BIBECHANA Vol. 22, No. 3, December 2025, 280–290 ISSN 2091-0762 (Print), 2382-5340 (Online) Journal homepage: http://nepjol.info/index.php/BIBECHANA Publisher:Dept. of Phys., Mahendra Morang A. M. Campus (Tribhuvan University)Biratnagar Thermodynamic and surface properties of Al-Cu-Fe-Si-Ti liquid alloy N. Dahal1,2,3, U. Mehta2, R. K. Gohivar2, R. P. Koirala2, S. K. Yadav2* 1Central Department of Physics,Tribhuvan University, Kirtipur 2Department of Physics, Mahendra Morang Adarsh Multiple Campus, Tribhuvan University Biratnagar, Nepal. 3Department of Physics,Sukuna Multiple Campus,Tribhuvan University, Sundarharaincha ∗Corresponding author. Email: sashit.yadav@mmamc.tu.edu.np Abstract The thermodynamic and surface properties of the Al-Cu-Fe-Si-Ti liquid alloy were system- atically investigated using theoretical models. These properties were investigated at different cross-sections from Fe and Ti corners. For the comparative study, the excess Gibbs free en- ergy of mixing for the liquid alloy was determined using the Muggianu, Kohler, and Chou models, based on the thermodynamic database of constituent binary subsystems available in the literature. The activity of the system was calculated using Chou model. The activi- ties of Al, Fe, Si, and Ti showed negative deviations from Raoult’s law, confirming strong complex-forming tendencies, whereas Cu exhibited positive deviations, highlighting its weaker interaction and tendency toward segregation. These deviations diminished with increasing temperature, indicating that elevated thermal energy reduces ordering interactions and pro- motes random mixing. The surface tension of the alloy was calculated using Butler equation with the aid of thermodynamic database. Present investigations revealed that compositions enriched with elements of intrinsically higher surface tension exhibited larger overall sur- face tension values. Surface segregation studies demonstrated that Al possesses the strongest surface affinity, followed by Si, while Ti is the least surface-active element. These findings provide crucial insights into the thermodynamic stability and interfacial behavior of multi- component Al–Cu–Fe–Si–Ti liquid alloys, which are essential for optimizing their processing and applications. Keywords Al-Cu-Fe-Si alloy, Chou model, thermodynamic modeling, R-K polynomial, surface tension. Article information Manuscript received: August 19, 2025; Revised: September 9, 2025; Accepted: September 12, 2025 DOI https://doi.org/10.3126/bibechana.v22i3.83332 This work is licensed under the Creative Commons CC BY-NC License. https://creativecommons. org/licenses/by-nc/4.0/ 280 http://nepjol.info/index.php/BIBECHANA sashit.yadav@mmamc.tu.edu.np https://doi.org/10.3126/bibechana.v22i3.83332 https://creativecommons.org/licenses/by-nc/4.0/ https://creativecommons.org/licenses/by-nc/4.0/ N. Dahal et al./ BIBECHANA 22 (2025) 280-290 281 1 Introduction The development of alloys has been driven by the need to engineer materials with tailored properties for scientific and technological applications. Among these, Al-based multicomponent alloys are widely used in aerospace and automotive industries due to their lightweight, high strength, wear resistance, and cost-effectiveness [1]. Their recyclability prop- erties further make them superior to polymer-based materials. The addition of Fe to Al enhances me- chanical strength [2], while Al-Cu alloys can form quasicrystalline structures, exhibiting low thermal conductivity and high corrosion resistance [3]. In- corporating Si into Al-Cu-Fe alloys promotes qua- sicrystalline phase formation, improving fluidity, reducing porosity, and enhancing strength [4–6] . Similarly, Ti-based alloys are favored in aeronau- tics and aerospace for their high strength-to-weight ratio, low density, excellent corrosion resistance and high melting temperature. However, their poor ox- idation resistance at high temperatures can be mit- igated by surface modification, where Ti concentra- tion is reduced by alloying with oxidation-resistant elements that preferentially segregate to the sur- face [7]. Experimental investigation of alloys in molten states faces significant challenges, includ- ing high reactivity of elements at elevated temper- atures, time-consuming procedures, high costs, and the need for advanced instrumentation [8]. The theoretical modeling complements the experimen- tal study by exploring a vast range of compositions and temperature-dependent structures, saving time and resources. In this regard, different theoretical models such as Collinet [9], Hillert [9, 10], Kohler [9, 11, 12], Muggianu [9, 12, 13], Toop [11, 12, 14] and Chou’s (also known as General Solution Model, GSM) [12,15,16] models are collectively recognized as geometric models, have been developed to ex- plore mixing properties of ternary and higher order liquid alloys. Notably, the Chou model and sym- metric geometric models like Muggianu and Kohler are often