The surface science of titanium dioxide - Niser

66 U. Diebold / Surface Science Reports 48 (2003) 53±229
and, more recently, atomic force microscopy (AFM), studies have revealed the complexity of the
seeminglysimple rutile (1 1 0) surface, hence the section on TiO 2 (1 1 0) commences with a
recommendation on the best wayto prepare this surface. The two other low-index planes, rutile (1 0 0)
and (0 0 1) are described in Sections 2.3 and 2.4, respectively. Until fairly recently the (1 3)
reconstruction of the rutile (1 0 0) seemed well understood, but inconsistencies in theoretical
calculations as well as new interpretations of X-raydiffraction data show that a closer look on the
structure of this phase maybe needed (Section 2.3.2.2). New developments on structural investigations
of anatase samples are included at the end.
2.1. Bulk structure
Titanium dioxide crystallizes in three major different structures; rutile (tetragonal, D 14
4h -P4 2/mnm,
a ˆ b ˆ 4:584 AÊ , c ˆ 2:953 AÊ [49]), anatase (tetragonal, D 19
4h -I4 1/amd, a ˆ b ˆ 3:782 AÊ , c ˆ 9:502 AÊ )
and brookite (rhombohedrical, D 15
2h -Pbca, a ˆ 5:436 A Ê , b ˆ 9:166 AÊ , c ˆ 5:135 AÊ ) [65]. (Other
structures exist as well, for example, cotunnite TiO 2 has been synthesized at high pressures and is one
of the hardest polycrystalline materials known [66].) However, onlyrutile and anatase playanyrole in
the applications of TiO 2 and are of anyinterest here as theyhave been studied with surface science
techniques. Their unit cells are shown in Fig. 2. In both structures, the basic building block consists of a
titanium atom surrounded bysix oxygen atoms in a more or less distorted octahedral con®guration. In
each structure, the two bonds between the titanium and the oxygen atoms at the aspices of the
octahedron are slightlylonger. A sizable deviation from a 908 bond angle is observed in anatase. In
rutile, neighboring octahedra share one corner along h1 10iÐtype directions, and are stacked with
their long axis alternating by908 (see Fig. 2 as well as Fig. 6). In anatase the corner-sharing octahedra
form (0 0 1) planes. Theyare connected with their edges with the plane of octahedra below. In all three
TiO 2 structures, the stacking of the octahedra results in threefold coordinated oxygen atoms.
Rutile TiO 2 single crystals are widely available. They can be bought in cut and polished form from
companies such as Commercial Crystal Laboratories, USA; Kelpin Kristallhandel, Germany;
Goodfellow, UK; Earth Jewelry, Japan and many others. A very small roughness is achieved by
grinding the sample, and then polishing the surface for manyhours with a chemo-mechanical treatment.
This is also referred to as epitaxial polish. Practical aspects of surface preparation and handling are
discussed in [67].
Ramamoorthyand Vanderbilt [68] calculated the total energyof periodic TiO 2 slabs using a selfconsistent
ab initio method. The (1 1 0) surface has the lowest surface energy, and the (0 0 1) surface
the highest. This is also expected from considerations of surface stability, based on electrostatic and
dangling-bonds arguments discussed in Section 2.2.1.1. below. The thermodynamic stability of the
(1 0 0) surface was also considered, and was found to be stable with respect to forming (1 1 0) facets.
The (0 0 1) surface was almost unstable with respect to the formation of macroscopic (1 1) (0 1 1)
facets. From the calculated energies a three-dimensional (3D) Wulff plot was constructed, see Fig. 3.
The Wulff construction [69] gives the equilibrium crystal shape of a macroscopic crystal. For
comparison with experimental crystal shapes one has to take into account that only four planes were
considered and that the calculations are strictlyvalid onlyat zero temperature.
The experimental results on the three low-index rutile surfaces discussed below ®t rather well with
the stabilityexpected from these calculations. For rutile, the (1 1 0), (0 0 1) and (1 0 0) surfaces have
been studied, with (1 1 0) being the most stable one. These three surfaces are discussed in this section.