Materials science

Edge effects

How do crystal structures terminate at 'flat' surfaces? New developments in electron crystallography mean that the detailed atomic structure of surfaces in complex crystals can be determined — with surprising results.

Anyone who has made a model of a crystal structure, or even just a drawing of one, must surely be struck by the fact that there is rarely, if ever, a satisfactory way of terminating the structure. Almost invariably, atoms with missing bonds are left dangling at the surface, and the chemist, at least, will immediately conclude that there must be some rearrangement at the surface to produce a more satisfactory bonding configuration. Remarkably, except for a handful of elemental and simple binary materials, until now we have had no knowledge of the real structure of most crystal surfaces, despite their enormous importance. But on page 55 of this issue, Erdman et al.1 show how direct-methods electron crystallography coupled with ab initio electronic structure calculations can be used to determine a complex surface structure of strontium titanate, SrTiO3. The results are surprising (although, with hindsight, perhaps to be expected) and they suggest that a new era of surface crystallography is beginning.

Surface structures are important in understanding processes such as catalysis, in which chemical reactions occur at the interface between a solid and a liquid or gas phase. These reactions are ubiquitous in the chemical industry, as well as at electrodes in fuel cells and in the dissolution (corrosion) of solids. Crucial to understanding the mechanisms of all these processes is a knowledge of the structure of the interface between the solid and the fluid medium. This last point leads to the observation that a surface is an interface between two phases, and in general the surface of a solid might have a different structure when it is the interface between a crystal and, for example, a vacuum or water or reacting gases.

Oxides are very important in this respect, and Erdman et al.1 have chosen a particularly appropriate material for their study: SrTiO3 is an example of a perovskite material, perhaps the most studied class of oxide. The parent crystal structure is relatively simple and consists of a cubic framework of corner-connected TiO6 octahedra, with Sr atoms in the cavities of the structure (Fig. 1). Related members of its large family exhibit a remarkable range of compositions and structures2. Perovskites include ferroelectric materials such as BaTiO3 (the prototypical oxide ferroelectric) and related high-dielectric-constant materials. Other transition-metal perov-skites exhibit exceptional electronic properties such as colossal magnetoresistance and (in oxygen-deficient copper oxides) high-temperature superconductivity. SrTiO3 is often used as a substrate for epitaxial growth of such materials, and this makes its surface structure particularly interesting.

Figure 1: The crystal structure of SrTiO3.

Each titanium atom is bonded to six oxygen atoms, forming an octahedral structure that is connected at its corners to its neighbours. Combining calculations and crystallographic images, Erdman et al.1 show that, at a surface in the horizontal plane of this crystal, the structure is reorganized, terminating in a double Ti–O layer with connections between polyhedral edges as well as corners.

Because of their much stronger interaction with matter, electrons (rather than X-rays or neutrons) are the preferred probe for the examination of surface structure. An early use of electron microscopy was the determination of simple metallic surface structures from end-on ('profile') images3. Shortly thereafter, the structure of the famous Si '7 × 7' surface was determined4 from transmission electron diffraction combined with scanning tunnelling microscopy data.

In determining the structure of crystals by X-ray diffraction, a major problem is that one knows only the intensities and not the phases of the diffracted beams. So direct inversion of the diffraction pattern by Fourier analysis to recover the electron density (which scattered the X-rays) is not possible. However, by recognizing that the electron density is not an arbitrary function but has special properties (for example, it is always positive and, as atomic electron density peaks strongly near the nucleus, is close to zero between atoms), relationships between the phases of diffracted beams can be established. These can then be factored into 'direct methods' of crystallographic analysis, which have made routine the determination of structures of moderately complex crystals (some hundreds of atoms in the unit cell). Electron crystallography is in principle similar — the scattering now occurs by the electrostatic potential of the atom, but this is simply related to the charge density by Poisson's equation — and direct methods have been used here too5.

It is not straightforward to apply direct methods to the solution of surface structures by electron crystallography, but Erdman et al.1 show that direct-methods techniques developed by Marks and colleagues6 lead directly to a projection of the surface structure. They then use ab initio electronic-structure calculations to refine the coordinates normal to the surface to obtain a full three-dimensional structure.

In the SrTiO3 structure (Fig. 1), there are alternating SrO and TiO2 layers normal to the cubic axes. So one might expect a surface in that plane to terminate either with a TiO2 layer or a SrO layer. In fact, in the observed structure1 the crystal terminates with two TiO2 layers, and with substantial reorganization in the outermost layer. The origin of the reorganization can be seen as follows. In the bulk structure each O atom is bonded to two Ti atoms. If this pattern were to persist in a surface of composition TiO2, each Ti atom would have to be 4-coordinated (that is, forming four bonds to oxygen) in contrast to the octahedral 6-coordination in the bulk. The surface reconstruction is such that coordination polyhedra share edges (rather than just vertices as in the bulk) so that the Ti atoms in the surface layer are 5-coordinated.

Such behaviour might have been expected from crystal chemistry. In the tungsten oxide WO3, for example, the structure is the same as the TiO3 framework of SrTiO3. WO3 is easily reduced to phases WO3−x in which, instead of having oxygen vacancies, the crystal reorganizes to eliminate the vacancies and maintain the octahedral coordination of the metal by edge-sharing between the octahedra. Similar behaviour is observed in the fantastically rich and highly organized structure of the many other oxides of the early transition metals (such as Ti, Nb, Mo and W)7.

It should be emphasized that the work under discussion is the beginning of a long and surely very interesting story. Even for SrTiO3 there is strong evidence8 for other reconstructions of the surface; in addition, as well as the perovskites A2+B4+O3 (such as SrTiO3), there are other families A+B5+O3 (such as NaNbO3) and A3+B3+O3 (such as LaFeO3). And then, of course, there are many thousands of other oxide structures.


  1. 1

    Erdman, N. et al. Nature 419, 55–58 (2002).

    ADS  CAS  Article  Google Scholar 

  2. 2

    Mitchell, R. H. Perovskites: Modern and Ancient (Almaz, Thunder Bay, Ontario, 2002).

    Google Scholar 

  3. 3

    Marks, L. D. Phys. Rev. Lett. 51, 1000–1002 (1983).

    ADS  CAS  Article  Google Scholar 

  4. 4

    Takayanagi, K., Tanishiro, Y., Takahashi, S. & Takahashi, M. Surf. Sci. 164, 367–392 (1985).

    ADS  CAS  Article  Google Scholar 

  5. 5

    Dorset, D. L. Structural Electron Crystallography (Plenum, New York, 1995).

    Google Scholar 

  6. 6

    Marks, L. D., Erdman, N. & Subramanian, A. J. Phys. Condens. Matter 13, 10677–10688 (2001).

    ADS  CAS  Article  Google Scholar 

  7. 7

    Hyde, B. G. & Andersson, S. Inorganic Crystal Structures (Wiley, New York, 1989).

    Google Scholar 

  8. 8

    Jiang, Q. D. & Zegenhagen, J. Surf. Sci. 425, 343–354 (1999).

    ADS  CAS  Article  Google Scholar 

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Correspondence to Michael O'Keeffe.

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O'Keeffe, M. Edge effects. Nature 419, 28–29 (2002).

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