Cation Ordering and Dielectric Properties of PMN-PSN Relaxors

Cation Ordering and Dielectric Properties of PMN-PSN Relaxors P. K. Davies, L. Farber, M. Valant *, and M. A. Akbas ** Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104 * Dept. of Ceramics, Jozef Stefan Institute, Ljubljana, Slovenia ** Currently at Vishay/Vitramon Inc., Monroe, CT 0648-1610, USA Abstract. Extended thermal annealing treatments were used to modify the B-site cation order in the (1-x)PMN - (x)psn perovskite system. Extensive 1:1 ordering could be induced in compositions with x 0.1. The substitution of PSN into PMN produces a large increase in the thermal stability of the 1:1 ordered phase, with the maximum disordering temperature of ~1360 C being observed for x = 0.5. The order-disorder transition temperature for pure PMN was calculated to be 913 C. The changes in stability could be rationalized using the random site model for the cation order. The well ordered, large chemical domain ceramics exhibited relaxor behavior up to x ~ 0.6, for higher values normal ferroelectric behavior was observed. Alterations in the size of the chemical domain size had no significant effect on the properties of the lower x compositions, but induced a transition to relaxor behavior for x > ~ 0.6. INTRODUCTION The chemistry and stability of the B-site ordering and its relevance to the relaxor ferroelectric behavior of the Pb(Mg 1/3 Nb 2/3 )O 3 (PMN) family of perovskites has been the subject of considerable debate. For several years the observation of a two-phase assemblage of nano-sized 1:1 ordered domains and disordered perovskite matrix in PMN was interpreted using the space charge model.[1] In this model the ordered doubled perovskite structure was claimed to be charge imbalanced and to contain a 1:1 ratio of Mg and Nb. However, recent experimental and theoretical studies of tantalate (Pb(Mg 1/3 Ta 2/3 )O 3 - PMT) and niobate (PMN) members of the PMN family have provided convincing support for an alternate charge balanced ordering scheme.[2-11] For this model, the random site structure, the β" position in the 1:1 ordered Pb(β' 1/2 β" 1/2 )O 3 phase is occupied solely by the "active" ferroelectric B-site cation (Nb or Ta), and the β' site by a random distribution of Mg and the remaining Nb/Ta cations. According to this model the ordered structure of PMT, for example, can be represented as Pb(Mg 2/3 Ta 1/3 ) 1/2 (Ta) 1/2 O 3. The primary experimental support for the random site model has come from new investigations of the ordered structures [10,11] and from the observation of extensive increases in the size of the chemical domains and the degree of order in samples equilibrated at elevated temperature.[2-6] Additional support has been provided by calculations of the relative stabilities of different possible B-site ordering schemes.[7-

9] The preparation of large chemical domain relaxors has also clarified the relationship between the crystal chemistry of the B-site ordering and the dielectric response. In contrast to the behavior of the Pb(Sc 1/2 Ta 1/2 )O 3 (PST) and Pb(Sc 1/2 Nb 1/2 )O 3 (PSN) systems, the large domain PMT systems retained their relaxor behavior.[2,3,6] This result implied that the chemical randomness (and associated random fields) on the β' sub-lattice, and not the actual ordered domain size, is critical in mediating the ferroelectric coupling. These new experimental studies also revealed that small concentrations of solid solution additives have a large effect on the conditions required to promote chemical ordering and domain coarsening in PMN and PMT. For example, the addition of 5-10 mole % PbZrO 3 to PMT induced an order of magnitude increase in the size of the chemical domains after appropriate thermal annealing.[2] Although the crystal chemistry of niobate and tantalate members of the PMN family is quite similar, the stability of their chemical order was found to be quite different. In PMT the cation ordering is stable up to ~1375 C; however, the absence of any increase in the order or domain size in pure PMN at any accessible temperature was proposed to result from a much lower order-disorder temperature, perhaps below 950 C.[6] This suggestion was also supported by recent calculations of the stability of the ordering in these and other related perovskite systems.[8,9] In this paper we investigate the cation ordering and properties of solid solutions in the (1-x)Pb(Mg 1/3 Nb 2/3 )O 3 - (x)pb(sc 1/2 Nb 1/2 )O 3 (PMN-PSN) system. By examining the thermal stability of the cation order across the system we provide evidence for an order-disorder temperature in PMN between 900-950 C. We also demonstrate that the alterations in the chemistry of the random site position induce a crossover from relaxor to normal ferroelectric behavior between x = 0.5 and 0.7. RESULTS AND DISCUSSION Structure and Stability Of The B-site Order In PMN-PSN. As we have reported previously [6], experiments aimed toward enhancing the degree of ordering in pure PMN, by annealing samples at temperatures from ~ 900 to 1350 C, met with no success. In all cases the degree of order (~ 20 volume % in small 2-3nm domains) was essentially the same as that observed in the as-sintered (1225 C, 3 hours) specimens. However, for the (1-x)PMN (x)psn solid solution system the cation order was responsive to thermal treatment for compositions with x 0.1. For most compositions the as-sintered samples exhibited very limited cation order; in all cases longer-term annealing and/or slow-cooling treatments induced extensive order. The maximum degree of order was typically attained through a 24- hour heat treatment at 1250 C followed by a slow cool at 10 /hr to 900 C (full details will appear elsewhere); see figure 1. The thermal stability of the cation order in each composition was examined by re-annealing and quenching the well-ordered samples at temperatures up to 1350 C. The degree of order was monitored by scaling the intensity of the (1/2,1/2,1/2) supercell reflection to the (001) sub-cell reflection.

