Competing Cation–Anion Interactions and Noncentrosymmetry in

Nov 26, 2013 - College of Arts and Sciences, Aurora University, 347 South Gladstone Avenue, Aurora, Illinois 60506-4892, United States. #. Department ...
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Competing Cation−Anion Interactions and Noncentrosymmetry in Metal Oxide-Fluorides: A First-Principles Theoretical Study Abhishek Kumar Mishra,*,†,‡ Michael R. Marvel,§ Kenneth R. Poeppelmeier,# and Umesh V. Waghmare‡ †

Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, United Kingdom Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India § College of Arts and Sciences, Aurora University, 347 South Gladstone Avenue, Aurora, Illinois 60506-4892, United States # Department of Chemistry, Northwestern University, Evanston, Illinois 60208-3113, United States ‡

S Supporting Information *

ABSTRACT: Anomalous Born dynamical charges in perovskite oxides, such as BaTiO3 and KNbO3, are known to be indicators of their tendency to turn polar through cation off-centering and measure of the interaction between d states of transition metal and p states of oxygen. Here, we use first-principles density functional theory based calculations to determine Born charges of noncentrosymmetric KNaNbOF5 and centrosymmetric CsNaNbOF5 with a goal to assess the cation−anion interactions relevant to the breaking of their centrosymmetry. We find that while noncentrosymmetry is favored by the primary Nb−O interaction, covalency in the competing interaction of Cs with anions suppresses it stabilizing the centrosymmetric structure and is reflected clearly in the deviation of Born effective charges (BECs) from their nominal ionic values. We identify specific features in the electronic structure that correlate with stability of the centrosymmetric structure and show that polarization of the noncentrosymmetric KNaNbOF5 estimated using the Berry phase method is rather weak ∼0.21 μC/cm2, consistent with the finding that it originates from the competition between the primary and secondary electronic distortions.

1. INTRODUCTION Materials with a polar noncentrosymmetric (NCS) structure, characterized by a nonzero electric dipole moment, possess technologically important physical properties such as piezoelectricity, pyroelectricity, and second harmonic generation,1,2 making them useful in a variety of applications ranging from pollution monitors, thermal detectors,1 multifunctional devices3,4 to photonic technology.5 The polar structural symmetry allows such a material to couple directly with an electric field (its energy is directly proportional to the electric field). A subclass of such materials is ferroelectrics, in which their dipole moment or polarization can be reversed with an applied electric field, making them useful in nonvolatile memory applications.6 A material on the brink of breaking inversion symmetry exhibits anomalously large response properties such as dielectric constant6 and are more suitable for applications. The breaking of centrosymmetry is typically a result of a delicate balance between short- and longrange interactions,6 and the chemical factors influencing these interactions are of fundamental interest in materials chemistry.7,8 Structures with a lack of center of inversion are typically insulating; for example, GaN,9 ZnO,9 and ferroelectric perovskite oxides10 are among the well-known noncentrosymmetric materials. Indeed, oxides have been studied intensely as noncentrosymmetric materials. Partial substitution of fluorine © 2013 American Chemical Society

for oxygen and the richness in chemical ordering among F and O lead to complicated crystal structures, which possibly involve deviation in Pauling’s second crystal rule.11 The mechanisms of centrosymmetry of such materials are expected to be different from the ones in perovskites. For example, interactions of the [NbOF5]2− anion with the combination of Na/K or Na/Cs were shown to differ significantly12 and be responsible for the structural ordering in noncentrosymmeric KNaNbOF5 and centrosymmetric CsNaNbOF5 structures. To be able to predict novel polar materials of this type, it is desirable to identify properties that are (a) indicative of the nature of such interaction and (b) that can be readily determined either experimentally or theoretically. Born effective charge (Z*) of an ion in an insulating material gives the electric dipole moment induced by its off-centering displacement (u): p = Z*u. It is fairly well established that Born effective or dynamical charges are indicators of the tendency of a perovskite oxide (e.g., BaTiO3)13 and a rocksalt group IV chalcogenide (e.g., GeTe)14 to become ferroelectric or polar. In the former, they reveal the hybridization between d orbitals of the Received: August 28, 2013 Revised: November 22, 2013 Published: November 26, 2013 131

