Geoscience Reference
In-Depth Information
where
π
a
0
5
π
0
ð
a
i
;
y
i
Þ;
K
a
5
π
0
ð
a
i
;
y
i
Þ;
is the thermodynamic equilibrium constant,
y
i
5
activity coefficient,
a
i
5
initial nonequilibrium activity of the nutrient component in the solution,
a
i
5
equilibrium activity of the nutrient components in the solution.
From
Eq. (4.12)
it is observed that
a
0
Δ
G depends upon the relative values of
π
and K
a
when
a
0
,
π
K
a
;
Δ
G
,
0
ð
4
:
13
Þ
a
0
5
π
K
a
;
Δ
G
0
ð
4
:
14
Þ
5
a
0
.
π
K
a
;
Δ
G
0
ð
4
:
15
Þ
.
For example, in
Eq. (4.13)
the process is irreversible and the reaction takes place
from left to right. In the case of
Eq. (4.14)
, the reaction takes place under equilib-
rium condition and, for example, in
Eq. (4.15)
the process becomes reversible. As a
result,
Δ
the changes in
G in
Eq. (4.12)
, for example, can be represented as
follows:
a
i
Þ
Δ
G
RT ln
ð
a
i
=
5
a
i
is the analogue of the relative supersaturation.
If the activity coefficient y
where a
=
1 or, in the given region, y does not depend upon
the concentration then, for example in
Eq. (4.12)
, the activity coefficient can be
replaced by the mol fraction. Then the ratio a
i
=
a
i
S
i
;
is replaced by S
i
=
where
S
i
5
:
Equilibrium concentration of the supersaturated solution should be achieved.
The ratio S
i
=
undersaturated solubility
S
i
is called the relative supersaturation or degree of supersaturation.
In recent years, there has been good progress on the experimental side. Much
credit goes to the Russian hydrothermal crystal growers. Balitsky and Bublikova
[4a] have studied the physicochemical foundation of malachite synthesis. Similarly,
Kuznetsov [4b] has reviewed the physical chemistry of hydrothermal crystal
growth and the crystallization of some A
2
B
6
crystals. Further, Popolitov [4c] has
reviewed the physical chemistry of the hydrothermal growth of tellurium dioxide
crystals. The reader can get valuable information in the topic Hydrothermal
Growth of Crystals
[5]
. These studies on the said works, along with the pioneering
works by Hegleson, Pitzer, Frank, Seward, Kaufman, etc. set a new trend for ther-
mochemical computation leading to the intelligent engineering of materials through
the generation of stability field diagrams for a variety of systems followed by their
experimental validation.
