J O U R N A L O F C H E M I S T R Y Materials Ionic conductivity, ferroelectricity and chemical bonding in TKWB type ceramics of the K6Li4Ta10O30–Pb5Ta10O30 system Virginie Hornebecq,* Jean-Maurice Re�au, Antoine Villesuzanne, Catherine Elissalde and Jean Ravez ICMCB-CNRS-Avenue du Dr. A. Schweitzer-33608 Pessac, France Received 6th May 1998, Accepted 3rd August 1998 Correlations between Curie temperature and chemical bonding were found in ferroelectric tetragonal potassium tungsten bronze type ceramics [TKWB] using the extended Hu�ckel tight-binding (EHTB) method.The influence of Pb for K,Li substitution is shown. AC complex impedance measurements were performed on ceramics with compositions corresponding to Pb5xK6(1-x)Li4(1-x)Ta10O30 (PKLT) in a wide temperature range. The conductivity relaxation parameters of Li+ conducting PKLT ceramics were determined.Transport properties in these materials appear to be due to a Li+ ion hopping mechanism. The influence of the substitution 6K++4Li+�5Pb2+ on the mobility is discussed with the assistance of the results obtained from EHTB calculations. frequency range, the permittivities were determined, under Introduction vacuum, from capacitance and dielectric losses tan d (the ratio Ferroelectric ceramics are of great interest for applications between the imaginary part er and the real part e¾r of the such as dielectrics for capacitors, infrared detectors, electro- relative permittivity) using a Wayne–Kerr Component mechanical converters, electrooptical modulators, etc.Analyser Model 6425.The temperature range was 100 to Dielectric losses often need to be reduced when the sample 300 K. The heating rate was close to 0.2 K min-1. has to be polarized or for high quality capacitors. In contrast, the conductivity may also be at the origin of other applications Results such as CTP (coeYcient temperature positive), CTN The temperature dependence of the real permittivity e¾r shows (coeYcient temperature negative), microwave absorbants, etc.a maximum corresponding to the ferroelectric–paraelectric Recent works have therefore been devoted to the study of transition temperature for the various compositions studied conductivity in ferroelectrics.1,2 (x=0.10; 0.25; 0.50; 0.65; 0.75; 0.80). Fig. 1 gives as an The aim of the present work is to prepare and to characterize example the curve (e¾r versus temperature) obtained for the new ferroelectric ceramics with ionic conductivity only.The composition corresponding to x=0.75 at 103 Hz. The trans- cation Ta5+, whose oxidation state is very stable, was chosen ition temperature increases significantly when K+ and Li+ are to prevent electronic conductivity. replaced by Pb2+ (6K++4Li+�5Pb2+).Furthermore, the The compositions PKLT selected here belong to the maximum of e¾r is wide and implies a diVuse ferroelectric– K6Li4Ta10O30 (Tc=7 K)–Pb5Ta10O30(Tc=538 K) system.3,4 paraelectric phase transition which can be explained by Furthermore, the relation between the Curie temperature Tc a domain of variable composition implying a distribution and chemical bonding has been recently determined in ferroof transition temperatures.Fig. 2 gives the variation of electric perovskites. The approach in the present paper consists the ferroelectric–paraelectric transition temperature versus firstly of research into the relation between the transition composition. temperature and chemical bonding in TKWB tantalates. Secondly, EHTB calculations were also helpful in understand- Correlation between the Curie temperature and the chemical ing the eVect of cationic substitution on the Li+ ionic bonding conductivity.Recent works have been devoted to the role of chemical bonding in the Curie temperature and microwave relaxation Preparation frequency in tantalates.7,8 It was shown that, in significantly PKLT samples with composition Pb5xK6(1-x)Li4(1-x)Ta10O30 are prepared from K2CO3, Li2 CO3, PbO and Ta2O5.The