Liquid Binary Alloys Research Articles

Thermodynamic modeling of liquid binary alloys of the Al–Er system

The paper presents the results of a study of the thermochemical properties of the Al–Er system. The thermodynamic characteristics were evaluated (△fH0298, S0298, (H0298−H00), Cp(T) and Cp(liq)) for the intermetallic compounds Al3Er, Al2Er, AlEr, Al2Er3, AlEr2. The values of△fH0298 calculated based on the semiempirical Miedema model adapted for the group of Al–REM alloys were taken for calculations and amounted to –47.7, –58.4, –63, –55.2, –46.8 kJ/mol∙at, respectively. The mixing characteristics of liquid alloys of this system were evaluated by Terra software package for modeling the equilibrium states of heterogeneous inorganic systems with an extensive database of properties of individual substances. The model of ideal solutions of interaction products was used as a computational model. Modeling of equilibrium composition and properties of melts was carried out in the temperature range of 1900–2100 K, in an argon atmosphere at a total pressure of 0.1 MPa in the system. Comparison of the obtained results with the simulation results in the approximation of an ideal solution, allowed us to determine the excess integral thermodynamic properties of liquid alloys (Gibbs energy, enthalpy, and entropy). It is shown that in the studied temperature range, with an increase of temperature, there is a natural, though not significant, decrease in the values of these parameters by absolute value. It is established that the formation of liquid alloys of the Al–Er system is accompanied by significant heat release: the value of the integral enthalpy of mixing at a temperature T = 2100 K is –58.9 kJ/ mol∙at. When comparing the thermochemical properties of the Al–Er system with the binary systems Al–Y and Al–Sc studied by the same methods, it is shown that all energy curves pass through the extremum at XSc,Y,Er ≈ 0.5. The strongest interaction of the components is observed in the Al–Y system, (ΔHmix = –58.9 kJ/mol∙at), which is close enough to the maximum modulo value of the enthalpy of mixing in the Al–Er system. The weakest interaction is observed in the Al–Sc system (ΔHmix = –44.8 kJ/mol·at). The results obtained in this work provide a theoretical basis for further experimental study of erbium–containing aluminum alloys.

Surface Tension of Cu-Ti Alloys and Wettability in a Liquid Alloy-Refractory Material-Gaseous Phase System.

The study involved measurements of surface tension of liquid binary copper-titanium alloys with respect to their chemical composition and temperature as well as investigations of the liquid alloy-refractory material-gaseous phase system wettability using usual refractory materials, i.e., graphite, aluminum oxide and magnesium oxide. The experiments were performed with the use of the sessile drop method and a high-temperature microscope coupled with a camera and a computer. The aim of this study was to determine the influence of titanium content in the Cu-Ti alloy on the surface tension and contact angle at the interface between the liquid alloy and the refractory material. The influence of temperature on these parameters was also examined. The tests were carried out for copper-titanium alloys with a maximum content of 1.5% wt. Ti, in the temperature range of 1373 to 1573 K. The test results indicate that as the titanium content in the alloy increases, its surface tension increases slightly. However, an increase in temperature causes a decrease in the surface tension of the alloys. In the case of an alloy containing 1.5% wt. Ti, surface tension at a temperature of 1373 K reaches 1351 mN∙m-1, and at a temperature of 1573 K, it decreases to 1315 mN∙m-1. As the temperature and titanium content in the alloy increase, a decrease in the contact angle is observed. The highest values of contact angles were recorded in the case of contact of the liquid alloy with graphite. For an alloy containing 0.1% wt. Ti at a temperature of 1373 K, the contact angle reaches 132°, while at a temperature of 1573 K, it decreases to 128°. For an alloy containing 1.5% wt. Ti, the values of contact angles are 100° and 96°, respectively. However, the contact angles have the lowest values for magnesium oxide. In the case of a temperature of 1573 K and an alloy containing 1.5% wt. Ti, the contact angle reaches 49°. Such a significant impact of titanium content on the contact angles may be due to its high affinity for oxygen (contact with a substrate made of Al2O3 and MgO and its reactivity with carbon (contact with graphite).

