The surface science of titanium dioxide - Niser

100 U. Diebold / Surface Science Reports 48 (2003) 53±229
Table 4
Comparison of calculated surface formation energies (J/m 2 ) for relaxed, unreconstructed TiO 2 surfaces a
Rutile (1 1 0) Anatase
(1 0 1) (1 0 0) (0 0 1) (1 0 3)f (1 0 3)s (1 1 0)
0.31 0.44 0.53 0.90 0.84 0.93 1.09
a Two different structures for the (1 0 3) surfaces (a `faceted' and a `smooth' one) have been considered. From [216,217].
Interestingly, the average surface energy of an equilibrium-shape anatase crystal is smaller than the one of
rutile [216,217], which might explain the fact that nanoscopic TiO 2 particles are less stable in the rutile
phase.
Experimental investigations on single-crystalline anatase are just starting. Meaningful surface
science investigations necessitate single-crystalline samples. While rutile crystals are readily available,
suf®cientlylarge and pure anatase crystals are more dif®cult to obtain. Because anatase is a metastable
phase, it transforms into rutile at relativelylow temperatures [210], with the transition temperature
dependent on impurities, crystal size, sample history, etc. From the recent progress in synthesizing
single-crystalline anatase samples with high purity [209] as well as the successful growth of epitaxial
thin-®lms on appropriate substrates [218±221] one can expect a rapid increase in the interest in anatase
TiO 2 in the near future.
2.6.1. Anatase (1 0 1)
Two reports on the structure of anatase (1 0 1) surfaces have appeared veryrecently[220,222]. The
(1 0 1) surface on an anatase sample grown bychemical transport [209] showed a (1 1) surface after
mild sputtering and annealing [222]. A mineral sample similar to the one displayed in Fig. 27 was used
in an STM studybyHebenstreit et al. [220]. In order to avoid the contaminations in this natural single
crystal, a 700 AÊ thick, epitaxial ®lm was grown on the surface, as described in [221]. Sputtering and
Fig. 27. (a) The equilibrium shape of a TiO 2 crystal in the anatase phase, according to the Wulff construction and surface
energies calculated in [216] (from Lazzeri et al. [216], # 2001 The American Physical Society). (b) Picture of an anatase
mineral crystal.