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Figure 1. Crystal structure (1 × 1 × 1 cell) of KNaNbOF5(NCS) (a) and CsNaNbOF5(CS) (b), showing asymmetric coordination environment surrounding the [NbOF5]2− anion in xy-plane.

transition metal and p orbitals of oxygen as the chemical mechanism responsible for broken centrosymmetry, while the chemical mechanism in the latter is based on covalent interactions between p states of a chalcogen and sp orbitals of group IV ion. Born charge also gives a force felt by an ion in the presence of applied electric field: F = −ZE; thus, they determine

the oscillator strengths relevant to absorption of IR radiation and can be determined experimentally, in principle. In complex materials, however, it is difficult to measure individual ionic Born charges experimentally, while it is readily possible to obtain them from a first-principles calculations within density functional theory (DFT). 132

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simulated structures of KNaNbOF5, F1 and F3 fluoride anions, which occupy positions bonding with two eight-coordinated K+ cations and one six-coordinated Na+ cation, retain the most negative potentials (0.45 and 0.22 v.u., respectively), while three remaining fluorides have lower negative potential 0.18, 0.17, and 0.15 v.u. for F2, F4, and F5 respectively and are singly or doubly coordinated. Similarly, the triply coordinated anionic sites are occupied by the three most negatively charged ions, F1, F3, while F2, F4, and F5 are singly or doubly coordinated in the centrosymmetric CsNaNbOF5. With a goal to understand the mechanism of broken centrosymmetry and to be able to design new materials, we investigated Cs substituted for K in KNaNbOF5 with Pna21 structure and K substituted for Cs in CsNaNbOF5 with Pbcn structure, at different concentrations x. We find that the same cation and anion ordering and observance of Pauling’s Second Crystal Rule is maintained even after replacing all of the K (or Cs) ions by Cs (or K), (K1−xCsxNaNbOF5 with x = 1 and Cs1−xKxNaNbOF5 with x = 1). We calculated the energy of mixing for noncentrosymmetric structure KNaNbOF5 as

Thus, the focus of our work here is to determine Born charges of noncentrosymmeric KNaNbOF5 and centrosymmetric CsNaNbOF5 structures using first-principles calculations and to identify the chemical interactions that are relevant to their structural ordering, with close examination of their electronic structure. Our work connects with the ideas of primary and secondary distortions highlighted in earlier work12 and highlights how the interaction between Cs or K with NbOF52− is reflected in their Born charges, competes with the Nb−O interaction, and determines the bonding and structural symmetry in these compounds. As Born charges are measurable, uniquely defined, and readily accessible to first-principles calculations, they can be effectively used in analysis and design of novel materials that would lack the center of inversion symmetry.

2. METHODOLOGY We used the Perdew−Zunger (PZ) functional for the local density approximation (LDA) of exchange-correlation energy within DFT as implemented in the Quantum ESPRESSO package,15 and ultrasoft pseudopotentials16 to model the interaction between valence electrons and ionic cores.17 Kohn−Sham wave functions were represented with a plane wave basis truncated with an energy cutoff of 25 Ry (and charge density with a cutoff of 150 Ry). The structural parameters are obtained with the Broyden−Fletcher−Goldfarb−Shenno (BFGS)18−20 scheme to minimize total energy using Hellmann−Feymann forces21,22 on cations, with a tolerance of 0.001 Ry/Bohr on force on each of cations. For structural optimizations, integrations over the Brillouin zone were sampled with Monkhorst−Pack23 uniform meshes of 2 × 4 × 3 and 3 × 2 × 2 k points for KNaNbOF5 and CsNaNbOF5 crystals respectively. Polarization values were calculated using Berryphase method24 with 4 × 8 × 6 and 6 × 4 × 4 meshes of k-points for KNaNbOF5 and CsNaNbOF5 crystals respectively. Such kpoint sampling of the Brillouin zone is adequately converged as these are materials with large band gaps. The optical dielectric constant and Born effective charges were computed using a DFT linear response.25

