Anomalous Synchrotron X-ray Scattering Studies of Nanodomains in Pb(Mg 1/3 Nb 2/3 )O 3 A. Tkachuk, Haydn Chen, P. Zschack and E. Colla Department of Materials Science and Engineering and Frederick Seitz Materials Research Laboratory University of Illinois, Urbana, Illinois 61801 USA Abstract. A systematic study of the temperature dependence of superlattice reflections in the reciprocal space of a single crystal Pb(Mg 1/3 Nb 2/3 )O 3 (PMN) was performed using anomalous x-ray scattering technique. Our studies confirm the existence of the two types of nanoregions in PMN: a) chemically ordered nanodomains, and b) polar nanodomains formed by short-range correlated ionic displacements. No detailed temperature dependence of these superlattice reflections has been reported in the past. From monitoring the superlatttice reflections corresponding to polar nanodomains (i.e. α spots) over the temperature range 15K-800K, we found freezing temperature (T f )of correlated atomic displacements was near 200 K. In contrast, chemically ordered nanodomains, which give rise to F type superlattice peaks, exhibited spherical shape over the entire temperature interval 15-800 K. This leads us to suspect that chemically ordered regions might be different and independent of polar nanodomains. In this paper we explain the contributions of different atomic displacements to α and F superlattice reflections in PMN. Correlation and competition between Pb displacements and the tilting of oxygen octahedra network are presented to understand the microstructural origin of the relaxor ferroelectric behavior. INTRODUCTION Lead magnesium niobate Pb(Mg 1/3 Nb 2/3 )O 3 (PMN)is a relaxor ferroelectric with dielectric constant >30,000 near T m =270 K [1,2]. Temperature dependence of the dielectric constant is diffuse and very sensitive to the frequency of the applied electric field. Although the dielectric constant of PMN shows a maximum at T m,it has been inferred from x-ray and neutron scattering experiments that PMN doesn t show any noticeable macroscopic structural phase transition in the temperature range 15-600 K [3]. Instead it was proposed, that the system undergoes a transition into a glass-like state at the so-called freezing temperature, T f =200-230 K [4]. Importance of the local disorder and different kinds of local fluctuations (chemical and dipolar)in PMN and other related relaxors was demonstrated to be intimately
related to the relaxor ferroelectric behavior. Correlation of these fluctuations is responsible for formation of different nanoregions, which may be studied through the associated superlattice reflections they produce [5,6]. The focus of this work is to investigate the behavior of these nanodomains as a function of temperature and x-ray energy, leading to an improved understanding of the microstructure and the underlying physical principles responsible for the relaxor ferroelectric behavior. METHODS AND MATERIALS Measurements were performed on the UNICAT undulator beamline (Sector 33- ID)at the Advanced Photon Source (APS), Argonne National Laboratory. The energy of the incoming x-rays was tuned near Pb L III edge (13.055 kev)for anomalous scattering measurements. See Figure 1. Three values of the energies were chosen: 13.045 kev, 13.005 kev and 12.855 kev, to emphasize the contribution of Pb to the superlattice peaks. Figure 1 depicts energy dependence of the fluorescence taken from the PMN sample. White beam from the undulator was monochromatized by two Si (111)single crystals and focussed with two mirrors. Mirrors also serve as high-order harmonic rejection devices. The energy was calibrated with a standard Pb foil in the transmission mode, then checked with the actual sample. Scintillation detector was used to detect the diffracted beam. The size of the beam in the diffraction plane of the conventional four-circle Huber diffractometer was about 0.2 mm at the sample position. All measurements were performed with constant 0.12 0.10 Fixed Q=(-0.8,1.5,2.5) energy scan Fluorescence (arb. units) 0.08 0.06 0.04 0.02 12.855 kev Pb L III =13.055 kev 13.005 kev 13.045 kev 0.00 12.80 12.85 12.90 12.95 13.00 13.05 13.10 Energy (kev) FIGURE 1. Energy dependence of the fluorescence from PMN
monitor counts. Displex cryostat has been used for low temperature measurements in the range of 15-300 K. Measurements were done during heating of the sample from 15 K to room temperature. Size of the PMN single crystal was 3 x 3 x 1 mm 3 with a surface normal oriented in the [001] direction. FWHM for 003 Bragg reflection is 0.003 in reduced reciprocal lattice units (r.l.u.)for L direction scan. Resolution in reciprocal space is better than 0.001 r. l. u. along the H, K and L directions. Supplemental data were taken at X-18A beamline, NSLS, and on the in-house hot-stage rotating anode x-ray machine. RESULTS ANDDISCUSSION Two types of nanoregions exist in PMN: a)chemically ordered nanodomains, and b)polar nanodomains, due to correlated ionic displacements. Each type of nanodomains gives rise to superlattice reflections at different positions in the reciprocal space. Reflections on the body-centered positions are called F spots and on the face-centered positions are called α spots [7]. In-phase rotations of oxygen octahedra produce α spots. However, F spots have their origin in both 1:1 chemical order of B-site atoms, and the out-of-phase rotations of oxygen octahedra. It is expected that oxygen octahedra rotation causes Pb atoms to be displaced, thereby producing local dipoles. Temperature dependence of the F spots is weaker than that of the α spots. Intensity at the position of the α spots gradually decreases and reaches a constant value above T f =200 K (Figure 2). 