considered more appropriate than asym- metric geometric models for analyzing highly in- tricate multi-component alloys [9]. These compu- tational approaches have been widely employed to assess the thermo-physical properties of ternary liq- uid alloys [11–14, 17, 18] and quaternary systems [8, 19–21]. Notably, Arslan and Dogan [9] applied these models to predict the thermodynamic behav- ior of the Fe-Cr-Ni-Mg-O quinary system, while Dogan et al. [13] investigated the Ni-Cr-Co-Al-Mo system. Extending this further, Dogan and Ar- slan [22] analyzed the Ni-Cr-Co-Al-Mo-Ti-Cu sys- tem, leveraging thermodynamic databases of con- stituent binary subsystems to enhance predictive accuracy. Moreover, a comprehensive investigation of the Al-Cu-Fe-Si-Ti liquid alloy remains unex- plored, with no theoretical or experimental data re- ported to date. Therefore, this study is designed to explore the thermodynamic and surface properties of Al-Cu-Fe- Si-Ti liquid alloy using theoretical modeling equa- tions. The common fundamental concept of these models is that the behavior of alloys is the cumula- tive effects of their binary subsystems with a spe- cific weightage assigned to each. 2 Formalism 2.1 Thermodynamics properties Excess Gibbs free energy of mixing ∆Gxs M is a ther- modynamic function that has a strong influence on the mixing behavior of alloys. For binary liq- uid alloys, the respective parameter ∆Gxs ij is ex- pressed in the form of Redlich-Kister (R-K) poly- nomial as [10–12,23] ∆Gxs ij = XiXj ∑ Aν ij(Xi −Xj) ν (1) where Xi and Xi are the concentrations of the com- ponents in the binary alloys. Aν ij are the coefficients of the R-K polynomials. The expression for ∆Gxs M of multi-component liquid alloy is obtained by adding ∆Gxs ij with suit- able probability weight assigned to each [11, 14, 20, 21,24] ∆Gxs M = Σm ij,i ̸=jWij∆Gxs ij (2) where, i, j = 1, 2, 3, ....m depending upon the com- ponents of the alloy. For quinary alloy, m=5 and hence ∆Gxs M can be expressed as ∆Gxs M = W12∆Gxs 12 +W13∆Gxs 13 +W14∆Gxs 14 +W15∆Gxs 15 +W23∆Gxs 23 +W24∆Gxs 24 +W25∆Gxs 25 +W34∆Gxs 34 +W35∆Gxs 35 +W45∆Gxs 45 (3) The term Wij is the probability weight assigned to binary pairs of the multi-component alloy, ex- pressed as Wij = xixj Xi(ij)Xj(ij) (4) where xi and xj are the concentrations of the com- ponents in the quinary system and Xi and Xj are the concentrations of the components in the con- stituent binary subsystem. The selection of later two terms depends upon the preferred theoretical model. For example, Muggianu model [9, 13] Xi(ij) = ( 1 + xi − xj 2 ) , Xj(ij) = ( 1 + xj − xi 2 ) (5) N. Dahal et al./ BIBECHANA 22 (2025) 280-290 282 Kohler model [9, 13] Xi(ij) = xi xi + xj , Xj(ij) = xj xi + xj (6) Chou model [9, 13] Xi(ij) = xi +Σm k=1,k ̸=i,jx kξki(ij) (7) Herein, ξki(ij) are the similarity indices of compo- nent k to component i in ij subsystem, expressed as [14,17,21] ξki(ij) = η(ij, ik) η(ij, ik) + η(ji, jk) (8) The term η(ij,ik) in Equation (8) is the square of deviation, expressed in the form η(ij,ik) = ∫ 1 0 (∆Gxs ij −∆Gxs ik ) 2dXi (9) The activity coefficient γi of ith component in the multi-component liquid alloy is related to partial excess Gibbs free energy (∆Gxs i ) as [12,25] RT ln γi = ∆Gxs i (10a) Once γi is calculated, the activity (ai) of the respec- tive component can be calculated using the relation ai = xiγi (10b) ∆Gxs i is calculated in terms of integral excess Gibbs free energy of mixing (∆Gxs M ) of the quinary system as [9] ∆Gxs i = ∆Gxs M + m∑ j=1 (δij − xj) ∂∆Gxs M ∂xj (11) where δij is the Kronecker delta function. 2.2 Surface properties The surface tension (σ) of a quinary liquid alloy is calculated using the analytical expression of But- ler’s model [11,12,14,23,26,27] σ = σi + RT Ai ln xs i xb i + ∆Gxs i,s −∆Gxs i,b Ai (12) Here, σi(i = 1, 2, 3, 4, 5) is the surface tension of the individual component at temperature of interest T, R is the molar gas constant, and xs i and xb i are the concentrations of the component i in the sur- face phase and the bulk phase respectively. ∆Gxs i,s and ∆Gxs i,b are respectively the partial excess free energy for the surface phase and the bulk phase of the individual component, and are related as ∆Gxs i,s = β∆Gxs i,b [11,20,26,28] . The term β is semi- empirical parameter and its value depends upon the state and type of the atoms of the liquid mixture. Ai is the surface area of the monolayer of one mole of pure element i and it can be calculated using the relation [23,26] Ai = fN 1/3 A (Mi/ρi) 2/3 (13) where f is called geometric factor and its value de- pends upon the type of crystal of the atoms in the mixture and the terms NA, Mi and ρi are the Avo- gadro’s number, molar mass of element i and den- sity of the element i respectively. The value of f is calculated from the relation [17,23,26] f = (3fb/4) 2/3(π1/3/fs) (14) with fb and fs are the volume and surface packing fractions respectively. 