Competing Cation–Anion Interactions and Noncentrosymmetry in Metal Oxide-Fluorides: A...

Competing Cation−Anion Interactions and Noncentrosymmetry inMetal Oxide-Fluorides: A First-Principles Theoretical StudyAbhishek 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 perovskiteoxides, such as BaTiO3 and KNbO3, are known to be indicatorsof their tendency to turn polar through cation off-centering andmeasure of the interaction between d states of transition metaland p states of oxygen. Here, we use first-principles densityfunctional theory based calculations to determine Born chargesof noncentrosymmetric KNaNbOF5 and centrosymmetricCsNaNbOF5 with a goal to assess the cation−anion interactionsrelevant to the breaking of their centrosymmetry. We find thatwhile noncentrosymmetry is favored by the primary Nb−Ointeraction, covalency in the competing interaction of Cs withanions suppresses it stabilizing the centrosymmetric structureand is reflected clearly in the deviation of Born effective charges(BECs) from their nominal ionic values. We identify specificfeatures in the electronic structure that correlate with stability of the centrosymmetric structure and show that polarization of thenoncentrosymmetric KNaNbOF5 estimated using the Berry phase method is rather weak ∼0.21 μC/cm2, consistent with thefinding 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, possesstechnologically important physical properties such as piezo-electricity, pyroelectricity, and second harmonic generation,1,2

making them useful in a variety of applications ranging frompollution monitors, thermal detectors,1 multifunctional devi-ces3,4 to photonic technology.5 The polar structural symmetryallows such a material to couple directly with an electric field (itsenergy is directly proportional to the electric field). A subclass ofsuch materials is ferroelectrics, in which their dipole moment orpolarization can be reversed with an applied electric field, makingthem useful in nonvolatile memory applications.6 A material onthe brink of breaking inversion symmetry exhibits anomalouslylarge response properties such as dielectric constant6 and aremore suitable for applications. The breaking of centrosymmetryis typically a result of a delicate balance between short- and long-range interactions,6 and the chemical factors influencing theseinteractions are of fundamental interest in materials chemistry.7,8

Structures with a lack of center of inversion are typicallyinsulating; for example, GaN,9 ZnO,9 and ferroelectric perovskiteoxides10 are among the well-known noncentrosymmetricmaterials. Indeed, oxides have been studied intensely asnoncentrosymmetric materials. Partial substitution of fluorine

for oxygen and the richness in chemical ordering among F and Olead to complicated crystal structures, which possibly involvedeviation in Pauling’s second crystal rule.11 The mechanisms ofcentrosymmetry of such materials are expected to be differentfrom the ones in perovskites. For example, interactions of the[NbOF5]

2− anion with the combination of Na/K or Na/Cs wereshown to differ significantly12 and be responsible for thestructural ordering in noncentrosymmeric KNaNbOF5 andcentrosymmetric CsNaNbOF5 structures. To be able to predictnovel polar materials of this type, it is desirable to identifyproperties that are (a) indicative of the nature of such interactionand (b) that can be readily determined either experimentally ortheoretically.Born effective charge (Z*) of an ion in an insulating material

gives the electric dipole moment induced by its off-centeringdisplacement (u): p = Z*u. It is fairly well established that Borneffective or dynamical charges are indicators of the tendency of aperovskite oxide (e.g., BaTiO3)

13 and a rocksalt group IVchalcogenide (e.g., GeTe)14 to become ferroelectric or polar. Inthe former, they reveal the hybridization between d orbitals of the

Received: August 28, 2013Revised: November 22, 2013Published: November 26, 2013

Article

pubs.acs.org/crystal

© 2013 American Chemical Society 131 dx.doi.org/10.1021/cg401296f | Cryst. Growth Des. 2014, 14, 131−139

pubs.acs.org/crystal

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

the oscillator strengths relevant to absorption of IR radiation andcan be determined experimentally, in principle. In complexmaterials, however, it is difficult to measure individual ionic Borncharges experimentally, while it is readily possible to obtain themfrom a first-principles calculations within density functionaltheory (DFT).

