Analytical and experimental study of electrical conductivity in the lithium tantalate nonstoichiometric structure

Transcription

1 M. J. CONDENSED MATTER VOLUME 5, NUMBER June 004 Analytical experimental study of electrical conductivity in the lithium tantalate nonstoichiometric structure S. Jebbari,, S. El Hamd, F. Bennani 3, A. Jennane, M. Hafid N. Masaif L.M.M, Laboratoire de Magnétisme et des Matériaux, Département de Physique Appliquée, Faculté des Sciences et Techniques, B.P. 577 Settat, Morocco LPTN, Département de Physique, Faculté des Sciences Semlalia, B.P. S5 Marrakech, Morocco 3 LPVC, Département de Physique, Faculté des Sciences, B.P. 33 Kénitra, Morocco We have been interested to experimental analytical studies of ionic conductivity of nonstoichiometric LiTaO 3 solid solutions. Theoretical approach combined with lithium tantalate vacancy models has been performed. A comparative study between the calculated measured values is presented taking into account the temperature composition effects on the conductivity. I. Introduction Lithium tantalate has been the subject of many theoretical practical investigations due to their properties in electro-optics, electo-acoustics non-linear optics. This material shows a ferroelectric behaviour well known to deal nonstoichiometric compound. In LiTaO 3, the solid solubility range extends from about 46 to 50.4 mol % of Li O at room temperature []. The structure of ferroelectric s LiTaO 3 belongs to space group R3c can be considered as a superstructure of the α-al O 3 corundum structure + 5+ with Li Ta cations along the c-axis []. Several studies have reported on the changes in electrical conductivity of the lithium tantalate solid solutions [3-6]. By complex impedance spectroscopy; Huanosta et al [4] studied the variation of the conductivity as a function of the stoichiometry in Li -5x Ta +x O 3 compounds. In previous work [7], the successive phase transitions corresponding to the various compositions in LiTaO 3 system have been reexamined. In brief, ceramic specimens of LiTaO 3 with different compositions are studied by the impedance spectroscopy in the Hz-MHz frequency range the K temperature range. The temperature dependence of the dielectric permittivity of these specimens was measured in order to determine the temperature of the phase transition. So, the ionic conductivity is determined for all compositions from Cole-Cole diagrams. The analysis of the ceramic samples, which are prepared from Li O Ta O 5, indicates that there is a modification of the ionic conductivity of LiTaO 3 with compositions. To find which defect is involved in this phenomenon, we have proposed a theoretical description of the defect structure in LiTaO 3 on the basis of a set of vacancy models combined with a ferroelectric phase transition theory. As LiTaO 3 is isomorphous with LiNbO 3, several defect models have been proposed for LiNbO 3. Fay et al. [8] describe a ceramic sample assumed containing oxygen lithium vacancies by the oxygen vacancy model having a formula [Li -x x ][Nb][O 3-x x ] where [.] represent the sublattice denotes the vacancies. This model cannot describe the density variation in function of the composition. In order to correct this anomaly, Lerner et al. [9] have predicted that an excess of niobium ions might occupy the lithium sites. This is, the lithium vacancy model, which is given by the formula [Li -5x Nb x 4x ][Nb]O 3 where the lithium vacancies are introduced taking into accounts the charge compensation. However, Peterson Carnevale [0] observed a new defect structure corresponding to the Nb-site vacancy type using the NMR technique. Then, their niobium vacancy model is arranged as follows: [Li -5x Nb 5x ][Nb -4x 4x ]O 3. Contrarily to the result pointed out by Abrahams Marsh [], Donnerberg et al. [] proved that the niobium vacancy model is unfavorable to compare the energetic aspect of the defect structure models. A comparative study between the densities of these models allows Iyi et al. [3] to reject the oxygen vacancy model. From this result, we have only used lithium tantalate vacancy models to describe the defect structures effects on the conductivity. A theory of ferroelectric s phase transition in the crystal LiNbO 3 has been performed to underst predict the properties of this crystal [4]. In this system, the solution of the dynamic problem of the crystal planes system exhibits the existence of the "soft mode" at the ferroelectric s transition. II. Experimental results The Moroccan Statistical Condensed Matter Society