cationic substitution corresponds to 6K++4Li+�5Pb2+. A special process was used in order to keep the initial stoichiometry, in particular to prevent PbO losses by volatilization. Details of the ceramic densification are given elsewhere.5 The samples are discs of diameter about 7 mm and thickness about 1 mm.X-Ray diVraction analysis revealed the ceramics to be single phase for 0x0.80. They crystallise with a tetragonal tungsten bronze structure.6 Ferroelectric study of PKLT ceramics Experiments The dielectric measurements were performed on ceramic discs. Electrodes were formed by depositing gold on the top and Fig. 1 Temperature dependence of e¾r ( f=103 Hz). bottom of circular surfaces by sputtering.In the 102–2×105 Hz J. Mater. Chem., 1998, 8(11), 2423–2428 2423Table 1 Extended Hu� ckel parameters: atomic orbital energies and Slater-type exponents and coeYcients. Double-f expansions are used for d orbitals Element Orbital Hii/eV f1 c1 f2 c2 Ta 5d -12.10 4.760 0.6597 1.940 0.5589 6s -10.10 2.280 1 6p -6.86 2.241 1 O 2s -32.30 2.275 1 2p -14.80 2.275 1 K 4s -4.34 1.000 1 4p -2.73 1.000 1 Pb 6s -15.70 2.350 1 6p -8.000 2.060 1 Li 2s -5.400 0.650 1 2p -3.500 0.650 1 Fig. 2 Composition variation of the ferroelectric–paraelectric transition temperature. but correspond to the K++Li+=Pb2+ substitution mode in covalent systems such as tantalates and niobates, covalency K6Li4Ta10O30. They were chosen in order to define a tractable tends to inhibit the ferroelectric distortion, by strengthening unit cell for the computation and to allow the study of the Pb the metal–oxygen bond and stabilizing the paraelectric phase.for K,Li substitution eVects. For ionic radius reasons, Pb In tantalates and niobates, this eVect appears to dominate the atoms were located in the A1 site (C.N.=12) (Fig. 3) for the well known softening eVect of covalency on short-range second composition and in both A1 and half A2 (C.N.=15) interatomic repulsions.9 sites for the third one.Here, covalency means the amount of mixing of metal d The extended Hu�ckel parameters used in the present work orbitals and oxygen 2p orbitals to form valence bands. This are given in Table 1. is a more complete view than the one given by electronegativity Fig. 4 shows the density of states and COOP curves for scales, for which covalency only means the departure from the K4Pb2Li2Ta10O30, calculated with the EHTB method. Li- and purely ionic picture. The bond covalencies were evaluated by K-character bands are located well above the Fermi level EF the computation of crystal orbital overlap populations and are out of the energy range of this figure.All bonding (COOPs) in the framework of the extended Hu�ckel tight- Pb–O and Ta–O bands lie below EF; the upper occupied band binding (EHTB) method.10,11 This quantum chemistry semi- corresponds to very covalent crystal orbitals with both Pb 6s empirical method is particularly well suited for the study of and O 2p atomic orbital contributions.It is of strong antibondthe interplay between chemical bonding and electronic struc- ing character against Pb–O bonds. Those very covalent Pb–O ture of molecules or crystals.12–17 Valence Slater-type atomic interactions are expected to weaken the Ta–O bond covalency. orbitals are attached to each atom; the Fock matrix elements The COOP values for Ta–O and Li–O bonds, summed up are computed, using the Wolfsberg–Helmholz formula,18 on to EF, are given in Table 2.The COOP, i.e. the covalency of the basis of atomic orbital overlaps and tabulated energies. Ta–O bonds decreases when the Pb content increases. The COOP is the extension to the crystalline solid of the Moreover, this increase is more significant for those Ta–O Mulliken overlap population for molecules.19,20 It is pro- bonds close to Pb atoms in the structure (competing bonds portional to two quantities closely related to covalency: the eVect).16 This evolution of Ta–O