Figure 1 shows an example of the x-ray data (for x = 0.5) collected from a wellordered sample after the initial annealing and slow cooling, and after successive quenching treatments at different temperatures. The intensity and width of the supercell peaks reflect the high degree of order and large chemical domain size in the slow-cooled specimen. These peaks show a continuous weakening and broadening after at heating higher temperatures and it is apparent that the disordering reaction shows second order character. By conducting similar experiments on compositions across the system we were able to delineate the order-disorder boundary. This is shown in figure 2 where the boundary is plotted for ~ 20% residual order, i.e. I (1/2,1/2,1/2)/(100)T /I (1/2,1/2,1/2)/(100)maximum = 0.2. 1350/2 1400 disordered 1300/6 1200 T ( C) 1250/24 1000 1:1 ordered ordered (1250 / 3 / -10 o C/h) 15 17 19 21 23 25 2-Theta 800 0 20 40 60 80 100 mole % PSN FIGURE 1. X-ray scans for x =0.5 FIGURE 2. Experimental order-disorder boundary with maximum ordering, and after for the PMN-PSN system subsequent high T treatments. From the data in figure 2 it is apparent that the introduction of Sc into PMN induces a large increase in the thermal stability of the cation order; for 10% PSN the orderdisorder boundary is close to 1150 C. The maximum stability of the ordering occurs at x = 0.5 where the order-disorder temperature is approximately 1360 C; this is significantly higher than the reported temperature for the PSN end-member (T dis = 1210 C). Simple extrapolation of the boundary to pure PMN yields a transition close to 950 C, a temperature that is apparently too low for the cations to retain any reasonable kinetic activity.

The microstructures of the well-ordered samples with x = 0.1, 0.5, 0.7, and 0.9 are shown in the dark-field TEM images in figure 3. Although all the samples show high levels of order, the size of the chemically ordered domains is clearly different in each sample. The largest ordered regions (~200nm) are observed in x = 0.5, which also has the highest order-disorder temperature, and the variation in the domain size is similar to the trend in the ordering temperatures. A B 200 nm C D FIGURE 3. Dark field images collected from well-ordered samples of (1-x)PMN - (x)psn with: (A) x = 0.1; (B) x = 0.5; (C) x = 0.7; (D) x = 0.9. Scale marker holds for all figures. Additional information on the stability of the ordering and its relationship to the domain coarsening was obtained by utilizing simple thermodynamic models to describe the cation mixing. The enthalpic stability of the 1:1 ordered Pb(β' 1/2 β" 1/2 )O 3 phases in the PMN-PSN system, and also of all other ordered mixed-metal perovskites, is derived from the valence difference of the β' and β" sites and the difference in the average β'-o and β"-o bond lengths. The substitution of PSN into PMN (where the effective replacement scheme is xsc 3+ = (2x/3)Mg 2+ + (x/3)nb 5+ on the β' site) does not change the average valence of the two ordered positions (which remain +3 and +5 for all values of x); however, the incorporation of the larger Sc cations onto the β' position (r(sc 3+ ) = 0.745Å, [2/3r(Mg 2+ ) + 1/3r(Nb 5+ )] = 0.693Å) does increase their size difference. The random distribution of metal cations on the β' sub-lattice also introduces a significant configurational entropic contribution to the