Emix1 = E NC[(K1 − xCsx)4 (NaNbOF5)4 ] − [(1 − x)E NC[KNaNbOF5]4 + xE NC[(CsNaNbOF5)4 ]]

where ENC[(K1−xCsx)4(NaNbOF5)4] is the energy of the mixed compound in the noncentrosymmetric structure, x being the concentration. ENC[KNaNbOF5]4 and ENC[(CsNaNbOF5)4] are the energies of the two end-member compounds in the noncentrosymmetric structure. Similarly, energy of mixing of centrosymmetric structures is Emix2 = EC[(Cs1 − xK x)8 (NaNbOF5)8 ] − [xEC[CsNaNbOF5)8 + (1 − x)EC[(KNaNbOF5)8 ]]

where EC[(Cs1−xKx)8(NaNbOF5)8] is the energy of the mixed compound in the centrosymmetric structure, and EC[CsNaNbOF5)8] and EC[(KNaNbOF5)8 are the energies of the two compounds in the centrosymmetric structure. From these mixing energies, which are all positive (given in Table S4 in Supporting Information), it is clear that the K-compound is most stable in the noncentrosymmetric space group, while the Cscompound is most stable in the centrosymmetric space group. We now examine the composition (x) dependent relative stability of mixed compounds in noncentrosymmetric structure with respect to the centrosymmetric one (see Figure 2):

3. RESULTS AND DISCUSSION 3.1. Structure and Stability of K1−xCsxNaNbOF5 and Cs 1−x K x NaNbOF 5 . Both noncentrosymmetric KNaNbOF5(NCS) and centrosymmetric CsNaNbOF5(CS) occur in orthorhombic crystal structure with space groups Pna21 and Pbcn and lattice parameters12 a = 11.8653(11) Å, b = 5.8826(6) Å, c = 8.1258(8) Å, and a = 8.3155(7) Å, b = 13.3176(11) Å, c = 11.314(9) Å, respectively. Theoretical structures were determined by starting with experimental structures and minimizing their total energy with respect to size and shape of the unit cell as well as the internal ionic positions. Our estimates of the lattice parameters are a = 11.5 Å, b = 5.68 Å, c = 7.92 Å and a = 8.02 Å, b = 12.86, c = 10.85 Å for KNaNbOF5(NCS) and CsNaNBOF5(CS) structures, respectively. The errors in our estimates are a little larger than the typical errors in LDA calculations, and this is probably because our calculations simulate perfectly ordered and stoichiometric compounds, while the experimental sample can contain of some disorder in cation site occupancies. We determined anionic bond valence and cationic bond valences of KNaNbOF5 and CsNaNbOF5 in the theoretical structures and observe that these structures follow Pauling’s Second Crystal Rule which states that anions with the largest negative potentials should occupy sites having the largest positive potentials. In our

ΔE = {2E NC[K1 − xCsxNaNbOF5] − EC[K1 − xCsxNaNbOF5]}1/8

noting that z = 4 and z = 8 in the two structures, respectively. It is clear that the noncentrosymmetric structure is relatively more stable up to a value of x ≈ 0.6 and the centrosymmetric structure becomes more stable for x > 0.6. Thus, we find that the mixed compounds are metastable and may be driven kinetically to form. Second, xc = 0.6 is the point of crossover for the stability of structure with Pna21 space group to that with Pbcn, which is close to 0.5 expected from the fact that the calculated anionic and cationic bond valences values and cation−anion ordering in mixed compounds are similar to that of the pure (parent) structures [KNaNbOF5 and CsNaNbOF5]. 133