COOPs is due to the decrease overlap of atomic orbitals and the product of the correspond- of electron density (Fig. 5) along those Ta–O bands aVected ing LCAOch is maximal for equal coeYcients.by the Pb for K substitution. The very low COOP values for The band structure and the Ta–O and Li–O COOPs were calculated with the EHTB method, for the compositions K6Li4Ta10O30, K4Pb2Li2Ta10O30 and K2Pb4Ta10O30. The two latter compositions are close to K6(1-x)Pb5xLi4(1-x)Ta10O30, Fig. 4 Density of states and COOP curves for K4Pb2Li2Ta10O30. The main atomic orbital contributions to the bands are indicated. 6s and 6s* bands are very covalent with both Pb 6s and O 2p character. B1 Fig. 3 Structure used to model the TKWB network. and B2 are two crystallographic sites occupied by Ta ions (Fig. 3). 2424 J. Mater. Chem., 1998, 8(11), 2423–2428Table 2 COOP values for PKLT ceramics calculated with the EHTB PbTa0.5Sc0.5O3 and PbNb0.5Sc0.5O3; in these significantly method.B1 and B2 are two crystallographic sites occupied by Ta ions covalent systems, the bulk energy stabilisation and the metal– (see Fig. 3) oxygen bond strengthening, due to covalency, tends to inhibit the ferroelectric distortion.8 The transition temperature can be COOP (e-/bond) increased by any chemical means leading to an increase of the Composition Ta(B1)–O Ta(B2)–O Li–O metal–oxygen network ionicity.K6Li4Ta10O30 0.6444 0.6299 -0.0111 Impedance study of PKLT ceramics K4Pb2Li2Ta10O30 0.6324 0.5882 -0.0176 K2Pb4Ta10O30 0.5953 0.5663 In the Pb5xK6(1-x)Li4(1-x)Ta10O30 solid solution, it is probable that, as in Ba5Li2(Ti2Nb8)O30, Li+ ions occupy only the triangle sites with 9-fold coordination (sites C).21 The partial presence of Li+ ions in those sites is favorable for the occurrence of Li+ ionic conductivity in the direction parallel to the c-axis.Experiments AC measurements were performed on the same samples as those used for dielectric measurements; they were carried out under vacuum. Each experimental temperature was maintained by a Eurotherm-902-S Controller for 0.5 hour with an accuracy of ±0.5 K before collecting data.AC measurements were recorded out using a 1260 Solartron frequency analyser in the frequency range 102–106 Hz for several temperature cycles between 300 and 700 K. Results Complex impedance diagrams of Z/V as a function of Z¾/V, i.e. Cole–Cole plots, are presented in Fig. 6 for the composition corresponding to x=0.75 at various temperatures: the bulk ohmic resistance corresponding to each experimental temperature is the intercept on the real axis of the zero phase angle extrapolation of the highest frequency curve.22,23 Fig. 5 (Top) Contours (logarithmic scale) of the computed valence electron density for K6Ta10O30.A and B sites are occupied by K and The temperature dependence of conductivity between Ta atoms, respectively. The C site is occupied by Li atoms in the 300 and 700 K is given in Fig. 7 for some PKLT series. K atoms in A1 (A2) sites lie 2.10 A° (2.07 A° ) above and Pb5xK6(1-x)Li4(1-x)Ta10O30 compositions as a plot of log(sT ) 1.83 A° (1.86 A° ) below the figure plane. Ta and O atoms lie within against inverse temperature: an Arrhenius type behavior is 0.16 A° and 0.02 A° from the figure plane, respectively. (Bottom) clearly exhibited.A linear fit to sT=s0 exp(-DEs/kT ) is Contours ( logarithmic scale) of the diVerence in computed valence shown, with correlation coeYcient R=0.98. Electrical data electron density between Pb4K2Ta10O30 and K6Ta10O30. Pb atoms are located in A1 and A2* sites. Solid lines: positive values. Dashed lines: relative to the samples are listed in Table 3: a slight increase negative values. of activation energy DEs and a decrease of conductivity can be observed when x increases.Conductivity relaxation parameters have been calculated Li–O bonds confirm their almost purely ionic character; the slight antibonding Li–O interactions (from the covalency