Peculiarities of PMN structure below temperature of relaxor phase transition

Materials Science and Engineering B83 (2001) 119– 122 www.elsevier.com/locate/mseb

Peculiarities of PMN structure below temperature of relaxor phase transition A.R. Lebedinskaya a, M.F. Kupriyanov a, R. Skulski b,* b

a Physics Faculty, Rosto6 on Don State Uni6ersity, 5 Zorge Street, Rosto6 on Don 344090, Russia Department of Materials Science, Faculty of Technics, Uni6ersity of Silesia, ul. 2 Sniezna Street, 41 -200 Sosnowiec, Poland

Received 19 April 2000; accepted 22 December 2000

Abstract The results of investigations of PMN single crystal atomic structure at temperatures 103, 183 and 203 K (i.e. below the temperature of dielectric permittivity maximum — Tm) shown that elementary cell parameters change non-monotonically at temperatures lower then Tm (Tm :240 K). By that Debay– Waller factors (DWF’s) of Pb atoms are considerably greater than DWF’s of another atoms in PMN, also it has been stated that disordered shifts of Pb atoms in x- and y-directions increase with decreasing temperature (for T BTm). © 2001 Elsevier Science B.V. All rights reserved. Keywords: PMN structure; Relaxor phase transition; Debay– Waller factor

1. Introduction Structural models of relaxor properties of oxide perovskites (OP) have been presented in [1 – 6] (including PbMg1/3Nb2/3O3-PMN). In some of these papers, variations of the structure with temperature and the external electric field are also analyzed these works help us to understand the mechanisms of arising of relaxor properties in OP. However, many questions concerning the PMN structure are not answered up to now. For example, in our opinion, the statement saying that in small regions of PMN (30 – 100 A, s) the Mg and Nb atoms are distributed as 1:1 is not proved enough. The superstructure reflexes observed in electron and X-ray diffraction [7–10] can be related with Mg/Nb ordering, but also with antiparallel shifts of Pb, Mg/Nb, O atoms. It is well known that in the electron diffraction the scattering possibility of oxygen atom is approximately equal to the scattering possibility of the heaviest atoms (Pb, Mg/Nb), and as a consequence the influence of antiparallel shifts of oxygen atoms is considerable. Besides, it is well known that the diffraction of electrons take place firstly in the surface layers and the * Corresponding author. E-mail address: [email protected] (R. Skulski).

results obtained in such a way do not describe the all volume of the sample well enough. Another problem related to relaxor ferroelectric (RF) properties of OP is discussed in [11]. This problem is as follows. The RF properties of PZT type solid solutions are analyzed from the point of view of structural phase transition related to oxygen octahedra rotations (systematized in [12]). As it is known from [11] the condensation of R25 and/or M3 modes is typical not only for the well known phase transitions in SrTiO3 and KMnO3 but also for solid solutions like PZT and PLZT. During the second order phase transitions related to rotation of oxygen octahedra (i.e. at which the tilting angle can be chosen as an ordering parameter) the RF properties can appear. In this paper, the results of investigations of PMN single crystal atomic structure at temperatures 103, 183 and 203 K (i.e. below the temperature of dielectric permittivity maximum — Tm) are presented. 2. Experiment PMN crystals were grown by R. Spinko from a solution of PMN synthesized by the solid state reaction in the melt PbO –B2O3 using the flux-growing technique.

0921-5107/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 5 1 0 7 ( 0 1 ) 0 0 4 9 9 - 8