3 Results and Discussion 3.1 Thermodynamic properties Table 1: Interaction energy parameters of the bi- nary sub-system of Al-Cu-Fe-Si-Ti liquid alloy System Aν ij [Jmol−1] Reference A0 ij -67094+8.56*T Al-Cu A1 ij 32148-7.12T T [29] A2 ij 5915-5.89 T A0 ij -91976.5+22.13*T Al-Fe A1 ij -5672.58+4.8728*T A2 ij 121.9 A0 ij -11340.1-1.23*T Al-Si A1 ij -3530.93+1.35993*T A2 ij 2265.39 A0 ij -108250+38*T Al-Ti A1 ij -6000+5.00*T [30] A2 ij 15000 A0 ij 36088-2.33*T Cu-Fe A1 ij 324.53-0.0327*T A2 ij 324.53-0.033*T A0 ij -39688.86+14.27*T Cu-Si A1 ij -49937.13+29.79*T A2 ij -31810.6+18.008*T A0 ij -19330+7.651*T Cu-Ti A1 ij 0 [24] A2 ij 9382-5.45*T A0 ij -62273.8+5.70*T Fe-Si A1 ij -5491.468 A2 ij -18821.54+22.07*T A0 ij -164434.6 +41.98*T Fe-Ti A1 ij -21.52*T [30] A2 ij 0 A0 ij -255852.17+21.87*T Si-Ti A1 ij 25025.35-2.00*T A2 ij 83940.65-6.71*T N. Dahal et al./ BIBECHANA 22 (2025) 280-290 283 Figure 1: Excess Gibbs free energy of mixing (∆Gxs ij ) of binary sub-systems of Al-Cu-Fe-Si-Ti liq- uid alloy at 1950 K Experimental as well as theoretical studies of the binary subsystems of Al-Cu-Fe-Si-Ti are available in literature. Hultgren et al. [31] have compiled the experimental data of thermodynamic param- eters of many binary subsystems, which is one of the popularly cited sources in the study of al- loy. The previous studies showed that the binary sub-systems Al-Cu [32–34] , Al-Fe [23, 35–38] , Al- Si [32, 39] and Al-Ti [36, 40, 41] are ordering alloys whereas Cu-Fe sub-system is reported to have seg- regating nature [2,42–44]. Additionally, Cu-Si [45], Cu-Ti [46, 47], Fe-Si [48, 49] and Si-Ti [50–52] have been investigated to have ordering nature. The theoretical approaches applied in this study treat the thermodynamic and surface properties of a multicomponent liquid alloy as the sum of the corre- sponding properties of all binary subsystems, with specific weightages assigned to each. The excess parameters of a binary liquid alloy are expressed in terms of Redlich-Kister (R-K) polynomials. The optimized coefficients of the R-K polynomials for the binary subsystems of the Al-Cu-Fe-Si-Ti liq- uid alloy were obtained from the literature and are presented in Table 1. The excess Gibbs free en- ergy of mixings of the binary sub-systems (∆Gxs ij ) of the quinary liquid alloy were calculated at 1950 K using aforementioned and are plotted in Figure 1. Among the 10 binary sub-systems, Cu-Fe was found to have positive (∆Gxs ij ) with peak value of 7.880 kJmol−1 at Cu50Fe50. The rest of all were found to have negative (∆Gxs ij ) with the peak values of −13.00 kJmol−1 at Al40Cu60, −12.20 kJmol−1 at Al50Fe50, −2.230 kJmol−1 at Al50Si50, −8.540 kJmol−1 at Al50Ti50, −3.200 kJmol−1 at Cu40Si60, −1.100 kJmol−1 at Cu50Ti50, −20.60 kJmol−1 at Fe50Si50, −12.80 kJmol−1 at Fe50Ti50 and −53.30 kJmol−1 at Si50Ti50, Figure 1. These results in- dicate that the Cu-Fe subsystem is segregating in nature, whereas the others exhibit ordering behav- ior, with Si-Ti being the most ordering, followed by Cu-Ti, Fe-Si, Al-Cu, Al-Si, Al-Ti, Al-Fe, and Cu-Si. (a) (b) Figure 2: ∆Gxs M of Al-Cu-Fe-Si-Ti liquid alloy at 1950 K from (a) Fe corner at cross-section xAl : xCu : xSi : xTi = 4:1:2:3 (b) Ti corner at cross- section xAl : xCu : xSi : xTi = 1:2:3:4. As Cu-Fe is the only segregating subsystem and Si- Ti is the strongest ordering subsystem among all binaries, this work focuses on exploring the excess Gibbs free energy of mixing (∆Gxs M ) and the activ- ities of the components in the Al-Cu-Fe-Si-Ti liq- uid alloy from the Fe and Ti corners. In this re- gard, ∆Gxs M of system was calculated at 1950 K at cross-section xAl : xCu : xSi : xTi = 4:1:2:3 from Fe corner and at xAl : xCu : xFe : xSi = 1:2:3:4 from Ti corner in the framework of Chou, Muggianu and Kohler models for comparison process. For the purpose, Equations (2-9) along with the required parameters from Table 1 have been utilized. The calculated values of ∆Gxs M from the preferred mod- els are consistent with each other (Figure 2(a,b)) thereby validating the present computational ap- N. Dahal et al./ BIBECHANA 22 (2025) 280-290 284 proaches. (a) (b) Figure 3: Compositional variations of ∆Gxs M for Al-Cu-Fe-Si-Ti liquid alloy at 1950 K from (a) Fe corner (b) Ti corner at 1:2:3:4,4:1:2:3,3:4:1:2,2:3:4:1 and 1:1:1:1 fixed compositions of other atoms. Additionally, the values of ∆Gxs M were calcu- lated from the Fe and Ti corners at fixed com- positions of the remaining atoms in the ratios 1:2:3:4, 4:1:2:3, 3:4:1:2, 2:3:4:1 and 1:1:1:1 using the Chou model (Figure 3 (a,b)).The optimum val- ues of ∆Gxs M from the Fe corner were found to be −27.720, −20.340, −13.260, −15.460, and −19.580 kJmol−1 for the above-mentioned cross-sections xAl : xCu : xSi : xTi =1:2:3:4,4:1:2:3,3:4:1:2,2:3:4:1 and 1:1:1:1 respectively, Figure 3(a). These results suggest that, at a particular Fe concentration, the strength of interaction between the components in- creases with an increase in the concentrations of Si and Ti, whereas