point from the complex impedance data in the complex modulus formalism M*=1/e*=j(vC0)z*, where j2=-1, v (v=2pf ) of view) increase with the Pb content.The COOP evolution with Pb content can be related to the is the angular frequency and Co is the vacuum capacitance of the cell. This formalism discriminates against electrode polariz- changes of transition temperature. The lowest temperature (7 K) corresponds to the highest Ta–O covalency ation and other interfacial eVects in solid electrolytes.Plots of normalized modulus (M/M¾max) versus log( f ) are given at (K6Li4Ta10O30); the increase of transition temperature observed upon Pb insertion is correlated to the decrease of various temperatures for the composition corresponding to x=0.75, for instance, in Fig. 8: the curves are non-symmetric, Ta–O covalency. This eVect was already observed in the K(Ta1-xNbx)O3 system and in the comparison of in agreement with the non-exponential behavior of the conduc- Fig. 6 Complex impedance plots at various temperatures. J. Mater. Chem., 1998, 8(11), 2423–2428 2425When the temperature increases, modulus peak maxima shift to higher frequencies (Fig. 8). Fig. 9 gives the temperature dependence of the fp=1/2pts relaxation frequency relative to Mmax for the composition x=0.75: Arrhenius-type behavior is shown.The temperature dependence of conductivity is reported in Fig. 9: its behavior is also of Arrhenius-type. Both lines are quasi-parallel, the activation energies issued from the impedance (DEs) and modulus (DEf) spectra are very similar (Table 3), suggesting that the Li+ ion transport in the materials studied is probably due to a hopping mechanism.27 Analogous results were obtained for the other compositions studied (Table 3).The composition dependence of log (s600K ) is given in Fig. 10: log (s600K) slightly decreases, quasi-linearly, when x increases whereas DEs slightly increases (Table 3). In contrast, the b parameter appears to be independent of x (Table 3). Its value (b#0.75) can be attributed to the existence of a distribution of relaxation times.28,29 This carrier polarization mechanism appears as weakly dispersive, of the same order of magnitude as the lattice one.5 Discussion Conductivity. For a given ionic conductor, the low frequency Fig. 7 Inverse temperature dependence of log(sT ) for some limit sdc of the bulk AC conductivity determined by impedance Pb5xK6(1-x)Li4(1-x)Ta10O30 compositions.spectroscopy is governed mainly by the hopping rate of free charge carriers and by the charge carrier concentration N(T ): Table 3 Electrical data and conductivity relaxation parameters relative to some various Pb5xK6(1-x)Li4(1-x)Ta10O30 compositions studied sdc=eN(T )m(T ) sdc=e2N(T )ca2h(n0/kT )exp(Sm/k) exp(-Em/kT ) x=0.10 x=0.25 x=0.50 x=0.75 x=0.80 where ah is the hopping distance, c is a geometrical factor log s600K/V-1 cm-1 equal to 1/6 for isotropic media, n0 is an attempt frequency to (±0.02) -6.92 -7.05 -7.25 -7.55 -7.58 overcome potential barriers, Sm is the migration entropy, Em DEs/eV (±0.02) 0.84 0.84 0.91 0.92 0.93 is the migration energy, the other parameters having their log s0/V-1 cm-1 conventional meaning.30–32 Equating DEs to Em, the pre- (±0.02) 2.91 2.78 3.17 2.96 3.18 exponential factor s0 in the sT=s0 exp(-DEs/kT ) equation DEf/eV can be given by the following expression: (±0.02) 0.85 0.85 0.93 0.91 0.94 b 0.77 0.76 0.73 0.77 0.74 s0=(e2a2hn0/6k)N(T )exp(Sm/k) Considering all Li+ ions as charge carriers in the partial tivity relaxation, which is well described by the empirical range (0.10x0.80) of the Pb5xK6(1-x)Li4(1-x)Ta10O30 solid stretched exponential Kohlrausch function Q(t)=exp[-t/ts]b solution, a maximum of charge carriers could correspond to (0<b<1).24–26 In this expression, ts and b are the conductivity the composition relative to x=0.50 where the C-sites are halfrelaxation time and the Kohlrausch exponent, respectively.occupied by Li+ ions.Such a result cannot be deduced from The smaller the value of b, the larger the deviation of the the small composition dependence of log(s0) (Table 3), which relaxation with respect to a Debye-type relaxation (b=1). Whatever the temperature, the full width at half-height (FWHH) of the M/M¾max spectrum is wider than the breadth of a Debye peak (1.14 decades) (Fig. 8) and it results in a value of b=1.14/FWHH for the Kohlrausch parameter, which can be considered as independent of temperature in the range studied.Fig. 9 Temperature dependences of log(sT ) and log fp, where fp is Fig. 8 Plots of normalized modulus (M/M¾max) versus log f at various temperatures. the Mmax peak frequency. 2426 J. Mater. Chem., 1998, 8(11), 2423–2428Fig. 10 Variation of log s600K with x for Pb5xK6(1-x)Li4(1-x)Ta10O30.depends on both charge carrier concentration and migration bonding of Li atoms is then weakened and their mobility increases with x. entropy parameters. The variation of electrical properties inside the Pb5xK6(1-x)Li4(1-x)Ta10O30 solid solution is relatively weak. Mobility. Charge density maps were obtained with the EHTB method. Calculations were performed for the In order to pinpoint precisely the relative importance of various steric and electronic eVects, it would be interesting to Pb4K2Ta10O30 and K6Ta10O30 compositions, in order to visualise the changes in electron density induced by Pb for K study the eVect of the insertion of lead on compounds containing a same number of Li+ cations.Work is in progress to substitution. Li atoms were omitted in these calculations in order to visualise, without the perturbation due to the lithium correlate insertion of lead, mobility of Li+ cations and ionic conductivity.charge density, the evolution of the electron density in the triangular tunnel section connecting C sites, which will be important in the remainder of this paper. The Fermi level for Conclusions K6Ta10O30 was located at the top of the 2p oxygen bands in The EHTB method was used to investigate the chemical order to reproduce the electron count of K6Li4Ta10O30. bonding in TKWB type ceramics.The eVect of the Pb for Fig. 5 shows the calculated valence electron density for K,Li substitution was studied in PKLT tantalate compounds. K6Ta10O30 in the TaO2 planes (containing both the equatorial Considerations such as covalency allowed us to compare Ta–O Ta–O bonds and the triangular tunnel sections) and the bonds in these compounds.diVerence in electron density between Pb4K2Ta10O30 and A correlation between chemical bonding and Curie K6Ta10O30. No significative valence charge density occurs in temperature was evidenced: the Curie temperature increases A sites for K6Ta10O30 since the 4s and 4p potassium bands when Pb atoms are inserted in the network. The very covalent are empty.Pb 6s charge density clearly appears in A1 and lead–oxygen bonds appear to have a significant influence on A2* sites even if Pb atoms are not in the plane of the figure. the metal–oxygen network, decreasing its covalency and fav- The decrease of electron density in those Ta–O bonds close to ouring the ferroelectric distortion.Pb atoms leads to the decrease in the Ta–O COOP calculated Furthermore, the conductivity parameters DEf and b were above. However, Ta–O bonds close to K atoms appear to be determined in the complex modulus formalism for various Li+ reinforced by the Pb for K substitution. The decrease in containing PKLT ceramics.The activation energies taken from electron density in the triangular tunnel section connecting C the impedance and modulus spectra are very similar, suggesting sites, when the Pb content rises, could play a role in the Li that Li+ ion transport is probably due to a hopping mechan- ion mobility. ism. The conductivity relaxation is well described by a Several antagonist eVects can aVect the mobility of Li+ ions Kohlrausch function Q(t)=exp[-t/ts]b.The value