BIBECHANA 18 (1) (2021) 184-192 184 Thermodynamic, structural, surface and transport properties of Au-Ni liquid alloy at 1150 K S. K. Yadav, N. Chaudhary, D. Adhikari* Department of Physics, Mahendra Morang Adarsh Multiple Campus, Tribhuvan University, Biratnagar, Nepal. *Email: adksbdev@yahoo.com Article Information: Received: July 14, 2020 Accepted: November 8, 2020 Keywords: Thermodynamic properties Surface properties Transport properties Au-Ni alloy ABSTRACT Thermodynamic, structural, surface and transport properties of Au-Ni liquid alloy at 1150 K were computed using different theoretical approaches. The thermodynamic properties, such as excess Gibbs free energy of mixing, enthalpy of mixing, activity and excess entropy of mixing and structural properties, such as concentration fluctuation in long wavelength limit and Warren-Cowley short range order parameter were computed in the frame work of Flory’s model. The effect of positive and negative values of the interchange energy parameter on the excess Gibbs free energy of mixing and concentration fluctuation in long wave length limit was also observed. The surface tension and surface concentration of the system were calculated using Butler’s model. In transport property, the viscosity of the system was calculated using Kaptay and Budai-Benko-Kaptay (BBK) models. DOI: https://doi.org/10.3126/bibechana.v18i1.30546 This work is licensed under the Creative Commons CC BY-NC License. https://creativecommons.org/licenses/by-nc/4.0/ 1. Introduction The comprehensive knowledge of the mixing behaviours of binary and multi-component liquid alloys are mandatory in order to develop new materials with desired characteristics. The study and explanation of the hetero-coordinating and homo- coordinating tendencies of the liquid alloys leading to different phase stabilities in the solid states are the most promising research directions in the metallurgical science and engineering. Several researchers [1-16] working in this field have long been attempting to reveal these behaviours by developing different modelling equations or by correlating them. Therefore, an attempt has been made in this work to study and explain the mixing and demixing behaviours of Au-Ni liquid alloy at 1150 K using different theoretical approaches. The thermodynamics of Au-Ni system have been studied by different authors [17–26]. But the complete set of mixing properties of the system is lacking till date. In this regard, the mixing behaviours of Au-Ni liquid alloy at 1150 K have been explained in terms of the thermodynamic, structural, surface and transport properties. The BIBECHANA ISSN 2091-0762 (Print), 2382-5340 (Online) Journal homepage: http://nepjol.info/index.php/BIBECHANA Publisher: Department of Physics, Mahendra Morang A.M. Campus, TU, Biratnagar, Nepal mailto:adksbdev@yahoo.com https://doi.org/10.3126/bibechana.v18i1.30546 https://creativecommons.org/licenses/by-nc/4.0/ http://nepjol.info/index.php/BIBECHANA S.K. Yadav et al. / BIBECHANA 18 (1) (2021) 184-192 185 thermodynamic and structural properties of the system were computed on the basis of Flory’s model [11, 27]. The mixing and demixing behaviours of the binary liquid alloys are