free energy of the random site structure, which we have previously noted can produce large changes in bulk stability.[2, 12]] Using a simplified approach in which the ordering reactions are assumed to be first order transitions (which they are not), the enthalpy of ordering can be calculated using classical thermodynamic treatments. The composition of the 1:1 ordered (1-x)PMN- (x)psn structure is given by Pb[(Mg (2-2x)/3 Nb (1-x)/3 Sc x ] 1/2 [Nb] 1/2 O 3 and the disordered perovskite by Pb(Mg (1-x)/3 Nb (4-x)/6 Sc x/2 )O 3. Therefore, the configurational entropy of the random site structure (S RS ) can be calculated from: S RS = -R/2[{(2-2x)/3}ln{(2-2x)/3} + {(1-x)/3}ln{(1-x)/3} + (x)ln(x)] (1) and the entropy of a fully disordered perovskite (S dis ) from: S dis = -R[{(1-x)/3}ln{(1-x)/3} + {(4-x)/6}ln{(4-x)/6} + (x/2)ln(x/2] (2) By using this mixing model to calculate the entropy of ordering ( S ord = S RS - S dis ), the enthalpy associated with the cation order ( H ord ) can be determined from the experimental order-disorder transition temperature (T dis ) by equating H ord and T dis S ord. The resultant enthalpies, plotted as a function of composition in figure 4, show an almost linear variation across the system and range from an extrapolated value of 3137 J/mole for pure PMN to 8547 J/mole for PSN. The predicted enthalpy for PMN yields an ordering temperature of 913 C. -2000-3000 -4000-5000 Hord -6000-7000 -8000-9000 0.0 0.2 0.4 x(psn) 0.6 0.8 1.0 FIGURE 4. Enthalpy of ordering, H ord (J/mole), calculated from the experimental transition temperatures using the mixing models described in the text.

Even though these calculations rely on a classical first order treatment of the disordering reactions, they provide useful additional information on the crystal chemical stability of the system. As mentioned above the incorporation of Sc onto the random site position would be expected to stabilize the cation order by increasing the difference in the size of the β' and β" sub-lattices. Although this expectation is supported by the increase in the enthalpy of ordering for increasing x, if the average size difference is the only factor affecting H ord the magnitude of the increase is surprisingly large. However, for the random site type of ordering unfavorable "excess" contributions to H ord must arise from the mixing of ions with different sizes and charges on the β' position. This excess contribution will be maximized for the ordered PMN end-member where the β' position would contain a 2:1 mixture of cations with the largest size and charge difference (r(mg 2+ )= 0.72Å, r(nb 5+ ) = 0.64Å). When the increase in the size difference of the β' and β" positions and the reduction in the charge/size mismatch on the β' sub-lattice are considered, the very large enhancement in H ord with x seems reasonable. The overall change in the free energy of the ordered 1:1 structure and the variation in the transition temperature, which is maximized close to x =0.5, is ultimately a compromise between the composition with the highest enthalpic stability (PSN) and the least negative entropy of ordering (PMN). Having established the changes in stability of the 1:1 order we return to the issue of the variations in domain size highlighted in figure 3. Although extensive ordering could be induced for compositions with 0.1 x 1.0, the domain size in the annealed samples shows a non-linear variation with x. It is evident that the degree of domain coarsening parallels the trend in the energetics of the system with the maximum domain size and stability occurring for x =0.5. An increase in the stability of the cation order necessarily increases the excess energy of boundaries (APB's) separating different translational variants of the ordered structure and of the interfaces between ordered and disordered regions of the sample. Therefore, while kinetics clearly play a very significant role in permitting these systems to approach an equilibrated state, the effect of Sc on the domain coarsening can be rationalized in terms of the thermodynamic stability and crystal chemical ideas proposed above. Dielectric Properties The response of the dielectric properties to the alteration in chemistry and order was examined by collecting weak field data from well-ordered and disordered compositions of (1-x)PMN-(x)PSN with x 0.1. Data collected from the ordered ceramics, with the microstructures shown previously in figure 3, appear in figure 5(A). For x 0.5 the frequency dependent behavior of the permittivity spectra are characteristic of a relaxor type response. For x 0.7 the dielectric properties are similar to those of pure PSN and PST, and the domain-coarsened samples exhibit a normal ferroelectric response. It is important to note that the crossover from relaxor to normal behavior is not associated with differences in the size of the chemical domains in the ordered samples. The largest domains are observed for x = 0.5 (figure 3), which is a relaxor, while x = 0.2 and x = 0.9 have similar domain sizes but very different dielectric responses. We have also confirmed that the behavior is not affected by Pb vacancies. This suggests that the alterations in the properties are induced by the

changes in the chemistry of the ordered structure, specifically the composition of the β' site. 14000 12000 10000 8000 6000 4000 2000 0.2 0.5 0.7 0.9 0-80 -60-40 -20 0 20 40 60 80 100120140 Temperature, ºC 14000 0.9 0.2 0.7 12000 10000 8000 6000 4000 2000 (A) (B) 0-80 -60-40 -20 0 20 40 60 80 100120140 Temperature, ºC FIGURE 5. Real part of the dielectric permittivity as a function of temperature for samples of (1- x)pmn-(x)psn. (A) ordered ceramics, (B) disordered ceramics. The dielectric behavior of the disordered PMN-PSN ceramics is shown in figure 5(B). The properties of compositions with x 0.5, which exhibit relaxor behavior in their ordered forms, show very little change with the reduction in the degree of order and domain size (see figure 5(B) and figure 6). However, for x 0.7 (normal

