Geology Reference
In-Depth Information
c. the notation
½
A
... is variously used for both mole fractions and molar con-
centrations (cf. Kröger
1974
, p 34).
It is to be further noted that in any ionization process in which an electron is
interchanged between a localized state for the defect and the collective population
of delocalized electrons, the chemical potential for the latter is given by the Fermi
level, to be used in determining DG
0
3. Write down the condition for electrical neutrality of the crystal, taking into
account the effective charge of each defect and including electrons added to the
conduction band and electron holes added to the valance band by the reactions
(the effective charge of a defect is the difference in charge of a crystal with the
defect and of the perfect crystal; the cryptic symbols
, prime, and x are com-
monly used for positive, negative, and zero effective charges to avoid confusion
with the usual absolute or formal charge states designated +, -, and 0).
4. Solve the simultaneous equations of (2) and (3) in order to obtain whatever is
being sought in the way of relationships between defect concentrations or
expressions for unknown concentrations in terms of experimentally controlled
quantities such as temperature and the activities of components in the envi-
ronment. In carrying through these calculations, it is often convenient to
introduce approximations for particular ranges of the variables, first by taking
into account the relative magnitudes of the equilibrium constants K, some of
which may be assumed to be negligibly small compared with others even if
absolute values are not known, and second by only considering the most
abundant defect of each charge sign when writing the condition of electro-
neutrality (Brouwer's approximation). The latter approximation often enables
particular ranges to be defined in which the logarithm of a defect concentration
can be expressed as a simple power of the activity or partial pressure of a
component in the environment (for example, the oxygen fugacity).
For an example of such considerations in the case of olivine, see Stocker
(
1978a
,
b
).
1.2.3 Order-Disorder
In some crystal structures, it can happen that certain types of sites in the unit cell
can be occupied nearly equally favorably by two different species of atom. It is
then possible that, from unit cell to unit cell or among sites within a unit cell, these
sites can be occupied by the two species non-randomly, in which case the crystal
structure is said to be ordered. For reasons of entropy, there tends to be a fairly
sharp transition from the ordered to the disordered state as the temperature is
increased, the sharpness of the transition being a result of its ''cooperative'' nature
(Christian
1975
, p. 206 et seq; Massalski
1983
). If the ordering consists simply of a