Figure 1. Crystal structure (1 × 1 × 1 cell) of KNaNbOF5(NCS) (a) and CsNaNbOF5(CS) (b), showing asymmetric coordination environmentsurrounding the [NbOF5]

2− anion in xy-plane.

Crystal Growth & Design Article

dx.doi.org/10.1021/cg401296f | Cryst. Growth Des. 2014, 14, 131−139132

Thus, the focus of our work here is to determine Born chargesof noncentrosymmeric KNaNbOF5 and centrosymmetricCsNaNbOF5 structures using first-principles calculations andto identify the chemical interactions that are relevant to theirstructural ordering, with close examination of their electronicstructure. Our work connects with the ideas of primary andsecondary distortions highlighted in earlier work12 and highlightshow the interaction between Cs or K with NbOF5

2− is reflectedin their Born charges, competes with the Nb−O interaction, anddetermines the bonding and structural symmetry in thesecompounds. As Born charges are measurable, uniquely defined,and readily accessible to first-principles calculations, they can beeffectively used in analysis and design of novel materials thatwould lack the center of inversion symmetry.

2. METHODOLOGY

We used the Perdew−Zunger (PZ) functional for the localdensity approximation (LDA) of exchange-correlation energywithin DFT as implemented in the Quantum ESPRESSOpackage,15 and ultrasoft pseudopotentials16 to model theinteraction between valence electrons and ionic cores.17

Kohn−Sham wave functions were represented with a planewave basis truncated with an energy cutoff of 25 Ry (and chargedensity with a cutoff of 150 Ry). The structural parameters areobtained with the Broyden−Fletcher−Goldfarb−Shenno(BFGS)18−20 scheme to minimize total energy using Hell-mann−Feymann forces21,22 on cations, with a tolerance of 0.001Ry/Bohr on force on each of cations. For structuraloptimizations, integrations over the Brillouin zone were sampledwith Monkhorst−Pack23 uniform meshes of 2 × 4 × 3 and 3 × 2× 2 k points for KNaNbOF5 and CsNaNbOF5 crystalsrespectively. Polarization values were calculated using Berry-phase method24 with 4 × 8 × 6 and 6 × 4 × 4 meshes of k-pointsfor KNaNbOF5 and CsNaNbOF5 crystals respectively. Such k-point sampling of the Brillouin zone is adequately converged asthese are materials with large band gaps. The optical dielectricconstant and Born effective charges were computed using a DFTlinear response.25

3. RESULTS AND DISCUSSION

3.1. Structure and Stability of K1−xCsxNaNbOF5 andCs1−xKxNaNbOF5. Both noncentrosymmetric KNaN-bOF5(NCS) and centrosymmetric CsNaNbOF5(CS) occur inorthorhombic crystal structure with space groups Pna21 and Pbcnand 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 deter-mined by starting with experimental structures and minimizingtheir total energy with respect to size and shape of the unit cell aswell as the internal ionic positions. Our estimates of the latticeparameters 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 CsNaN-BOF5(CS) structures, respectively. The errors in our estimatesare a little larger than the typical errors in LDA calculations, andthis is probably because our calculations simulate perfectlyordered and stoichiometric compounds, while the experimentalsample can contain of some disorder in cation site occupancies.We determined anionic bond valence and cationic bond valencesof KNaNbOF5 and CsNaNbOF5 in the theoretical structures andobserve that these structures follow Pauling’s Second CrystalRule which states that anions with the largest negative potentialsshould occupy sites having the largest positive potentials. In our

