Geoscience Reference
In-Depth Information
If the process of dissolution of the solid components continues, then the free
energy dG becomes:
G
dG
5
ð
n
A
2
dn
Þμ
A
1
ð
n
lA
1
dn
Þμ
lA
1
n
B
μ
B
ð
4
:
9
Þ
1
The change in the free energy corresponding to this, under constant P and T,
becomes:
5
ðμ
1A
2
μ
A
Þ
ð
:
Þ
dG
dn
4
10
or
dG
=
dn
5
μ
1A
2
μ
A
ð
4
:
11
Þ
μ
1A
,
μ
A
, then dG/dn is negative and the process occurs on its own, since the
free energy decreases. When
If
μ
1A
.
μ
A
, the crystallization of the substance from
solution B takes place and the chemical potential decreases, and when
μ
1A
5
μ
A
,
the process reaches the equilibrium state. Consequently, the solute component
changes over from the phase wherein its chemical potential is higher into the phase
where its chemical potential is lower. The phase transition stops when the chemical
potential of the component becomes equal in both phases. It is observed that the
above-considered mechanism is realized only when, in the nonequilibrium process,
the changes in dG do not depend upon the chemical potential and concentration of
other components of the solution. However, consideration of the above relationship
may help in understanding the physicochemical principles of the hydrothermal
process.
Most hydrothermal crystal growth experiments are carried out under the condi-
tions of temperature gradient in standard autoclaves. The growth of a single crystal
into the seed can be carried out in two ways:
1. Recrystallization of the solid substance, including its dissolution in the liquid phase, con-
vective mass transfer of the dissolved part of the substance to the growth zone or seed.
2. Dissolution of the mixture of the nutrient components with the help of their convective
mass transport into the growth zone and interaction of the dissolved components on the
seed surface.
The methodology of the growth of single crystals on a seed is the establishment of
growth conditions in which the process is represented by the sum of macro- and
microprocesses occurring between the interface boundary of the solution and the crys-
tal. The composition and concentration of the solution, temperature and pressure,
hydrodynamic conditions, and surface contact of the phases are some of the basic
physical and chemical parameters which determine the regime and rate of dissolution
of the nutrient, mass transport, and the possibility of the formation of new phases.
The isothermal chemical reaction can be expressed in terms of the van't Hoff
equation:
a
0
Δ
G
P
;
T
5
RT ln
π
RT ln K
ai
ð
4
:
12
Þ
