rev. Lett. 116, 055901 (2016).
- Y. Hinuma, G. Pizzi, Y. Kumagai, F. Oba, and I. Tanaka, Band structure diagram paths based on crystallography, Comput. Mater. Sci. 128, 140 (2017).
- P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo et al., Quantum espresso: a modular and open-source software project for quantum simulations of materials, J. Phys.: Condens. Matter 21, 395502 (2009).
- P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. B. Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M. Cococcioni et al., Advanced capabilities for materials modelling with quantum espresso, J. Phys.: Condens. Matter 29, 46 (2017).
- J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces, Phys. Rev. Lett. 100, 136406 (2008).
- G. Pizzi, A. Cepellotti, R. Sabatini, N. Marzari, and B. Kozinsky, AiiDA: Automated interactive infrastructure and database for computational science, Comput. Mater. Sci. 111, 218 (2016).
- S. P. Huber, S. Zoupanos, M. Uhrin, L. Talirz, L. Kahle, R. Häuselmann, D. Gresch, T. Müller, A. V. Yakutovich, C. W. Andersen et al., AiiDA 1.0, a scalable computational infrastructure for automated reproducible workflows and data provenance, Sci. Data 7, 300 (2020).
- M. Uhrin, S. P. Huber, J. Yu, N. Marzari, and G. Pizzi, Workflows in AiiDA: Engineering a high-throughput, event-based engine for robust and modular computational workflows, Comput. Mater. Sci. 187, 110086 (2021).
- P. Sc. H. Ghosez, X. Gonze, and J. P. Michenaud, phonon dispersion curves and interatomic force constants of barium titanate, Ferroelectrics 206, 205 (1998).
- Ph. Ghosez, E. Cockayne, U. V. Waghmare, and K. M. Rabe, Lattice dynamics of , , and : A comparative first-principles study, Phys. Rev. B 60, 836 (1999).
- M. Paściak, S. E. Boulfelfel, and S. Leoni, Polarized cluster dynamics at the paraelectric to ferroelectric phase transition in , J. Phys. Chem. B 114, 16465 (2010).
- H. T. Stokes, D. M. Hatch, and B. J. Campbell, Isodistort, isotropy software suite, https://iso.byu.edu/ (2021).
- B. J. Campbell, H. T. Stokes, D. E. Tanner, and D. M. Hatch, Isodisplace: a web-based tool for exploring structural distortions, J. Appl. Crystallogr. 39, 607 (2006).
- R. E. Cohen and H. Krakauer, Lattice dynamics and origin of ferroelectricity in : Linearized-augmented-plane-wave total-energy calculations, Phys. Rev. B 42, 6416 (1990).
- R. Armiento, B. Kozinsky, G. Hautier, M. Fornari, and G. Ceder, High-throughput screening of perovskite alloys for piezoelectric performance and thermodynamic stability, Phys. Rev. B 89, 134103 (2014).