2 3 ANALYTICAL AND EXPERIMENTAL STUDY OF ELECTRICAL The experimental technique the preparation of the solid solutions have been described elsewhere [7]. By the conventional mixed oxide method, the nonstoichiometric LiTaO 3 samples were prepared from Li CO 3 Ta O 5. Powders were isostatically pressed at 500 bars to give pellets of 3 mm in diameter mm in thickness were sintered at 500 K for 4h with a heating rate of 00 K/h. Ceramics were characterised by X-ray diffraction the microstructure of these samples were Li/Ta Experimental formula LiTaO 3 Li 0.98 Ta.005 O 3 Li Ta.008 O 3 Li 0.90 Ta.0 O 3 Proposed formula (b) (c) [Li.0 ][Ta.0 ]O 3 [Li.0 Ta.0 ]O 3 [Li 0.98 Ta 0.0 ][Ta 0.985! 0.05 ]O 3 [Li 0.98 Ta 0.005! 0.05 ][Ta]O 3 [Li Ta 0.04 ][Ta 0.966! ]O [Li Ta 0.008! ][Ta]O 3 3 [Li 0.90 Ta 0.0 ][Ta 0.9! 0.08 ]O 3 [Li 0.90 Ta 0.0! 0.08 ][Ta]O 3 Table : Chemical formula obtained by the analysis the proposed formula according to (b) (c) models with different Li/Ta ratios. Among of the electrical measurements investigated, we have interested about the variation of the conductivity σ by complex impedance spectroscopy. The isothermal measurements were carried out between K with temperature steps of 50 or 00 K except in T c range where steps were reduced to 0 K. The range of measuring frequencies was Hz- MHz for ceramic samples. A Pt(Rh 0%)/Pt thermocouple located near the sample is connected to a Keithley 000 electrometer to measure temperatures; reported temperatures are estimated as accurate to ± K. The ionic conductivity is determined for all compositions from Cole-Cole diagrams the variation vs temperature is studied as a function of the Li/Ta ratio [7]. The measured conductivities for nonstoichiometric LiTaO 3 with different compositions were shown in FIG. the form of Arrhenius plots for the temperature range from 830 to 50 K. The curves are essentially linear permit to determine the activation energy of the studied concentrations. The obtained values are presented in table. examined using scanning electron microscopy (SEM). The chemical composition of the samples was obtained using inductively coupled plasmaatomic emission spectroscopy (ICP-AES). The formulae obtained, which estimated to be about 0.8% for Li 0.% for Ta, are reported in Table. We denote by (a), (b) (c) the oxygen, tantalate lithium vacancy models. log(σ)(ω- cm -) -3,6-3,8-4,0-4, -4,4-4,6-4,8-5,0-5, -5,4-5,6-5,8-6, , 0,90 0,95,00,05,0,5,0 03/T ( K -) FIG. : Variation of log(σ) as a function of 0 3 /T.The full circles, squares, triangles crosses are experimental data the solid lines are the linear fits to the data.

3 S. JEBBARI, F. BENNANI, A. JENNANE, M. HAFID AND N. MASAIF 4 III. Theoretical approach In this work, we suppose that ceramic samples of LiTaO 3 are single crystal. Such an assumption is based on the experimental fact that the ferroelectric s phase transition occurred in the ceramic samples which are formed by parallel planes along the polar "c" axis. In Figure, distances between planes (Li, Ta O at T=0 K) are denoted as follow: R O-O (b=.30å), R Li-O (R 0 = 0.60 Å), R Ta-O (R 0 = Å), R Li-Ta (R =b - R 0 - R 0 ) [5]. The essential of the theory of ferroelectric s transition in LiTaO 3 is reported in reference [4]. Here we only report the useful expressions in the appendix. At 0 K, the soft mode frequency, ω, is proportional to the Curie temperature. Substituting ω by expression A.0 to obtain the following relation that allows calculating the Curie temperature: T M + M + M MM M 0 P P = 0 ( )( )( ) () T M M M M M M P P with P = 3q 0 R qr 0 q R0 (R R ) (R R ) P 0 ( ) 0 = + + M M q 0 q (R R ) ( + ) ( + ) M M 0 3q 0 M M The elements X X related to exactly stoichiometric nonstoichiometric compositions respectively. This expression allows to determinate Curie temperatures of the defect structure models. Li/Ta Activation energy (ev) log(σ o ) (Ω - cm - ) Table : Values of the activation energy log(σ o ) of the LiTaO 3 for the different Li/Ta ratios studied. Electrical conductivity can be described by the law Arrhenius, ΔE σ = σ o exp(- ) () k BT where σ 0 is the pre-exponential factor, E the activation energy, k B the Boltzmann constant T is the temperature (K). We introduce the conductivity, σ, to explain the role of defect structure in nonstoichiometric lithium tantalate compound. ΔE σ = σ o exp(- ) (3) k BT Although the expression of the T is determinate at Curie temperature point, this relation seems again O - Li + Ta FIG. : Different planes in an elementary cell of crystal LiTaO 3. correct to calculate the conductivity about T. Taking into account of the experimental results, we have proposed two possible models: tantalate lithium vacancy models. However, we represent these models, described previously, in the following condensed form, [Li α Ta α α3 ][Ta β β ][O 3γ γ ]; K = g K with K=M, q g= α, β or γ. Here α, β γ allow identifying two models as follows: i) Tantalum vacancy model corresponds to α =-5x, α =5x, β =-4x, β =4x γ =; K = ( 5x ) K + 5xK, K = ( 4x)K K 0 = K 0. ii) Lithium vacancy model corresponds to α =- 5x, α =x, α 3 =4x, β = γ =; K = ( 5x )K + xk, K = K K 0 = K0. In this representation α=β=γ=0 signified that ions vacancies are absent in these nonstoichiometric models.

