Microsoft Word - SHASHIT FINAL (--) S.K. Yadav et al../ BIBECHANA 16 (2019) 106-121 RCOST p. 106 (Online Publication: Dec., 2018) BIBECHANA A Multidisciplinary Journal of Science, Technology and Mathematics ISSN 2091-0762 (Print), 2382-5340 (0nline) Journal homepage: http://nepjol.info/index.php/BIBECHANA Publisher: Research Council of Science and Technology, Biratnagar, Nepal Mixing properties of Ni-Al liquid alloys at different temperatures S. K. Yadav1*, P. Sharma2, R. P. Koirala2, A. Dhungana2, D. Adhikari2 1Department of Physics, Suryanarayan Satyanarayan Morbaita Yadav Multiple Campus, Tribhuvan University, Siraha, Nepal. 2Department of Physics, Mahendra Morang Adarsh Multiple Campus, Tribhuvan University, Biratnagar, Nepal. *E-mail: yadavshashit@yahoo.com Article history: Received 6 September, 2018; Accepted 25 September, 2018 DOI: http://dx.doi.org/10.3126/bibechana.v16i0.21138 This work is licensed under the Creative Commons CC BY-NC License. https://creativecommons.org/licenses/by-nc/4.0/ Abstract The validity of simple statistical model or simple theory of mixing has been first established by explaining the experimental values of the thermodynamic and structural properties of Ni-Al melt at 1873 K. Secondly, the linear temperature dependence of ordering energy parameter has been assumed to extend the model for predicting the mixing behaviours of the melt at different temperatures in correlation with R-K polynomials. The surface tension of the system has been explained and predicted with the help of Renovated Butler model. Theoretical investigations correspond that alloy is found to be strongly interacting or hetero-coordinating at its melting temperature. This tendency, however, gradually decreases at higher temperatures. Being more specific, the system shows ideal behaviours with respect to mixing properties at elevated temperatures. Keywords: Mixing behaviours, Renovated Butler model, hetero-coordinating, surface tension. 1. Introduction Alloying phenomenon has been evolved as a robust tool in the field of material science and engineering in order to develop new materials with predetermined characteristics. As a result, the alloys have numerous uses in household, industrial, medicinal, military and commercial fields. Similarly, Ni-Al being super alloy has high thermal conductivity, high melting temperature, low density, offers good resistance to oxidation and corrosion and accessible costs. Due to which they have profound utilizations in the modern day technological devices [1, 2]. The details of the uses of the alloy can be found from references 1 and 2. Moreover, the thermal processing routes together with the governing parameters, such as pressure, S.K. Yadav et al../ BIBECHANA 16 (2019) 106-121 RCOST p. 107 (Online Publication: Dec., 2018) temperature and micro-granules determine the microstructure of an alloy. The in-depth understanding of the mixing properties of the initial melts of alloy is thus mandatory in this field. This information cannot be exclusively obtained from the experimental measurements only as being expensive, time consuming, tedious and often face difficulties with regard to the reactivity of the walls of the container at high temperatures [3]. Even to perform experimental measurements, most of the governing parameters are computed by theoretical approximations. With due regards, several theoretical models [1, 3-18] so far have been developed to explain and predict the mixing properties of binary liquid alloys at a temperature or different temperatures. We, therefore, intend to study and explain thermodynamic, structural and transport properties of Ni-Al liquid alloy at 1873 K on the basis of simple theory of mixing (STM) in this work. The surface tension and surface segregation of the alloy have been explained using Renovated Butler model (RBM) [3, 14, 19]. The desirable properties and multi-disciplinary uses of Ni-Al alloy, as stated earlier, have drawn considerable attentions of the several researchers [1, 2, 20-27] working in the field of material science. Ansara et