it decreases with an increase in Cu concentration. This is because higher Si and Ti concentrations promote the formation of the most energetic and ordering complexes of Si– Ti, Fe–Si, and Fe–Ti. Conversely, increasing the Cu concentration reduces the number of ordering pairs, which lowers the magnitude of the negative ∆Gxs M value. The present investigation also reveals that the strength of quinary interaction in the alloy is dominated by binary pairs interactions of Si–Ti in the cross-sections xAl : xCu : xSi : xTi=1:2:3:4, 4:1:2:3 and 1:1:1:1, Fe-Si and Fe-Ti interactions in 3:4:1:2 and 2:3:4:1. The maximum negative values of ∆Gxs M calcu- lated from the Ti corner are −29.280, −25.010, −17.900, −14.500, and −21.950 kJmol−1 for the cross-sections xAl : xCu : xFe : xSi = 1:2:3:4, 4:1:2:3, 3:4:1:2, 2:3:4:1 and 1:1:1:1 respectively, Fig- ure 3(b). These results indicate that increment in the concentrations of Fe and Si have greater influ- ence on increasing ∆Gxs M of the system from the Ti corner. The maximum ∆Gxs M values in the quinary compositions are lower than the maximum ∆Gxs ij value of the Si-Ti binary system at the composi- tion Si50Ti50. This suggests that the robustness of the quinary interaction is surpassed by that of the Si–Ti binary interaction. Further, the strength of the quinary interaction is dominated by Si–Ti in- teractions in the cross-sections 1:2:3:4, 4:1:2:3, and 1:1:1:1; by Cu–Ti, Fe—Si, and Si—Ti interactions in 3:4:1:2; and by Cu—Ti and Fe—Ti interactions in 2:3:4:1. 3.2 Activity The activities of the components of the Al–Cu–Fe– Si–Ti liquid alloy were calculated at 1950 K and higher temperatures in the aforementioned cross- sections using Equations (10) and (11) within the framework of the Chou model. The activities of the components calculated from the Fe corner at the cross-section xAl : xCu : xSi : xTi = 3:4:1:2 are illustrated in Figure 4(a). It can be observed that the activity of Fe (aFe) exhibits a small negative deviation from ideal be- havior, indicating its tendency to form complexes with other components. At xFe = 0.1, the activi- ties are aAl = 0.10, aCu = 0.31, aSi = 0.008 and aTi = 0.043. As the Fe concentration increases (i.e., the concentrations of the other components decrease), the activities of Al, Si, and Ti decrease steadily, whereas the activity of Cu initially in- creases despite its decreasing concentration, Figure 4(a). After reaching a maximum of 0.46, aCu de- creases with further increases in Fe concentration. This behavior can be explained by the segregating nature of the Cu-Fe system and the ordering ten- dency of the other binary subsystems. Increasing the Fe concentration favors the formation of com- plexes between Fe and the other elements, except Cu. Consequently, Cu shows a stronger tendency to leave the solution, which initially raises its ac- N. Dahal et al./ BIBECHANA 22 (2025) 280-290 285 tivity. However, at higher Fe concentrations, the very low concentrations of all other components are available in the liquid mixture, including Cu which leads to a reduction in the activities of Al, Cu, Si and Ti. Moreover, aFe increases gradually with increase in its concentration as expected. (a) (b) Figure 4: Activity of components of Al-Cu-Fe-Si-Ti liquid alloy at 1950 K (a) Fe corner at cross-section xAl : xCu : xSi : xTi = 3:4:1:2 (b) Ti corner at cross-section xAl : xCu : xFe : xSi = 1:2:3:4. The activity of Ti (aTi), calculated from the Ti cor- ner, shows a negative deviation from ideal behav- ior (Figure 4b), indicating its strong tendency to form complexes throughout the entire concentra- tion range. At xTi = 0.1, the activities of the other components are found to be aAl = 0.05, aCu = 0.46, aFe = 0.09 and aSi = 0.08. With increasing Ti con- centration or decreasing concentrations of Al, Cu, and Fe, the activities of Al, Cu, and Fe increased, reaching maximum values of aAl = 0.064, aCu = 0.599 and aFe = 0.110, before decreasing again with further reductions in their respective concen- trations. This trend arises from the strong complex- forming tendency of Si and Ti, as evidenced by their large negative ∆Gxs M , which dominates over the weaker ordering tendencies of the other binary subsystems. At equiatomic composition, the activ- ities follow the order aCu>aAl>aFe>aTi>aSi. Figure 5: Variation of activity of com- ponents with temperature at composition Al20Cu20Fe20Si20Ti20. The variation of the component activities with temperature at equiatomic composition (Al20Cu20Fe20Si20Ti20) was also studied in the present work. The activities of Al, Fe, Si, and Ti increase with rising temperature whereas that of Cu decreases (Figure 5). Al, Fe, Si, and Ti exhibit negative deviations from ideality, indicating their complex-forming nature in this alloy. However, this tendency diminishes at elevated temperatures, lead- ing to an increase in their activities. In contrast, Cu shows a positive deviation from Raoult’s law, reflecting its segregating behavior. Consequently, the activity of Cu decreases as temperature rises. 