Prediction of azeotropic behavior using physicochemical properties for Sn-based binary liquid alloys in vacuum distillation

Crude tin must undergo separation from impurities to enhance its value and expand its applications. The phase diagrams and physical properties in liquid state of Sn-based alloys are the theoretical basis for vacuum impurity removal from crude tin. The formation of azeotrope affects the effect of impurity removal in vacuum distillation. This study focuses on the correlation between the azeotropic region and the parameters of the Wilson equation of 13 Sn-based binary systems under 10 Pa. The results reveal that the Al–Sn, Cu–Sn, and Ti–Sn systems can form azeotropes that are challenging to separate through straightforward vacuum distillation. In contrast, the other Sn-based binary alloys could not form azeotropes at the experimental conditions, thereby facilitating their removal through vacuum distillation. This method provides a reliable support for the separation and purification of crude tin by vacuum distillation.

A Theoretical and Computational Study of Structure‐Property Relationship in Five Binary Liquid Alloys

AbstractA theoretical model is proposed in this work for the evaluation of composition‐dependent thermophysical properties such as the isothermal compressibility, velocity of sound and Debye temperature of liquid binary alloys. Using a square‐well (SW) model potential function under mean spherical model approximation, the composition‐dependent atomic‐level structural functions of Al1‐xCux, Ag1‐xCux, Au1‐xCux, Ag1‐xAlx, and Au1‐xAgx alloys have been determined and compared with available experimental data. An extensive computation was done to calculate the composition‐dependent isothermal compressibility through the structure factor in the long wavelength limit (k→0), and then we employed this data to investigate the velocity of sound in the considered melts. This yields the fundamental maximum frequency with which the constituent particles are vibrating in the melts and is used to determine the composition‐dependent Debye temperature, ΘD. The computed Debye temperature of considered melts using the Square‐well potential function is found to be in satisfactory agreement with the available DFT and MD simulation results.

Thermodynamic activity in Zn–Cu–Sn–In liquid solder alloys: a comprehensive analysis using the molecular interaction volume model

The molecular interaction volume model (MIVM) was employed to estimate the activity of each component in Zinc–Copper–Tin–Indium (Zn–Cu–Sn–In) quaternary liquid alloys at 1023 K, keeping indium content constant, i.e. xIn = 0.1, and varying molar ratios of Cu and Sn (xCu/xSn). Furthermore, the model has been used to determine the activity of each component of all sub-binary systems, namely Cu–Zn at 1200 K, Sn–Zn at 750 K, In–Zn at 700 K, Cu–Sn at 1400 K, Cu–In at 1073 K, In–Sn at 700 K, and Zn–Cu–In liquid ternary alloys at 1023 K for three molar ratios of Cu and In, i.e. xCu/xIn = 1:2, 1:1, and 2:1. We found that the activity deviations of Zn from Raoult’s law transform from positive to negative as the xCu/xIn ratio changes from 1:2 to 2:1. The estimated values were analyzed with the correspondent experimental results in the case of ternary and all the binary liquid alloys. There is a notable agreement observed between theoretical forecasts and practical findings in both binary and ternary systems. This work provides a thorough thermodynamic study of the Zn, Cu, Sn, and In quaternary systems.

Estimation of Activity and Molar Excess Gibbs Energy of Binary Liquid Alloys Pb-Sn, Al-Sn and In-Zn from the Partial Radial Distribution Function Simulated by Ab Initio Molecular Dynamics

