BIBECHANA 18 (1) (2021) 149-158 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: [email protected] Article Information: ABSTRACT Received: June 29, 2020 This research explores mixing behaviour of liquid In – Tl system through Accepted: August 8, 2020 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 Keywords: interaction parameters are found to be positive, concentration independent and Mixing properties temperature dependent. Theoretical results are in a good agreement with the Ordering energy corresponding literature data which support homo-coordinating tendency in the Complex formation model liquid In-Tl alloy. Segregation 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 also used in nuclear reactor control rod alloys, low pressure sodium lamps and alkaline Indium is a substance which is used in solder alloys batteries. Additions of indium to lead–tin bearings which are applied in electronics for assembling are utilized in piston type aircraft engines, high semiconductor chips to a base and hybrid integrated performance automobile engines and in turbo– circuits and to seal glass to metal in vacuum tubes. diesel truck engines. The addition of indium to gold Fusible indium alloys are used to bend thin walled dental alloys recuperates their mechanical tubes without wrinkling the wall or changing the properties and increases resistance to discoloring. original cross-section. These alloys are not only Small amount of indium is used to improve the used in fire control system, restraining links that machinability of gold alloys for jewelry [1].The hold alarm, water valve and door operating indium–thallium alloy is a classic type of shape mechanism but also used as temperature indicators memory alloy with a low melting temperature. It in situations where other methods of temperature has wide range of practical applications in the field measurements are impracticable and infeasible [1]. of metallurgy which includes the use in 149 I. B. Bhandari et al. / BIBECHANA 18 (1) (2021) 149-158 thermostats, hydraulic lines and electrical circuits total number of atoms is N = NA + NB. When [2]. Thallium alone is improper for direct use components A and B are amalgamated together to because of its properties of toxicity, unfavorable form a binary A-B solution, thermodynamic mechanical properties and significant tendency to properties are changed. The liquid alloy is oxidize. Thallium contains the most constant considered to be ternary mixture of three species; A atomic vibration so far experimented. This property atom, B atom and chemical complex AuBv, is also of Tl preceded it to be used in atomic clocks. called conformal solution. The number of free Thallium immediately forms alloys with most other atoms will be reduced due to compound formation metals. There is incomplete mutual insolubility in the melt. Now for n1g atoms of A, n2g atoms of with iron and limited solubility in the liquid state B and n3g atoms of AuBv, with copper, aluminum, zinc, arsenic, manganese 푛1 = 푥 − 푢푛3 and 푛2 = (1 − 푥) − 푣푛3 (1) and nickel. Gold, silver, cadmium and tin formulate simple eutectic point with thallium. Thallium also The total number of atoms after mixing can be forms binary alloys with antimony, barium, given as calcium, cerium, cobalt, germanium, lanthanum, 푛 = 푛1 + 푛2 + 푛3 = 1 − (푢 + 푣 − 1)푛3 (2) lithium, magnesium, strontium, tellurium, bismuth The free energy of mixing of the binary A-B and indium. The ternary alloys of thallium Tl–Pb– mixture can be written as [23], Bi, Tl–Al–Ag, In–Hg–Tl, Sn–Cd–Tl, Bi–Sn–Tl and ′ 퐺푀 = −푛3푔 + 퐺 (3) Bi–Cd–Tl are used as semiconductors in ceramic compounds. Thallium has good wear resistance Here,−푛3푔 stands for lowering of free energy due when it is used in bearing shafts. Thallium to compound formation, g is the formation energy containing alloys are frequently recommended for of complex. 