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 mostnegative potentials (0.45 and 0.22 v.u., respectively), while threeremaining fluorides have lower negative potential 0.18, 0.17, and0.15 v.u. for F2, F4, and F5 respectively and are singly or doublycoordinated. Similarly, the triply coordinated anionic sites areoccupied by the three most negatively charged ions, F1, F3, whileF2, F4, and F5 are singly or doubly coordinated in thecentrosymmetric CsNaNbOF5.With a goal to understand the mechanism of broken

centrosymmetry and to be able to design new materials, weinvestigated Cs substituted for K in KNaNbOF5 with Pna21structure and K substituted for Cs in CsNaNbOF5 with Pbcnstructure, at different concentrations x. We find that the samecation and anion ordering and observance of Pauling’s SecondCrystal Rule is maintained even after replacing all of the K (orCs) ions by Cs (or K), (K1−xCsxNaNbOF5 with x = 1 andCs1−xKxNaNbOF5 with x = 1). We calculated the energy ofmixing for noncentrosymmetric structure KNaNbOF5 as

=

− −

+

−E E

x E

xE

[(K Cs ) (NaNbOF ) ]

[(1 ) [KNaNbOF ]

[(CsNaNbOF ) ]]

x xmix1 NC 1 4 5 4

NC 5 4

NC 5 4

where ENC[(K1−xCsx)4(NaNbOF5)4] is the energy of the mixedcompound in the noncentrosymmetric structure, x being theconcentration. ENC[KNaNbOF5]4 and ENC[(CsNaNbOF5)4] arethe energies of the two end-member compounds in thenoncentrosymmetric structure. Similarly, energy of mixing ofcentrosymmetric structures is

=

−

+ −

−E E

xE

x E

[(Cs K ) (NaNbOF ) ]

[ [CsNaNbOF )

(1 ) [(KNaNbOF ) ]]

x xmix2 C 1 8 5 8

C 5 8

C 5 8

where EC[(Cs1−xKx)8(NaNbOF5)8] is the energy of the mixedcompound in the centrosymmetric structure, andEC[CsNaNbOF5)8] and EC[(KNaNbOF5)8 are the energies ofthe two compounds in the centrosymmetric structure. Fromthese mixing energies, which are all positive (given in Table S4 inSupporting Information), it is clear that the K-compound is moststable in the noncentrosymmetric space group, while the Cs-compound is most stable in the centrosymmetric space group.We now examine the composition (x) dependent relative

stability of mixed compounds in noncentrosymmetric structurewith respect to the centrosymmetric one (see Figure 2):

Δ =

−−

−

E E

E

{2 [K Cs NaNbOF ]

[K Cs NaNbOF ]}1/8x x

x x

NC 1 5

C 1 5

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



3.2. Electronic Structure.We now present an analysis of theelectronic structure of noncentrosymmetric K1−xCsxNaNbOF5and centrosymmetric Cs1−xKxNaNbOF5. From the electronicdensity of states of the KNaNbOF5 and CsNaNbOF5 (Figure3a,b), we find that KNaNbOF5 is an insulator with an indirect

energy band gap of 4.67 eV, and its band gap decreased only by0.1 eV after complete substitution of Cs cations at K-sites.Second, the centrosymmetric CsNaNbOF5 structure is aninsulator with an indirect band gap of 4.57 eV (Figure 3b), andcomplete substitution of K atoms at Cs-sites results in an increasein the band gap by only 0.03 eV. A relatively smaller gap of the

Cs-compound reflects a slightly stronger, covalent interaction ofCs 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 examinedthe projected density of states of these structures (see Figure3a,b). It is clear that the top of the valence band is mostlycontributed by 2p states of oxygen with a bandwidth of 0.5 eV.This is indeed much narrower than the typical bandwidth (about4−5 eV) of oxygen bands in perovskite oxides. Indeed thatcompares well with the bandwidth of bands constituted of 2porbitals of fluorine just below the oxygen bands. Similar to theperovskites, the bottom of the conduction band is constitutedessentially of the 4d states of Nb cations, although it is split upinto two sub-bands that are rather sharp. This reflects stronglyionic character of Nb and O, while fluorine states are expected tobe involved in some covalent bonding. Further analysis of theprojected density of states clearly reveals mixing between 5porbitals 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 Kcompound (see Figure 3a,b). Interestingly, both the valence andconduction bands arise from the anion [NbOF5]

