Browsing by Subject "Liquid alloys"
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Item Ordering and Segregation in Liquid Alloys(Faculty of Physics, 2018) Yadav, Shashit KumarThe design and fabrication of new alloys is usually approached by a method that combines theoretical analysis and experimental observation (composition−structure− property), but in many cases, due to the experimental difficulties related to high temperatures, the theoretically predicted property values are of key importance. This is particularly relevant for all industrial processes, such as casting, joining, crystal growth, etc. that involves the presence of the liquid phase, i.e. liquid metals and alloys. Alloying processes have been evolved as one of robust tool to achieve desired materials with required characteristics. The thermal treatments of materials, chemical compositions and operating parameters (temperature, pressure and working atmosphere) overrule the microstructure of an alloy. The in−depth knowledge of thermodynamics, kinetics and thus, the energetic of the alloy prototypic process has great significance in metallurgical science and engineering. In view of the aforementioned, we have studied and explained the mixing behaviour of two Al−based (Al−Fe at 1873 K and Al−Mg at 1073 K) as well as two Bi−based (Bi−Tl at 750 K and In−Bi at 900 K) liquid binary alloys with the help of theoretical modeling. The thermodynamic properties, such as free energy of mixing (G ), activity (a), enthalpy of mixing (H ) and entropy of mixing (S vii ), structural properties, such as concentration fluctuation in long wave length limit (S (0)), chemical short range order parameter (α ) and ratio of diffusion coefficients (D ) for above mentioned liquid alloys at chosen temperatures have been analyzed in the fame work of regular associated solution model. For this purpose, we have determined the model parameters which are the interaction energy parameters (ω , , ω , and ω /D , ), equilibrium constant (k), mole fractions of complex (x ) and free monomers (x and x ). The compositional contribution from the heat associated with the formation of the complex and the heat of mixing of species to the net enthalpy change has been studied for each system. The comparative studies of the thermodynamic properties of these systems reveal that the Al−Fe being the most interacting system followed by the Bi−Tl, the Al−Mg and the In−Bi, in which the viii ABSTRACT interactions are the weakest. Theoretical investigations of structural properties show that all the preferred liquid alloys show complete ordering nature at least close to their respective melting temperatures. The interaction energy parameters are found to be temperature dependent. The surface properties of the chosen liquid alloys have been explained with the help of Renovated Butler model. The trends of surface segregations in these liquid binary alloys have been studied by computing surface tension (σ) and surface concentrations (x and x ). Theoretical investigations confirm the segregation of the alloy component having a lower surface tension, i.e. the extent of segregation of Bi−atoms at the surface layer, which is more pronounced in In−Bi melts with respect to that of liquid Bi−Tl alloys. Moreover, in case of two Al−based melts, the Al−atoms segregate on the Al−Fe surface phase whereas they remain in the bulk region of Al−Mg. Additionally, the regular associated solution model has been extended to study and predict the thermodynamic and structural properties of concerned liquid alloys at different temperatures. For this purpose, ω , , ω , and ω for each of the system have been computed at different temperatures keeping x , , x , x and k invariant. The modeling equations obtained by the polynomial fitting of different orders along with the values of parameters to forecast these properties have also been included in this work. Theoretical computations indicate that the excess Gibbs free energy of mixing (G ) of the alloys gradually decreases with an increase in temperature above melting temperatures. Accordingly, at higher temperatures, the ordering or the compound formation tendencies of these alloy systems gradually decrease and sometimes show segregating nature. These findings are further supported by decrease in deviations between the computed and observed values of S (0) at higher temperatures. The liquid alloys thus show the maximum tendency towards complex formation at their respective melting temperatures, however, these tendencies significantly decreases at elevated temperatures. Thermodynamic properties have been then correlated with the Renovated Butler model to explain the surface properties at different temperatures. The computed values for the surface concentrations of the segregating components of the liquid alloys approach respective ideal values at higher temperatures. Similarly, the surface tension of metallic melts metals and alloys, decrease at elevated temperatures.Item Theoretical modeling to access the surface phenomenon of liquid ternary alloys(Institute of Science and Technology, Physics, 2023) Mehta, UpendraThe 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 vii 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.Item Thermodynamic artifacts in liquid alloys(Institute of Science and Technology, Physics, 2023) Gohivar, Ramesh KumarThe experimental and literature values of the excess free energy of mixing of Al–Fe, Al–Mn, Al–Ti, and Li–Mg binary and Al–Li–Zn ternary liquid alloys were modeled in terms of self-consistent interaction energy parameters within the framework of RedlichKister (R-K) polynomials. Initially, these parameters were assumed to be linearly dependent on temperature (T-dependent). The linear T-dependent interaction parameters were used to study various thermodynamic properties, such as free energy of mixing, enthalpy of mixing, activity, and concentration fluctuation in long wavelength limit of the aforementioned liquid alloys at various temperatures. At temperatures close to the melting point, it was found that the thermodynamic properties of the liquid alloys agree well with the corresponding experimental values. However, at higher temperatures, thermodynamic properties of the liquid alloys showed unusual phase equilibrium conditions. These conditions were referred to be artifacts or artificial inverted miscibility gaps because they were only observed in theoretical calculations and not in experimental measurements. The linear T-dependent optimised parameters of R-K polynomials were, therefore, considered inadequate at higher temperatures to account for the presence of such artifacts in the thermodynamic properties of liquid alloys. Consequently, it became clear that the interaction energy parameters must be re-optimized in order to produce parameters appropriate throughout a broad range of T-dependence. The interaction parameters for the respective excess free energy of mixing of the aforementioned liquid alloys were then re-optimized within the R-K polynomial framework, considering the exponential T-dependence of the parameters. Again, the optimized exponential T-dependent interaction parameters were utilized to assess the thermodynamic properties of the liquid alloys. As in the prior case, the thermodynamic properties of the alloys were found to agree well with the corresponding experimental values at temperatures close to the melting point. In addition, the thermodynamic properties of the liquid alloys computed at higher temperatures with T-dependent exponential parameters were free of artifacts. This study, thus, shows clearly that the poor modelling of interaction energy parameters is responsible for the appearance of artifacts in the properties of liquid alloys. It was also found that the exponential T-dependent parameters can be used over a wide temperature range for the evaluation of the thermodynamic properties of liquid alloys without producing artifacts. In addition, the ternary Al–Li–Zn liquid alloy showed the critical mixing behaviour at a Li concentration of 0.3 and a temperature of 973 K at the x Al : x = 1 : 1 cross section from the Li corner. This interesting behaviour in the ternary Al–Li–Zn liquid alloy is recommended for further investigation.