BIBECHANA 18 (1) (2021) 149-158 149 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 Investigation on thermo-physical properties of liquid In-Tl alloy I. B. Bhandari1,2, N. Panthi1,3 , I. Koirala1* 1Central Department of Physics, Tribhuvan University, Kirtipur, Nepal 2Department of Applied Sciences, Purwanchal Campus, Tribhuvan University, Dharan, Nepal 3Department of Physics, Patan Multiple Campus, Tribhuvan University, Lalitpur, Nepal *E-mail: ikphysicstu@gmail.com Article Information: Received: June 29, 2020 Accepted: August 8, 2020 Keywords: Mixing properties Ordering energy Complex formation model Segregation ABSTRACT This research explores mixing behaviour of liquid In – Tl system through thermodynamic and the structural properties on the basis of Complex Formation Model. The properties like surface tension and viscosity have been analyzed through simple statistical model and Moelwyn – Hughes equation. The interaction parameters are found to be positive, concentration independent and temperature dependent. Theoretical results are in a good agreement with the corresponding literature data which support homo-coordinating tendency in the liquid In-Tl alloy. DOI: https://doi.org/10.3126/bibechana.v18i1.29531 This work is licensed under the Creative Commons CC BY-NC License. https://creativecommons.org/licenses/by-nc/4.0/ 1. Introduction Indium is a substance which is used in solder alloys which are applied in electronics for assembling semiconductor chips to a base and hybrid integrated circuits and to seal glass to metal in vacuum tubes. Fusible indium alloys are used to bend thin walled tubes without wrinkling the wall or changing the original cross-section. These alloys are not only used in fire control system, restraining links that hold alarm, water valve and door operating mechanism but also used as temperature indicators in situations where other methods of temperature measurements are impracticable and infeasible [1]. Indium is also used in nuclear reactor control rod alloys, low pressure sodium lamps and alkaline batteries. Additions of indium to lead–tin bearings are utilized in piston type aircraft engines, high performance automobile engines and in turbo– diesel truck engines. The addition of indium to gold dental alloys recuperates their mechanical properties and increases resistance to discoloring. Small amount of indium is used to improve the machinability of gold alloys for jewelry [1].The indium–thallium alloy is a classic type of shape memory alloy with a low melting temperature. It has wide range of practical applications in the field of metallurgy which includes the use in http://nepjol.info/index.php/BIBECHANA mailto:ikphysicstu@gmail.com https://doi.org/10.3126/bibechana.v18i1.29531 https://creativecommons.org/licenses/by-nc/4.0/ I. B. Bhandari et al. / BIBECHANA 18 (1) (2021) 149-158 150 thermostats, hydraulic lines and electrical circuits [2]. Thallium alone is improper for direct use because of its properties of toxicity, unfavorable mechanical properties and significant tendency to oxidize. Thallium contains the most constant atomic vibration so far experimented. This property of Tl preceded it to be used in atomic clocks. Thallium immediately forms alloys with most other metals. There is incomplete mutual insolubility with iron and limited solubility in the liquid state with copper, aluminum, zinc, arsenic, manganese and nickel. Gold, silver, cadmium and tin formulate simple eutectic point with thallium. Thallium also forms binary alloys with antimony, barium, calcium, cerium, cobalt, germanium, lanthanum, lithium, magnesium, strontium, tellurium, bismuth