al. (1988) compared the different thermodynamic model to compute the different phases of Ni-Al alloy and concluded that the results obtained from sub-lattice model are more close to experimental predictions. Maret et al. (1990) have determined the Bhatia-Thornton and Faber-Ziman structure factors by neutron diffraction method for Al80Ni20 liquid alloy. Their work further corresponds that the chemical short-range order is quite more prominent in Al80Ni20 than in Al80[Mnx(FeCr)1-x]20 phase. Pasturel et al. (1992) have shown that the phase diagram of the alloy computed using ab initio approximations are in agreement with experimental information. After reviewing the available phase equilibrium and thermodynamic data from different literatures for Ni-Al, two thermodynamic models were devised by Huang and Chang (1998) which have fewer and more reasonable model parameters as compared to others. They well explained the phase equilibrium and defect concentration of disordered fcc phase γ(-Ni, Al) are modeled by substitutional solution model and the ordered fcc γ' (-Ni3Al) are modeled with two-sublattice model. Asta et al. (2001) studied the atomic and electronic structure and diffusion coefficients in liquid Ni-Al alloys by ab initio molecular dynamics simulations. Moreover, Adamiec (2007) determined the brittleness temperature range for the examined Ni3Al alloy to be 1340 0C both for the liquidus heating stage and cooling stage. The thermodynamic database for the mixing properties of the considered system at different temperatures throughout the entire concentration range, however, is lacking in the literatures. Even though, Grigorovitch and Krylov (1998) used a new high- temperature calorimeter method to study the enthalpies of mixing of nickel-rich Al-Ni melts at 1823 K only in the concentration range Al< 0.22. They computed the other thermodynamic properties, such as integral enthalpy of mixing and activities of Al and Ni at very few temperatures on the basis of quasi-ideal solution model. Their results are in accordance with the findings of the present work. Recently, Yadav et al. (2016) have explained the thermodynamic and structural properties of Ni-Al liquid alloy at 1873 K using regular associated solution model and quasi-lattice model. Ahmed et al. (20018) presented self-consistent results of molecular dynamics simulations for the temperature and concentration dependence of the self-diffusion and interdiffusion coefficients, thermodynamic factor, Manning factor and the reduced heat of transport of the Ni-Al liquid alloy. But the phase determining mixing properties at different temperatures for the preferred system are unavailable in the literatures. Eventually, we have extended STM by considering the linear temperature dependence of the interaction energy parameter to predict thermodynamic, structural and transport properties of the liquid alloy at S.K. Yadav et al../ BIBECHANA 16 (2019) 106-121 RCOST p. 108 (Online Publication: Dec., 2018) temperatures 1873 K, 1973 K, 2073 K and 2173 K, 1873 K being the melting temperature of the system. Redlich-Kister (R-K) polynomials [28, 29] have been associated with this approximation to determine the modeling parameters at different temperatures. The thermodynamic properties at different temperatures so computed have been correlated with RBM to predict the surface properties of the liquid alloy at above mentioned temperatures. The brief procedures to obtain the theoretical modeling equations are presented in the Section 2, the results and discussion are outlined in the Section 3 and the conclusions of the work are highlighted in the Section 4. 