The δ-phase of SrTeO3 at 780 K1

As part of a structural investigation of strontium tellurate(IV) (STO), SrTeO3, with particular emphasis on the crystal chemistry and phase transitions, the structure of the δ-phase has been determined at 780 K using a single-crystal analysis. Both structural and non-linear optical measurements indicate that STO undergoes a γ→δ second-order ferroelectric phase transition at 633 K from the C2 (γ) to the C2/m (δ) modification. Systematic differences between the similar γ- and δ-phase structures were determined and it was found that this phase transformation can be described by a displacive mechanism.


Comment
The origin of unusual ferroelectric properties and several phase transitions between α-β (350 K), β-γ (590 K) and γ-δ (760 K) polymorphs of STO were hotly debated long time (Yamada & Iwasaki, 1973;Yamada, 1975;Simon et al., 1979;Ismailzade et al., 1979;Libertz & Sadovskaya, 1980, Antonenko et al., 1982Kudzin et al., 1988) but the detailed structure data are lacking. Recently, in our several papers of the present series (Zavodnik et al., 2007a,b,c,) the structures of α (T < 363 K), β (363 K < T < 563 K) and γ (563 K < T <633 K) phases STO were reported. The purpose of the present communication is to report on the structure of δ-phase and clarify the nature of γ-δ ferroelectric phase transition at 633 K. There is a number of experimental studies of dielectric, elastic, piezoelectric and optical properties near well known reversible γ-δ phase transition at 633 K (Ismailzade et al., 1979;Libertz & Sadovskaya, 1980;Kudzin et al., 1982Kudzin et al., , 1988Antonenko et al., 1982). All the measured constants exhibit significant changes but the lack of thermal hysteresis or phase coexistence at this transition is indicative of a second order transformation. Around 633 K the SHG signal vanishes indicating that the δ-structure is centrosymmetrical. No success was obtained in earlier attempts to determine the δ phase structure using X-ray and neutron powder diffraction studies (Simon et al., 1979;Ismailzade et al., 1979;Dityatiev et al., 2006). The structure of δ-phase STO forms a three-dimensional lattice consisting types of irregular n-vertex SrOn (n = 6, 7, 8) polyhedra sharing corners or faces and TeO 3 pyramidal units which share edges with Sr-polyhedra but are not connected to each other. The projection along the b axis ( Fig. 1) shows two sorts of tunnels running along that direction. Te 4+ cations are located inside the tunnels of different sizes and shapes which represent the required space for the lone-electron pairs within the structure. From a comparison of atomic coordinates of comparable atoms in γ and δ phases the atomic polar displacements required to achieve centrosymmetry were determined. The structures of these polymorphs are similar and the phase transformation can be realised by the orientation and tilts of the TeO 3 pyramids and also by the variation in n-vertex SrO n polyhedra without a serious changing the building structural blocks. The Te6-O31 bond length is located at distance greater than 2.8 Å and does not contribute to the first coordination sphere of Te 4+ . Probably, γ-δ phase transition in STO can be described by displacive mechanism rather than by order-disorder model. The structure-property correlation in STO is in progress and will be reported later.

Experimental
The single crystals of STO were grown by Czochralski technique as described earlier (Libertz & Sadovskaya, 1980;Avramenko et al., 1984). The products were characterized in a scanning electron microscope (Jeol 820) with an energy-dispersive spectrometer (LINK AN10000), confirming the presence and stoichiometry of Sr and Te. SHG measurements showed that there is a symmetry centre in δ-phase (which is stable above 633 K) in a full agreement with the results (Libertz & Sadovskaya, 1980).
The atomic coordinates of all Sr and Te cations in γ-phase were used as starting parameters. The O atoms were localized by difference Fourier maps. The selection of space group C2/m for description of crystal structure of δ-phase STO was based on the experimental data of second harmonic generation (SHG) obtained on tested single crystals. The temperature dependence of SHG signal confirms that the structure of δ-phase STO is centrosymmetric. Precise X-ray diffraction study of single crystals at high temperatures is a challenging task because there is usually only a small number of measured X-ray reflections in the data and they cover a rather limited range of sinθ/λ. At 780 K it was impossible to registrate any reflections with sinθ/λ > 0.54. The thermal vibration parameters for oxygen anions were very high and strongly anisotropic. It was difficult to use an anisotropic approximation in this high-temperature refinement because the ratio of statistically reliable reflections to a number of refined parameters was very far from an optimal value. The positive definite refinements with anisotropic atomic displacement parameters were impossible for O atoms at 780 K. It was a main reason why the oxygen atoms were refined isotropically. A special attention must be given to the accuracy of interatomic distances of Te-O which are not rather similar as in the case of α, β and γ-phases (Zavodnik et al., 2007a,b,c). But all these Te-O bond lengths can be found acceptable if we take into account the standard deviation. The highest residual electron density peak is located 0.87 Å from atom Sr1 and the deepest hole is located 0.12 Å from atom Te4. Several atoms (Sr6, O12, O22 and O52) have increased isotropic atomic displacement parameters. These atoms are located inside significant voids which are larger than the voids for the rest of the atoms. The same peculiarity was also observed for the α-β and γ-STO structures. Fig. 1. The crystal structure of δ-SrTeO3 at 780 K. The sequence of Sr polyhedra are presented, Te cations occupy two different kinds of voids in a three-dimensional lattice.

Special details
Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.
Refinement. Refinement of F 2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F 2 , conventional R-factors R are based on F, with F set to zero for negative F 2 . The threshold expression of F 2 > σ(F 2 ) is used only for calculating Rfactors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F 2 are statistically about twice as large as those based on F, and R-factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å 2 )
x y z U iso */U eq  (10)