Stability of intrinsic defects and defect clusters in LiNbO 3 from density functional theory calculations Haixuan Xu (徐海譞, 1 Donghwa Lee (이동화, 1 Jun He (贺峻, 1, * Susan B. Sinnott, 1 Venkatraman Gopalan, 2 Volkmar Dierolf, 3 and Simon R. Phillpot 1,† 1 Department of Materials Science and Engineering, University of Florida, Gainesville, Florida 32611, USA 2 Department of Materials Science and Engineering, Pennsylvania State University, University Park, Pennsylvania 16802, USA 3 Department of Physics, Lehigh University, Bethlehem, Pennsylvania 18015, USA Received 19 May 2008; revised manuscript received 22 September 2008; published 6 November 2008 A large experimental body of literature on lithium niobate, a technologically important ferroelectric, suggests that nonstoichiometric defects dominate its physical behavior, from macroscale switching to nanoscale wall structure. The exact structure and energetics of such proposed intrinsic defects and defect clusters remains unverified by either first-principles calculations or experiments. Here, density functional theory DFT is used to determine the dominant intrinsic defects in LiNbO 3 under various conditions. In particular, in an Nb 2 O 5 -rich environment, a cluster consisting of a niobium antisite compensated by four lithium vacancies is predicted to be the most stable defect structure, thereby verifying what was thus far a conjecture in the literature. Under Li 2 O-rich conditions, the lithium Frenkel defect is predicted to be the most stable, with a positive defect formation energy DFE. This is proposed as the underlying reason that the vapor-transport equilibration VTE method can grow stoichiometric LiNbO 3 . The effects of temperature and oxygen partial pressure are also explored by combining the DFT results with thermodynamic calculations. These predictions provide a picture of a very rich defect structure in lithium niobate, which has important effects on its physical behavior at the macroscale. DOI: 10.1103/PhysRevB.78.174103 PACS numbers: 61.72.J-, 71.15.Mb, 61.82.Ms I. INTRODUCTION LiNbO 3 is an important ferro-, pyro-, and piezoelectric material with many promising physical properties. 1 Its appli- cations include use as a second-harmonic generator, a para- metric oscillator, a transducer, and nonvolatile memory. 2,3 Nonstoichiometric intrinsic defects and defect clusters have been identified as the origin of substantial differences in properties between materials with slightly different Li / Nb ratios. While a large body of experimental literature exists, and some theoretical investigations have been performed, many of the key conjectures in the literature, especially on defect clusters, remain unverified by either experiments or theory. The purpose of this work is to systematically analyze the intrinsic defects and defect clusters in lithium niobate using density functional theory DFT calculations combined with thermodynamic calculations. It appears that the growth process affects the type of de- fects produced. The typical composition of LiNbO 3 grown from congruent melting is Li / Li+Nb = 0.485, which indi- cates a lithium-deficient defect structure. 4 More nearly stoi- chiometric compositions have been achieved through vapor- transport equilibration VTERefs. 5 and 6 and double- crucible Czochralski DCCZRefs. 7 and 8 methods. The change in composition from 0.485 congruent to 0.5 stoi- chiometric causes large shifts in the Curie temperature, 9 co- hesive field for domain reversal, 8–10 built-in internal field, 11 and other properties. 4 In particular, it has been conjectured that the temperature stability and field dynamics of a defect cluster consisting of a niobium antisite surrounded by four lithium vacancies can explain much of the observed macros- cale switching behavior in congruent lithium niobate. 4 How- ever, no experimental verification or detailed theoretical analysis of this intrinsic defect cluster has been presented to date. Thus, a fundamental understanding of this and other intrinsic defects in LiNbO 3 is essential. Based on the experimental data, several defect models in congruent LiNbO 3 have been proposed. Prokhorov and Kuzminov 12 proposed that oxygen vacancies surrounded by two lithium vacancies the so-called model I dominate at room temperature. However, it was soon determined from experiments that the density of LiNbO 3 increases with in- creasing Li 2 O deficiency, 13 which is inconsistent with model I. Schirmer et al. 14 concluded that niobium antisites compen- sated by niobium vacancies model II are the dominant de- fects, and that oxygen vacancies are present in negligible concentration. However, Donnerberg et al., 15 using atomic- level simulations, showed that the formation of niobium va- cancies to compensate for the niobium antisites is energeti- cally less favorable than the formation of lithium vacancies. This leads to model III consisting of Nb Li .... +4V Li ' Fig. 1. Model III was supported by x-ray- and neutron-diffraction studies. 16–19 On the one hand, Schirmer et al. 14 pointed out that the niobium vacancy model model II and lithium va- cancy model model III can be reconciled if it is assumed that there are ilmenite-type stacking faults in congruent LiNbO 3 . On the other hand, nuclear-magnetic-resonance NMR studies 20,21 concluded that a combination of model I and model III provides both qualitative and quantitative agreement with Li NMR spectra. Inconsistent with this is the assumption that only model III can be used to explain the temperature dependence of experimental Li and Nb NMR spectra. 20,21 These contradictory experimental results demon- strate that the nature of intrinsic-defect arrangements in LiNbO 3 is still not fully understood. In order to understand intrinsic-defect complexes, it is first necessary to understand the formation of individual PHYSICAL REVIEW B 78, 174103 2008 1098-0121/2008/7817/17410312 ©2008 The American Physical Society 174103-1