2−. A cleansignature of the centrosymmetry appears in the relative height ofthe two Nb sub-bands immediately above the gap: the lowerenergy d-conduction band is weaker than the one above it inKNaNbOF5, while it is exactly reversed in CsNaNbOF5.We further investigated these interesting sub-bands through

visualization of the charge contained in them. The weaker low-energy sub-band of KNaNbOF5 and on the reverse stronger sub-band of CsNaNbOF5 (Figures 4a and 5a) comprises 4dzy orbitalsof Nb and a weak overlap with p orbitals of the equatorial fluorineanions (2p orbitals), while there is no component of orbitals ofoxygen. The higher energy sub-band in both materials (which isalso more sharp, of smaller bandwidth in of KNaNbOF5 than inCsNaNbOF5) is constituted of 4dxz and 4dx2−y2 orbitals of Nb(see Figures 4b and 5b) coupled with 2p orbitals of connectingfluorides as well as of oxygen cation. This represents a relativelyweak Nb dπ−O pπ interaction termed as the primary electronicdistortion.7 Weaker overlap between 2p orbital of oxygen and 4dorbital of Nb in the upper sub-band of CsNaNbOF5 than that inKNaNbOF5 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) inCsNaNbOF5 which relates to the secondary distortion, competeswith Nb−O interaction (the inherent primary electronicdistortion in [NbOF5]

2−) and stops the ordering that breaksits inversion symmetry. On the other hand, we do not find anysuch hybridization between K cationic states and fluorine anionicstates in the DOS of KNaNbOF5, and hence KNaNbOF5maintains higher primary electronic distortion and results in anoncentrosymmetric structure. Thus, Nb−O interaction favors astronger primary distortion and noncentrosymmetric structure,and its suppression by the competing interaction of Cs withanions results in the centrosymmetric structure.Previously reported bond valence data support the idea that

competition between the Nb−O dπ−pπ interactions (primarydistortions) and O−K/Cs interactions (secondary distortions)weakens the former distortions.12 For example, the CsNaNbOF5oxide ion makes more/stronger contacts to surrounding alkalications than the KNaNbOF5 oxide ion owing to a highersurrounding positive potential (0.48 v.u. versus 0.38 v.u.).Indeed, the predominant lattice-derived secondary distortion inCsNaNbOF5 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.

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



primary distortion and mitigates the Nb−O dπ−pπ interaction.In contrast, no significant secondary distortion is observablealong the O−Nb−F1 bond axis in KNaNbOF5 , and the Nb−Odπ−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−F3bond length is large compared to other equatorial Nb−F bondlengths) compared to that in CS polymorph (all equatorial Nb−F bond lengths are same). Second, [Nb-OF5]

2− anion moiety inthe CS polymorphmakes six cationic contacts with Na comparedto five in NCS polymorph.26 Thus, while Nb−O primarydistortion must be preserved for NCS space group, it does notguarantee crystallization in an NCS space group, and it is thecovalency in the competing interaction of cations (K/Na/Cs)with anions that suppresses it stabilizing the centrosymmetricstructure. Pauling’s Second Crystal Rule (PSCR) predicts local

electroneutrality in ionic structures. Deviations from PSCR maymanifest as secondary, symmetry-breaking distortions in metaloxide fluorides12 and do in the present work. The equatorial Nb−F bond lengths are equal and the equatorial fluoride ligands haveequal residual negative potentials in the CS polymorph owing tosymmetry in the surrounding cationic bond network. The localsymmetry precludes preferential cation−anion interactions, i.e.ones that are markedly stronger than the others, and represents alocal adherence to PSCR: a symmetric (equal) distribution ofpositive potential. In contrast, an equatorial fluoride ligand in theNCS polymorph makes stronger/shorter contacts to the cationicbond network owing to asymmetry therein. The secondarydistortion of the equatorial fluoride towards the cationic bondnetwork is a significant structural element and signals a localdeviation from PSCR.