of b (b= in such a system. Steric eVects: (i) a slight decrease of the 0.75) can be attributed to the existence of a distribution of lattice constants, perpendicular to the tunnel direction, when relaxation times; it shows that the charge carrier polarization x increases, leads to a diminution of the tunnel sections mechanism is weakly dispersive. The eVects of the substitution containing Li+ cations.5 This eVect tends to increase the 6K++4Li+�5Pb2+ on the Li+ ion mobility were also potential barrier and to reduce the mobility of Li+ cations, discussed.but is expected to be weak (Da/a#Db/b<1%); (ii) as Pb is inserted in the network, a transfer of electron density from Ctunnels (around Li atoms) to Pb–O bonds is expected because References Pb–O bonds are more covalent than K–O bonds and because 1 M.Dong, J. M. Re�au, J. Ravez and P. Hagenmuller, J. Solid State Pb2+ is more polarizing than K+ (Fig. 5). Furthermore Pb, Chem., 1995, 116, 185. K, Li and O atoms are in the same plane (structure). This 2 M. Dong, J. M. Re�au and J. Ravez, Solid State Ionics, 1996, leads to a higher mobility of Li+ cations.Electronic eVects: 91, 183. (iii) the Li–O COOP has been calculated with the EHTB 3 T. Fukuda, Jpn. J. Appl. Phys., 1970, 9, 599. method (Table 2). It clearly shows that Li–O bond is fully 4 E. C. Subarrao and G. Shirane, Acta. Crystallogr., 1960, 13, 226. 5 V. Hornebecq, C. Elissalde, J. M. Re�au and J. Ravez, Phys. Status ionic, with a very low antibonding covalent contribution which Solidi, submitted.increases with x, giving a slight increase of Li ion mobility; 6 A. Magne�li, Arkiv Kemi, 1949, 1, 213. (iv) from an electrostatic point of view, the replacement of 7 C. Elissalde, A. Villesuzanne, J. Ravez and M. Pouchard, K+ ions by Pb2+ tends to decrease the absolute value of the Ferroelectrics, 1997, 99, 131.negative Madelung potential in C-tunnels, because of the 8 A. Villesuzanne, C. Elissalde, M. Pouchard and J. Ravez, Eur. diVerence of charge of the two ions and because the O2- ions Phys. J. (B), in press. 9 R. E. Cohen, Nature, 1992, 358, 136. net charge is reduced (covalency eVect). The electrostatic J. Mater. Chem., 1998, 8(11), 2423–2428 242710 R.HoVmann, J. Chem. Phys., 1963, 39, 1397. 22 K. S. Cole and R. H. Cole, J. Chem. Phys., 1941, 9, 341. 23 J. E. Bauerle, J. Phys. Chem. Solids, 1969, 30, 2657. 11 M.-H. Whangbo and R. HoVmann, J. Am. Chem. Soc., 1978, 24 G. Williams and D. C.Watts, Trans. Faraday Soc., 1970, 23, 625. 100, 6093. 25 K. L. Ngai and S. W. Martin, Phys. Rev. B, 1989, 40, 10550. 12 R. HoVmann, Solids and Surfaces: A Chemist’s View of Bonding in 26 F. S. Howell, R. A. Bose, P. B. Macedo and C. T. Moynihan, Extended Structures, VCH, New York, 1988. J. Phys. Chem., 1974, 78, 639. 13 J. K. Burdett and S. A. Gramsh, Inorg. Chem., 1978, 33, 4309. 27 B. V. R. Chowdari and R. Gopalakrishnan, Solid State Ionics, 14 E. Canadell and M.-H. Whangbo, Chem. Rev., 1991, 91, 965. 1987, 23, 225. 15 J. K. Burdett, Chemical Bonding in Solids, Oxford University 28 B. V. R. Chowdari and K. Radhakrishnan, J. Non. Cryst. Solids, Press, New York, 1995. 1989, 108, 323. 16 A. Villesuzanne and M. Pouchard, C. R. Acad. Sci. Paris, 1996, 29 J. Kawamura and M. Shimoji, Mater. Chem. Phys., 1989, 23, 72. 310, Se� rie II, 155. 30 N. F. Uvarov and E. F. Hairetdinov, J. Solid State Chem., 1986, 17 A. Simon, Angew. Chem., Int. Ed. Engl., 1997, 36, 1788. 62, 1. 18 J. H. Ammeter, H.-B. Bu� rgi, J. C. Thibeault and R. HoVmann, 31 D. P. Almond and A. R.West, Solid State Ionics, 1987, 23, 27. J. Am. Chem. Soc., 1978, 100, 3686. 32 N. F. Uvarov, E. F. Hairetdinov, J. M. Re�au, J. M. Bobe, 19 T. Hughbanks and R. HoVmann, J. Am. Chem. Soc., 1983, 105, J. Se�ne�gas and M. Poulain, Solid State Ionics, 1994, 74, 195. 3528. 20 R. S. Mulliken, J. Chem. Phys., 1955, 23, 1833. 21 M. Dong, Thesis, 1997, Universite� Bordeaux I, France. Paper 8/03412E 2428 J. Mater. Chem., 1998,