generally explained in terms of the thermodynamic and structural properties. The compound forming liquid alloys are characterised by high negative values of excess free energy of mixing (∆𝐺𝑀 𝑥𝑠) and enthalpy of mixing (∆𝐻𝑀). The activities (𝑎) of such systems show negative deviation from the Raoult’s law. Meanwhile, the liquid alloys showing demixing behaviours have positive or very low negative values of ∆𝐺𝑀 𝑥𝑠 and ∆𝐻𝑀, and their activities show positive deviation from the Raoul’ts law [4, 28, 29]. Likewise, the study of structural properties has been developed as an important tool to explain and predict the nature of the local arrangements of liquid alloys. If the computed values of concentration fluctuation in long wavelength limit (𝑆𝐶𝐶(0)) is less than the ideal value (𝑆𝐶𝐶 𝑖𝑑 (0)), i.e., if 𝑆𝐶𝐶(0) < 𝑆𝐶𝐶 𝑖𝑑 (0), then hetero- coordinating or ordering nature of the system is expected and if 𝑆𝐶𝐶(0) > 𝑆𝐶𝐶 𝑖𝑑 (0), then homo- coordinating or segregating nature of the system is expected. Consequently, the value of Warren- Cowley short range order parameter (𝛼1) is found to be non-zero and negative (𝛼1 < 0) for ordering system, 𝛼1 > 0 is found for segregating system and 𝛼1 = 0 represents random mixing. The surface properties and the viscosity of the liquid alloys are the direct consequences of their thermodynamic properties. Hence the surface properties, such as surface tension (𝜎) and the extent of surface segregation (𝑥𝑖 𝑠) of the system were computed using Butler’s model [30-34]. The viscosity (𝜂) of the system was computed on the basis of Kaptay [34, 35] and Budai-Benko-Kaptay (BBK) [36] models. The necessary theoretical formulations of the work are presented in the Section 2, the results and discussion are presented in the Section 3 and the conclusions are outlined in the Section 4. 2. Modeling Equations Thermodynamic properties In thermodynamic properties, excess free energy of mixing (∆𝐺𝑀 𝑥𝑠), activities of monomers Al (𝑎𝐴𝑙) and Ni (𝑎𝑁𝑖), enthalpy of mixing (∆𝐻𝑀) and excess entropy of mixing (∆𝑆𝑀 𝑥𝑠) have been analysed using Flory’s model [11, 22]. This model is fundamentally used to explain the properties of alloys showing like- atoms clusters or self-associates. The preferred liquid alloy, Au-Ni at 1100 K also show the same behaviour. If 𝜇 atoms of 𝐴 (=Al) and 𝑣 atoms of 𝐵 (=Ni) are mixed near to their melting temperatures, then there are preferable associations among the like atoms in the metallic mixture of the types 𝜇𝐴 ⇋ 𝐴𝜇 and 𝑣𝐵 ⇋ 𝐵𝑣, called self-associates. The expression for ∆𝐺𝑀 𝑥𝑠 on the basis of the selected model can be given as ∆𝐺𝑀 𝑥𝑠 = 𝑅𝑇 [ln (1−𝛽)𝑥 (1−𝛽𝑥) + 𝑥(1−𝑥) (1−𝛽𝑥) 𝜔] (1) where 𝑅 is the real gas constant, 𝑇 is the absolute temperature, 𝑥 is the composition of Al and 𝜔 is the interchange energy. The term 𝛽 is the size factor and is given as 𝛽 = (𝜙−1) 𝜙 with 𝜙 = ΩNi ΩAu (2) where Ω is the atomic size of the atom. The free energy of mixing (∆𝐺𝑀) and excess free energy of the mixing (∆𝐺𝑀 𝑥𝑠) are related as ∆𝐺𝑀 = ∆𝐺𝑀 𝑥𝑠 + 𝑅𝑇[𝑥 ln 𝑥 + (1 − 𝑥) ln(1 − 𝑥)] (3) The activity (𝑎𝑖; 𝑖 = 1,2) of the ith component of the binary liquid alloy in terms of ∆𝐺𝑀 is expressed as 𝑅𝑇 ln(𝑎𝑖) = ∆𝐺𝑀 + (1 − 𝑥) ( 𝜕∆𝐺𝑀 𝜕𝑥 ) (4) Using Equations (1) and (3) in Equation (4), the expression for 𝑎𝑖 can be obtained as ln 𝑎𝑖 = ln[(1 − 𝛽)(1 − 𝑥)𝛾(𝑥)] + 𝛽(1 − 𝑥)𝛾(𝑥) + 𝜔 𝑅𝑇 (1 − 𝑥)2[𝛾(𝑥)]2 (5) where 𝛾(𝑥) = 1/(1 − 𝛽𝑥). The standard thermodynamic relation relating enthalpy of mixing, excess entropy of mixing and free energy of mixing are given as ∆𝐻𝑀 = ∆𝐺𝑀 − 𝑇 ( 𝜕∆𝐺𝑀 𝜕𝑇 ) (6) and ∆𝑆𝑀 𝑥𝑠 = − ( 𝜕∆𝐺𝑀 𝑥𝑠 𝜕𝑇 ) (7) S.K. Yadav et al. / BIBECHANA 18 (1) (2021) 184-192 186 Using Equations (1) and (3) in Equation (7), one can yield the respective expressions for ∆𝐻𝑀 and ∆𝑆𝑀 𝑥𝑠 as ∆𝐻𝑀 = 𝑥(1−𝑥)𝜔 (1−𝛽𝑥) − 𝑇 𝑥(1−𝑥) (1−𝛽𝑥) 𝜕𝜔 𝜕𝑇 + 𝑅𝑇2 𝑥(1−𝑥) (1−𝛽𝑥) [ 𝛽 (1−𝛽) − 𝑥 (1−𝛽𝑥) 𝜔 𝑅𝑇 ] 𝜕𝛽 𝜕𝑇 (8) ∆𝑆𝑀 𝑥𝑠 = 𝑅𝑇𝑥(1−𝑥) (1−𝛽𝑥) [ 𝛽 (1−𝛽) − 𝜔𝑥 𝑅𝑇(1−𝛽𝑥) ] 𝜕𝛽 𝜕𝑇 − 𝑥(1 − 𝑥) 1 (1−𝛽𝑥) 𝜕𝜔 𝜕𝑇 − 𝑅[𝑥 ln(1 − 𝛽) − ln(1 − 𝛽𝑥) (9) where 𝜕𝜔 𝜕𝑇 and 𝜕𝛽 𝜕𝑇 are the temperature derivative terms of interchange energy and size factor respectively. Structural properties To analyse the local arrangements of atoms in the metallic mixture, the concentration fluctuation in long wavelength limit (𝑆𝐶𝐶(0)) and Warren-Cowley short range order parameter (WCSROP), 𝛼1, were calculated. 𝑆𝐶𝐶(0) in terms of ∆𝐺𝑀 can be expressed by standard thermodynamic relation as [37, 38] 𝑆𝐶𝐶(0) = 𝑅𝑇 ( 𝜕2𝐺𝑀 𝜕𝑥2 ) −1 (10) Using Equations (1) and (3), the relation for 𝑆𝐶𝐶(0) can be obtained as 𝑆𝐶𝐶(0) = 𝑥(1−𝑥) 1−𝑥(1−𝑥)𝑓(𝛽,𝜔) (11) where 𝑓(𝛽, 𝜔) = [ 2𝜔 𝑅𝑇 (1−𝛽) (1−𝛽𝑥)3 − 𝛽2 (1−𝛽𝑥)2] (12) Putting 𝑓(𝛽, 𝜔) = 0 in Equations (11) and (12), the expression for ideal value of 𝑆𝐶𝐶(0) can be obtained as 𝑆𝐶𝐶 𝑖𝑑 (0) = 𝑥(1 − 𝑥) (13) The experimental value of 𝑆𝐶𝐶(0) can be calculated by the following relation 𝑆𝐶𝐶(0) = (1 − 𝑥) 𝑎𝑖 ( 𝜕𝑎𝑖 𝜕𝑥 ) = 𝑥 𝑎𝑗 ( 𝜕𝑎𝑗 𝜕(1−𝑥) ) (14) Herein, 𝑎𝑖 and 𝑎𝑗 are the experimental values of the activity of ith (𝑎𝐴𝑢) and jth (𝑎𝑁𝑖) respectively. The Warren-Cowley short range order parameter (𝛼1) for binary liquid alloys can be given as [37, 38] 𝛼1 = (𝑆−1) [𝑆(𝑍−1)+1] (15) where 𝑍 is the coordination number and its value is taken to be 10 in present work and 𝑆 = 𝑆𝐶𝐶 𝑖𝑑 (0) 𝑆𝐶𝐶(0) . Surface properties According to the Butler model, the surface tension (𝜎) of the binary liquid alloy in the initial melt can be expressed as [30-32] 𝜎 = 𝜎1 0 + 𝑅𝑇 𝜑1 [ln 𝑥1 𝑆 − ln 𝑥1] + ∆𝐺𝑠,1 𝑥𝑠−∆𝐺1 𝑥𝑠 𝜑1 (16) 𝜎 = 𝜎2 0 + 𝑅𝑇 𝜑2 [ln 𝑥2 𝑆 − ln 𝑥2] + ∆𝐺𝑠,2 𝑥𝑠−∆𝐺2 𝑥𝑠 𝜑2 (17) where 𝜎𝑖 0 (𝑖 = 1, 2) is the surface tension of the pure atom 𝑖, 𝜑𝑖 is the molar surface area of pure atom 𝑖 and 𝑥𝑖 𝑆 and 𝑥𝑖 are the surface and bulk concentrations of atoms 𝑖 in the surface phase and bulk phase of the liquid alloy respectively. ∆𝐺𝑠,𝑖 𝑥𝑠 is the surface partial excess free energy of atom 𝑖 and ∆𝐺𝑖 𝑥𝑠 is the bulk partial excess free energy of atom 𝑖 and they are related as ∆𝐺𝑠,𝑖 𝑥𝑠 = 𝛽∆𝐺𝑖 𝑥𝑠, where 𝛽 is constant and 𝛽 = 0.83 [28, 32, 34, 39] is taken for calculations in the present work. The molar surface area of ith atom is expressed as 𝜑𝑖 = 1.091 (𝑉𝑖 0) 2/3 (𝑁𝐴)1/3 (18) where 𝑉𝑖 0 is the molar volume of ith atom and 𝑁𝐴 = 𝑁 is the Avogadro’s number. The molar volume (𝑉𝑖 0) of ith atom is calculated by taking the ratio of its mass (𝑚𝑖) and density (𝜌𝑖 0) at the required temperature (𝑇𝐾). The temperature dependent expressions of 𝜎𝑖 0 and 𝜌𝑖 0 can be given as [40] 𝜎𝑖 0 = 𝜎0 + (𝑇𝐾 − 𝑇0) 𝑑𝜎 𝑑𝑇 and 𝜌𝑖 0 = 𝜌0 + (𝑇𝐾 − 𝑇0) 𝑑𝜌 𝑑𝑇 (19) Herein, 𝜎0 and 𝜌0 are the