For the present, it is difficult to obtain thermodynamic data for binary liquid alloys by experimental measurements. In this study, the molecular dynamics processes of the binary liquid alloys Pb50-Sn50, Al50-Sn50, and In50-Zn50 were simulated by using the ab initio molecular dynamics (AIMD) principle, and their partial radial distribution functions (PRDF) were obtained at different simulation steps. Combined with the relevant binary parameters of the Molecular Interaction Volume Model (MIVM), Regular Solution Model (RSM), Wilson Model, and Non-Random Two-Liquid (NRTL) models. The integral terms containing the PRDF were computed using the graphical integration method to obtain the parameters of these models, thus estimating their activity and molar excess Gibbs energy. The total average relative deviations (ARD) of the activity and molar excess Gibbs energy estimates of the four models for the binary liquid alloys Pb50-Sn50, Al50-Sn50, and In50-Zn50 at full concentration when the PRDF is obtained by the symmetry method are MIVM: 21.59% and 59.35%; RSM: 21.63% and 60.27%; Wilson: 24.27% and 86.7%; NRTL: 23.9% and 83.24%. When the PRDF is obtained by the asymmetric method: MIVM: 22.86% and 68.08%; RSM: 32.84% and 68.66%; Wilson: 25.14% and 82.75%; NRTL: 24.49% and 85.74%. This indicates that the estimation performance of the MIVM model is superior to the other three models, and the symmetric method performs better than the asymmetric method. The present study also derives and verifies the feasibility of Sommer’s equation for estimating the molar excess Gibbs energy and activity of binary liquid alloy systems in the Miedema model by using different equations of enthalpy of mixing versus excess entropy given by Tanaka, Ding, and Sommer. The total ARD of Tanaka, Ding, and Sommer’s relational equations in the Miedema model for estimating the activities and molar excess Gibbs energies of the binary liquid alloys Pb-Sn, Al-Sn, and In-Zn are 3.07% and 8.92%, 6.09% and 17.1%, and 4.1% and 14.77%. The results indicate that the estimation performance of the Miedema model is superior to the other four models.

Calorimetric study of the enthalpy of mixing in the liquid systems Li-Zn and Li-Sn-Zn

Partial and integral molar enthalpies of mixing of binary liquid Li-Zn alloys and ternary liquid Li-Sn-Zn alloys were determined by drop calorimetry at 823 K. The binary system was investigated up to xZn = 0.85 and the integral mixing enthalpy was described with a Redlich-Kister-polynomial. Li-Zn shows an exothermic behavior and a minimum molar mixing enthalpy of about ΔHmix = -11.7 kJ⋅mol−1 at xZn = 0.6. The mixing enthalpy along nine ternary sections of Li-Sn-Zn (A: xLi/xSn ≈ 9:11, B: xLi/xSn ≈ 1:4, C: xSn/xZn ≈ 9:1, D: xSn/xZn ≈ 7:3, E: xSn/xZn ≈ 1:1, F: xLi/xZn ≈ 1:3, G: xLi/xZn ≈ 1:1, H: xLi/xZn ≈ 3:2, I: xLi/xZn ≈ 7:3) was investigated. Solid pieces of Li, Sn, and Zn respectively were dropped to the liquid binary starting alloys in the calorimeter at 823 K. The integral values at the crossing points of the various sections show excellent agreement. The course of the partial and integral enthalpy values along the sections A, D, E, F, G, H, and I indicate multiple-phase regions. The occurrence of such partially liquid and de-mixed liquid regions is discussed and compared with a calculated version of the isothermal section at 823 K which exhibits a large ternary liquid miscibility gap. The experimental ternary data allocated to the fully liquid monophasic regions was numerically fitted based on a Redlich-Kister-Muggianu polynomial for substitutional solutions including ternary interactions. In addition, a comparison with enthalpy values from the extrapolation methods based on binary data according to the Muggianu and Toop model, respectively, is shown. Both models fail to accurately reproduce the experimental values. Iso-enthalpy plots of calculated integral mixing enthalpy for stable and metastable fully homogeneous liquid alloys for the entire ternary system are shown.

Theoretical Investigation of the Thermodynamic Properties of Lead-free Ternary Alloys Sn-Sb-Bi and their Subsystems

The concentration-dependent properties, like the constituents’ activities for the binary liquid alloys like Sb-Sn at 905 K, Bi-Sn at 600 K, and Bi-Sb at 1200 K, and the integral Gibbs free energy of mixing, ΔGXS, of the correspondent alloys were computed using the molecular interaction volume model (MIVM). Further, the model has been used to compute the activities of the component Sn in the ternary Sn-Sb-Bi system at 900K at the three cross-sections, i.e., Sb:Bi = 1:3, 1:1, and 3:1. The theoretical data have been analyzed with the corresponding experimental data accessible in the literature. An acceptable concurrence has been obtained, with some inconsistencies. The activities of the ternary alloys along the three cross-sections, i.e., Sb:Bi = 1:3, 1:1, and 3:1, show that the deviations change from positive to negative with increasing Sb content. The results confirm that MIVM is a good model for estimating the thermodynamic properties of binary and ternary systems.