and indium. The ternary alloys of thallium Tl–Pb– Bi, Tl–Al–Ag, In–Hg–Tl, Sn–Cd–Tl, Bi–Sn–Tl and Bi–Cd–Tl are used as semiconductors in ceramic compounds. Thallium has good wear resistance when it is used in bearing shafts. Thallium containing alloys are frequently recommended for bearings, electronics industry such as in solid state rectifiers, electrical fuses and soldering materials [1]. The study of In-Tl alloy is also useful to investigate the corresponding higher order alloy through different approaches [3]. There is difficulty in studying the properties of alloys in liquid state due to lack of long range atomic order. Therefore, theoreticians have exercised different models to understand the properties of various binary liquid alloys [4–22]. The different properties were studied at fixed temperature of 723 K through different models. In present work, we have explored the energetic of In – Tl alloy at a temperature of 723K using complex formation model [23]. The outcomes are analyzed and compared with literature data [24] to explicate the accuracy of this method in thermodynamic and structural description of the presented binary system. 2. Theory Thermodynamic properties If a binary alloy contains NA = x number of A atoms and NB = (1-x) number of B atoms, so that total number of atoms is N = NA + NB. When components A and B are amalgamated together to form a binary A-B solution, thermodynamic properties are changed. The liquid alloy is considered to be ternary mixture of three species; A atom, B atom and chemical complex AuBv, is also called conformal solution. The number of free atoms will be reduced due to compound formation in the melt. Now for n1g atoms of A, n2g atoms of B and n3g atoms of AuBv, 𝑛1 = 𝑥 − 𝑢𝑛3 and 𝑛2 = (1 − 𝑥) − 𝑣𝑛3 (1) The total number of atoms after mixing can be given as 𝑛 = 𝑛1 + 𝑛2 + 𝑛3 = 1 − (𝑢 + 𝑣 − 1)𝑛3 (2) The free energy of mixing of the binary A-B mixture can be written as [23], 𝐺𝑀 = −𝑛3𝑔 + 𝐺′ (3) Here,−𝑛3𝑔 stands for lowering of free energy due to compound formation, g is the formation energy of complex. 𝐺′ is the free energy of mixing of the ternary mixture of A, B and AuBv. If the ternary mixture is an ideal solution, 𝐺′ = 𝑅𝑇 ∑ 𝑛𝑖𝑙𝑛 ( 𝑛𝑖 𝑛 ) (4) If the effects of differences in sizes of the various constituents in the mixture cannot be ignored and the interaction 𝜔𝑖𝑗 are small but not zero, the theory of regular solutions in the zeroth approximation [25] or the conformal solution approximation [26] is valid. For regular solution 𝐺′ = 𝑅𝑇 ∑ 𝑛𝑖𝑙𝑛 ( 𝑛𝑖 𝑛 ) + ∑ 𝜔𝑖𝑗 ( 𝑛𝑖𝑛𝑗 𝑛 ) (5) This equation is concerned to conformal solution approximation. Where 𝜔𝑖𝑗= 0 (for i = j) are termed as the interaction energies and by definition are independent of concentration, although they are depended upon temperature and pressure. Now the expression for free energy of mixing GM for the compound forming binary alloy is 𝐺𝑀 = −𝑛3𝑔 + 𝑅𝑇 ∑ 𝑛𝑖𝑙𝑛 ( 𝑛𝑖 𝑛 )3 𝑖=1 + ∑ ∑ ( 𝑛𝑖𝑛𝑖 𝑛 )𝑖<𝑗 𝜔𝑖𝑗 (6) I. B. Bhandari et al. / BIBECHANA 18 (1) (2021) 149-158 151 The expression for heat of mixing HM is given by[23] 𝐻𝑀 = 𝐺𝑀 − 𝑇 ( 𝜕𝐺𝑀 𝜕𝑇 ) 𝑃 (7) Substituting for GM, 𝐻𝑀 = −𝑛3𝑔 + 𝑅𝑇 ∑ 𝑛𝑖𝑙𝑛 ( 𝑛𝑖 𝑛 ) 3 1 + ∑ ∑ ( 𝑛𝑖𝑛𝑗 𝑛 ) 𝜔𝑖𝑗 𝑖<𝑗 − 𝑇 𝜕 𝜕𝑇 [−𝑛3𝑔 + 𝑅𝑇 ∑ 𝑛𝑖 3 𝑖=1 𝑙𝑛 ( 𝑛𝑖 𝑛 ) + ∑ ∑ ( 𝑛𝑖𝑛𝑗 𝑛 ) 𝜔𝑖𝑗 𝑖<𝑗 ] 𝐻𝑀 = −𝑛3 [𝑔 − 𝑇 ( 𝜕𝑔 𝜕𝑇 ) 𝑃 ] + 1 𝑛 ∑ ∑(𝑛𝑖𝑛𝑗)𝑖<𝑗 [𝜔𝑖𝑗 − 𝑇 ( 𝜕𝜔𝑖𝑗 𝜕𝑇 ) 𝑃 ] (8) The expression for entropy of mixing SM can be obtained as [23] 𝑆𝑀 = 𝑛3 𝜕𝑔 𝜕𝑇 − 𝑅 ∑ 𝑛𝑖𝑙𝑛 𝑛𝑖 𝑛 − ∑ ∑ 𝑛𝑖𝑛𝑗 𝑛 𝜕𝜔𝑖𝑗 𝜕𝑇𝑖<𝑗 3 𝑖=1 (9) The equilibrium value of 𝑛3 at a given pressure and temperature is given by[23] ( 𝜕𝐺𝑀 𝜕𝑛3 ) 𝑇,𝑃,𝑁,𝐶 = 0 (10) Substituting the value of GM from Equation (6) and after some algebraic calculation 