Environmental Engineering Reference
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through detailed thermodynamic treatment of defects that the law of constant
proportion is a special case. In principle, it is an exception rather than the rule.
Thus, it is more correct to speak of ''nonstoichiometry'' in compounds, i.e., all
compounds, referred to as bertholides, exhibit deviation from stoichiometry.
However, the extent of deviation is very small (undetectable) in the so-called
stoichiometric compounds. Therefore, any compound should always be repre-
sented by M 1 δ X (e.g., FeO, NiO, CoO, Cu 2 O, etc.) or MX 2 δ (e.g., UO 2 )or
MX 2 δ or M 2 X 5 δ (e.g., SiO 2 , TiO 2 , ZrO 2 ,Ta 2 O 5 ,Nb 2 O 5 , etc.) or M 1 δ X (e.g.,
ZnO, CdO, BeO, Al 2 O 3 , etc.), where X represents the electronegative component.
At a specific temperature and P x 2 (s), the compound would be stoichiometric. The
deviation from stoichiometry,
δ
, is related to P x 2 (g) and n i , the intrinsic defect
concentration. The variations of
as a function of P x 2 (g)/ P x 2 (s) for two different
compounds having different n i values are presented in Fig. 5.8 [10].
It can be seen that for low intrinsic defect concentrations, it is necessary to
have X 2 (g) pressures different from the pressure above the stoichiometric com-
pound by several orders of magnitude before one can obtain measurable devia-
tions from stoichiometry. In contrast, if n i is high, relatively small changes in
the pressure of X 2 only will cause significant deviation from the stoichiometric
composition. For example, if n i is considered to be 10 4 , increasing the X 2 pres-
sure 10,000 times the pressure that is in equilibrium with the stoichiometric com-
pound will cause a change of 0.01 in
δ
10 3 , the deviation
is 0.015 when P x 2 (g) is only 10 times P x 2 (s). As examples, one can consider the
compounds like KCl, AgBr, TiO, and FeO. At 25
δ
. In contrast, at n i
5
C, n i for KCl is known to be
10 17 . Thus, one would have to change the pressure of chlorine by many orders
of magnitude before any change in stoichiometry could be detected. Even at 973
K, the intrinsic defect concentration is only 4
°
10 5 for which the compound
is considered to be stoichiometric. In the cases of FeO and TiO, the deviation
from stoichiometry is readily detectable. In AgBr, the deviation is small at and
around room temperature ( n i
10 6 at 293 K), but heating the crystal to
573 K would make it susceptible to measurable deviations from stoichiometry
( n i
8
4
10 3 ).
5.4.3 Defect Structure in Stoichiometric Compounds
Kr ¨ger and Vink [11] have provided a list of six basic types of defect structure
(internal atomic disorder, thermal disorder, and intrinsic defects) that are possible
in a stoichiometric compound of type MO. These include:
1. Cation and anion vacancies (V M
V O ),
2. Vacancies and interstitial ions of the same component (V O
O i )or(V M
M i ),
3.
Misplaced atoms (M O
O M , antistructure),
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