2. Theoretical modeling equations 2.1 Thermodynamic properties Simple statistical model is based upon pairwise interaction and conditional probabilities of occupation of neighbouring sites by the atoms of constituent elements which can be expressed in terms of interchange energy or interaction energy or ordering energy by applying grand partition function for binary alloys [30-32]. According to simple statistical method, the partition function for binary alloy of type A-B consisting of NA and NB atoms type of A and B element under the criteria NA+NB = N, where N=total number of each type atoms, is given by Ξ=∑ q����T� q ���T�exp ����������� ��� � (1) where μi represents the chemical potential of ith component and qiNi represents atomic partition functions for ith components provided i = A or B. KB and T are Boltzmann constant and absolute temperature, E is the configurational energy of alloy. The thermodynamic relation between free energy of mixing (GM) and excess free energy of mixing (G���) can be written as G� = G��� + RT ∑ x� log x�� (2) where x� is the concentration of each component. The excess free energy of mixing is also given as [30-32] !"#$� = % log σ'dx = x� log γ� + x log γ *+ (3) where σ is expressed as σ = �β + 2x� − 1� exp 0 �12���3 /2x� (4a) γ� = [�β − 1 + 2x�� x��1 + β�]⁄ 89 (4b) γ = [�β + 1 − 2x�� x �1 + β�]⁄ 89 (4c) β = 1 + 4x�x [exp�2ω ZK T⁄ � − 1]> '⁄ (4d) At equiatomic concentration (x� = x = 0.5), the expression for G���/RT can be written as !"#$� = ln {2D 'E [1 + exp �−ω zK T�]⁄ �D '⁄ } (5) We have used “ω” notation for ordering energy of alloy and “Z” for co-ordination number. Then following Equation (2), the expression for free energy of mixing can be written as G� = NK T[x�x 1��� + x� ln x� + x ln x ] (6) The standard thermodynamic for heat of mixing (H�) in terms of G� can be expressed as H� = G� − T 0I !I� 3 (7) S.K. Yadav et al../ BIBECHANA 16 (2019) 106-121 RCOST p. 109 (Online Publication: Dec., 2018) Using Equation (5) in Equation (6), we get the expression for the heat of mixing as H� = NK T Jx�x 1��� − >�� x�x I1I�K (8) The activity (a�) of the monomers of the binary liquid alloys in terms G� of is given as [30] NK T ln a� = G� + �1 − x�� 0M !MNO 3�,Q,� (9) For each of the component (A and B) the expressions for activity are ln a� = ln x� + x ' 1��� (10) ln a = ln x + x�' 1��� (11) 2.2 Structural properties The atomic arrangement of constituents of the liquid alloys can be investigated by using the parameters like concentration fluctuation in the long wave length limit (Scc(0)) and Warren-Cowley short range order parameter (α1) [17, 15, 33]. Scc(0) can be related with the two thermodynamic parameters namely, free energy of mixing (G�) and activity (ai) [15] as S**�0� = K T 0M9 !MN9 3�>�,Q,� (12a) = x a� 0MS�MN�3�> = x�a� 0MS�MN�3�> (12b) Using the Equation (5) in Equation (12a) yields S**�0� = x�x J1 + D'T �1 − β�K�> (13) where z represents the coordination number and we have taken it to be 10 for our work. Moreover, the expression for the ideal value of S**�0� can be given as [10, 15] S**�I = x�x (14) Warren-Cowley short range order parameter (α1) in terms of S**�0� can be expressed as [10, 15] α> = ���>�[��D�>��>] (15) where S = S**�0�/x�x = S**�0�/S**�I �0� (16) 2.3 Surface properties Following Kaptay (2015), according to Renovated Butler model, the surface tension (σ) of the binary liquid alloy of the type A-B can be given as [3, 14] σ = σ�+ V�WV� + $�V� ln XN�#N�Y + ∆ #,�"# �∆ �"#V� = σ + V�WV� + $�V� ln XN�#N�Y + ∆ #,�"# �∆ �"#V� (17a) where σ�+ is the surface tension of the pure ith component of the liquid mixture. λ�+ and λ� are the molar surface areas of ith component in the pure liquid and in the liquid solution respectively. ∆G�,��� and ∆G ��� are the surface partial excess free energy and bulk partial free energy of ith component; and x�� and x� surface mole fraction and bulk mole fraction of the same component respectively in the liquid mixture such that x�� + x� = 1. But the molar surface area of component in the pure liquid is equal to the molar surface area of the component in the liquid solution, i.e. λ�+ = λ� [3, 14]. The molar surface area of a pure liquid metal i is expressed as λ� = f ]V�+_'/`�N�a�>/` (17b) S.K. Yadav et al../ BIBECHANA 16 (2019) 106-121 RCOST p. 110 (Online Publication: Dec., 2018) where N�a = 6.022 × 10'`mol> is the Avogadro's number, V�+ is the molar volume of pure metal i at its melting temperature and f is the geometrical constant which is expressed as f = 0` efg 3'/` hi/jek (17c) where fl and fm are the volume and surface packing fractions and their values depend upon the type of crystal structure of the pure components of the liquid alloys. The value of f is taken to be 1.06 for this work [3, 14, 34]. 