surface tension and density of the pure atom at its melting temperature, 𝑇0 is the melting temperature of the pure atom and 𝑑𝜎 𝑑𝑇 and 𝑑𝜌 𝑑𝑇 are the temperature derivative terms of surface tension and density respectively. Transport property In transport property, the viscosity (𝜂) of the system was calculated using Kaptay equation [34,35] and S.K. Yadav et al. / BIBECHANA 18 (1) (2021) 184-192 187 Budai-Benko-Kaptay (BBK) model [36]. According to the Kaptay model, the expression for the viscosity of the binary liquid alloys can be given by 𝜂 = ( ℎ 𝑁𝐴 ∑ 𝑥𝑖𝑉𝑖 0 𝑖 +𝑉𝐸) exp ( ∑ 𝑥𝑖𝐺𝑖 ∗ 𝑖 −(0.155±0.015)𝐻𝑀 𝑅𝑇 ) (20) where ℎ is Planck’s constant and 𝑉𝐸 is the excess volume of alloy formation which can be neglected. The term 𝐺𝑖 ∗ stands for the Gibb’s energy of activation of the viscous flow of ith component and is expressed as 𝐺𝑖 ∗ = 𝑅𝑇 ln ( 𝜂𝑖 0 𝑉𝑖 0 ℎ𝑁𝐴 ) (21) where 𝜂𝑖 0 is the viscosity of the pure component of the metallic mixture and can be given as [40] 𝜂𝑖 0 = 𝜂0 exp( 𝐸 𝑅𝑇 ) (22) where 𝜂0 is the viscosity of the pure atom at its melting temperature and 𝐸 is the activation energy. The ideal value of the viscosity of the liquid mixture can be expressed as 𝜂𝑖𝑑 = ∑ 𝑥𝑖𝑖 𝜂𝑖 0 (23) Following Budai-Benko-Kaptay [36], the expression for the viscosity of binary liquid alloy can be given as 𝜂 = 𝐴. (∑ 𝑥𝑖𝑀𝑖𝑖 )1/2 (∑ 𝑥𝑖𝑉𝑖+𝑉𝐸 𝑖 )2/3 𝑇1/2 exp [ 𝐵 𝑇 (∑ 𝑥𝑖𝑇𝑚,𝑖 ∗ −𝑖 ∆𝐻𝑀 𝑞.𝑅 )] (24) where 𝑞 = 25.4 is the semi-empirical parameter which is related to the cohesion energy of the pure liquid metal and 𝑇𝑚,𝑖 ∗ is defined as effective melting point of the pure component. The values of the coefficients 𝐴 and 𝐵 can be taken as (1.8 ± 0.39) × 108 and (2.34 ± 0.2) respectively 3. Results and Discussion The value of 𝜙 = 1.63 was first calculated using Equation (2) and then the effect of interchange energy (𝜔) on free energy of mixing (∆𝐺𝑀) was observed. For this purpose, the values of ∆𝐺𝑀 were computed using Equations (1-3) for different values of 𝜔, such as ±3𝑅𝑇, ±2𝑅𝑇 and ±1𝑅𝑇. The plot of the isotherms of the compositional dependence of ∆𝐺𝑀 for aforementioned values of 𝜔 at 1150 K is portrayed in Fig. 1(a). It can be observed that the negative values ∆𝐺𝑀 gradually increases with the increase in the negative values of 𝜔 and decreases with increase in the positive values of 𝜔. The value of ∆𝐺𝑀 is found to be positive for 𝑥𝐴𝑢 = 𝑥 < 0.8 for 𝜔 = +3𝑅𝑇. The optimised value of 𝜔 = 15400 and 𝛽 = 0.32886 were then obtained using Equations (1-3) and the experimental value of ∆𝐺𝑀 𝑥𝑠 [29] employing the method of successive approximation. The experimental and the calculated values of ∆𝐺𝑀 𝑥𝑠 were found to be in well agreement (Fig. 1(b)). Both of these values are found to be positive which correspond that the Au-Ni liquid alloy at 1150 K is a homo-coordinating or segregating system. Hence, the system shows demixing tendency with respect to the thermodynamic functions. The like-atoms clusters or self-associates are favourable in the liquid state and the system exhibit liquid miscibility gaps [4]. The activity of the system was computed using Equations (5) and above determined model parameters. The experimental [29] as well as the theoretical values of activities of the monomers Au (𝑎𝐴𝑢) and Ni (𝑎𝑁𝑖) were