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Cs-compound reflects a slightly stronger, covalent interaction of Cs with anions than K. To understand how the orbitals contribute to the total density of states and to get an idea of the nature of bonding, we examined the projected density of states of these structures (see Figure 3a,b). It is clear that the top of the valence band is mostly contributed by 2p states of oxygen with a bandwidth of 0.5 eV. This is indeed much narrower than the typical bandwidth (about 4−5 eV) of oxygen bands in perovskite oxides. Indeed that compares well with the bandwidth of bands constituted of 2p orbitals of fluorine just below the oxygen bands. Similar to the perovskites, the bottom of the conduction band is constituted essentially of the 4d states of Nb cations, although it is split up into two sub-bands that are rather sharp. This reflects strongly ionic character of Nb and O, while fluorine states are expected to be involved in some covalent bonding. Further analysis of the projected density of states clearly reveals mixing between 5p orbitals of Cs with 2p orbitals of F (in the lower valence band), while orbitals of K do not have much mixing with F orbitals, evident in relatively sharper peaks in the lower valence band of K compound (see Figure 3a,b). Interestingly, both the valence and conduction bands arise from the anion [NbOF5]2−. A clean signature of the centrosymmetry appears in the relative height of the two Nb sub-bands immediately above the gap: the lower energy d-conduction band is weaker than the one above it in KNaNbOF5, while it is exactly reversed in CsNaNbOF5. We further investigated these interesting sub-bands through visualization of the charge contained in them. The weaker lowenergy sub-band of KNaNbOF5 and on the reverse stronger subband of CsNaNbOF5 (Figures 4a and 5a) comprises 4dzy orbitals of Nb and a weak overlap with p orbitals of the equatorial fluorine anions (2p orbitals), while there is no component of orbitals of oxygen. The higher energy sub-band in both materials (which is also more sharp, of smaller bandwidth in of KNaNbOF5 than in CsNaNbOF5) is constituted of 4dxz and 4dx2−y2 orbitals of Nb (see Figures 4b and 5b) coupled with 2p orbitals of connecting fluorides as well as of oxygen cation. This represents a relatively weak Nb dπ−O pπ interaction termed as the primary electronic distortion.7 Weaker overlap between 2p orbital of oxygen and 4d orbital of Nb in the upper sub-band of CsNaNbOF5 than that in KNaNbOF5 confirms weaker primary distortion in the former. We note that greater hybridization of 5p states of Cs cations with fluorine anions (F1 and other equatorial fluorine anions) in CsNaNbOF5 which relates to the secondary distortion, competes with Nb−O interaction (the inherent primary electronic distortion in [NbOF5]2−) and stops the ordering that breaks its inversion symmetry. On the other hand, we do not find any such hybridization between K cationic states and fluorine anionic states in the DOS of KNaNbOF5, and hence KNaNbOF5 maintains higher primary electronic distortion and results in a noncentrosymmetric structure. Thus, Nb−O interaction favors a stronger primary distortion and noncentrosymmetric structure, and its suppression by the competing interaction of Cs with anions results in the centrosymmetric structure. Previously reported bond valence data support the idea that competition between the Nb−O dπ−pπ interactions (primary distortions) and O−K/Cs interactions (secondary distortions) weakens the former distortions.12 For example, the CsNaNbOF5 oxide ion makes more/stronger contacts to surrounding alkali cations than the KNaNbOF5 oxide ion owing to a higher surrounding positive potential (0.48 v.u. versus 0.38 v.u.). Indeed, the predominant lattice-derived secondary distortion in CsNaNbOF5 occurs along the same O−Nb−F1 bond axis as the

Figure 2. Relative stability of noncentrosymmetric structure [K1−xCsxNaNbOF5] with respect to centrosymmetric structure [K1−xCsxNaNbOF5] as a function of mixing x.