2.4 Transport properties The transport properties of liquid alloys can be interpreted by using two parameters namely, viscosity (η) and ratio of mutual to intrinsic diffusion coefficients (D�/D�I). According to simple statistical approach, viscosity (η) for liquid alloy can be expressed as [30, 31] η = η�I J1 − x�x 0 '1���3K (18) where η�I is ideal viscosity which is given by η�I = �x�η�+ + x η + �; η�+ stand for the viscosity of pure component in the liquid mixture. The mutual diffusion coefficient (D�� in terms of intrinsic diffusion coefficient (D�I) can be expressed as [35]. D� = D�I I pq SOINO (19a) where the terms carry their meanings as mentioned earlier. Above Equation can also be written as [10, 15, 29] r!rOs=t�uuOs �+��uu�+�v (19b) where D� = x�D + x D�; and D� and D are self-diffusion coefficients of pure component. Further, the expression for D�/D�I can be expressed in term of ordering energy (ω) as D� = D�I J1 − x�x 0 '1���3K (20) 3 Results and Discussion 3.1 Thermodynamic properties The thermodynamic model fit parameter, ω, called ordering energy for Ni-Al liquid alloy at 1875 K is computed using Equations (2-5) in order to explain the observed excess free energy of mixing (G���) [36]. The optimized value of ordering energy so obtained is ω = −7.03 RT. The negative value of ω corresponds that the liquid system is found to be complete ordering in nature at least at its melting temperature, which is 1873 K. The compositional dependence of isotherm plots of the computed and observed G���/RT is portrayed in Figure 1. It can be observed that both of these values are in excellent agreement throughout the entire concentration range (Figure 1). The extremum values of G���/RT (=−2.0602, theoretical and = −2.0584, experimental [36]) at equiatomic concentration (x> = x' = 0.5) which corresponds that the system is strongly interacting and symmetric in nature at near to its melting temperature. The similar results were also obtained by Yadav et al. (2016) [1]. The ordering energy is assumed to be only temperature dependent in simple theory of mixing. The temperature dependent model parameter (dω/dT) is obtained from Equation (8) with the aid of above determined ω and experimental value of H� [36] by successive approximation method. The best fit value S.K. Yadav et al../ BIBECHANA 16 (2019) 106-121 RCOST p. 111 (Online Publication: Dec., 2018) dω/dT is found to be 47.25 for the system at 1873 K. Eventually, the theoretical value of H� is computed from Equation (8) using the determined values of model parameters. Figure 1 displays the isotherm plots of experimental as well as theoretical values of H�/RT as a function of concentration for the system. This figure further corresponds that both of these values are in good agreement. The minimum values of H�/RT (=−3.1780, theoretical and −3.2111, experimental [36]) are found to be at x> = x' = 0.5. The theoretical findings thus communicates that the preferred system is symmetric with respect to H� and there appears strong bonding between the constituent atoms of the complex at 1873 K. Activity (a) is an important thermodynamic property which is directly measured from the experiments. The strength of compound formation tendency can also be interpreted on the basis of activity. Moreover, any observed deviation in the thermodynamic properties of the system can incorporated into the activity. The activities (a�� and a�p) of both the monomers (Ni and Al) of the liquid system are computed using Equations (10 and 11) with the help of above determined model parameter. The isotherm plots of both the theoretical and experimental [36] values of a�� and a�p as a function of concentration are presented in Figure 1. It can be observed that both the computed and observed values of a�� and a�p are in excellent agreement at all