Estimation of Activity and Molar Excess Gibbs Energy of Binary Liquid Alloys Al-Cu, Al-Ni, and Al-Fe from the Partial Radial Distribution Function Simulated by Ab Initio Molecular Dynamics

To accurately and conveniently obtain the thermodynamic data of binary liquid alloys, a new method is proposed in this study. It combines ab initio molecular dynamics (AIMD) simulation with a thermodynamic model to estimate the activity and molar excess Gibbs energy of binary liquid alloys. Additionally, two methods of grouping the partial radial distribution function (PRDF) of 5000 steps obtained by simulation are proposed for the first time. The PRDF of Al50Cu50, Al50Ni50, and Al50Fe50 is obtained by AIMD simulation. These PRDF are combined with four thermodynamic models to estimate the activity and molar excess Gibbs energy. Furthermore, the estimation results of the four models are compared with those of the Miedema model. The results show that when the first peak of the PRDF is obtained by the symmetric method, the average relative deviation (ARD) of the activity and molar excess Gibbs energy of the four models are, respectively: 28% and 32% for Molecular Interaction Volume Model (MIVM); 162% and 38% for Regular Solution Model (RSM); 508% and 65% for Wilson model; 562% and 67% for Non-Random Two-Liquid (NRTL). When the first peak of PRDF is obtained by non-symmetric method, the average ARD of the activity and molar excess Gibbs energy of the four models are, respectively: 64% and 20% for MIVM; 115% and 26% for RSM; 661% and 70% for Wilson; 727% and 72% for NRTL. In addition, the average ARD of the activity and molar excess Gibbs energy of the Miedema model are 113% and 33%. These data indicate that the estimation performance of the MIVM model is superior to the other four models, and the symmetric method performs better than the non-symmetric method. The grouping treatment of PRDF data effectively improves estimation performance.

Estimation of Two Component Activities of Binary Liquid Alloys by the Pair Potential Energy Containing a Polynomial of the Partial Radial Distribution Function

An investigation of partial radial distribution functions and atomic pair potentials within a system has established that the existing potential functions are rooted in the assumption of a static arrangement of atoms, overlooking their distribution and vibration. In this study, Hill’s proposed radial distribution function polynomials are applied for the pure gaseous state to a binary liquid alloy to derive the pair potential energy. The partial radial distribution functions of 36 binary liquid alloy from literatures were used to obtain the binary model parameters of four thermodynamic models for validation. Results show that the regular solution model (RSM) and molecular interaction volume model (MIVM) outperform other models when the asymmetric method calculates the partial radial distribution function. RSM demonstrates an average SD of 0.078 and an ARD of 32.2%. Similarly, MIVM exhibits an average SD of 0.095 and an average ARD of 32.2%. Wilson model yields an average SD of 0.124 and an average ARD of 226%. Nonrandom two-liquid (NRTL) model exhibits an average SD of 0.225 and an average ARD of 911%. On applying the partial radial distribution function symmetry method, MIVM and RSM outperform the other models, with an average SD of 0.143 and an average ARD of 165.9% for MIVM. RSM yields an average SD of 0.117 and an average ARD of 208.3%. Wilson model exhibits average values of 0.133 and 305.6% for SD and ARD, respectively. NRTL model shows an average SD of 0.200 and an average ARD of 771.8%. Based on this result, the influence of the symmetry degree on the thermodynamic model is explored by examining the symmetry degree as defined by the experimental activity curves of the two components.