퐺′ is the free energy of mixing of the bearings, electronics industry such as in solid state ternary mixture of A, B and AuBv. If the ternary rectifiers, electrical fuses and soldering materials mixture is an ideal solution, [1]. The study of In-Tl alloy is also useful to 푛 퐺′ = 푅푇 ∑ 푛 푙푛 ( 푖) (4) 푖 푛 investigate the corresponding higher order alloy through different approaches [3]. There is difficulty If the effects of differences in sizes of the various in studying the properties of alloys in liquid state constituents in the mixture cannot be ignored and due to lack of long range atomic order. Therefore, the interaction 휔푖푗 are small but not zero, the theoreticians have exercised different models to theory of regular solutions in the zeroth understand the properties of various binary liquid approximation [25] or the conformal solution alloys [4–22]. The different properties were studied approximation [26] is valid. For regular solution at fixed temperature of 723 K through different 푛 푛 푛 퐺′ = 푅푇 ∑ 푛 푙푛 ( 푖) + ∑ 휔 ( 푖 푗) (5) models. In present work, we have explored the 푖 푛 푖푗 푛 energetic of In – Tl alloy at a temperature of 723K This equation is concerned to conformal solution using complex formation model [23]. The approximation. Where 휔푖푗= 0 (for i = j) are termed outcomes are analyzed and compared with as the interaction energies and by definition are literature data [24] to explicate the accuracy of this independent of concentration, although they are method in thermodynamic and structural depended upon temperature and pressure. description of the presented binary system. Now the expression for free energy of mixing GM for the compound forming binary alloy is 2. Theory 푛 퐺 = −푛 푔 + 푅푇 ∑3 푛 푙푛 ( 푖) + Thermodynamic properties 푀 3 푖=1 푖 푛 푛푖푛푖 If a binary alloy contains NA = x number of A ∑ ∑ ( ) 휔 (6) 푖<푗 푛 푖푗 atoms and NB = (1-x) number of B atoms, so that 150 I. B. Bhandari et al. / BIBECHANA 18 (1) (2021) 149-158 The expression for heat of mixing HM is given of atomic order. The concentration fluctuation at by[23] long wavelength limit is related with free energy of 휕퐺푀 mixing by the expression [27], 퐻푀 = 퐺푀 − 푇 ( ) (7) 휕푇 푃 푅푇 푆푐푐(0) = 2 (13) Substituting for GM, 휕 퐺푀 2 3 휕푐 푛푖 퐻푀 = −푛3푔 + 푅푇 ∑ 푛푖푙푛 ( ) 푅푇 푛 ( ) 1 푆푐푐 0 = 2 (푛′) ′ 2 ′ 푛 ′ 푛 푛 3 푖 (푛 ) 푛푖 푗 푖 푗 푅푇 ∑푖=1( − )+2푛 ∑푖<푗 ∑ 휔푖푗( ) ( ) + ∑ ∑ ( ) 휔 푛푖 푛 푛 푛 푛 푖푗 푖<푗 (14) 3 휕 푛 Theoretically computed values of 푆푐푐(0) can be − 푇 [−푛 푔 + 푅푇 ∑ 푛 푙푛 ( 푖) 휕푇 3 푖 푛 compared with the observed values computed from 푖=1 activity data by the expression, −1 −1 푛푖푛푗 휕푎퐴 휕푎퐵 + ∑ ∑ ( ) 휔 ] 푆푐푐(0) = (1 − 푥)푎퐴 ( ) = 푥푎퐵 ( ) 푛 푖푗 휕푐 푇,푃,푁 휕푐 푇,푃,푁 푖<푗 (15) 휕푔 1 퐻푀 = −푛3 [푔 − 푇 ( ) ] + ∑푖<푗 ∑(푛푖푛푗) [휔푖푗 − The ideal value of Scc(0) can be expressed as, 휕푇 푃 푛 푆푖푑(0) = 푥(1 − 푥) (16) 휕휔푖푗 푐푐 푇 ( ) ] (8) 휕푇 푃 The Warren–Cowley short range order parameter The expression for entropy of mixing SM can be quantify the degree of local order in the binary obtained as [23] alloy [28,29]. The theoretical values of this 휕푔 3 푛푖 푛푖푛푗 휕휔푖푗 parameter can be calculated as 푆푀 = 푛3 − 푅 ∑푖=1 푛푖푙푛 − ∑푖<푗 ∑ 휕푇 푛 푛 휕푇 (s−1) Scc(0) α1 = ,S = id (17) (9) s(z−1)+1 Scc(0) The equilibrium value of 푛3 at a given pressure and where z is coordination number, which is taken as temperature is given by[23] 10 for our calculation. 휕퐺 ( 푀) = 0 (10) Transport Properties 휕푛 3 푇,푃,푁,퐶 Substituting the value of GM from Equation (6) and The mixing behaviour of the alloys forming molten after some algebraic calculation alloy can also be studied at the microscopic level in 푔 푙푛(푛 푛푢+푣−1푛−푢푛−푣) + 푌 = (11) terms of coefficient of diffusion. The mutual 3 1 2 푅푇 The Equation (11) is called equilibrium equation, diffusion coefficient (DM) of binary liquid alloys where can be expressed in terms of activity (ai) and self- 푛 푛 푛 푛 휔 diffusion coefficient (Did) of pure component with 푌 = [ 1 2 (푢 + 푣 − 1) − 푢 2 − 푣 1] 12 + 푛2 푛 푛 푅푇 the help of Darken’s equation [30] 푛2푛3 푛3 푛2 휔23 푑푙푛푎 [ (푢 + 푣 − 1) − 푣 + ] + 퐷 = 퐷 푥 푖 (18) 푛2 푛 푛 푅푇 푀 푖푑 푑푥 푛1푛3 푛3 푛1 휔13 [ (푢 + 푣 − 1) − 푢 + ] (12) with 퐷푀 = 푐퐴퐷퐵 + 푐퐵퐷퐴 푛2 푛 푛 푅푇 where DA and DB are the self – diffusion Structural Properties coefficients of pure components A and B The concentration fluctuation at long wavelength respectively, limit is of good interest because any deviation from The expression for DM in terms of Scc(0) can be 푖푑 given as ideal value 푆푐푐 (0) is significant in describing the 퐷 푆푖푑(0) nature of ordering and phase segregation in molten 푀 = 푐푐 (19) 퐷 푆 (0) alloys.