concentrations of Ni (x�� = 0.1 − 0.9). The modeling equations and model fit parameter have not only explained G��� and H� but also have reproduced activity successfully. This establishes the validity of the simple theory of mixing. To predict the mixing behaviours of the liquid system at different temperatures, above stated thermodynamic properties of the liquid system have been computed at 1873 K, 1973 K, 2073 K and 2173 K; 1873 K being its melting temperature. As the model parameter ω depends on temperature, their values at different temperatures have been computed assuming dω/dT to be constant and using the following equations [3, 29] d[ω�T�]NO = 0I1I�3 dT (21a) and, ω]Tz_ = ω�T� + 0I1I�3 dT (21b) where Tz (= 1973 K, 2073 K and 2173 K) are the temperatures of interests and T (=1873 K) is the melting temperature of the alloy. The ordering energies determined from Equation (21) at different temperatures are presented in Table 1. It can be observed that the negative values of ω gradually decreases with increase in temperature of the liquid alloy which indicates that the compound forming tendency gradually decreases at elevated temperatures. Table 1: Ordering energies (ω) at different temperatures Temperature (K) ω �Jmol�>� 1873 −109472 1973 −104747 2073 −100022 2173 −95296.9 The compositional dependence of activities of the free monomers Ni (a��) and Al (a�p) of the liquid alloy at different temperatures are then predicted using Equations (10 and 11) with the help of ω (determined from Equation (21)) and are plotted in Figure 2. It can be observed that the activities of the monomers of the liquid alloy increases with increase in its temperature indicating the decrease in the compound. forming tendency at elevated temperatures. The theoretical findings of this work are in accordance with that of others [3, 29, 37-39, 40]. S.K. Yadav et al../ BIBECHANA 16 (2019) 106-121 RCOST p. 112 (Online Publication: Dec., 2018) Fig. 1: Isotherm plots of excess free energy of mixing (G���), heat of mixing (H�) and activities of Ni (a��) and Al (a�p) versus concentration of Ni (x��) for Ni-Al liquid alloy at 1873 K. Fig. 2: The plots of activities of Ni (ln� |}~�) and Al (ln� |���) versus concentration of Ni (x��) at different temperatures for Ni-Al liquid alloy. To predict the excess free energy of mixing at the above mentioned different temperatures, R-K polynomials are fitted. On the fundamentals of R-K polynomials, excess free energy of mixing (G���) as a function of concentration and temperature is expressed as [28, 29, 40, 41] G����x, T� = x� ∑ kp�T��x> − x'�p�p�+ (22) where kp�T� = Ap + BpT + CpTln T + DpT' + - - - and kp has the same temperature dependence as G���. A, B, C and D are the fitting coefficients. The partial excess free energies of each monomers of the liquid system are expressed as G����x, T� = x'' ∑ kp�T�[�1 + 2l�x> − x']�x> − x'�p�>�p�� (23a) G ���x, T� = x>' ∑ kp�T�[x> − x'�1 + 2l�]�x> − x'�p�>�p�� (23b) The optimized coefficients set of G��� for Ni-Al liquid alloy are tabulated in the Table 2. These coefficients are obtained by the method of least square fitting. Table 2: Optimized coefficient set of G��� for Ni-Al liquid alloy l A��10�Jmol�>� B��10gJmol�>K�>� C��10`Jmol�>K�>� D��Jmol�>K�'� 0 -80.3198 59.1000 -77.3906 18.6736 1 -1.92735 1.42178 -1.86200 0.449363 2 136.606 -100.755 131.948 -31.8373 3 59.3994 -43.8099 57.3728 -13.8431 S.K. Yadav et al../ BIBECHANA 16 (2019) 106-121 RCOST p. 113 (Online Publication: Dec., 2018) Fig. 3: The predicted values of G��� versus concentration of Ni (x��) for Ni-Al liquid alloy at different temperatures. Fig. 4: The predicted values of H�/RT versus concentration of Ni (x��) for Ni-Al liquid alloy at different temperatures. The excess free energy of mixing of the liquid alloy at above mentioned temperatures are then computed using Equation (22) with the help of the fitting coefficients in Table 1 and its compositional plots are displayed in Figure 3. It can be observed that the plots of G��� gradually shallows up with the increase in the temperature of the system