3.3. Born Effective Charges. A small structural distortioncan be represented by displacements of atoms from their

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



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

* =∂∂αβ

α

εβ =

ZF

Jj

u

,,

0

where the derivative is calculated at zero cationic displacement.14

A large BECmeans that a large electric force is felt by an ion evenif the field is small and thus indicates the tendency of a materialtoward a polar ground state. A large value of the BEC was shownto be an indicator of a material which is on the verge of aferroelectric transition.13,27−29 In these materials, Z* is

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



anomalously large in the centrosymmetric structure and becomesless so in a noncentrosymmetric one.The nature of bonding we uncovered from atomic and

electronic structure and the origin of breaking of centrosymme-try is clearly seen in our calculated BECs of KNaNbOF5 andCsNaNbOF5. Anomalous BEC on trans fluoride F1 (up to−1.92) (ZXX = −0.90, ZYY = −0.92, ZZZ = −1.92) in thecentrosymmetric structure of CsNaNbOF5 is a indicative of thepresence of large secondary distortion. This secondary distortionlowers the primary electronic distortion and thus results in anoverall centrosymmetric structure. In contrast, we find lowervalues of BECs on trans fluoride F1 (ZXX = −1.54, ZYY = −1.06,ZZZ = −0.87) in KNaNbOF5. We saw in section 3.2 from theelectronic bands that O−pπ and Nb−dπ interactions arestronger in the noncentrosymmetric KNaNbOF5 than the onein the centrosymmetric CsNaNbOF5. From Table 1, we see that

oxygen anion possesses higher magnitude (more anomalous) ofBECs in CsNaNbOF5, consistent with its weaker the primaryelectronic 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 non-centrosymmetric structure of KNaNbOF5, consistent withstronger covalency of Cs with fluorine anions, as seen earlier inour analysis of the electronic density of states. Higherhybridization of Cs cations with fluorine anions is very importantand results in a large secondary distortion (indicated by thecoordination number of oxygen) and hence a centrosymmetricstructure.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 thecentrosymmetric CsNaNbOF5 than those in noncentrosym-metric KNaNbOF5. Large values of Born effective charges offluorine anions too are indicative of the centrosymmetry andcorrelate with the presence of large secondary distortion inCsNaNbOF5.Born effective charges also clearly explain bonding in these two

structures. As we discussed in section 3.1 that in bothKNaNbOF5(NCS) and CsNaNbOF5(CS) compounds, equato-rial fluoride F3 and fluoride F1 which is trans to the oxygen anionhave three cationic contacts, while other three fluorides, namely,F2, F4, and F5, have only one or two cationic contacts. Our

calculated BECs bear reflection of this trend, as we see inKNaNbOF5, 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 theremaining three equatorial fluorides F2, F4, and F5 (Table 1). So,F1 which has the largest magnitude of BEC and F3 which has alarger value of BEC among all other equilateral fluorides arefound to be coordinated with three cationic sites. Similarly, BECsof 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 largerin magnitude and are coordinated with three cationic sites, incontrast to doubly or singly coordinated sites of remainingfluorides, whose BECs are smaller in magnitude.

3.4. Dielectric Constant and Polarization. Dielectricconstant diverges near a ferroelectric transition at which theinversion symmetry is broken. In the present case, though we donot have a symmetry breaking transition in the same sense (thereare no small atomic displacements that connect the twostructures), we expect the electronic dielectric behavior to reflectthe change in bonding at the crossover between noncentrosym-metric KNaNbOF5 and centrosymmetric CsNaNbOF5. Wedetermined electronic dielectric constants (square of refractiveindex) of both noncentrosymmetric KNaNbOF5 and centrosym-metric CsNaNbOF5 and of mixed noncentrosymmetric andcentrosymmetric structures. A variation of dielectric constantswith varying mixing of K/Cs cations is shown in Figure 6. From

the relative stability of the two structures in Figure 2, we knowthat the material transforms from K-rich noncentrosymmetricstructure to Cs-rich centrosymmetric structure at x = 0.6. Indeed,we find that the dielectric constant increases as x approaches thecrossover value of 0.6 from both sides, and there is a peak (withdiscontinuity) in the dielectric constant as a function ofconcentration x of Cs/K ions (shown by thick dotted line inFigure 6).We calculated polarization of noncentrosymmetric KNaN-

bOF5 using the Berry phase method20 and find that it is rather

weak, ∼0.21 μC/cm2 along the z-direction (and of course zeroalong the x and y directions due to symmetry) (see Figure 7a).When we replace all K cations by in noncentrosymmetric