ferroelectrics in their ordered forms) the reduction in domain size promotes a transition to frequency dependent relaxor behavior (figure 5B). This change is accompanied by an increase in the magnitude of the permittivity and the temperature of the permittivity maximum (e.g. ~ 35 C for x = 0.9, figure 6). The behavior of these PSN-rich samples is similar to that reported previously for pure PMN and PST. 15000 x = 0.2 10000 5000 ordered 0 x = 0.9 10000 5000 ordered 0-50 0 50 100 FIGURE 6. Comparison of the real part of the permittivity for ordered and disordered samples of (1- x)pmn-(x)psn with x= 0.2 (upper plot), and x = 0.9 (lower plot). The alterations in the dielectric response of the ordered samples highlight the importance of the composition of the random site position in mediating the ferroelectric transitions. For low values of x the fields associated with the random distribution of "active" (Nb) and "inactive" (Mg,Sc) cations on the β' sub-lattice are effective in frustrating long-range ferroelectric coupling. The dilution of active Nb cations on this site for higher x enhances the long-range coupling and increases the temperature of the permittivity maxima. At a critical dilution limit, or critical correlation length, the concentration of Nb is apparently low enough to permit the barriers to long-range coupling to be overcome. In the PMN-PSN system this occurs for x between 0.5 and 0.7 under weak field conditions. Because the coupling lengths

in the ordered PMN-rich samples are so short, reductions in the size of the chemical domains have no significant effect on the dielectric response. The correlation lengths are much longer in the ordered PSN-rich samples and the size of the chemical domains now becomes an important factor. In this case the coupling can be frustrated, and relaxor behavior induced, by disordering the samples and reducing the size of the chemically domains below the critical correlation length. We are currently exploring these ideas in more detail using TEM to examine the relationship between the ordered domain and the polar domain structures, particularly in the region of relaxor to normal ferroelectric cross-over. CONCLUSIONS Relatively low-level substitutions of PSN (10 mole %) are effective in stabilizing extensive 1:1 B-site chemical ordering in PMN. Large alterations in the thermodynamic stability of the cation ordering are observed across the system with the maximum disordering temperature occurring for 50% substitution. Relaxor behavior is observed in both ordered and disordered forms of samples with ~ 60 mole % PSN. At higher levels of substitution the dielectric response is dependent upon the degree of order and domain size; disordered samples are relaxors and ordered samples exhibit normal ferroelectric behavior. ACKNOWLEDGMENTS This work has been supported by the Office of Naval Research through grant N00014-98-1-0583, and by the National Science Foundation through grant DMR 98-09035 and grant INT 98-11609 (MV). The work also made use of the MRSEC shared experimental facilities supported by the NSF under grant DMR96-32598. REFERENCES 1. Cross, L. E., Ferroelectrics, 151, 305-320 (1994) and references therein. 2. Akbas, M. A. and Davies, P. K., J. Amer. Ceram. Soc., 80, 2933-2936 (1997) 3. Davies, P. K. and Akbas, M. A., Ferroelectrics, 221, 27-36 (1999) 4. Montgomery, J. K., Akbas, M. A., and Davies, P. K., J. Amer. Ceram. Soc., 82, 3193-3198 (1999) 5. Davies, P. K. and Akbas, M. A., J. Phys. Chem. Solids., 61, 159-166 (2000) 6. Akbas, M. A. and Davies, P. K., J. Amer. Ceram. Soc., 83, 119-123 (2000) 7. Bellaiche, L., Padilla, J., and Vanderbilt, D., Phys. Rev. B., 59, 1834-1839 (1999) 8. Burton, B., and Cockayne, E., Phys. Rev. B (Rapid Comm.), 60, R12542-12545 (1999) 9. Burton, B., Phys. Rev. B., 59, 6087-6091 (1999) 10. Yan, Y., Pennycook, S. J., Xu, Z., and Viehland, D., Appl. Phys. Lett., 72, 3145-3147 (1998) 11. Egami, T., Dmowski, W., Teslic, S., Davies, P. K., Chen, I-W., and Chen, H., Ferroelectrics, 206, 231-244 (1998) 12. Davies, P. K., Tong, J., and Negas, T., J. Amer. Ceram. Soc., 80, 1727-1740 (1997)