indicating the decrease in the values of G���. At x> = x' = 0.5, the computed values of G��� are −32.0820, −30.2981, −28.5837 and −26.9302 kJmol-1 respectively at 1873 K, 1973 K, 2073 K and 2173 K. G��� thus gradually decreases at higher temperature and is maximum at 1873 K which is the melting temperature of the system. The compound forming tendency, therefore, decreases at elevated temperatures and the system is found to be most interacting at its melting temperature. These results further strengthen the previous predictions of activity at different temperatures. The heat of mixing (H�/RT) of the system at different temperatures are computed using Equations (7 and 8) with the aid of above determined values of G���. Figure 4 represents the compositional dependence of H�/RT of the liquid alloy at different temperatures. Like G���, the plots of H�/RT too gradually shallow up with the increase in the temperature of the system above 1873 K (Figure 4) which corresponds the decrease in H�/RT. At x> = x' = 0.5, the computed values of H���/RT are −3.17830, −3.01721, −2.87166 and −2.73951 respectively at 1873 K, 1973 K, 2073 K and 2173 K. Theoretical predictions thus indicate that the strength of bonding between the atoms of the complex gradually decreases at elevated temperatures. 3.2 Structural properties To have greater insight of the atomic arrangements in the disordered liquid mixture, we have computed concentration fluctuation in long wavelength limit ]S**�0�_ and Warren-Cowley short range order parameter (Alpha1= α>) in the frame work of STM at 1873 K. The ordering or compound forming S.K. Yadav et al../ BIBECHANA 16 (2019) 106-121 RCOST p. 114 (Online Publication: Dec., 2018) tendency and segregating or demixing tendency of the atoms of liquid mixture can also be interpreted on the basis of S**�0� and α>. At a given concentration and temperature, if S**�0� < S**�I �0� for which α> < 0, then the system shows ordering (hetero-coordinating) tendency and if S**�0� > S**�I �0� for which α> > 0, then it shows segregating (homo-coordinating) tendency. Theoretical and ideal values of S**�0� are computed using Equations (13 and 14) with the help of determined values of model parameters. The experimental values of S**�0� are computed using Equation (12) and observed values of activity [36]. The theoretical values of α1 are computed using Equations (15 and 16) with the help of determined values of essential ingredients. The isotherm plots of S**�0� and α> as a function of concentration are portrayed in Figure 5. It can be observed that both the theoretical and experimental values of are less than ideal values, i.e. S**�0� < S**�I �0� and α> < 0 which correspond that the system is complete ordering in nature at its melting temperature. Moreover, both the theoretical and experimental values of S**�0� are in good agreement which proves the validity of the theoretical modeling equations. It has been already mentioned that we have also computed theoretical values of S**�0� and α> at different temperatures within the constrained curtained of STM. These values are obtained using Equations (13-16) with the help of above determined parameters at different temperatures. The compositional and temperature dependence of S**�0� and α> for the liquid alloy are presented in Figures 6 and 7. The values of S**�0� < S**�I �0� and α> < 0 at all concentrations and temperatures indicating that the ordering tendency still prevail in the liquid system. At x> = x' = 0.5, the deviation between S**�0� and S**�I �0� are found to be 0.209010, 0.204286, 0.199324 and 0.194113 at 1873 K, 1973 K, 2073 K and 2173 K respectively which predicts the decrease in the compound forming tendency of liquid alloys at elevated temperatures. However, this tendency is the maximum at 1873 K, the melting temperature of the alloy. Additionally, computed values of S**�0� gradually gets closure to the ideal values at elevated temperatures. The perusal of Figure 7 communicates that the curves of α> gradually shallows up at elevated temperatures which indicates the decrease in compound forming tendency. Likewise, the values of α> at equiatomic composition are found to be -0.337710, -0.308860, -0.282290 and -0.257790 at 1873 K, 1973 K, 2073 K and 2173 K respectively predicting the similar nature as above. 