Geoscience Reference
In-Depth Information
chemical reactions are either controlled by thermodynamic or kinetics. Present
generation researchers are using such thermodynamic data for a given precursor
system to design the experiments. There are several commercial available softwares
having such a thermodynamic database for a wide range of compounds, which
can be utilized to calculate the thermodynamic properties for a given system.
Thermodynamic processing variables, such as temperature, pH, concentrations of
reactants, and additives, determine not only the processing space for a given mate-
rial, but also influence both reaction and crystallization kinetics. To some extent
even the size and morphology could also be predicted using such a thermodynamic
model, especially based on the concentration and temperature of the hydrothermal
medium.
Thermodynamic modeling has been successfully used for the synthesis of a
wide range of metal oxides, HAp, PZT family of materials, amongst others. Riman
and coworkers
[76,77,107
111]
have done a pioneering work in this area for the
past two decades. It is even popularly called Lencka
Riman model for hydrother-
mal materials processing. A few other groups are also working on the thermody-
namic modeling of hydrothermal reactions and kinetics
[112
115]
. For the benefit
of readers, only a selected systems have been discussed here briefly.
The optimal approach to control the chemical phases under hydrothermal condi-
tions is to calculate the stability and yield conditions by a thermodynamic model.
Commercial softwares are available for both aqueous and nonaqueous systems with
different ranges of applicability in terms of species concentration, pressure, and tem-
perature. Usually, any thermodynamic model requires the following information for
all species in the solution: the standard Gibbs energies
Δ
H
f
of
formation, entropies S
o
at a reference temperature (298.15 K), and the partial molar
volumes V
o
and heat capacities C
p
as functions of temperature. Equilibrium equa-
tions for all the species in the solution are set up. The model considers all the activity
coefficients of aqueous species, for example, the data bank from OLI Systems Inc.
[116]
, and in the absence of thermodynamic values, estimation methods are used to
obtain such values
[77,117]
. The results of the calculation of the model are the equi-
librium concentrations of all species as a function of pH, temperature, and initial
reagent concentrations. The key to representing the standard-state properties over
substantial temperature and pressure ranges is the accurate knowledge of the heat
capacity and volume. For this purpose, the Helgeson
Δ
G
f
and enthalpies
Tanger
(HKFT) equation of state is used
[27,118]
. This equation accurately represents the
standard-state thermodynamic functions for aqueous, ionic, and neutral species as
functions of both temperature and pressure. In the case of solid compounds, solubility
data in pure water as well as in alkaline or acidic solutions at different temperatures
are the best source of data for standard-state properties. These data are available in
ttopics of Seidell and Linke
[119,120]
. Whenever possible, regression of solubility
data are performed using the OLI software
[116]
to obtain accurate and consistent
thermochemical data for solid compounds.
The main objective of these thermodynamic modelings is to calculate the opti-
mum synthesis conditions for the formation of phase-pure materials with con-
trolled size and shape to some extent. This information can be obtained from the
Kirkham
Flowers