3.2. Electronic Structure. We now present an analysis of the electronic structure of noncentrosymmetric K1−xCsxNaNbOF5 and centrosymmetric Cs1−xKxNaNbOF5. From the electronic density of states of the KNaNbOF5 and CsNaNbOF5 (Figure 3a,b), we find that KNaNbOF5 is an insulator with an indirect

Figure 3. Calculated density of states (DOS) of KNaNbOF5(NCS) (a) and CsNaNbOF5(CS) (b) with the Fermi energy set to zero. We have marked the specific atomic states which contribute maximum to the bands.

energy band gap of 4.67 eV, and its band gap decreased only by 0.1 eV after complete substitution of Cs cations at K-sites. Second, the centrosymmetric CsNaNbOF5 structure is an insulator with an indirect band gap of 4.57 eV (Figure 3b), and complete substitution of K atoms at Cs-sites results in an increase in the band gap by only 0.03 eV. A relatively smaller gap of the 134

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Figure 4. Charge density associated with LUMO (a) and LUMO+1 (b) of KNaNbOF5(NCS).

electroneutrality in ionic structures. Deviations from PSCR may manifest as secondary, symmetry-breaking distortions in metal oxide fluorides12 and do in the present work. The equatorial Nb− F bond lengths are equal and the equatorial fluoride ligands have equal residual negative potentials in the CS polymorph owing to symmetry in the surrounding cationic bond network. The local symmetry precludes preferential cation−anion interactions, i.e. ones that are markedly stronger than the others, and represents a local adherence to PSCR: a symmetric (equal) distribution of positive potential. In contrast, an equatorial fluoride ligand in the NCS polymorph makes stronger/shorter contacts to the cationic bond network owing to asymmetry therein. The secondary distortion of the equatorial fluoride towards the cationic bond network is a significant structural element and signals a local deviation from PSCR. 3.3. Born Effective Charges. A small structural distortion can be represented by displacements of atoms from their

primary distortion and mitigates the Nb−O dπ−pπ interaction. In contrast, no significant secondary distortion is observable along the O−Nb−F1 bond axis in KNaNbOF5 , and the Nb−O dπ−pπ interaction is preserved. A comparison of bonding network between NCS and CS polymorph of KNaNbOF526 shows that there is significant distortion in the equatorial plane in NCS polymorph (Nb−F3 bond length is large compared to other equatorial Nb−F bond lengths) compared to that in CS polymorph (all equatorial Nb− F bond lengths are same). Second, [Nb-OF5]2− anion moiety in the CS polymorph makes six cationic contacts with Na compared to five in NCS polymorph.26 Thus, while Nb−O primary distortion must be preserved for NCS space group, it does not guarantee crystallization in an NCS space group, and it is the covalency in the competing interaction of cations (K/Na/Cs) with anions that suppresses it stabilizing the centrosymmetric structure. Pauling’s Second Crystal Rule (PSCR) predicts local 135

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Figure 5. Charge density associated with LUMO (a) and LUMO+1 (b) of CsNaNbOF5(CS).

reference (typically equilibrium) positions. In an ionic or polar material, a displacement of an atom generates an electric dipole, which gives long-range dipole−dipole interactions which show up as the splitting between transverse and longitudinal optic modes in the phonon spectrum. Born effective charge (BEC or, Z*), defined earlier, is also known as the transverse or dynamic or effective charge and can also be defined as the linear coupling between the electric field ε and the force Fj on ion j exerted by the field j:

Z*J , αβ =

∂Fj , α ∂εβ

u=0

where the derivative is calculated at zero cationic displacement.14 A large BEC means that a large electric force is felt by an ion even if the field is small and thus indicates the tendency of a material toward a polar ground state. A large value of the BEC was shown to be an indicator of a material which is on the verge of a ferroelectric transition.13,27−29 In these materials, Z* is 136

