research papers 402 DOI: 10.1107/S010876730401726X Acta Cryst. (2004). A60, 402±408 Acta Crystallographica Section A Foundations of Crystallography ISSN 0108-7673 Received 8 March 2004 Accepted 14 July 2004 # 2004 International Union of Crystallography Printed in Great Britain ± all rights reserved Extinction-free electron diffraction refinement of bonding in SrTiO 3 Jesper Friis, a * Bin Jiang, b John Spence, b Knut Marthinsen c and Randi Holmestad a a Department of Physics, Norwegian University of Science and Technology (NTNU), N-7491 Trondheim, Norway, b Department of Physics and Astronomy, Arizona State University, Tempe, AZ 85287-1504, USA, and c Department of Materials Technology, Norwegian University of Science and Technology (NTNU), N-7491 Trondheim, Norway. Correspondence e-mail: jesper.friis@material.ntnu.no Accurate low-order Fourier coef®cients of the crystal potential of SrTiO 3 are measured by quantitative convergent-beam electron diffraction. The accuracy in the corresponding derived X-ray structure factors is about 0.1% for the strong low-order re¯ections (sin = < 0.3 A Ê 1 ). This accuracy is better than for conventional X-ray diffraction and equivalent to the accuracy of the X-ray Pendello È sung method. Combination of these structure factors with high-order X-ray diffraction measurements allows accurate bonding information to be obtained from a multipole model ®tted to the experimental data. It is shown that TiÐO has a covalent component and that the SrÐO bond is mainly ionic. The role of Ti 3d electrons in TiÐO bonding is also discussed. 1. Introduction Strontium titanate (SrTiO 3 ) is a typical perovskite structure, with incipient ferroelectric properties at ambient temperature and a displacive phase transition from a cubic to a tetragonal structure at around 106 K. The cubic phase structure of SrTiO 3 is shown schematically in Fig. 1. The covalent component of the chemical bonding in perovskites is considered important for understanding their physical properties, such as incipient ferroelectricity. Theoretical calculations using density func- tional theory (DFT) show that the TiÐO bonding is polar covalent, while the SrÐO bonding has mainly ionic character (Weyrich & Siems, 1985). Despite being quantitatively very different, the experimental deformation density maps of Buttner & Maslen, (1992) and Abramov et al. (1995) show a charge accumulation in the TiÐO bonds. Similar results were also obtained by X-ray powder diffraction experiments analyzed with the maximum-entropy method (Ikeda et al., 1998). A more detailed quantitative characterization of the charge density was performed by Zhurova & Tsirelson (2002), based on a multipole analysis of X-ray experiments at 145 K (Abramov et al. , 1995). It is well known that low-order structure factors contain signi®cant information on the valence-charge distribution (Zuo et al. , 2000), important for chemical bonding. Fig. 2 shows the valence scattering in SrTiO 3 from the Sr, Ti and O atoms. There are only three re¯ections contributing to the valence scattering of Sr (sin = < 0:25 A Ê 1 ) and 14 contri- buting to the valence scattering of Ti (sin = < 0:5A Ê 1 ). Unfortunately, most of these re¯ections are strong (Q > 1:30 m 1 , see Table 1) and therefore strongly affected by extinction. This makes multipole re®nements based on X-ray diffraction dif®cult. In the present work, we overcome this problem by measuring the structure factors affected by Figure 1 Schematic drawing of the unit cell of SrTiO 3 in the cubic phase. The Sr and Ti atoms are at cubic site-symmetry positions m  3m, while the O atoms have the site symmetry 4=mmm. Figure 2 Valence-electron scattering factors of Sr(4s 2 ), Ti(3d 2 4s 2 ) and O(2s 2 2p 4 ) atoms. Note: all scattering factors are normalized to one.