120

A.R. Lebedinskaya et al. / Materials Science and Engineering B83 (2001) 119–122

To rule out the effect of mechanical treatment on the PMN crystal structure we did not give the crystal a spherical or cylindrical shape for facilitating the recording of the X-ray absorption. The crystal having the form of rectangular parallelepiped with dimension of 0.11× 0.06×0.05 cm3 was studied on the X-ray CAD4 Diffractometer with Mo– Ka radiation (Sin q/uB 1.01 A, − 1) from a graphite monochromator at the temperatures of 293, 183 and 103 K by Dr B. Merinov at the Institute of Crystallography and at the temperature of 203 K by Dr A. Gubaidulin at the A.E. Arbuzov Institute of Organic and Physical Chemistry of Kazan Scientific Centre of the Russian Academy of Sciences. The total number of the measured reflections was 1102 (293 K), 700 (203 K), 1016 (183 K) and 1173 (103 K). Lorentz-polarization corrections were made in the usual manner. The absorption coefficient was v = 667.1 cm − 1. Application of all the corrections gave F(hkl) exp. The extinction corrections were not introduced because the comparison of F(hkl) calc with F(hkl) exp did not reveal any clearly defined extinction effects. During the measurements of integral intensities of the reflections by the method of q, 2q scanning the temperature was stabilized to an accuracy of 9 0.5 K. Attempts to reliably determine the atomic parameters for the crystals with a perovskite structure having the phase transitions of different types (first-order ferroelectric, relaxor-type diffuse ferroelectric, ferroelastic etc.) confronts with some difficulties. On the one hand, such phase transitions are, usually, small variations of the atomic structure in the vicinity of the transition temperature. It is quite evident, that these variations are accompanied by small variations of structure amplitudes. To determine these variations successfully it is necessary, 1. to make the precision measurements of integral intensities of reflections; 2. to classify the reflections by their sensitivity to small variations of structural models; 3. to use a special procedure of processing the experimental evidence and to take into account sensitivity

to the shifts and Debay–Waller factors (DWFs) of the atoms in PMN. On the other hand, a real state of crystals related to the presence of defects of different types in them due both to the conditions of their growth and their arising at phase transitions may lead to marked variations of the form and integral intensities of the reflections. In the first stage of our investigations special attention was given to all these problems. In particular, to rule out the effect of mechanical treatment on the PMN crystal structure we did not give the crystal a spherical or cylindrical shape for facilitating the recording of the X-ray absorption. Also, we made a detailed analysis of the PMN crystal structure at room temperature and it has been established that the PMN atomic parameters are in accord with those reported in [13] with the accuracy of observation. In refining the PMN structure at low temperatures this enabled us to rule out the structural characteristics of the real PMN crystal state (occupation factor, Pb and O vacancies, etc.) as the parameters for refinement. As criteria of the quality of refining the PMN structure we used a functional S- and a R-factor, that estimate on the next formulas: N

− F calc % kF exp i i R=

i=1

,

N

% kF

exp i

i=1 N

calc 2 S= % (k F exp ) , i − F i i=1

where k is scale factor.

3. Results and discussion The results of the refinement of PMN single crystal structure at 103, 183, 203 and 293 K are presented in Table 1. The model has been used at which Pb, Mg/Nb and O atoms occupy their ideal positions (Pb [0, 0, 0], Mg/ Nb[1/2, 1/2, 1/2], O[1/2, 1/2, 0], [1/2, 0, 1/2], [0, 1/2,

Table 1 Perovskite cell parameters and DWF’s of the PMN atoms at different temperatures; space group Pm3m Structural parameters

103 K

183 K

203 K

293 K*

A (A, ) B (A, ) C (A, ) h= i=k (°) B(Pb) (A, 2) B(Mg/Nb) (A, 2) B(O) (A, 2) R-factor S-factor

4.034 (1) 4.035 (1) 4.033 (7) 90.0 (1) 4.23 (4) 0.47 (2) 0.76 (4) 0.103 9.034

4.028 (1) 4.028 (1) 4.028 (1) 90.0 (1) 4.35 (2) 0.56 (2) 0.98 (2) 0.091 9.154

4.029 (3) 4.030 (2) 4.029 (3) h =90.17 (5), i =k = 90.04 (5) 4.21 (6) 0.61 (3) 1.21 (2) 0.047 5.443

4.033 (2) 4.034 (1) 4.033 (7) 90.0 (1) 3.80 (2) 0.66 (2) 1.70 (7) 0.046 2.651

A.R. Lebedinskaya et al. / Materials Science and Engineering B83 (2001) 119–122 Table 2 DWFs of all atoms and shifts of the Pb and O atoms in PMNa Parameters