Viscosity database for ternary Cu–Cr–X (X=Ni, Si, Zr) alloys based on CALPHAD-type modeling

A viscosity model with composition and temperature dependence for the liquid alloys of the Cu–Cr–X (X = Ni, Si, Zr) systems was developed using the CALPHAD (CALculation of PHAse Diagrams) approach. Based on the critical review of the available experimental data for pure metal viscosity, the viscosities of pure liquid Cu, Cr, Zr, Ni and Si were simulated with the Arrhenius formula. The viscosities of the binary liquid alloys of the Cu–Ni, Cu–Si, Cu–Zr, Cr–Ni, Cr–Si and Ni–Zr systems at different temperatures were evaluated using the CALPHAD-type formalism. The non-linear viscosity behavior resulting from chemical short-range order was described using temperature-dependent binary interaction parameters. The viscosities of the Cu–Cr and Cr–Zr liquid alloys were predicted employing the Hirai equation. The viscosities of the Cu–Cr–Zr, Cu–Cr–Ni and Cu–Cr–Si ternary liquids were directly extrapolated using the Redlish-Kister-Muggianu equation from the parameters of the binary systems. A comprehensive understanding of the temperature-composition-solidification phase-viscosity relationship was established for ternary melts. The satisfactory agreement observed between calculations and experimental data validates the use of CALPHAD-type viscosity modeling, supporting the suitability of the constructed viscosity database for predicting the viscosity of high-performance Cu-based alloys.

Temperature-Dependence of Mixing Properties of Cu-Ti Liquid Alloy

In this study, the temperature-dependence of thermodynamic and surface properties of Cu-Ti binary liquid alloy were studied. In thermodynamic properties, excess Gibbs free energy of mixing, enthalpy of mixing, excess entropy of mixing, and activity of the system were computed at 1873 K. The surface properties were analyzed by computing the surface tension and surface concentration of the system. Thermodynamic properties were computed in the framework of the Redlich-Kister polynomial, and the surface properties were computed using the Butler model. At its melting point, the system exhibited a tendency for the formation of compounds, and as the Cu concentration was increased, the surface tension of the system gradually decreased. The excess Gibbs free energy of mixing, activity and surface tension of the system were also computed at different temperatures, in the range 1873-2173 K. With the increase in temperature of the system, the compound forming tendency of the system gradually decreased.

Estimation of Component Activities and Molar Excess Gibbs Energy of 19 Binary Liquid Alloys from Partial Pair Distribution Functions in Literature

This work proposes a new method for estimating the molar excess Gibbs energy and activity of liquid alloy based on recent research. The local composition theory provides a connection between the structures of liquid alloys and the thermodynamic models. The partial pair distribution function (PPDF) was utilized to calculate the parameters of the MIVM, RSM, Wilson, and NRTL. The statistics of the number of molecular pairs of MIVM and RSM were rewritten, which resulted in new forms of the two models. To enhance the NRTL’s estimation performance, the coordination number was incorporated into it (M-NRTL). The aforementioned model and Quasi-chemical model (QCM) were utilized to estimate the excess Gibbs energy and activity of 19 alloys. The alloys contained multiple sets of PPDFs, which enabled the calculation of multiple sets of model parameters. The work examined the impact of expressing the model parameters as first-order linear functions of the components or as constants on the accuracy of the estimation. The parameters were treated as constants. MIVM, RSM, and M-NRTL provided an average relative deviation (ARD) of activity of less than ±20% for 15, 10, and 9 alloys by estimation. When model parameters were expressed as a function of components, QCM showed the best estimation performance, having nine alloys with an ARD of less than ±20%. The number of alloys with an ARD of less than ±20% corresponding to MIVM, RSM, Wilson, NRTL, and M-NRTL was six, five, three, five, and two, respectively. This new method offers simplicity, numerical calculation stability, and excellent reproducibility.