found to be in well agreement (Fig. 1(c)). Both of these values show positive deviation from Raoult’s law indicating that the preferred system is segregating in nature. Theoretical investigations show that the model parameters have successfully reproduced excess free energy of mixing and activity of the system. The temperature derivative terms of model parameters ( 𝜕𝜔 𝜕𝑇 = −7.2000 and 𝜕𝛽 𝜕𝑇 = −0.00001) were optimised using Equation (8) and the experimental value of the enthalpy of mixing (∆𝐻𝑀) [29]. The enthalpy of mixing (∆𝐻𝑀) and the excess entropy of mixing (∆𝑆𝑀 𝑥𝑠) were then computed using Equations (8) and (9) respectively with the aid of abovementioned model parameters. Both of these values are found to be in good agreement with their respective experimental values (Fig. 1 (b)). Moreover, the positive value of ∆𝐻𝑀 reveals the demixing tendency of the system. S.K. Yadav et al. / BIBECHANA 18 (1) (2021) 184-192 188 (a) (b) (c) Fig. 1(a-c): Plots of the compositional dependence of thermodynamic functions for Au-Ni liquid alloys at 1150 K. (a) Effect of positive and negative values of 𝜔 𝑅𝑇⁄ on ∆𝐺𝑀, (b) ∆𝐺𝑀 𝑥𝑠, ∆𝐻𝑀 and ∆𝑆𝑀 and (c) 𝑎𝐴𝑢 and 𝑎𝑁𝑖. The greater insight of the homo-coordinating and hetero-coordinating nature of the liquid alloys can be obtained by computing and analysing the structural functions. For this purpose, the theoretical, ideal and experimental values of the concentration fluctuation in long wavelength limit (𝑆𝐶𝐶(0)) were computed using Equations (11-14) with the help of abovementioned model parameters and the experimental value of activity [29]. The effect of the positive and the negative values of 𝜔 on 𝑆𝐶𝐶(0) were studied by arbitrarily varying the values of as 𝜔 = ±4𝑅𝑇, ±3𝑅𝑇, ±2𝑅𝑇 and ±1𝑅𝑇. It can be observed that with gradual increase in the negative values of 𝜔, the deviation between the ideal and the theoretical values of 𝑆𝐶𝐶(0) gradually increases (Fig. 2(a)). These results predict that the preferred system would turn into segregating to ordering nature with increase in the negative value of 𝜔. Likewise, the effect of positive values of 𝜔 on 𝑆𝐶𝐶(0) as a function of concentration is presented in Fig. 2(b). It indicates that the computed values of 𝑆𝐶𝐶(0) gradually increases and reaches the peak value at 𝑥 = 0.4 for 𝜔 = +1𝑅𝑇. For 𝜔 = +2𝑅𝑇, 𝑆𝐶𝐶(0) is found to have negative value in the range 0.1 < 𝑥 < 0.53. Likewise, for 𝜔 = +3𝑅𝑇, 𝑆𝐶𝐶(0) is found to be negative in the range 𝑥 < 0.9 and for 𝜔 = +4𝑅𝑇, it is found to be negative in the range 0.1 < 𝑥 < 0.62, 0.69 < 𝑥 < 0.9. As 𝑆𝐶𝐶(0) cannot have negative values, the value of interchange energy should be in between 1 and 2, i.e., +1𝑅𝑇 < 𝜔 < +2𝑅𝑇. The same result (𝜔 = +1.6107𝑅𝑇) was found during the investigation of the thermodynamic properties. The theoretical as well experimental computed values of 𝑆𝐶𝐶(0) are in excellent agreement and are found to be grater than the ideal value at all concentrations (Fig. 2(c)). Therefore, it can be concluded that the liquid Au-Ni at 1150 K shows complete homo-coordinating tendency. The theoretical values of WCSROP (𝛼1) were computed using Equation (15) and plotted in Fig. 2(d). The value of 𝛼1 > 1 at all compositions revealing the similar nature as by 