3.3 Surface properties The surface tension (σ) of the liquid alloy was cal- culated at 1950 K and higher temperatures using the Butler equation. For this purpose, the surface tensions, densities, their temperature variations, and melting temperatures of the individual alloy components, listed in Table 2, were taken from the literature [53]. By employing these parameters along with the determined values of partial excess Gibbs free energy of mixing (∆Gxs i ) of the indi- vidual components in Equations (11) and (12), the surface tension of the quinary system was evalu- ated from both Fe and Ti corners by varying the concentration of the corner element from 0.1 to 0.9. These values were calculated at aforementioned cross-sections as a function of concentration and are displayed in Figure 6(a,b). N. Dahal et al./ BIBECHANA 22 (2025) 280-290 286 Table 2: Input physical parameters for surface tension at melting temperature (T0) [53] Parameter Element Al Cu Fe Si Ti Tm [K] 933 1360 1809 1683 1958 ρ0 [kg m−3] 2385 8000 7030 2524 4110 ∂ρ ∂T [kg m−3 K−1] -0.28 -0.801 -0.833 -0.3487 -0.226 σ0 [N m−1] 0.914 1.285 1.872 0.865 1.65 ∂σ ∂T [N m−1 K−1] -0.00035 -0.00013 -0.00049 -0.00013 -0.00026 (a) (b) Figure 6: Surface tension of the Al-Cu-Fe-Si-Ti liq- uid alloy at 1950 K calculated from (a) Fe corner and (b) Ti corner. In the Fe corner, calculations were performed for the cross-sections xAl : xCu : xSi : xTi = 1:2:3:4, 4:1:2:3,3:4:1:2, 2:3:4:1 and 1:1:1:1, as illustrated in Figure 6(a). At xFe = 0.1, the computed σ val- ues are 1.12, 0.84, 0.95, 0.92, and 0.94 Nm−1 for the respective cross-sections. With increasing bulk concentration of Fe, the surface tension of the liq- uid alloy gradually increases in each cross-section. Among the alloy components, Ti exhibits the high- est surface tension (σTi = 1.6487 Nm−1) and Al the lowest (σAl = 0.558 Nm−1) at 1950 K, Table 2. Therefore, at a given Fe concentration, the alloy’s surface tension is maximized in the cross-section with the largest proportion of Ti and minimized in the cross-section with the largest proportion of Al. This demonstrates that the surface tension of the quinary liquid alloy increases with increasing Ti concentration and decreases with increasing Al concentration. The surface tension of the liquid alloy was also cal- culated from the Ti corner for the cross-sections xAl : xCu : xFe : xSi = 1:2:3:4, 4:1:2:3, 3:4:1:2, 2:3:4:1 and 1:1:1:1, shown in Figure 6(b). At xTi = 0.1, the computed values of σ are 1.043, 0.81, 0.90, 1.07, and 0.94 Nm−1 for the respective cross- sections. The maximum surface tension, observed at the cross-section xAl : xCu : xFe : xSi = 2:3:4:1, is attributed to the higher proportions of Cu and Fe, both of which have relatively large surface tensions, Table 2. Conversely, the minimum surface tension is observed at the cross-section xAl : xCu : xFe : xSi = 4:1:2:3, resulting from the lower proportions of Cu and Fe and the higher proportions of Al and Si, which have comparatively lower surface tensions. These findings demonstrate that the surface tension of the liquid alloy increases in compositions where elements with inherently higher surface tensions are present in greater proportions. Figure 7: Variation of surface tension of Al–Cu–Fe– Si–Ti liquid alloy with temperature. N. Dahal et al./ BIBECHANA 22 (2025) 280-290 287 Variation of surface tension of the quinary alloy with temperature was studied at different compo- sitions, out of which variation at five different as- sembly of atoms of the liquid alloy is demonstrated in Figure 7. Surface tension of the liquid alloy is observed to decrease at elevated temperature, implying the decrease in the atomic interactions among the constitute atoms of the liquid mixture. This result further justifies the the mixing tendency predicted by the previously determined thermody- namic functions of the system at elevated tempera- tures. (a) (b) Figure 8: Surface concentrations of components of Al-Cu-Fe-Si-Ti of liquid alloy calculated from (a) Fe corner at cross-section xAl : xCu : xSi : xTi = 3:4:1:2 (b) Ti corner at cross-section xAl : xCu : xFe : xSi = 1:2:3:4. The surface concentrations of the components (xs i , i = Al,Cu, Fe, Si, T i) of the quinary system were computed as a function of Fe and Ti concen- trations in different cross-sections. As shown in Fig- ure 8(a), at the cross-section xAl : xCu : xSi : xTi = 3:4:1:2, the surface concentrations of atoms at 1950 K are found to be xs Al = 0.66359, xs Cu = 0.20645, xs Fe = 0.0.034397, xs Si = 0.07484 and xs T i = 0.020699, while the corresponding bulk concen- trations are xAl = 0.24, xCu = 0.32, xFe = 0.20, xSi = 0.08 and xTi = 0.16. These results indicate a strong tendency of Al atoms to segregate at the surface, while the other atoms preferentially remain in the bulk phase. The surface concentration of Fe increases gradually at first