Self-Diffusion Coefficients of Components in Liquid Binary Alloys of Noble Metals

An accurate determination of transport coefficients in liquids, such as diffusivity, is crucial for studying fundamental chemical processes, for constructing and verifying model theories of liquid, and for the optimization of technological processes. However, a reliable experimental determination of the diffusivity is a difficult and sometimes nearly impossible task. In this regard, the development of model theories that allow calculating characteristics of atomic transport is of special interest. Here, the concentration dependencies of the self-diffusion coefficients of the components in Cu-Ag, Cu-Au, and Ag-Au liquid alloys at T = 1423 K and T = 1573 K are calculated in the framework of the linear trajectory approximation in conjunction with the square-well model and the semi-analytical representation of the mean spherical approximation. We reveal that peculiarities in the behavior of the obtained dependencies are related to the peculiarities of the phase diagrams of the alloys under consideration. Additionally, we verify our calculation method on Al80-Cu20 and Al80-Au20 liquid alloys. The results obtained are in good agreement with available experimental and molecular-dynamic simulation data. In the cases when the experimental information is not available, the presented results can be considered as predictive to estimate the quantities under consideration approximately.

Correlation between structures and atomic transport properties of compound forming liquid Cu-In alloys

The Lebowitz solution of the Percus-Yevick hard-sphere mixture is invoked with the square-well potential function to determine Ashcroft-Langreth type three partial correlation functions in binary Cu-In liquid alloys. These computed partial correlation functions have been employed to generate Bhatia-Thornton fluctuations in the considered melts. Using these structural parameters we investigate the temperature and composition-dependent diffusion coefficients of considered melts. The computed values of concentration-concentration fluctuations, in the long-wavelength limit, and the Warren-Cowley short-range order parameter, show the formation of chemical compounds between unlike atoms in the In-rich region of Cu-In melts. We find a very good agreement between theoretically formulated and computed data of with the corresponding experimental values. Computed results of and suggest that hetero coordination is favorable over homo coordination in the investigated melts. The validity of the Stokes-Einstein relation was observed over a wide range of temperatures and compositions in the investigated melts. Further, a new correlation between two body pair excess entropy and the Stoke-Einstein relation has been formulated for square-well binary liquid alloys. Surface tension and compressibility as a function of In composition have been computed through microscopic structural functions of the alloys. Computed surface tension and ratio of mutual to intrinsic diffusion (D m /D id ) are found comparable to available simulated data. The computed values of shear viscosity are in good agreement with the experimental data. Calculated results suggest that the combination of hard sphere potential with square-well tail under mean spherical model approximation is one of the good method for determining the structures and transport coefficients of compound forming binary liquid alloys.

High Temperature Stability of K-Pb Liquid Alloy

The study explores the thermo-physical properties of complex binary liquid potassium-lead alloy at temperature 848 K as a function of concentration by considering complex using different model equations. The Quasi Chemical approximation and the R-K equation are used to investigate features such as free energy, heat of mixing, chemical activity, and concentration fluctuation in the long wave limit at temperature of 848 K. However, at 900 K and 1000 K, these are exclusively examined using the R-K equation. The temperature dependent exponential interaction parameters proposed by Kaptay are taken into account in the RK equation. The study goes on to look at the alloy's viscosity and surface tension using the Budai-Benko-Kaptay model and the Kaptay's improved derivation of Butler equation. The mixing nature of the system is investigated in depth, with a focus on the interaction energy parameters between the alloy's surrounding atoms. The work investigates the fact that the liquid alloy has a moderately interacting as well as ordering character throughout a whole concentration range, and the computed theoretical thermodynamic facts are in reasonable agreement with the corresponding experimental data at 848 K. At greater temperatures, the alloy's tendency goes from ordering to segregating. The alloy's viscosity and surface tension decrease as the temperature rises.

Accurate interatomic potential for the nucleation in liquid Ti-Al binary alloy developed by deep neural network learning method