1/2(135) F spot showed about 20% reduction in intensity from 15K to room temperature with a noticeable cusp near T f (Figure 3). Detailed analysis revealed that α peaks vanish above T f (Figures 2 and 4), and the remaining intensity is from soft <110> T phonon mode. FWHM of the F spots is temperature independent over the whole temperature range 15-800K. See inset of Figure 3. Small dependence on the energy of the x-rays tuned near Pb L III edge is attributed to the contribution from correlated Pb atomic displacements. See Figures 2 and 3. From the temperature dependence of the α superlattice peak profile (Fig. 2 and Fig. 4), corresponding to polar regions, we found the freezing temperature (T f )of the correlated atomic displacements near 200K. Decrease in the intensity of the α superlattice peaks is accompanied by reduction of thermal diffuse scattering corresponding to the soft <110> T mode. See inset of Figure 4. This suggests the importance of the phonon coupling with the origin of the α spots. The ridges were found not only near reflections with the sum of Miller indices h+k+l=even, as was reported before [8], but near all the Bragg reflections. Structure factor calculations were carried out to include two types of correlated oxygen octahedra rotations in PMN: 1)in-phase, and 2)out-of-phase. These two types of rotations displace Pb atoms in two different ways, which were modeled in this work and the results are in good agreement with the experimental observations. In-phase BO 6 rotations, coupled with corresponding Pb displacements, contribute to the intensity of the α spots below T f. Out-of-phase rotations, coupled with a different Pb displacement pattern, contribute to the F spots. We attribute the
0.14 0.13 Intensity 1/2(035) α spot 12.085 kev 13.005 kev Lorentzian Hight/Monitor counts 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0 50 100 150 200 250 300 T (K) No change up to 800 K T f FIGURE 2. Intensity of the 1/2(035) α spot vs. temperature. 1/2(-135) F spot 0.100 13.005 kev 12.855 kev 0.19 0.095 0.090 0.085 Lorentzian Hight / Monitor counts 0.18 0.17 0.16 0.15 0.14 FWHM 0.080 0.075 0.070 0.065 0.060 0.055 0 50 100 150 200 250 300 550 600 650 700 750 800 T(K) 0 50 100 150 200 250 300 T (K) T f FIGURE 3. Intensity of the 1/2(135) F spot vs. temperature. Inset shows the width (FWHM) of the 1/2(035) peak in the 15-800 K temperature range.
increase in the α spot intensity on cooling below T f to the increased angle of the rotations due to freezing of the corresponding zone boundary phonon mode, and due to the increased magnitude of coupled anti-parallel Pb displacements. From the disappearance of the α spots on heating we suggest that there is no contribution from Pb displacements to the intensity of the α spots above T f. Independence of the intensity above T f measured at the position of the α spot from the x-ray energy tuned near Pb L III absorption edge further supports this fact (Figure 2). Two different zone boundary phonon modes corresponding to in-phase and out-of-phase rotations, gradually freeze on cooling, which is evident from the intensity increase of α and F superlattice reflections, shown in Fig. 2 and Fig. 3 respectively. Freezing of the in-phase rotations below T f, as seen from Fig. 2, may stiffen the lattice due to corresponding static displacements, therefore making out-of-phase rotation more difficult. This may explain the small drop in the intensity of the 1/2(135) F spot seen in Fig. 3 just below T f. Intensity contribution to α and F spots due to short-range correlated anti-parallel Pb displacements can be viewed as a result of competing interactions preventing long-range ferroelectric order at low temperatures. Tendency for the whole crystal to order may compete with displacements caused by oxygen octahedra rotations below T f. Instead, system is subdivided into randomly oriented frozen nanoregions of the polar phase [1 3]. Appearance of the α spots below T f is related to the competing anti-parallel Pb displacements caused by oxygen octahedra rotations [9]. It was suggested that polar nanoregions exist at 0.60 0.55 0.50 0.45 FWHM 1/2(035) α spot <100>* <011>* <01-1>* FWHM (r.l.u) 0.40 0.35 0.30 0.25 0.20 0.15 0.10 L 013 023 2.80 2.60 2.40 2.20 012 1.20 1.40 1.60 1.80 022 0 100 200 300 550 600 650 700 750 800 T (K) K <011>* H <01-1>* FIGURE 4. Width of the 1/2(035) α spot in different directions vs. temperature. Inset shows (100) plane scan of the α spot with strong thermal. diffuse scattering in [10 1] direction.