and then rises sharply with increasing bulk Fe concentration. In contrast, the surface concentration of Al decreases markedly, whereas Si and Ti concentrations decrease gradu- ally. Interestingly, the surface concentration of Cu initially increases despite a decrease in its bulk con- centration, but after reaching a maximum value, it decreases again. This unusual behavior of Cu can be attributed to the strong ordering tendency of the other elements with Fe, which reduces the like- lihood of Cu forming bonds with them. As a result, Cu atoms preferentially migrate toward the surface phase. A similar variation in the surface concentra- tion of Al atoms has been reported in the Ti-Al-Si ternary liquid alloy by Yadav et al. [28]. In the Ti corner at the cross-section xAl : xCu : xFe : xSi = 1:2:3:4, the surface concentrations are found to be xs Al = 0.351316, xs Cu = 0.159499, xs Fe = 0.04691, xs Si = 0.419739 and xs T i = 0.022489, cor- responding to bulk concentrations of xAl = 0.08, xCu = 0.16, xFe = 0.24, xSi = 0.32 and xTi = 0.20 (Figure 8(b)). In this region, Al and Si exhibit a strong tendency to segregate into the surface phase, while Cu, Fe, and Ti preferentially remain in the bulk phase. Moreover, the surface concentration of Ti increases gradually at first and then rises sharply with increasing bulk Ti concentration. Conversely, xs Si decreases as bulk concentration of Ti increases. The concentrations of Al, Cu, and Fe at the surface initially rise with decreasing bulk concentration, reaching a peak before declining again. This un- usual behavior is attributed to the dominant pres- ence of Si and the strong ordering tendency of the Si-Ti system, which influences the distribution of Al, Cu and Fe at the surface. At equiatomic com- position, the overall extent of surface segregation tendency of the alloying elements follows the order Al>Si>Cu>Fe>Ti>. We have also calculated the temperature depen- dence of the surface concentrations at a fixed com- position, Al20Cu20Fe20Si20Ti20, Figure 9. The surface surface concentrations of the components at this composition are found to be xs Al = 0.620774, xs Cu = 0.139894, xsFe, = 0.031593, xs Si = 0.186671 and xs T i = 0.021066 at 1950 K. This implies the highest surface segregating nature of Al and lowest surface segregating nature of Ti among the com- ponents in this composition too. Further, the sur- face concentration of Fe and Ti appears to be en- N. Dahal et al./ BIBECHANA 22 (2025) 280-290 288 hanced with rise in temperature, whereas, surface concentration of Al, Cu and Si appears to decrease at higher temperature. Figure 9: Variation of surface concentrations of the components of Al–Cu–Fe–Si–Ti liquid alloy with temperature. 4 Conclusion The thermodynamic analysis of the Al-Cu-Fe-Si-Ti liquid alloy reveals that its multicomponent behav- ior is primarily governed by the interactions within its binary subsystems. Among the ten binaries, Cu-Fe exhibits a segregating tendency with posi- tive excess Gibbs free energy of mixing, while the remaining systems show ordering behavior, with Si- Ti being the strongest ordering pair. The calculated quinary ∆Gxs M values from both Fe and Ti corners confirm the consistency of Chou, Muggianu, and Kohler models, thereby validating the present com- putational approach. The quinary alloy exhibits stronger negative ∆Gxs M values when Si and Ti con- centrations are high, emphasizing the dominance of Si-Ti, Fe-Si, and Fe-Ti interactions. Conversely, higher Cu concentration reduces ordering, leading to weaker interactions. Comparison with binary interactions shows that the robustness of quinary ordering does not surpass the strong Si-Ti binary interaction at 1950 K. Overall, the alloy’s thermo- dynamic stability is strongly influenced by the co- operative effects of ordering pairs, particularly Si- Ti, Fe-Si, and Fe-Ti, while Cu tends to weaken the interaction strength due to its segregating na- ture with Fe. This tendency of the quinary system is further justified by the results of activity, the other thermodynamic function. The surface ten- sion of the quinary system increases at each cross- section with the increase in concentrations of Fe and Ti. The surface tension rises in alloy compo- sitions enriched with elements that naturally pos- sess higher surface tensions. At the cross-section xAl : xCu : xSi : xTi = 3:4:1:2 and from Fe cor- ner, Al atoms segregate at the surface, while the other atoms preferentially remain in the bulk phase. From Ti corner at xAl : xCu : xFe : xSi=1:2:3:4, Al and Si exhibit a strong tendency to segregate into the surface phase, while Cu, Fe, and Ti preferen- tially remain in the bulk phase. At equiatomic com- position, the overall extent of surface segregation tendency of the alloying elements follows the order Al>Si>Cu>Fe>Ti>. Temperature elevation sys- tematically decreases both surface segregation and deviations in activities, confirming that the system approaches an ideal random distribution at higher temperatures. References [1] C. Corti. 