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arises from interaction with the implanted metal ions rather than local structural modification due to high-energy implantation.
Recent work has indicated that doping with Ag, Rb, y, and la is likewise ineffective in shifting the absorption spectrum [62],
evidently because the incompatible ionic radii prevent occupation of Ti lattice sites.
Doping TiO 2 with anions likewise increases light absorption and photocatalytic activity, but in this case the dopants occupy
substitutional O sites in the lattice [63]. Thin films deposited by sputtering in a low-pressure N 2 /Ar atmosphere and powders
heat-treated in NH 3 /Ar were more photoreactive than the same materials in the undoped condition [64]. Nanocrystalline pow-
ders doped with N have been prepared by different synthesis routes from a wide variety of precursors [16, 17]. Proposed
methods include hydrolysis of tetra-butyl titanate in an aqueous NH 3 solution [65] and the synthesis of nanopowders with con-
trolled levels of N by sequential reaction of Ticl 4 in toluene with H 2 O and NH 3 followed by final calcination [66]. Visible light
photocatalysis was demonstrated in B-doped and B-/N-codoped nanopowders prepared by a sequential reaction method [67]
and by the sol-gel process [68]. Synthesis of c-doped anatase nanoparticles with visible light photoreactivity has been carried
out by a modified sol-gel technique [69]. The sol-gel process has also been used to produce N-/f-codoped nanopowders [70,
71] (with NH 4 f and NH 4 cl as precursors). N-/c-codoped TiO 2 photocatalysts (with NH 3 vapor as the N precursor and alcohols
as the c precursor) have been prepared by a hydrothermal method [72].
crystal shape is a major determining factor in the photocatalytic behavior of anatase TiO 2 because of the influence of the
highly reactive {001} facets. On the basis of the standard Wulff construction, less than 6% of the total surface area of a typical
anatase crystal is composed of these facets, while more stable {101} surfaces constitute the predominant fraction [73]. Substantial
research efforts are therefore currently dedicated to the methods for controlled growth of TiO 2 nanocrystals containing an ele-
vated percentage of high-energy {001} facets with the aim of increasing their photocatalytic activity. Before discussing methods
of tailoring crystal morphology it is first necessary to consider the underlying thermodynamic principles that govern crystal
shape due to the preferential growth of low-energy facets. It should also be remarked that it has recently been discovered [74]
that, at variance with the generally accepted explanation, clean {001} surfaces are under certain conditions less reactive than
{101} in photooxidation reactions that produce hydroxide radicals and photoreduction reactions that generate hydrogen.
10.5
Particle shaPe calculatioN
A thermodynamic model has been developed that allows calculation of the particle shape and phase stability of faceted TiO 2
nanocrystals [75-77]. On the basis of this model it has been established that there is a size dependence of the shape as a result
of the increasing surface contribution to the total free energy of the crystal with decreasing diameter. The model takes into
account the variation of the free energy with crystal size and shape due to the increasing contribution of surface effects as the
crystal size is decreased.
for a nanoparticle of a specific phase, the total free energy G 0 can be derived from the sum of the bulk and surface
components:
0 =
bulk
surf
(10.6)
GG G
+
The free energy in the formation of a nanocrystal is determined by summing the weighted values of the individual
surfaces:
qf ii
i
γ
(
)
0
0
(10.7)
GGMe
=
fi
+
1
-
ρ
where Δ fi G 0 is the free energy of formation of bulk material, M is the molar mass, e is the volume dilation due to surface tension,
q is the surface to volume ratio, fi i is a weighting factor, γ i is the surface energy of surface i , and ρ is the density. The size
dependence of the free energy arises due to the increase in the surface to volume ratio and the volume dilation with decreasing
crystal size. The shape dependence results from the changes in the surface to volume ratio and the surface free energy term
related to the fraction of a given surface present in the crystal.
The average surface tension σ can be calculated from the weighted sum of the individual values σ i of each surface of the
crystal:
= fi i
σ
σ
(10.8)
i
i
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