𝑙𝑛(𝑛3𝑛𝑢+𝑣−1𝑛1 −𝑢𝑛2 −𝑣) + 𝑌 = 𝑔 𝑅𝑇 (11) The Equation (11) is called equilibrium equation, where 𝑌 = [ 𝑛1𝑛2 𝑛2 (𝑢 + 𝑣 − 1) − 𝑢 𝑛2 𝑛 − 𝑣 𝑛1 𝑛 ] 𝜔12 𝑅𝑇 + [ 𝑛2𝑛3 𝑛2 (𝑢 + 𝑣 − 1) − 𝑣 𝑛3 𝑛 + 𝑛2 𝑛 ] 𝜔23 𝑅𝑇 + [ 𝑛1𝑛3 𝑛2 (𝑢 + 𝑣 − 1) − 𝑢 𝑛3 𝑛 + 𝑛1 𝑛 ] 𝜔13 𝑅𝑇 (12) Structural Properties The concentration fluctuation at long wavelength limit is of good interest because any deviation from ideal value 𝑆𝑐𝑐 𝑖𝑑 (0) is significant in describing the nature of ordering and phase segregation in molten alloys. This has been used to investigate the nature of atomic order. The concentration fluctuation at long wavelength limit is related with free energy of mixing by the expression [27], 𝑆𝑐𝑐(0) = 𝑅𝑇 𝜕2𝐺𝑀 𝜕𝑐2 (13) 𝑆𝑐𝑐(0) = 𝑅𝑇 𝑅𝑇 ∑ ( (𝑛𝑖 ′) 2 𝑛𝑖 − (𝑛′) 2 𝑛 )3 𝑖=1 +2𝑛 ∑ ∑ 𝜔𝑖𝑗( 𝑛𝑖 𝑛 ) ′ ( 𝑛𝑗 𝑛 ) ′ 𝑖<𝑗 (14) Theoretically computed values of 𝑆𝑐𝑐(0) can be compared with the observed values computed from activity data by the expression, 𝑆𝑐𝑐(0) = (1 − 𝑥)𝑎𝐴 ( 𝜕𝑎𝐴 𝜕𝑐 ) 𝑇,𝑃,𝑁 −1 = 𝑥𝑎𝐵 ( 𝜕𝑎𝐵 𝜕𝑐 ) 𝑇,𝑃,𝑁 −1 (15) The ideal value of Scc(0) can be expressed as, 𝑆𝑐𝑐 𝑖𝑑(0) = 𝑥(1 − 𝑥) (16) The Warren–Cowley short range order parameter quantify the degree of local order in the binary alloy [28,29]. The theoretical values of this parameter can be calculated as α1 = (s−1) s(z−1)+1 ,S = Scc(0) Scc id(0) (17) where z is coordination number, which is taken as 10 for our calculation. Transport Properties The mixing behaviour of the alloys forming molten alloy can also be studied at the microscopic level in terms of coefficient of diffusion. The mutual diffusion coefficient (DM) of binary liquid alloys can be expressed in terms of activity (ai) and self- diffusion coefficient (Did) of pure component with the help of Darken’s equation [30] 𝐷𝑀 = 𝐷𝑖𝑑𝑥 𝑑𝑙𝑛𝑎𝑖 𝑑𝑥 (18) with 𝐷𝑀 = 𝑐𝐴𝐷𝐵 + 𝑐𝐵𝐷𝐴 where DA and DB are the self – diffusion coefficients of pure components A and B respectively, The expression for DM in terms of Scc(0) can be given as 𝐷𝑀 𝐷𝑖𝑑 = 𝑆𝑐𝑐 𝑖𝑑(0) 𝑆𝑐𝑐(0) (19) I. B. Bhandari et al. / BIBECHANA 18 (1) (2021) 149-158 152 The mixing behaviour of liquid alloys at microscopic level can also be understood in terms of viscosity. The Moelwyn – Hughes equation for viscosity of liquid alloy [31] is 𝜂 = 𝜂𝑖𝑑 [1 − 𝑥𝐴𝑥𝐵 ( 2𝑔 𝑅𝑇 )] (20) with 𝜂𝑖𝑑 = 𝑥𝜂𝐴 + (1 − 𝑥)𝜂𝐵 where 𝜂𝑖 is the viscosity of pure component i. At temperature T, it is given by [32] 𝜂𝑖 = 𝜂𝑖0exp ( 𝐸 𝑅𝑇 ) (21) Here 𝜂𝑖0 a constant in the unit of viscosity and E is the activation energy. Surface Properties The surface properties of the liquid mixture give insight into the metallurgical phenomenon, such as crystal growth, wielding, gas absorption and nucleation of gas bubbles [33]. The expressions for surface tension proposed by Prasad et al., [34,35], has been reduced in the simple form using zeroth approximation as 𝜏 = 𝜏𝐴 + 𝑘𝐵𝑇 𝜉 𝑙𝑛 𝑥𝑠 𝑥 + 𝑔 𝜉 [𝑝(1 − 𝑥𝑠)2 + (𝑞 − 1)(1 − 𝑥)2] (22) 𝜏 = 𝜏𝐵 + 𝑘𝐵𝑇 𝜉 𝑙𝑛 (1−𝑥𝑠) (1−𝑥) + 𝑔 𝜉 [𝑝(𝑥𝑠)2 + (𝑞 − 1)(𝑥)2] (23) where 𝜏𝐴 and 𝜏𝐵 are the surface tensions of pure components A and B respectively, 𝑥 and 𝑥𝑠 are the bulk and surface concentration of the components of alloy, p and q are called coordination fractions, which are defined as the fraction of the total number of nearest neighbors made by atom within its own layer and that in the adjoining layer. The coordination fractions p and q are related to each other by the relation 𝑝 + 2𝑞 = 1, for closed packed structure, 𝑝 = 0.5 and 𝑞 = 0.25 The expression for the mean atomic surface area 𝜉 is 𝜉 = ∑ 𝑐𝑖𝜉𝑖 (24) The atomic surface are for each component is 𝜉𝑖 = 1.102 ( 𝛺𝑖 𝑁𝐴 ) 2/3 (25) where 𝛺𝑖is the molar volume of the component i and 𝑁𝐴represents Avogadro number. Equating equations (22) and (23), we can solve