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calculated BECs bear reflection of this trend, as we see in KNaNbOF5, BECs of trans fluoride F1 (ZXX = −1.54, ZYY = −1.06, ZZZ = −0.87) and equatorial fluoride F3 (ZXX = −1.18, ZYY = −1.325, ZZZ = −0.72) are larger in magnitude than those of the remaining three equatorial fluorides F2, F4, and F5 (Table 1). So, F1 which has the largest magnitude of BEC and F3 which has a larger value of BEC among all other equilateral fluorides are found to be coordinated with three cationic sites. Similarly, BECs of F1 (ZXX = −0.90, ZYY = −0.92, ZZZ = −1.92) and F3 (ZXX = −0.74, ZYY = −1.99, ZZZ = −0.68) in CsNaNbOF5(CS) are larger in magnitude and are coordinated with three cationic sites, in contrast to doubly or singly coordinated sites of remaining fluorides, whose BECs are smaller in magnitude. 3.4. Dielectric Constant and Polarization. Dielectric constant diverges near a ferroelectric transition at which the inversion symmetry is broken. In the present case, though we do not have a symmetry breaking transition in the same sense (there are no small atomic displacements that connect the two structures), we expect the electronic dielectric behavior to reflect the change in bonding at the crossover between noncentrosymmetric KNaNbOF5 and centrosymmetric CsNaNbOF5. We determined electronic dielectric constants (square of refractive index) of both noncentrosymmetric KNaNbOF5 and centrosymmetric CsNaNbOF5 and of mixed noncentrosymmetric and centrosymmetric structures. A variation of dielectric constants with varying mixing of K/Cs cations is shown in Figure 6. From

anomalously large in the centrosymmetric structure and becomes less so in a noncentrosymmetric one. The nature of bonding we uncovered from atomic and electronic structure and the origin of breaking of centrosymmetry is clearly seen in our calculated BECs of KNaNbOF5 and CsNaNbOF5. Anomalous BEC on trans fluoride F1 (up to −1.92) (ZXX = −0.90, ZYY = −0.92, ZZZ = −1.92) in the centrosymmetric structure of CsNaNbOF5 is a indicative of the presence of large secondary distortion. This secondary distortion lowers the primary electronic distortion and thus results in an overall centrosymmetric structure. In contrast, we find lower values of BECs on trans fluoride F1 (ZXX = −1.54, ZYY = −1.06, ZZZ = −0.87) in KNaNbOF5. We saw in section 3.2 from the electronic bands that O−pπ and Nb−dπ interactions are stronger in the noncentrosymmetric KNaNbOF5 than the one in the centrosymmetric CsNaNbOF5. From Table 1, we see that Table 1. Diagonal Elements of the Born Effective Charge Tensors of Different Ions in One Formula Unit of KNaNbOF5(NCS) and CsNaNbOF5(CS) Born effective charges Z*αβ KNaNbOF5(NCS)

CsNaNbOF5(CS)

ion

ZXX

ZYY

ZZZ

ion

ZXX

ZYY

ZZZ

K

1.20

1.32

1.21

1.23 4.57 −2.02 −1.59 −0.69 −1.18 −0.71 −0.59

1.08 4.45 −1.07 −1.06 −0.76 −1.32 −1.65 −0.75

1.21 4.43 −0.79 −0.87 −1.70 −0.72 −0.73 −1.82

Cs1 Cs2 Na Nb O F1 F2 F3 F4 F5

1.32 1.40 1.23 4.49 −0.88 −0.90 −1.75 −0.74 −1.83 −0.74

1.40 1.40 1.19 4.62 −1.13 −0.92 −0.60 −1.99 −0.80 −1.53

1.46 1.38 1.21 4.85 −2.12 −1.92 −0.92 −0.68 −0.63 −0.98

Na Nb O F1 F2 F3 F4 F5

oxygen anion possesses higher magnitude (more anomalous) of BECs in CsNaNbOF5, consistent with its weaker the primary electronic distortion, and the centrosymmetric structure. It is also evident in Table 1 that the BECs of Cs cations are larger (up to 1.46) than those of K cations in the noncentrosymmetric structure of KNaNbOF5, consistent with stronger covalency of Cs with fluorine anions, as seen earlier in our analysis of the electronic density of states. Higher hybridization of Cs cations with fluorine anions is very important and results in a large secondary distortion (indicated by the coordination number of oxygen) and hence a centrosymmetric structure. From the Born effective charges of F (Table 1), we see that all the equatorial fluorine cations F2 (ZXX = −1.75, ZYY = −0.60, ZZZ = −0.92), F3 (ZXX = −0.74, ZYY = −1.99, ZZZ = −0.68), F4 (ZXX = −1.83, ZYY = −0.80, ZZZ = −0.63), and F5 (ZXX = −0.74, ZYY = −1.53, ZZZ = −0.98) exhibit clearly larger values of BECs in the centrosymmetric CsNaNbOF5 than those in noncentrosymmetric KNaNbOF5. Large values of Born effective charges of fluorine anions too are indicative of the centrosymmetry and correlate with the presence of large secondary distortion in CsNaNbOF5. Born effective charges also clearly explain bonding in these two structures. As we discussed in section 3.1 that in both KNaNbOF5(NCS) and CsNaNbOF5(CS) compounds, equatorial fluoride F3 and fluoride F1 which is trans to the oxygen anion have three cationic contacts, while other three fluorides, namely, F2, F4, and F5, have only one or two cationic contacts. Our