3.3 Surface properties The surface properties (surface tension (σ) and surface segregation (x��� and x�p� ))give the information about various mechanical properties such as, the catalytic activity of alloy catalysts and wettability. The surface properties of the preferred liquid alloy at 1873 K have been studied in the frame work of Renovated Butler model (RBM) [8, 14, 19, 29, 34]. The theoretical values of σ, x��� and x�p� are computed using Equation (17). The surface partial excess free energy (∆G�,���) required herein is computed using the expression ∆G�,��� = β�∆G ���� (24) where the values of ∆G ��� are taken from Table 2 and the value of β is taken to be 0.8181 [8, 14, 19, 29, 34]. The molar surface areas of the monomers of the liquid alloy (λ�) are computed using Equations (17b and 17c) by substituting f = 1.06 [3, 19]. The surface tensions of the pure components (σ�+) at the melting temperature (T=1873 K) of the liquid alloy are using the values from Table 3 and the following expression [42] S.K. Yadav et al../ BIBECHANA 16 (2019) 106-121 RCOST p. 115 (Online Publication: Dec., 2018) σ�+ = σ+ + �T − T+� I�I� (25) Fig. 5: The isotherm plots of computed values of S**�0� and α> versus concentration of Ni (x��) for Ni-Al liquid alloy at 1873 K. Fig. 6: The computed values of S**�0� versus concentration of Ni (x��) for Ni-Al liquid alloy at different temperatures. where σ+ is the surface tension of the pure component at its melting temperature, T+ is its melting temperature in absolute scale and dσ/dT is the temperature derivative of the surface tension. The molar volumes of the pure components (V�+) are determined from the ratio of their atomic masses to respective densities (m/ρ). The density of each component of the liquid mixture at T=1873 K is computed using the parameters from Table 3 and the expression [42] ρ = ρ+ + �T − T+� I�I� (26) where ρ+ is the density of the pure component at its melting temperature (T+) and dρ/dT is the temperature derivative of the density. Table 3: Input parameters for surface tension (σ) and viscosity (η� [42] Density Surface tension Viscosity Metal T+ ρ+ dρ/dT σ+ dσ/dT η+ E (K) (kg m-3) (kg m-3K-1) (mNm-1) (mNm-1K-1) (mNsm-2) (kJmol-1) Ni 1727 7905 −1.160 1778 −0.38 0.1663 50.2 Al 933 2385 −0.280 914 −0.35 0.1492 16.5 S.K. Yadav et al../ BIBECHANA 16 (2019) 106-121 RCOST p. 116 (Online Publication: Dec., 2018) Fig. 7: The computed values of α> versus concentration of Ni (x��) for Ni-Al liquid alloy at different temperatures Fig. 8: The computed values of σ versus concentration of Ni (x��) for Ni-Al liquid alloy at 1873 K. The isotherm graphical representations of surface tension (σ) and surface concentrations (x��� and x�p� ) as a function of concentration for the system at 1873 K are portrayed in Figures 8 and 9 respectively. The surface tension of the system is found to be less than ideal value throughout the entire concentrations (Figure 8). The perusal of Figure 9 corresponds that the surface concentration of Al is greater than its ideal value and that of Ni is less than that of its ideal value indicating that Al atoms segregate on the surface region whereas Ni atoms remain in the bulk phase of the liquid mixture at 1873 K. Fig. 9: The compositional dependence of isotherm plots of x��� and x�p� for Ni-Al liquid alloy at 1873 K. Fig. 10: The compositional dependence of computed values of σ for Ni-Al liquid alloy at different temperatures. S.K. Yadav et al../ BIBECHANA 16 (2019) 106-121 RCOST p. 117 (Online Publication: Dec., 2018) The theoretical values of σ, x��� and x�p� for the preferred liquid alloys at above mentioned different temperatures are computed using Equations (17, 24-26) with the help of ingredients from Tables 2 and 3. The compositional and temperature dependence of σ, x��� and x�p� are plotted in Figures 10, 11 and 12 