4 5 ANALYTICAL AND EXPERIMENTAL STUDY OF ELECTRICAL In order to provide an adequate description of defect structure in nonstoichiometric lithium tantalate we have analytically performed the calculations of the Curie temperature as function of the composition x that we illustrate in Table 3. Estimate values of T for LiTaO 3 have been obtained using the following values of charges masses of ions q 0 =, q =5, q =, M 0 =48, M =80.95, M =6.94. The conductivities for these vacancy models could, therefore, be calculated according to equation (3) taking into account the values of the σ 0 E for each composition x. (b) (c) T c ( 7.88 x)( x)( + 0 x) ( x) T c x x Table 3 : The Curie temperature T as a function of the nonstoichiometric composition x. (b) (c) represent the vacancy models. T c -3,5 ( ) -4,0-4,5-5,0-4, -4,4 ( ) lo σ) g ((Ω - cm - ) -5,5-6,0-6,5-7,0-4,6-7,5-4,8-8, log( σ) (Ω -.c m - ) -5,0-5, -5,4 0, 9 0 0, 9 5, 0 0, 0 5, 0, 5, /T (K - ) -5,6-5,8-6,0-6, 0,90 0,95,00,05,0,5,0 0 3 /T [K - ] lo g σ)(ω ( -.c m - ) -3,5-4,0 (3) -4,5-5,0-5,5-6,0-6,5-7,0-7,5-8,0-8, ,0 0,90 0,95,00,05,0,5,0 0 3 /T (K - ) lo g σ) ( (Ω -.cm - ) (4) ,90 0,95,00,05,0,5,0 0 3 /T ( K - ) FIG. 3 : Logarithmical conductivity of LiTaO 3 solid solutions as function of the reciprocal temperature with different composition x. () Li/Ta=, () Li/Ta=0.98, (3) Li/Ta=0.95 (4) Li/Ta=. The full circles, squares, triangles crosses are experimental data the solid lines represent the linear fits to the data. Dash dot lines indicate the linear fits of (b) (c) models respectively.