Figure 6. Variation of average electronic dielectric constants with mixing x (K/Cs) in the noncentrosymmetric structure of K1−xCsxNaNbOF5 and centrosymmetric structure of Cs1−xKxNaNbOF5. Dotted line shows the transition at a mixing value of about 0.6.

the relative stability of the two structures in Figure 2, we know that the material transforms from K-rich noncentrosymmetric structure to Cs-rich centrosymmetric structure at x = 0.6. Indeed, we find that the dielectric constant increases as x approaches the crossover value of 0.6 from both sides, and there is a peak (with discontinuity) in the dielectric constant as a function of concentration x of Cs/K ions (shown by thick dotted line in Figure 6). We calculated polarization of noncentrosymmetric KNaNbOF5 using the Berry phase method20 and find that it is rather weak, ∼0.21 μC/cm2 along the z-direction (and of course zero along the x and y directions due to symmetry) (see Figure 7a). When we replace all K cations by in noncentrosymmetric 137

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Figure 7. Weak polarization in the z-direction (Nb−F) in KNaNbOF5(NCS) structure (a); zero net polarization because of opposite direction of dipoles in CsNaNbOF5(CS) structure (b). We have reduced atomic radius and connectivity factor for clear visualization of polarization.

KNaNbOF5 (K1−xCsxNaNbOF5, with x = 1), we find a slightly larger value of polarization (Pz = −1.29 μC/cm2). Such small values of polarization are consistent with the fact that it arises from the competition between primary and secondary distortions. In the centrosymmetric structure of CsNaNbOF5 calculated polarization is zero in all three directions, as expected from the symmetry of the crystal (see Figure 7b).

structure that correlate with stability of their centrosymmetric structure and show that polarization of the noncentrosymmetric KNaNbOF5 estimated using the Berry phase method is rather weak, ∼0.21 μC/cm2, consistent with its origin in the competition between the primary and secondary electronic distortions.

4. CONCLUSION Using first-principles DFT-based calculations, we have analyzed the structure, electronic structure, polarization, and Born effective charges of noncentrosymmetric KNaNbOF5 and centrosymmetric CsNaNbOF5. We find that the Born charges clearly bear the difference between the interactions of Cs, K with anions, which are key to the structural centrosymmetry. We find that a strong Nb−O interaction relevant to the primary distortion favors a noncentrosymmetric structure. When the competing Cs/K interaction with F and O is strongly covalent enough, it suppresses the primary distortion favoring centrosymmetry. We identified the specific features in the electronic

* Supporting Information

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ASSOCIATED CONTENT

S

Calculated structural parameters (Table S1), bond valences (Tables S2 and S3), energy of mixing (Table S4), and dielectric constants values (Table S5). This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Present address: Department of Chemistry, University College London, 20 Gordon Street, London, United Kingdom WC1H 0AJ. E-mail: [email protected], mishra_lu@hotmail. com, [email protected]. Tel.: +44-7466106384. 138

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Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS A.K.M. acknowledges the Department of Science and Technology (DST), New Delhi, for a fellowship under Fast Track Scheme for Young Scientists (SR/FTP/PS-105/2009), and U.V.W. thanks the IUS-STF for funding through the Indo-US Joint Center between JNCASR and NU. This work was also supported by a grant from the National Science Foundation (Solid State Chemistry Award No DMR-1005827).

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REFERENCES

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