temperatures much higher than room temperature [2,6]. Chemical disorder of Nb 5+ and Mg 2+ ions is believed to play an important role in the formation of these polar regions [2]. Parallel displacements of Pb don t produce superlattice reflections, which appear only below T f when anti-parallel distortions are induced in the polar nanodomains by oxygen octahedra rotations. Interactions within and between the polar regions are expected to increase with decreasing temperature due to diminishing of thermal fluctuations. But competing anti-parallel Pb displacements induced by oxygen octahedra rotations below T f, weaken the parallel alignment of the dipoles within the nanodomains, and subsequently the interaction between the regions also reduces. Therefore the polar nanoregions become randomly frozen in the crystal without forming normal microscopic size ferroelectric domains. Coherence in anti-parallel Pb displacements is unlikely to spread beyond the boundaries of the individual polar regions and it appears to be independent of temperature below T f as evident from Fig. 4. Coherence length is inversely proportional to FHWM of the reflection peak and below T f corresponds to about 40 Å. Presence of atomic disorder and competing interactions are important properties of the dipolar glasses. PMN has intrinsic chemical disorder on the B sites, but we need better understanding about the microscopic origin of the competing interactions to explain its glass-like behavior. In this work we have studied the evolution of two types of nanodomains: a)chemical, and b)polar by following the temperature dependence of the corresponding superlattice reflections. Chemical domains, which give rise to F superlattice peaks, were found to be isotropic in space and temperature independent in size over the whole temperature interval 15-800 K. Their size was found to be slightly larger than that of the polar nanodomains (near 50 Å). We are not claiming that mixture of antiferroelectric and ferroelectric nanoregions exist in PMN. Instead, it is proposed that competing anti-parallel displacements of Pb are induced by freezing of corresponding oxygen octahedra rotations within the polar regions themselves below T f 200 K. These displacements disrupt the formation of the ferroelectric phase. ACKNOWLEDGEMENTS The research was supported by the US Department of Energy; grant No. DEFG02-96ER45439 through the Frederick Seitz Materials Research Laboratory. We thank the staff of UNICAT at the Advanced Photon Source, Argonne National Laboratory and MATRIX at NSLS, Brookhaven National Laboratory. We also would like to thank Dr. Zhongming Wu for his assistance during the experiments conducted at UNICAT. The UNICAT facilityat the Advanced Photon Source (APS)is supported by the University of Illinois at Urbana-Champaign, Materials Research Laboratory (U.S. Department of Energy, the State of Illinois-IBHE-HECA and the National Science Foundation), the Oak Ridge National Laboratory (U.S. Department of Energy under contract with Lockheed Martin Energy Research), the National Institute of Standards and Technology (U.S. Department of Commerce)
and UOP LLC. Use of the Advanced Photon Source was supported by the U.S. Department of Energy, Basic Energy Sciences, Office of Science, under Contract No. W-31-109-Eng-38. REFERENCES 1. G. A. Smolenskii et al., Ferroelectrics and related Materials, NewYork: Gordon and Breach, 1981 2. L. E. Cross, Ferroelectrics 151, 305-320 (1994). 3. P. Bonneau, P. Garnier, G. Calvarin, et al., Journal of Solid State Chemistry 91, 350-361 (1991). 4. D. Viehland, J.-F. Li, S. J. Jang, et al., Phys. Rev. B 43, 8316-8320 (1991) 5. A. D. Hilton, D. J. Barber, C. A. Randall, et al., J. Mater. Sci. 25, 3461-3466 (1990) 6. S. Vakhrushev, A. Naberezhnov, S. K. Sinha, et al., J. Phys. Chem. Solids 57, 1517-1523 (1996) 7. C. A. Randall, D. J. Barber, R. W. Whatmore, et al., J. Mater. Sci. 21, 4456-4462 (1986) 8. H. You, Q.M. Zhang, Phys. Rev. Lett. 79, 3950-3953 (1997) 9. V. Gosula, A. Tkachuk, K. Chung and Haydn Chen, J. Phys. Chem. Solids 61, 221-227 (2000)