it for 𝑥𝑠 as the function of x and hence compositional dependence of surface tension can be evaluated. where 𝜏𝐴 and 𝜏𝐵 are the surface tensions of pure components A and B respectively, 𝑥 and 𝑥𝑠 are the bulk and surface concentration of the components of alloy, p and q are called coordination fractions, which are defined as the fraction of the total number of nearest neighbors made by atom within its own layer and that in the adjoining layer. The coordination fractions p and q are related to each other by the relation 𝑝 + 2𝑞 = 1, for closed packed structure, 𝑝 = 0.5 and 𝑞 = 0.25 The expression for the mean atomic surface area 𝜉 is 𝜉 = ∑ 𝑐𝑖𝜉𝑖 (24) The atomic surface are for each component is 𝜉𝑖 = 1.102 ( 𝛺𝑖 𝑁𝐴 ) 2/3 (25) where 𝛺𝑖is the molar volume of the component i and 𝑁𝐴represents Avogadro number. Equating equations (22) and (23), we can solve it for 𝑥𝑠 as the function of x and hence compositional dependence of surface tension can be evaluated. 3. Results and Discussion Thermodynamic properties The experimental data on the thermodynamic properties as well as phase diagram information [24] have been used for the calculation of order energy parameters for liquid phase In–Tl system. The data set of the Gibbs energy of mixing (GM) were taken as input data to calculate by the CFM the interaction energy parameters, i.e. g, ω12, ω13, ω23. The starting values of g/RT and ωij/RT were obtained as suggested in ref. [23]. Equilibrium Equation (11) along with Equations (1) and (2) were applied to compute the number of complexes, I. B. Bhandari et al. / BIBECHANA 18 (1) (2021) 149-158 153 n3, as a function of concentration. The values of interaction energy parameters were adjusted to give the concentration dependence of free energy of mixing which fits well with the corresponding thermodynamic data. From the phase diagram [24] In-Tl alloy is expected to aggregate with stoichiometry In-Tl ( u = 1, v = 1).The calculations were done at temperature of 723 K. The interaction energy parameters for In–Tl liquid alloys are found to be g = 0.755 RT, ω12 =0.476 RT, ω13=1.610 RT and ω23= 1.481 RT. The positive interaction energies imply the repulsion between the corresponding species. The concentration dependence of the equilibrium values of chemical complexes, n3, (Fig. 1) displays the symmetry with the maximum value of 0.4178 at equiatomic composition. The curve describing the Gibbs free energy of mixing of the In–Tl liquid phase is symmetric with respect to the equiatomic composition (Fig. 2). Theoretical calculation of free energy of mixing for In-Tl liquid alloy shows that In - Tl alloy in liquid state is weakly interacting or homo-coordinating system. There is an excellent agreement between the experimental and calculated integral free energies. Very poor agreement of calculated values of HM and SM with experimental simply indicates the importance of the dependence of interaction energies on temperature. To account this, we have used Equations (8) and (9) to determine the variation in energy parameters with respect to temperature from experimental values of HM and SM [24]. The temperature dependent interaction energies at T=723K are found to be 1 𝑅 𝜕𝑔 𝜕𝑡 = 0.845, 1 𝑅 𝜕𝜔12 𝜕𝑡 = 0.383, 1 𝑅 𝜕𝜔13 𝜕𝑡 = 1.493, 1 𝑅 𝜕𝜔23 𝜕𝑡 = 1.430 It is found from the present analysis that the heat of mixing and entropy of mixing both are positive at all concentrations. Our theoretical calculation shows that the maximum value of the heat of mixing is 0.0512 RT at xIn = 0.6 (Fig.3) and the maximum value of entropy of mixing is 0.6107 at xIn = 0.5 (Fig.4). There is excellent agreement between experimental and calculated values of HM. The calculated values of SM deviates from experimental values by maximum percentage of 8.31 at xIn = 0.8 and by minimum percentage of 5.56 at xIn = 0.4. This deviation is because of the propagation of error from previous calculation. 