Environmental Engineering Reference
In-Depth Information
that they can meet at one of the interfaces, i.e., metal/oxide or oxide/oxygen,
and react with one another. The migration of reacting species through this barrier
layer is only possible if the oxide lattice is defective in nature, i.e., defective in
atomistic scale.
Imperfections or defects in solids may be divided into two groups: (1) point
or lattice defects and (2) line and surface defects. The point defects include vacan-
cies either on anion or cation sublattices or both, interstitials of either kind of
ions, misplaced atoms, as well as foreign cations or anions. The line and surface
defects include dislocations, grain boundaries, the inner and outer surfaces of the
product layer, etc. However, discussion here will be mainly focused on the types
of point imperfections and their concentrations, and the corresponding defect
equilibria, because they can help us to understand the oxidation behavior of the
various metal-oxidant systems.
In order to describe the point defects and to express their formation in terms
of reaction equations, it is absolutely necessary to follow a system of notation.
Several systems of notation exist in the literature of defect chemistry; however,
Kr¨ ger and Vink's method has found more or less universal acceptance. Accord-
ingly, this type of notation has been used in the present discussion.
In a compound MO, the point defects are represented by:
V
O
—anion vacancies
V
M
—cation vacancies
O
i
—anion interstitials
M
i
—cation interstitials
Atoms on normal lattice positions are written as O
O
,M
M
, i.e., oxygen atoms
and metal atoms are at their normal lattice sites. Correspondingly, an unoccupied
or vacant interstitial site is written as V
i
. Real crystals always contain some im-
perfections. When a foreign (F) cation occupies a regular M site, the foreign
atom is represented by F
M
. If it occupies an interstitial site, it is written as F
i
,
and when it occupies an oxygen site, it is written as F
O
.
The creation of a point defect in a perfect crystal increases both the internal
energy (hence enthalpy) and the entropy of the system. The equilibrium concen-
tration of the defects will be reached only when the free energy of the system
is at a minimum. Thermodynamically, point defects will always be present in a
crystal above zero Kelvin. Furthermore, all types of defects will, in principle, be
formed. However, the free energies of formation of the different types of defects
will usually have widely different values; correspondingly, it is found that one
type of defect structure commonly predominates in a particular solid. The relative
concentrations of the different types of defect will be a function of temperature
and other variables such as state and composition of the compound. Thus, defect
equilibria with a large positive enthalpy of formation, for instance, which are not