5 S. JEBBARI, F. BENNANI, A. JENNANE, M. HAFID AND N. MASAIF 6 IV. Results discussion By a linear fit of the experimental values the calculation of the slope of the curve logσ in the form of Arrhenius plot (figure ) we obtained σ 0 E for each composition x. Estimated activation energy at different Li/Ta ratio from equation () is reported in Table. Calculated experimental values of σ for various nonstoichiometric compositions are illustrated in Figures 3. A comparison of the measured conductivity with two vacancy models (Lithium tantalate vacancy models) is indicating. Observed curves log(σ) vs T - indicate that the lithium vacancy model is the best to describe the conductivity in nonstoichiometric LiTaO 3 solid solutions. Effect of the lithium defect is predominant over that of tantalate vacancies in the conductivity of the LiTaO 3. Thus, the number of Li vacancies connected with the composition Li/Ta ratio is mainly responsible for the increase found in conductivity. V. Conclusion We have presented conductivity as a function of temperature composition in nonstoichiometric LiTaO 3 ceramics. In this simple system, the theory of ferroelectric s phase transition gives a good quantitative description of the experimental results. A comparative study, between vacancy models experimental values of the conductivities, shows that the lithium vacancy model is the defect model, which can be suggested to describe the defect structure in nonstoichiometric lithium tantalate. Appendix The energy of electrostatic interaction of two charged long lines is, l W = e δiδ jb ln (A) R ij N q where δ i i i = with l, R ij, q i N i is the line l b length, the distance between lines, the charge of ions their number respectively. We deduce the full energy of interaction of planes such that: j l Bij U ij = ln + (A) b R n ij Rij j 0 n 0 where B ij = (Rij) with R ij is the equilibrium b n distance between planes. 0 If we put xij = Rij Rij, then the energy writes j l jn xij Uij = ( ln ) + (A3) b n 0 0 Rij b (Rij) j The coefficient Cij = n describes the 0 b (Rij) interaction between Li O planes (as well as for Ta O). However, the interaction between Li Ta will deduce from the total energy: j l Bij Uij = ln (A4) b 0 R R ij ij Finally, for LiTaO 3 crystal C ij coefficients are q 0q e CLi-O C0 = 3 n, b R 0 q0qe CTa-O C0 = 3 n, b R0 qq e CLi -Ta C = n (A5) b R where q, q q 0 are the electric charge of Nb 5+, Li +, O - ions, respectively. To solve the dynamic problem we reduced the structure of charged planes to system of vibration of linear lattice (FIG. 4). The displacements of the three ions are indicated by v s (Li + ), u s (Nb 5+ ) ξ s (O - ). Then, the system is described by the differential equations as M!! u s = C0 ( ξs+ u s ) + C(vs u s ) M!! vs = C(us vs ) + C0 ( ξs u s ) M0! ξ s = C0 (vs ξs ) + C0(vs- ξs ) (A6) where M, M, M 0 are the masses of elements Ta, Li 3O respectively. The choose of solutions in the form of plan waves, i( ω t+ a s k) gs = g e (Α7) with g = u, v or ξ leads to a system of linear equations. This system has a nontrivial solution. Then we put k=0 in the determinant equation ( =0) in order to obtain the fundamental frequencies of optical branches. Then we obtain the following equation, 4 ω - B ω + D = 0, where:

6 7 ANALYTICAL AND EXPERIMENTAL STUDY OF ELECTRICAL B = C0 ( + ) + C ( + ) M M 0 M M + C 0 ( + ) M M 0 M + M + M D = 0 MM M0 (C0 C0 + C0C + C C0 ) (A8) The two optical modes are given by / ω = B ± ( B D) (A9) 4 For small parameter ((4D/B )<<) we deduce, D ne M + M M0 P ω = = +, B b MM M0 P ω = B ω with P = 3q0R qr 0 q R0 (R 0R) (R0R) P = ( + ) + q M M0 q (R0R 0 ) ( + ) - ( + ) (A0) M M 0 3q 0 M M us 3O - Ta 5+ Li + vs FIG. 4: Displacement of Li +, Ta 5+ 3O - ions in a linear lattice. ξs References [] M. Paul, M. Tabuchi, A. R. West, Chem. Mater., 9 (997) 306. [] S. C. Abrahams, L. J. Bernstein, Phys. Chem. Solids, 8 (967) 685. [3] Y. Fujino, H. Tsuya, K. Sugibachi, Ferroelectrics, (97) 3. [4] A. Huanosta, A. R. West, J. App. Phys., 6 (987) [5] D. C. Sinclair, A. R. West, Phys. Rev. B, 39 (989) [6] I. Tomeno, S. Matsumura, Phys. Rev. B, 38 (988) 606. [7] F. Bennani, E. Husson, J of European Cearamic Society, (00) 847. [8] H. Fay, W. J. Alford, H. M. Dess, Appl. Phys. Lett., (968) 89. [9]P. Lerner, C. Legras, J. P. Dumas, J. Cryst. Growth, 3/4, (968) 3. [0] G. E. Peterson, A. Carnevale, J. Chem. Phys., 56 (97) [] C. S. Abrahams, P. Marsh, Acta Crystallogr. Sect. B, 4 (986) 6. [] H. Donnerberg, S. M. Tomlinson, C. R. A. Catlow, O. F. Schirmer., Phys. Rev. B, 40 (989) 909. [3] N. Iyi, K. Kitamura, F. Izumi, J. K. Yamamoto, T. Hayashi, H. Asano, S. Kimura., J. of Solid State chem., 0 (99) 340. [4] F. P. Safaryan, Physics Let. A, 9 (999) 55. [5] M. E. Lines, A. M. Glass, Principles application of ferroelectrics related materials. Clarendon Press, Oxford (977).