respectively. Figure 10 predicts that σ of the system gradually decreases with increase in its temperature which further strengthen the earlier findings of thermodynamic and structural properties. It can be observed that the predicted values of x��� gradually increases (Figure 11) whereas that of x�p� gradually decreases with increase in the temperature of the system. More precisely, Ni atoms gradually move from the bulk phase to the surface whereas Al atoms gradually move from surface phase to the bulk in order to maintain equilibrium. Moreover, the predicted values of x��� and x�p� gradually approaches their ideal values at elevated temperatures; and are accordance with findings of others [3, 29, 37-39, 40]. Fig. 11: The compositional dependence of computed values of x��� for Ni-Al liquid alloy at different temperatures. Fig. 12: The compositional dependence of computed values of x�p� for Ni-Al liquid alloy at different temperatures3.4Transport properties In transport properties, we have computed viscosity (η) and ratio of mutual to intrinsic diffusion coefficients (D�/D�I) for the preferred system at 1873 K and also at above mentioned different temperatures on the floor of STM. Theoretical values of η for the system at 1873 K and different temperatures are computed using Equations (18) with the help of essential parameters from Tables 1 and 3. The plots of η as a function of concentration and temperature are portrayed in Figures 13 and 14. The perusal of Figure 13 indicates that the viscosity of the liquid alloy at its melting temperature (1873 K) is less than its ideal value at all concentrations. It increases rapidly with increase in the concentration of Ni till about x�� = 0.75 and then decreases. The viscosity of the system decreases gradually with increase S.K. Yadav et al../ BIBECHANA 16 (2019) 106-121 RCOST p. 118 (Online Publication: Dec., 2018) in its temperature as one expects. As viscosity depends upon H� of the liquid alloy, similar trends are followed by their plots at elevated temperatures. Fig. 13: The compositional dependence of isotherm plot of viscosity (η) for Ni-Al liquid alloy at 1873 K. Fig. 14: The compositional dependence of predicted values of η for Ni-Al liquid alloy at different temperatures. Theoretical values of D�/D�I at 1873 K and also at higher temperatures are obtained using Equation (20) and the values of parameters from Table 1. The graphical representations of values so computed are displayed in Figures 15 and 16. Fig. 15: The computed values of D�/D�I versus concentration of Ni (x��) for Ni-Al liquid alloy at 1873 K. Fig. 16: The computed values of D�/D�I versus concentration of Ni (x��) for Ni-Al liquid alloy at different temperatures. S.K. Yadav et al../ BIBECHANA 16 (2019) 106-121 RCOST p. 119 (Online Publication: Dec., 2018) The study of D�/D�I helps to understand the compound forming or ordering tendency of the liquid alloy. At given temperature and concentration, if r!rOs > 1, then the liquid alloy shows ordering nature and if r!rOs < 1, then it shows segregating nature. The perusal of Figure 15 notifies that r!rOs > 1 throughout the entire concentrations at the melting temperature of the system indicating that there is strong tendency towards compound formation at this temperature. However, it can be observed that the predicted values of D�/D�I gradually decreases with increase in the temperature of the system which corresponds that the compound forming tendency gradually declines at elevated temperatures. 4. Conclusions The mixing behaviours of the preferred liquid alloy have been successfully explained and predicted at its melting and higher temperatures on the basis of theoretical modeling equations. Theoretical investigations forecast that the system shows strong tendency towards compound formation at least at its melting temperature, however, this tendency gradually declines at higher temperatures. More precisely, the system shows ideal behaviours with regards to mixing properties at elevated temperatures. 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