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 n 1 , n 2 , n 3 xIn n3 n1n2 Fig.1 Fig.1: Number of complexes (n1, n2, n3) vs. concentration xIn of liquid In - Tl alloy at 723K. -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 G M / R T Experimental Theoretical Fig.2 0.0 0.2 0.4 0.6 0.8 1.0 xIn Fig. 2: Free energy of mixing (GM/RT) vs. concentration (xIn) of liquid In - Tl alloy at 723K. Structural Properties It has been reported that when Scc(0) < Scc id(0), the existence of chemical ordering leading to complex I. B. Bhandari et al. / BIBECHANA 18 (1) (2021) 149-158 154 formation is expected while Scc(0) > Scc id(0), is an indication of segregation. The same interaction parameters used in the calculation of the thermodynamic properties were employed in the calculations of Scc(0) using Equation (14) while the experimental values of Scc(0) were obtained from Equation (15) using the experimental activity data. The results obtained from the above computations are plotted in Fig. (5). It is found that Scc(0) > Scc id(0) throughout the entire concentration range, this also confirms the presence of chemical segregation or a preference for like atoms to pair. The value of short range order parameter is positive through the whole concentration range which indicates that the alloy is segregating at all compositions. The value of short range order parameter has been found maximum (= 0.02438) at xIn = 0.5 at 723 K (Fig. (6)). 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.01 0.02 0.03 0.04 0.05 0.06 H M / R T xIn Experimental Theoretical Fig.3 Fig. 3: Heat of mixing (HM) vs. concentration of indium (xIn) in the liquid In - Tl alloy at 723K. Transport Properties The calculated values of Scc(0)) by Equation (17) can be applied to evaluate the ratio of the mutual and intrinsic-diffusion coefficients (DM/Did) using Equation (19), against the concentration of indium. We note that the ratio of diffusivities can also be used to indicate levels of order in the liquid binary alloys. The presence of chemical order is indicated by DM/Did>1. Similarly, DM/Did<1 suggests the tendency for segregation. Fig. (7) shows the plots DM/Did against concentration of indium. It can be observed that the ratio DM/Did is less than 1 throughout the whole concentration range. This indicates the homo – coordinating tendency in In– Tl alloys at the temperature of investigation. It is also noticed that DM/Did exhibits maximum peak at around the equi-atomic composition. The result predicted by DM/Did is in agreement with the results obtained from the free energy of mixing, concentration fluctuations and CSRO parameter. The viscosity of the In–Tl liquid alloy has been calculated numerically using Equation (20). From the plot of η verses bulk concentration of indium (Fig. 8) small negative deviation from the linear law (Raoult's law) in viscosity isotherms η(x) has been inspected. Surface Properties The surface concentrations and surface tension of In–Tl alloy have been computed numerically using Equations (22) and (23). The values of densities and surface tension at melting temperature (T0) of pure atoms are taken from ref. [32]. These values have been optimized at required temperature (T) by using the expressions 𝜌𝑖(𝑇) = 𝜌𝑖 0 + (𝑇 − 𝑇𝑖 0) 𝑑𝜌𝑖 𝑑𝑡⁄ (26) 𝜏𝑖(𝑇) = 𝜏𝑖 0 + (𝑇 − 𝑇𝑖 0) 𝑑𝜏𝑖 𝑑𝑡⁄ (27) where 𝑑𝜌𝑖 𝑑𝑡⁄ and 𝑑𝜏𝑖 𝑑𝑡⁄ represent temperature coefficients of density and