Temperature (K) 293

Shifts of Pb atoms (A, ) lx 0.11 (2) ly 0.11 (2) lz 0.28 (4)

203

183

103

0.24 (1) 0.09 (3) 0.27 (3)

0.26 (2) 0.09 (2) 0.28 (3)

0.24 (3) 0.18 (2) 0.26 (2)

DWFs of PMN atoms on the isotropic approximation (A, 2) Pb 0.91 (5) 1.28 (2) 1.37 (3) 0.69 (2) Mg/Nb 0.66 (3) 0.61 (3) 0.56 (2) 0.47 (2) O 1.00 (2) 0.98 (2) 0.98 (2) 0.74 (4) R-factor 0.037 0.051 0.043 0.047 S-factor 1.365 2.427 1.423 1.541 Shifts of O atoms (A, ) OI(0.5, 0.5, 0) lx 0.07 (2) ly 0.07 (2) lz 0.09 (1)

0.11 (2) 0.11 (2) 0.04 (1)

0.10 (2) 0.10 (2) 0.04 (1)

0.07 (1) 0.07 (1) 0.10 (2)

OII(0, 0.5, 0.5) lx ly lz

0.09 (1) 0.07 (2) 0.07 (2)

0.04 (1) 0.11 (2) 0.11 (2)

0.04 (1) 0.10 (2) 0.10 (2)

0.10 (2) 0.07 (1) 0.07 (1)

0.07 (2) 0.09 (1) 0.07 (2) 0.49

0.11 (2) 0.04 (1) 0.11 (2) 0.43

0.10 (2) 0.04 (1) 0.10 (2) 0.41

0.07 (1) 0.10 (2) 0.07 (1) 0.35

0.032

0.046

0.040

0.041

OIII(0.5, 0, 0.5) lx ly lz DWF’s of O atoms (A, 2) R-factor a

These data coincide with [13].

1/2]) in elementary cell. DWF’s have been calculated assuming that the Gaussian distribution around these positions take place. The isotropic approximation of DWF’s for all atoms has been used. Such initial structural model leads to the following conclusions, 1. the values of all parameters of PMN elementary cell at 183 and 203 K are smaller than the values at 103 and 293 K; 2. DWF’s of Pb atoms are considerably greater than DWF’s of another atoms. Decrease of the lattice parameters which have been observed, one can relate the structure compression connected to oxygen octahedra rotation. As a result of the rotation the chains of BOBOBO atoms become zigzag-like. Such collective correlated rotations of the octahedra (the result of antiparallel shifts of oxygen atoms) should lead to the superstructure with A= 2a. The full description of such possibility for perovskite type structure was presented in [12]. Such phase transitions are related to the condensation of R25 and/or M3 modes [14]. The example of such a phase transition is the transition in SrTiO3 at 105 K [16]. Calculations of the magnitude of shifts of atoms based on the data presented in Table 1 give the values 0.20 A, .

121

Neither we nor another authors have seen the superstructure reflections. This fact can be explained as follows. The contributions into X-ray reflection intensities from the oxygen atoms are rather not big when compared with contributions from another atoms. Moreover, in the case of PMN the long range ordering is limited to about 100 A, . If the superstructure is limited to such a small regions the superstructure reflexes are weak and broad. On the other hand, the superstructure reflexes from such a small regions can be observed (and are observed) in the electron diffraction pattern. DWF’s are sensitive to disordered shifts of atoms (Pb atoms in lead-containing compounds) in perovskite type structure. DWF’s values are a consequence of mean quadratic shifts of atoms during thermal vibrations as well as the static disordered shifts [15]. This approach provides good fit of experimental structural amplitudes to the theoretical data and leads to decrease the R-factor. The structural parameters of PMN at 103, 183 and 203 K are presented in Table 2. As it is seen from Table 2 in PMN single crystals the disordered shifts of Pb atoms in x- and y-directions increase with decreasing temperature (for TB Tm).