𝑆𝐶𝐶(0). Thus, the theoretical findings of thermodynamic and structural properties are in accordance and suggest the demixing behaviour of the system at selected temperature. S.K. Yadav et al. / BIBECHANA 18 (1) (2021) 184-192 189 The surface tension (𝜎) and the surface concentrations of the monomers Au (𝑥𝐴𝑢 𝑠 ) and Ni (𝑥𝑁𝑖 𝑠 ) were computed using Butler’s model [30]. The surface tensions and densities of the pure components of the system were computed using Equation (19) and the parameters in Table 1. The values of 𝜎, 𝑥𝐴𝑢 𝑠 and 𝑥𝑁𝑖 𝑠 were then computed using Equations (17) and (18). The ideal value of the surface tension (𝜎𝑖𝑑) of the liquid alloy is obtained as the additive sum of the surface tension of the pure atoms in it using the relation 𝜎𝑖𝑑 = ∑ 𝑥𝑖𝑖 𝜎𝑖 0. The surface concentration of Au atom is found to be higher whereas that of Ni is found to be lower than their respective ideal values (Fig. 3(a)). Therefore, Au atoms segregates on the surface phase and Ni atoms remains in the bulk phase in the initial melt. The computed values of the surface tension of the system is found to be less than the ideal value at all compositions (Fig. 3(b)). In transport property, the viscosity (𝜂) of the system was computed using Kaptay model [34,35] and Budai-Benko-Kaptay (BBK) model [36]. The viscosity is directly related to the enthalpy of mixing of the system and is the measure of the cohesion energy of the metallic solution. The viscosity (𝜂) and its necessary ingredients for the system was computed using Equations (20-24) with the help of the input parameters from Table 1. The computed values of the viscosity of the system from both of the preferred models are found to be less than the ideal value at all compositions (Fig. 4). (a) (b) (c) (d) Fig. 2(a-d): Plots of the compositional dependence of structural functions for Au-Ni liquid alloy at 1150 K. (a) Effect of negative values of 𝜔 𝑅𝑇⁄ on 𝑆𝐶𝐶(0), (b) Effect of positive values of 𝜔 𝑅𝑇⁄ on 𝑆𝐶𝐶(0), (c) 𝑆𝐶𝐶(0) and (d) WCSROP. S.K. Yadav et al. / BIBECHANA 18 (1) (2021) 184-192 190 (a) (a) (b) 3(a, b): Plots of the compositional dependence of the surface tension (𝜎) and surface concentrations (𝑥𝐴𝑢 𝑠 and 𝑥𝑁𝑖 𝑠 ) for Au-Ni liquid alloy at 1150 K. (a) Surface tension and (b) Surface concentrations Fig. 4: The compositional dependence of viscosity (𝜂) for Au-Ni liquid alloy at 1150 K. Table 1: Input parameters for surface tension (𝜎) and viscosity (𝜂) [40] Metal 𝑇0 (K) 𝜌0 (kg m−3) 𝜕𝜌 𝜕𝑇⁄ (kg m−3K−1) 𝜎0 (N m−1) 𝜕𝜎 𝜕𝑇⁄ (N m−1K−1) 𝜂0 (Nsm−2) 𝐸 (Jmol−1) Au 1336 17360 -1.50 0.1140 -0.00052 0.001132 15900 Ni 1727 7905 -1.160 0.1778 -0.00038 0.0001663 50200 S.K. Yadav et al. / BIBECHANA 18 (1) (2021) 184-192 191 4. Conclusion The computed values of the excess free energy of mixing and the enthalpy of mixing were found to be positive and the activity showed positive deviation from the Raoult’s law. The value of the concentration fluctuations in long wavelength limit was found to be greater than the ideal value and Warren-Cowley short range order parameter was found to be positive. These results correspond that the liquid Au-Ni alloy at 1150 K showed homo- coordinating behaviours. 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