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Model for B Site Ordering in PMN Eric Cockayne Benjamin P. Burton

Model for B Site Ordering in PMN Eric Cockayne Benjamin P. Burton Material Measurement Laboratory, NIST, Gaithersburg. Observed Cation Ordering in Various ABB'O 3 perovskites (Burton & Cockayne, PRB 60, R12542 (1999)). Randall & Bhalla (Jpn. J Appl. Phys. 29, 327 1990):

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Model for B Site Ordering in PMN Eric Cockayne Benjamin P. Burton

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  1. Model for B Site Ordering in PMN Eric Cockayne Benjamin P. Burton Material Measurement Laboratory, NIST, Gaithersburg

  2. Observed Cation Ordering in Various ABB'O3 perovskites (Burton & Cockayne, PRB 60, R12542 (1999))

  3. Randall & Bhalla (Jpn. J Appl. Phys. 29, 327 1990): short-range ordering correlated with relaxor behavior

  4. Coulomb model (Bellaiche and Vanderbilt PRL 81, 1318 (1998)): predicts 1:2 [111] ordering for AB1/3B'2/3O3 with heterovalent B cations Holds true for BMN (Dias and Luiz- Moreira, J. Appl. Phys. 94, 3414 (2003)). Akbar and Davies (J. Phys. Chem. Sol. 61, 159 (2000)): 1:1 Ordering in PMN: ``random site” model: One sublattice is Nb, the other a random arrangement of Mg2/3Nb1/3

  5. Ab-Initio-Calculation-Based Proposed Ground State of PMN Prosandeev et. al., PRB 70, 134110 (2004) 1:1 [111] A Example of ``1:1-type” structure”

  6. Calculated energies of Pb- and Ba- complex perovskites Burton & Cockayne, PRB (1999)

  7. Coulomb effects do not explain cation ordering in PMN. But Why Not? Various explanations for observed 1:1 ordering in PMN: 1. Pb4+ substitution on B sublattice (Bellaiche & Vanderbilt) 2. Theories with multibody terms Pb bonding to underbonded oxygen (Burton and Cockayne) empirical multibody terms (A. Y. Gufan, Phys. Solid State 47, 1134 (2005)) charge transfer to A site depending on surrounding B environment (Wu and Krakauer, PRB 63, 184113 (2001). This talk: simple quantitative ”multibody” model: Coulomb interactions + effect of local electric fields at A sites

  8. Starting point: existing effective Hamiltonian approach to local polarizations in Pb-based perovskites (Cockayne, Bellaiche and Burton, AIP Conf.l Proc. 2001)) Heff = Honsite(xi) + Hij(xi,xj) + H(xi,Eloc(s)) + H(xi,e) → Heff = Honsite(xi) + H(xi,Eloc(s)) + HCoulomb (s) Honsite(xi) → quartic; isotropic

  9. Ionic energetics vs. strength of local field “Centered” A site Ion; e.g. Ba DU ~ a E2 “Off-center” ion, eg. Pb DU ~ a1 |E| + a2 E2 Sitewise addition for electric fields in a configuration: U = UCoulomb + C1Si |Ei| + C2Si |Ei|2 (C1 = 0 for centered ions) This is physical origin of multibody terms in model C1 and C2 always negative: Similutaneously want low Coulomb energy (ordered) and strong local fields (disorder)!

  10. Calculations of local field strengths <|E|> and <E2> Plausibility argument for stability of 1:1 [111] A

  11. Methods • Configuration exploration • Brute force: 6x6x2 simulation cell; compute all 1:1-type structures • 36 sites on each Mg2/3Nb1/3 sublattice. • Explore all arrangements of Mn24Nb12 on these sites • (exploit symmetries to reduce burden) • Find ground state for various linear and quadratic coupling • constants • Map phase diagram; identify small-unit-cell candidates for PMN ground state. • Ab initio electronic structure VASP used (DFT) code Projector augmented wave pseudopotentials optimized to PBE version of GGA Run using PBEsol version of GGA 400 eV plane wave cutoff; Common k-point grid equivalent to 6x6x6 Monkhorst-Pack on primitive perovskite cell

  12. Results: qualitative phase diagram 1:1 C 1:1 B 1:1 A Magnitude of C1 1:1 A 1:1 C 1:1 B 1:2 1:2 Magnitude of C2

  13. Ab initio results Structure Atoms/cell Symmetry U/(5 atoms) (eV) 1:2 [111] 15 rhomb -36.616 1:1 [111] A 30 mono -36.603 1:1 [111] B 60 ortho -36.598 1:1 [111] C 60 mono -36.640 1:2 [110] 15 ortho -36.587 1:1 [001] 15 tetrag -36.520 1:1 [111] C has lowest energy of any known configuration! Caveat: only symmetry-preserving relaxation has been allowed further relaxation (e.g. oxygen octahedral tilting) could lower energy further.

  14. Conclusions • Simple quantitative model for cation ordering in complex pervoskites • Competition between Coulomb effects, favoring highly ordered structures, and relaxation due to strong local fields favoring disorder • Whether an ion tends to be central (Ba) or off-centered (Pb) affects the relative stability of the different configurations • Several ``random-site type” configurations are identified as candidates for the ground state of PMN and related materials • One of these structures has the lowest energy in DFT calculations

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