4. Conclusions The obtained results of PMN-single crystal structure behavior at low temperatures can account for the data obtained from diffuse X-ray scattering [5], polar metastability investigations [17,18] and hypersound anomalies [19] in PMN at 190–230 K. The possible reasons for the anomaly in the temperature dependence of lattice parameters below Tm at a relaxor ferroelectric phase transition in PMN in the vicinity of the phase transition may be the weakening of a long interaction in the electron crystal sublattice, which are a cause for the decrease of a radius of correlation interaction and leads to a relative ‘release’ of rotational modes of vibrations that is accompanied by the coordinated rotations of oxygen octahedra BO6 (B=Mg/Nb). Anomalies of elementary cell observed at 183–203 K are also in good agreement with Tm calculated for PMN in [20] (with assumption that PMN is an example of superparaelectric) and from the analysis of Gaussian distribution of relaxation times [21].

References [1] P. Bonneau, P. Garnier, G. Calvarin, E. Husson, J.R. Gavarri, A.W. Hewat, A. Morell, J. Solid State Chem. 91 (1991) 350. [2] H.D. Rosenfeld, T. Egami, Ferroelectrics 158 (1994) 351. [3] S. Vakhrushev, A. Nabereznov, S.K. Sinha, Y.P. Feng, T. Egami, J. Phys. Chem. Solids 57 (1996) 1517.

122

A.R. Lebedinskaya et al. / Materials Science and Engineering B83 (2001) 119–122

[4] Q.M. Zhang, H. You, M.L. Mulvihill, S.J. Jang, Solid State Commun. 97 (1996) 693. [5] H. You, Q.M. Zhang, Phys. Rev. Lett. 79 (1997) 3950. [6] N. de Mathan, E. Husson, G. Calvarin, A. Morel, Mater. Res. Bull. 26 (1991) 1167. [7] D.M. Fanning, I.K. Robinson, S.T. Jung, E.V. Colla, D.D. Viehland, D.A. Payne, J. Appl. Phys. 87 (2000) 840. [8] L. Yinmei, S. Chengyu, W. Baosong, HREM studies of ordered superstructure in PMN and PLMN ceramics, ISAF’94, in: Proceedings of the Ninth IEEE International Symposium on Applications of Ferroelectrics (Cat. No.94CH3416-5), IEEE, 1994, pp. 226 – 228. [9] C. Boulesteix, F. Varnier, A. Llebaria, E. Husson, J. Solid State Chem. 108 (1994) 141. [10] N. de Mathan, E. Husson, P. Gaucher, A. Morell, Mater. Res. Bull. 25 (1990) 427. [11] D. Xunhu, X. Zhengkui, D. Viehland, J. Am. Ceram. Soc. 78 (1995) 2815.

.

[12] A.M. Glazer, Acta Crystallogr. Sect. A: Cryst. Phys. Diffrac. Theor. Gen. Crystallogr. A31 (1975) 756. [13] A. Verbaere, Y. Piffard, Z.G. Ye, E. Husson, Mater. Res. Bull. 27 (1992) 1227. [14] R.A. Cowley, W.J.L. Buyers, G. Dolling, Solid State Commun. 7 (1969) 181. [15] R. Kolesova, V. Kolesov, M. Kupriyanov, R. Skulski, Phase Transitions 68 (1999) 62. [16] A.D. Bruce, R.A. Cowley, J. Phys. C: Solid State Phys. 6 (1973) 2422. [17] R. Sommer, N.K. Yushin, J.J. van der Klink, Phys. Rev. B 48 (1993) 13230. [18] Z.-G. Ye, H. Schmidt, Ferroelectrics 145 (1993) 83. [19] C.S. Tu, V.H. Schmidt, J.G. Siny, J. Appl. Phys. 78 (1995) 5665. [20] R. Skulski, Mater. Sci. Eng. B64 (1999) 39. [21] R. Skulski, Phys. A 274 (1999) 361.