For the traditional empirical potentials, the accuracy of chemical bonding in a wide temperature range is regrettable, and thereby they are not an appropriate choice to explore the nucleation process of crystals. As a developed superalloy in aerospace, the liquid structure and nucleation mechanism of Ti-Al alloy desire to be investigated to comprehend the solidification process deeply. This work develops an accurate deep neural network (DNN) potential for Ti-Al binary system by employing a machine-learning method. Then, the local structure and the nucleation process of liquid Ti-48 %Al and Ti-52 %Al (atomic percentage) alloys from the normal to the undercooled state are performed by molecular dynamics simulation with the DNN potential. It is found that the formation of the locally ordered structures depends on the Ti-Al atom pair during the solidification. The Honeycutt-Andersen indices of 1431,1541 and 1551 are dominant, and the liquid structure is mainly characterized by perfect and distorted icosahedral clusters. By Voronoi Polyhedron (VP) analysis, Ti-centered VPs favor the formation of body-centered-cubic (BCC) structure, while Al-centered VPs have the main contribution to the icosahedral structure. Besides, liquid Ti-52 %Al alloy prefers to form face-centered-cube (FCC) nuclei than BCC nuclei in a high undercooling, which is closely related to the ability to capture Ti-Al bonds. The favor of the nucleation of the γ phase causes the nuclei with non-equilibrium composition, comprised of Ti-rich BCC and Al-rich FCC coordinated atoms, respectively. Novelty, the FCC nuclei in liquid Ti-Al alloys are independently generated without the precursor of BCC coordinated atoms. High undercooling can transform the nucleation mechanism from two steps to one step.

A study of thermodynamics of mixing for Al[formula omitted]Zn[formula omitted] liquid binary alloy

Thermodynamics of mixing, namely, the energy of mixing (ΔF), enthalpy of mixing (ΔQ) and entropy of mixing (ΔS) for Al1−xZnx liquid binary alloys are calculated theoretically by using the electronic theory of metals (ETM) along with the perturbative approach and the statistical mechanics at T=1000 K. The electron-ion and ion-ion effective pair interactions, vital for any microscopic study, are described by a local pseudopotential. The results of our calculations for energy of mixing, however, agree very well with the available experimental data. In the case of entropy of mixing and the enthalpy of mixing agreement with experimental data is found to be good. We offer a prescription to lessen the discrepancy between theory and experiment in the case of enthalpy of mixing and entropy of mixing, and this project will be undertaken as our future work.

Thermophysical behavior of mercury-lead liquid alloy

Thermophysical properties of compound forming binary liquid mercury-lead alloy at temperature 600 K have been reported as a function of concentration by considering HgPb2 complex using different modelling equations. The thermodynamic properties such as the Gibbs free energy, enthalpy of mixing, chemical activity of each component, and microscopic properties such as concentration fluctuation in long-wavelength limit and Warren-Cowley short range order parameter of the alloy are studied by quasi-chemical approximation. This research paper places additional emphasis on the interaction energy parameters between the atoms of the alloy. The theoretical and experimental data are compared to determine the model’s validity. Compound formation model, statistical mechanical technique, and improved derivation of the Butler equation have all been used to investigate surface tension. The alloy’s viscosity is investigated using the Kozlov-Ronanov-Petrov equation, the Kaptay equation, and the Budai-Benko-Kaptay model. The study depicts a weak interaction of the alloy, and the theoretical thermodynamic data derived at 600 K are in good agreement with the experimental results. The surface tension is slightly different in the compound formation model than in the statistical mechanical approach and the Butler equation at greater bulk concentrations of lead. The estimated viscosities in each of the three models are substantially identical.

Microscopic Origin of Immiscibility and Segregation in Liquid Metallic Binary Alloys

Microscopic description in the study of immiscibility and segregating properties of liquid metallic binary alloys has gained a renewed scientific and technological interests during the last eight years for the physicists, metallurgists and chemists. Especially, in understanding the basic mechanisms, from the point of interionic interaction, and how and why segregation in some metallic alloys takes place at and under certain thermodynamic state specified by temperature and pressure. An overview of the theoretical and experimental works done by different authors or groups in the area of segregation combining electronic theory of metals, statistical mechanics and the perturbative approach is presented in this review. Main attention in this review is focused on the static effects such as the effects of energy of mixing, enthalpy of mixing, entropy of mixing and understanding the critical behavior of segregation of alloys from the microscopic theoretical approach. Investigation of segregating properties from the dynamic effects such as from the effects of shear viscosity and diffusion coefficient is just becoming available. However, we have restricted this review only on static effects and their variation of impacts on different alloys. Bangladesh Journal of Physics, 27(2), 1-25, December 2020