Table 1. Diagonal Elements of the Born Effective ChargeTensors of Different Ions in One Formula Unit ofKNaNbOF5(NCS) and CsNaNbOF5(CS)

Born effective charges Zαβ*

KNaNbOF5(NCS) CsNaNbOF5(CS)

ion ZXX ZYY ZZZ ion ZXX ZYY ZZZ

K 1.20 1.32 1.21 Cs1 1.32 1.40 1.46Cs2 1.40 1.40 1.38

Na 1.23 1.08 1.21 Na 1.23 1.19 1.21Nb 4.57 4.45 4.43 Nb 4.49 4.62 4.85O −2.02 −1.07 −0.79 O −0.88 −1.13 −2.12F1 −1.59 −1.06 −0.87 F1 −0.90 −0.92 −1.92F2 −0.69 −0.76 −1.70 F2 −1.75 −0.60 −0.92F3 −1.18 −1.32 −0.72 F3 −0.74 −1.99 −0.68F4 −0.71 −1.65 −0.73 F4 −1.83 −0.80 −0.63F5 −0.59 −0.75 −1.82 F5 −0.74 −1.53 −0.98

Figure 6.Variation of average electronic dielectric constants withmixingx (K/Cs) in the noncentrosymmetric structure of K1−xCsxNaNbOF5and centrosymmetric structure of Cs1−xKxNaNbOF5. Dotted line showsthe transition at a mixing value of about 0.6.



KNaNbOF5 (K1−xCsxNaNbOF5, with x = 1), we find a slightlylarger value of polarization (Pz = −1.29 μC/cm2). Such smallvalues of polarization are consistent with the fact that it arisesfrom the competition between primary and secondarydistortions. In the centrosymmetric structure of CsNaNbOF5calculated polarization is zero in all three directions, as expectedfrom the symmetry of the crystal (see Figure 7b).

4. CONCLUSION

Using first-principles DFT-based calculations, we have analyzedthe structure, electronic structure, polarization, and Borneffective charges of noncentrosymmetric KNaNbOF5 andcentrosymmetric CsNaNbOF5. We find that the Born chargesclearly bear the difference between the interactions of Cs, K withanions, which are key to the structural centrosymmetry. We findthat a strong Nb−O interaction relevant to the primarydistortion favors a noncentrosymmetric structure. When thecompeting Cs/K interaction with F and O is strongly covalentenough, it suppresses the primary distortion favoring centro-symmetry. We identified the specific features in the electronic

structure that correlate with stability of their centrosymmetricstructure and show that polarization of the noncentrosymmetricKNaNbOF5 estimated using the Berry phase method is ratherweak, ∼0.21 μC/cm2, consistent with its origin in thecompetition between the primary and secondary electronicdistortions.

■ ASSOCIATED CONTENT*S Supporting InformationCalculated structural parameters (Table S1), bond valences(Tables S2 and S3), energy of mixing (Table S4), and dielectricconstants values (Table S5). This material is available free ofcharge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*Present address: Department of Chemistry, University CollegeLondon, 20 Gordon Street, London, United Kingdom WC1H0AJ. E-mail: [email protected], [email protected], [email protected]. Tel.: +44-7466106384.

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



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mailto:[email protected]




NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSA.K.M. acknowledges the Department of Science and Technol-ogy (DST), New Delhi, for a fellowship under Fast TrackScheme for Young Scientists (SR/FTP/PS-105/2009), andU.V.W. thanks the IUS-STF for funding through the Indo-USJoint Center between JNCASR and NU. This work was alsosupported by a grant from the National Science Foundation(Solid State Chemistry Award No DMR-1005827).

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