22nd Santa Fe Symposium On Jew- ellery Manufacturing Technology, 18–21 May 2008 Albuquerque, New Mexico, USA. Gold Bulletin, 41(3):269–271, 2008. [2] H. Nishimura and C. Hisatsune. The con- stitution of the alloys of copper, aluminium, and iron. Memoirs of the College of Engineer- ing, Kyoto Imperial University, 10(5):163–172, 1939. [3] R. Babilas, A Bajorek, M. Spilka, A. Radoń, and W. Łoński. Structure and corrosion resis- tance of Al–Cu–Fe alloys. Progress in Natural Science: Materials International, 30(3):393– 401, 2020. [4] A.P. Tsai, A. Inoue, and T. Masumoto. Effects of preparation conditions and additional ele- ments on phason strains in stable icosahedral quasicrystals in Al-Cu-Fe systems. Journal of Materials Science Letters, 8(4):470–472, 1989. [5] M. Mitka, A. Góral, and L. Lityńska- Dobrzyńska. Synthesis and stability of qua- sicrystalline phase in Al-Cu-Fe-Si mechanically alloyed powders. Journal of Materials Science, 56(18):11071–11082, 2021. [6] S. Khalesi, R. Omidi, R. Taghiabadi, and M. Emami. Effect of Si addition on the weibull distribution of tensile properties of fe-bearing Al-Cu alloys. Silicon, 16(11):4609–4620, 2024. [7] T. Moskalewicz, M. Kot, and B. Wendler. Microstructure development and properties of the AlCuFe quasicrystalline coating on near- α titanium alloy. Applied Surface Science, 258(2):848–859, 2011. [8] Y. Ouyang, X. Zhong, Y. Du, Y. Feng, and Y. He. Enthalpies of formation for the Al– Cu–Ni–Zr quaternary alloys calculated via a combined approach of geometric model and N. Dahal et al./ BIBECHANA 22 (2025) 280-290 289 miedema theory. Journal of Alloys and Com- pounds, 420(1-2):175–181, 2006. [9] H. Arslan and A. Dogan. An analytical investi- gation for thermodynamic properties of the Fe- Cr-Ni-Mg-O system. Russian Journal of Phys- ical Chemistry A, 89(2):180–189, 2015. [10] M. Hillert. Partial gibbs energies from redlich- kister polynomials. Thermochimica acta, 129(1):71–75, 1988. [11] A. Dhungana, S.K. Yadav, and D. Adhikari. Thermodynamic and surface properties of Al– Li–Mg liquid alloy. Physica B: Condensed Mat- ter, 598:412461, 2020. [12] H. Arslan and A. Dogan. Determination of surface tension of liquid ternary Ni–Cu–Fe and sub-binary alloys. Philosophical Magazine, 99(10):1206–1224, 2019. [13] A. Dogan, H. Arslan, and T. Dogan. Esti- mation of excess energies and activity coeffi- cients for the penternary Ni-Cr-Co-Al-Mo sys- tem and its subsystems. The Physics of Metals and Metallography, 116(6):544–551, 2015. [14] U. Mehta, S.K. Yadav, I. Koirala, R.P. Koirala, and D. Adhikari. Thermodynamic and surface properties of liquid Ti–Al–Fe alloy at different temperatures. Physics and Chemistry of Liq- uids, 59(4):585–596, 2021. [15] K.C. Chou. A new solution model for predict- ing ternary thermodynamic properties. Cal- phad, 11(3):293–300, 1987. [16] K.C. Chou. A general solution model for predicting ternary thermodynamic properties. Calphad, 19(3):315–325, 1995. [17] U. Mehta, S.K. Yadav, I. Koirala, R.P. Koirala, G.K. Shrestha, and D. Adhikari. Study of sur- face tension and viscosity of Cu–Fe–Si ternary alloy using a thermodynamic approach. He- liyon, 6(8), 2020. [18] C. Costa, S. Delsante, G. Borzone, D. Zivkovic, and R. Novakovic. Thermodynamic and sur- face properties of liquid Co–Cr–Ni alloys. The Journal of Chemical Thermodynamics, 69:73– 84, 2014. [19] J. Wang, P. Hudon, D. Kevorkov, C. Patrice, I.H. Jung, and M. Medraj. Thermodynamic and experimental study of the Mg-Sn-Ag-In quaternary system. Journal of Phase Equilib- ria and Diffusion, 35(3):284–313, 2014. [20] D.K. Sah, U. Mehta, D. Adhikari, and S.K. Ya- dav. Model based study of temperature depen- dent thermodynamic and surface properties of Al-Ti-Ni-Cr system in liquid state. Physica B: Condensed Matter, 695:416471, 2024. [21] D.K. Sah, U. Mehta, R.K. Gohivar, D. Ad- hikari, and S.K. Yadav. Theoretical assess- ment of thermodynamic and surface proper- ties of Ag–Al–Au–Cu liquid alloy at different temperatures. Applied Physics A, 131(2):144, 2025. [22] A. Dogan and H. Arslan. Assessment of ther- modynamic properties of lead-free soldering Co–Sb–Sn, Ag–In–Pd–Sn, and Ni–Cr–Co–Al– Mo–Ti–Cu alloys. Physics of Metals and Met- allography, 119(10):976–992, 2018. [23] S.K. Yadav, L.N. Jha, and D. Adhikari. Model- ing equations to predict the mixing behaviours of Al- Fe liquid alloy at different temperatures. Bibechana, 15:60–69, 2018. [24] R. Arroyave, T.W. Eagar, and L. Kaufman. Thermodynamic assessment of the Cu–Ti–Zr system. Journal of Alloys and Compounds, 351(1-2):158–170, 2003. [25] M. Hillert. Empirical methods of predicting and representing thermodynamic properties of ternary solution phases. Calphad, 4(1):1–12, 1980. [26] G. Kaptay. Improved derivation of the but- ler equations for surface tension of solutions. Langmuir, 35(33):10987–10992, 2019. [27] J.A.V. Butler. The thermodynamics of the sur- faces of