surface tension respectively for the components of the metal alloys. The computed values of surface concentration for molten In–Tl alloys at 723 K are depicted in Fig. (9). Surface concentration of indium in In–Tl alloys is found to increase with the increase of bulk concentration of In. The computed surface tension for In–Tl alloys at 723 K is less than ideal values at all concentrations of indium; i.e., there is negative departure of surface tension from ideality (τ = τAx+τB(1−x)) throughout the bulk concentrations of indium in In–Tl alloys (Fig. 10). For the In-Tl melt, the surface tension of Tl is smaller than that of In atom. Therefore, Tl atoms having lower surface tension segregates on the surface phase but In I. B. Bhandari et al. / BIBECHANA 18 (1) (2021) 149-158 155 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 S M / R xIn Experimental Theoretical Fig.4 atoms remains in the bulk phase throughout the entire composition. Fig. 4: Entropy of mixing (SM) vs. concentration of indium (xIn) in the liquid In - Tl alloy at 723K. Experimental Theoretical Ideal 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 S c c (0 ) xInFig.5 Fig. 5: Concentration fluctuation at long wavelength limit (Scc(0)) vs. concentration of indium (xIn) in the liquid In - Tl alloy at 723K. 0.0 0.2 0.4 0.6 0.8 1.0 0.000 0.005 0.010 0.015 0.020 0.025 a 1 xInFig.6 Fig. 6: Chemical short range order (α1) vs. concentration of indium (xIn) in the liquid In - Tl alloy at 723K. 0.0 0.2 0.4 0.6 0.8 1.0 0.76 0.80 0.84 0.88 0.92 D M / D id xInFig.7 Fig. 7: Ratio of mutual and intrinsic diffusion coefficients (DM/Did) vs. concentration of indium (xIn) in the liquid In - Tl alloy at 723K. I. B. Bhandari et al. / BIBECHANA 18 (1) (2021) 149-158 156 0.0 0.2 0.4 0.6 0.8 1.0 0.0008 0.0010 0.0012 0.0014 0.0016 h N s m -2 xIn Theoretical alues Ideal values Fig.8 Fig. 8: Viscosity (η) vs. concentration of indium (xIn) in the liquid In - Tl alloy at 723K. 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 x s In xIn Theoretical values Ideal values Fig.9 Fig. 9: Surface concentration of indium ( xIn s ) vs. bulk concentration of indium (xIn) in the liquid In - Tl alloy at 723K. 4. Conclusions The theoretical analysis of the thermodynamic properties reveals that there is a tendency of like atom pairing in the liquid In–Tl alloys at all concentrations. The ordering energy is found to be positive and temperature dependent. The study of concentration fluctuation in long wavelength limit and CSRO show that there is tendency of phase separation in In –Tl liquid alloy. Negative deviation of viscosity isotherms from Raoult law is observed. Viscosity of the alloys decreases with increase in the concentrations of indium. The ratio of diffusion coefficients (DM/Did) is found to be greater than one at all compositions which also indicates segregating tendency of the system. At the temperature of investigation, the surface tension increases with the increase in the bulk concentration of In. The surface tension of the liquid In–Tl alloy is found to be smaller than ideal values. 0.0 0.2 0.4 0.6 0.8 1.0 0.46 0.48 0.50 0.52 t N m -1 xIn Theoretical Ideal Fig.10 Fig. 10: Surface tension (τ) vs. bulk concentration of indium (xIn) in the liquid In - Tl alloy at 723K. References [1] F. Habashi, ed., Alloys Preparation, Properties, Applications, First, Wiley-VCH (1998). [2] Z.P. Luo, An Overview on the Indium-Thallium (In-Tl) Shape Memory Alloy Nanowires, Metallogr. Microstruct. Anal. 1 (2012) 320. https://doi.org/10.1007/s13632-012-0046-4 [3] U. Mehta, S.K. Yadav, I. Koirala, D. 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