Theoretical modeling to access the surface phenomenon of liquid ternary alloys
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Institute of Science and Technology, Physics
Abstract
The Redlich-Kister (R-K) polynomial was used to optimise the linear temperature dependent
interaction energy parameters for excess Gibbs free energy of mixing of binary
subsystems of Fe–Si–Ti, Al–Sn–Zn and Al–Cu–Fe ternary liquid alloys using experimental
data for excess entropy of mixing and enthalpy of mixing. The optimised
parameters of binary subsystems were then used in the Chou equation (General Solution
Model) for the excess Gibbs free energy of mixing of ternary liquid alloys to evaluate the
partial excess free energy of mixing of components. These partial excess free energies
of components of ternary liquid alloys were then used in the Butler equation to compute
the surface concentrations of components and surface tensions of these ternary systems
from the corner of each element at cross-sections of 3 : 1, 1 : 1 and 1 : 3. In addition,
the excess surface tension of the binary subsystems at four different temperatures was
used to compute the temperature dependent coefficients of the R-K polynomial for the
binary subsystems of the previously mentioned ternary alloy. These coefficients were
then used in the Kohler, Toop, and Chou equation to obtain the surface tension of the
ternary alloys at different temperatures and concentrations. The obtained values of surface
tension using these geometrical models were then compared with those obtained
using the Butler equation.
It was found that the component with the lowest surface tension leads to the highest
surface concentration and the surface concentration of components increases as their
bulk concentration increases and vice versa. Furthermore, it was observed that the the
interaction between the binary pairings affected the surface concentration of a component
in these ternary alloys. All three binary subsystems of Fe–Si–Ti ternary system were
found to be ordering in nature and the surface concentration of the components was also
affected by the interaction between these binary pairs. The surface concentration of Ti
was found to increase with the decrease of its bulk concentration at the low content of Ti
in the alloys. This unusual behaviour was observed due to the higher interaction energy
between Fe and Si than between Fe and Ti in Fe–Si–Ti ternary liquid alloys.
It was observed that the surface concentration of each component in Al–Sn–Zn ternary
liquid alloy increased with increasing the respective bulk concentration at all crosssections.
In this case, surface concentration was determined by the surface tension of
the individual components, as all the binary sub-systems of this ternary alloys were of
segregating nature.
In case of Al–Cu–Fe liquid ternary alloys, binary sub-systems Al–Cu and Al–Fe are of
ordering in nature while Cu–Fe is strongly segregating. When observed from the Fe
corner, the surface concentration of Cu increased from 0.060 to 0.081 while the bulk
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concentration decreased from 0.225 to 0.088 at the cross-section x
Al
: x
= 3 : 1. This
unusual trend of increasing surface concentration of Cu with the decrease of its bulk
concentration may be due to the ordering tendency of Fe with Al and the segregating
nature of Fe with Cu.
The surface concentration of components changes towards the ideal value (bulk concentration)
at elevated temperatures. The surface concentration of Fe and Ti was found to
increase while that of Si was found to decrease when the temperature of the alloy was
increased from 1873 K to 2173 K. The surface concentration of Fe and Ti were found
less than their respective bulk concentration and mole fraction concentration of Si in the
surface was found to be much higher than the bulk phase. Similar results were noticed
for the variation of surface concentration with temperature in the case of Al–Sn–Zn and
Al–Cu–Fe ternary liquid alloys.
The surface tension of liquid ternary alloys was found to decrease rapidly with the rise in
bulk concentration of the component having the least surface tension in pure state. The
value of temperature coefficient of surface tension was found to vary with composition of
the alloys. The surface tension of all ternary liquid alloys studied in this work decreased
linearly with increase in temperature, regardless of composition.