solutions. Proceedings of the Royal Society of London. Series A, Containing Pa- pers of a Mathematical and Physical Charac- ter, 135(827):348–375, 1932. [28] S.K. Yadav, U. Mehta, and D. Adhikari. Opti- mization of thermodynamic and surface prop- erties of ternary Ti–Al–Si alloy and its sub- binary alloys in molten state. Heliyon, 7(3), 2021. [29] V.T. Witusiewicz, U. Hecht, S.G. Fries, and S. Rex. The Ag–Al–Cu system: Part i: Re- assessment of the constituent binaries on the basis of new experimental data. Journal of Al- loys and Compounds, 385(1-2):133–143, 2004. [30] I. Ansara, A.T. Dinsdale, and M.H. Rand. Thermochemical database for light metal al- loys. Office for Official Publications of the Eu- ropean Communities, 1998. [31] R.R. Hultgren, P.D. Desai, D.T. Hawkins, M. Gleiser, K.K. Kelley, and D.D. Wagman. Selected values of the thermodynamic proper- ties of binary alloys (ASM, Metals Park, OH, 1973). Search in, 2007. N. Dahal et al./ BIBECHANA 22 (2025) 280-290 290 [32] DS Kanibolotsky, OA Bieloborodova, NV Ko- tova, and VV Lisnyak. Thermodynamic prop- erties of liquid al-si and Al-Cu alloys. Jour- nal of Thermal Analysis and Calorimetry, 70(3):975–983, 2002. [33] R.K. Mishra, R. Lalneihpuii, and R. Venkatesh. Statistical mechanical studies of Al rich Al–Cu melts. Physica A: Statistical Mechanics and its Applications, 550:123901, 2020. [34] M. Trybuła, N. Jakse, W. Gąsior, and A. Pas- turel. Thermodynamics and concentration fluctuations of liquid Al-Cu and Al-Zn al- loys. Archives of Metallurgy and Materials, 60(2A):649–655, 2015. [35] A. Walnsch, M.J. Kriegel, O. Fabrichnaya, and A. Leineweber. Thermodynamic assess- ment and experimental investigation of the sys- tems Al–Fe–Mn and Al–Fe–Mn–Ni. Calphad, 66:101621, 2019. [36] A. Kostov, B. Friedrich, and D. Živković. Ther- modynamic calculations in alloys Ti-Al, Ti-Fe, Al-Fe and Ti-Al-Fe. Journal of Mining and Metallurgy, Section B: Metallurgy, 44(1):49– 61, 2008. [37] I.B. Bhandari, N. Panthi, S. Gaire, and I. Koirala. Effect of temperature on mixing be- havior and stability of liquid Al-Fe alloys. In Journal of Physics: Conference Series, volume 2070, page 012025. IOP Publishing, 2021. [38] D. Adhikari, S.K. Yadav, and L.N. Jha. Thermo-physical properties of Al–Fe melt. Journal of the Chinese Advanced Materials So- ciety, 2(3):149–158, 2014. [39] M. Bonnet, J. Rogez, and R. Castanet. Emf investigation of Al-Si, Al-Fe-Si and Al-Ni-Si liquid alloys. Thermochimica acta, 155:39–56, 1989. [40] R. Novakovic, D. Giuranno, E. Ricci, A. Tuissi, R. Wunderlich, H.J. Fecht, and I. Egry. Sur- face, dynamic and structural properties of liq- uid Al–Ti alloys. Applied Surface Science, 258(7):3269–3275, 2012. [41] R.G. Reddy, A.M. Yahya, and L. Brewer. Thermodynamic properties of Ti–Al inter- metallics. Journal of Alloys and Compounds, 321(2):223–227, 2001. [42] Y. Chuang, R. Schmid, and Y.A. Chang. Ther- modynamic analysis of the iron-copper system i: The stable and metastable phase equilibria. Metallurgical Transactions A, 15(10):1921– 1930, 1984. [43] M.A. Turchanin, P.G. Agraval, and I.V. Niko- laenko. Thermodynamics of alloys and phase equilibria in the copper-iron system. Journal of Phase Equilibria, 24(4):307–319, 2003. [44] Q. Chen and Z. Jin. The Fe-Cu system: A ther- modynamic evaluation. Metallurgical and Ma- terials Transactions A, 26(2):417–426, 1995. [45] X. Yan and Y.A. Chang. A thermodynamic analysis of the Cu–Si system. Journal of Al- loys and Compounds, 308(1-2):221–229, 2000. [46] T. Abbas and A.B. Ziya. Evidence of short- range order in the disordered Cu-Ti alloys. Journal of Materials Science, 28(18):5010– 5013, 1993. [47] P. Wei and L. Jie. Thermodynamics of Ti in Cu–Ti alloy investigated by the emf method. Materials Science and Engineering: A, 269(1- 2):104–110, 1999. [48] D. Kanibolotsky, O. Bieloborodova, N. Kotova, and V. Lisnyak. Thermodynamics of liquid Fe- Si and Fe-Ge alloys. Journal of Thermal Anal- ysis and Calorimetry, 71(2):583–591, 2003. [49] D. Adhikari, I.S. Jha, and B.P. Singh. Struc- tural asymmetry in liquid Fe–Si alloys. Philo- sophical Magazine, 90(20):2687–2694, 2010. [50] O.E. Awe, Y.A. Odusote, L.A. Hussain, and O. Akinlade. Temperature dependence of ther- modynamic properties of Si–Ti binary liquid alloys. Thermochimica Acta, 519(1-2):1–5, 2011. [51] S.H. Tabaian, M. Maeda, T. Ikeda, and Y. Ogasawara. Thermodynamic study of molten Si-Ti binary alloys. High Tempera- ture Materials and Processes, 19(3-4):257–264, 2000. [52] S.K. Yadav, U. Mehta, R.K. Gohivar, A. Dhungana, R.P. Koirala, and D. Ad- hikari. Reassessments of thermo-physical prop- erties of Si-Ti melt at different temperatures. Bibechana, 17:146–153, 2020. [53] J.J. Valencia and P.N. Quested. Thermophys- ical properties. Modeling for Casting and So- lidification Processing, 189, 2001. Introduction Formalism Thermodynamics properties Surface properties Results and Discussion Thermodynamic properties Activity Surface properties Conclusion