K. K. Mishra et al./ BIBECHANA 14 (2017) 54-65 : RCOST p.54 (Online Publication: Dec., 2016) 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 Thermodynamic, structural, surface and transport properties of Zn- Cd liquid alloy at 800 K K. K. Mishra1*, H . K. Limbu1, B. Yadav1, A. K. Khan2, I. S. Jha1, D. Adhikari1 Department of Physics, Mahendra Morang Aadarsh Multiple Campus, T. U., Biratnagar, Nepal 2Department of Physics, R.M. College, Saharsa, India *Email address: mailkaushalko@yahoo.com Article history: Received 25July, 2016; Accepted 18 September, 2016 DOI: http://dx.doi.org/10.3126/bibechana.v14i0.15715 This work is licensed under the Creative Commons CC BY-NC License. https://creativecommons.org/licenses/by-nc/4.0/ Abstract The mixing thermodynamic and structural properties of Zn-Cd liquid at 800K has been studied using Flory’s model. To explain the mixing properties of binary liquid alloys, size factor (ф) and ordering energy (ω) are taken into account. Thermodynamic properties like free energy of mixing (GM), activity (a), Heat of mixing (HM) and entropy of mixing (SM) and the microscopic properties like concentration fluctuation in the long wave length limit (Scc(0)) and chemical short range order parameter (α1) have been calculated. Surface property has also been studied with the help of Buttler’s model. The viscosity of the melt has been computed from Kaptay equation and BBK models. Both the viscosity and surface tension of the alloy increase with addition of zinc- component. Keywords: Thermodynamic properties; Structural properties; Surface properties; Transport properties 1. Introduction Zn-Cd alloy is a simple eutectic system which has been widely studied due to its low melting point and regular lamellar structure. Since cadmium is highly reactive element it has limited applications in its pure state. But the alloys of cadmium have several useful properties for industrial applications. When cadmium is alloyed with zinc, the properties of hardness, wear resistance, mechanical strength and fatigue strength are significantly improved. Cadmium and cadmium based alloys is the subject of both theoretical and experimental research studies [1-6]. Zinc–Cadmium alloys are used as solders at medium temperature which provide excellent corrosion resistance joints on most metals. Devices with such superior strength joints can work in high vibration http://nepjol.info/index.php/BIBECHANA mailto:mailkaushalko@yahoo.com http://dx.doi.org/10.3126/bibechana.v14i0.15715 https://creativecommons.org/licenses/by-nc/4.0/ https://creativecommons.org/licenses/by-nc/4.0/ https://creativecommons.org/licenses/by-nc/4.0/ K. K. Mishra et al./ BIBECHANA 14 (2017) 54-65 : RCOST p.55 (Online Publication: Dec., 2016) and high stress applications in electronics, lighting and electrical products. Moreover, use of cadmium in electroplating as in cyanide bath poses problems of environmental concern because cadmium is toxic. Zn- Cd alloys can be used in dry electroplating and can be a safer potential substitute for cadmium. In metallurgical science, the study of mixing properties of liquid alloys is important because a good knowledge of their mixing properties in the liquid state is necessary for preparation of desired materials. Surface properties are required to understand the surface related phenomena such as corrosion, wetting characteristics of solders and kinetics of phase transformation. Transport properties such as viscosity and diffusivity of metals in the liquid state are required for many metallurgical processes and heterogeneous chemical reactions. Many researchers [7-12] have been working with several models to explain the mixing properties of binary liquid alloys. The alloying behavior of binary liquid alloys can be studied theoretically by computing thermodynamic, structural, transport and surface properties of alloys in the liquid state. The mixing behavior of binary liquid has been explained by several theoreticians of the basis of several models [13-19]. In this work we have used Flory’s model [19, 20] to explain the thermodynamic and structural behavior of Zn-Cd liquid alloy at 800 K. In Flory’s model the interaction energy parameter is considered as temperature dependent and is determined by fitting experimental values of thermodynamic functions at different concentrations. 2. Formalism 2.1 Thermodynamic function 2.1.1 Free energy of mixing Flory’s model [19] is found to be the best applicable for the determination of thermodynamic and microscopic properties of those alloys which has greater size mismatch. Homogenous solution of binary liquid alloy A-B consists of cA (≡ c) mole of A and cB {≡ c(1-c)} mole of B respectively, where cA and cB are the mole fractions of A (≡ Zn) and B (≡ Sn) in the binary liquid solution of A and B. Thus free energy of mixing of those alloys whose constituent atoms differ widely in sizes can be expressed as [19] 𝐺𝑀 = 𝐺(𝑖𝑑𝑒𝑎𝑙) + 𝐺(𝑠𝑖𝑧𝑒) + 𝑐(1 − 𝑐)𝐺(𝜔) (1) where, 𝐺(𝑖𝑑) = [𝑐𝑙𝑛𝑐 + (1 − 𝑐)ln⁡(1 − 𝑐)]𝑅𝑇 (2) G (size) and G (ω) are contributions due to the size effect and the interchange energy (ω) respectively. From Flory’s model [19], we have 𝐺(𝑠𝑖𝑧𝑒) = 𝑅𝑇[𝑐𝑙𝑛(1 − 𝛽) − ln⁡(1 − 𝛽𝑐)] (3) 𝐺(𝜔) = 𝑐(1 − 𝑐)𝜔 (1 − 𝛽𝑐)⁄ (4) 𝛽 = 1 − 1/𝛷 (5) with𝛷 = 𝜗𝐵/𝜗𝐴 where⁡𝜗𝐴and 𝜗𝐵are atomic volumes of the pure species A and B respectively [20] Here ϑZn =ϑM [1+𝛼p (T-TM)] and ϑCd = ϑM [1+𝛼p (T-TM)] (6) where, ϑM = atomic volume at melting point K. K. Mishra et al./ BIBECHANA 14 (2017) 54-65 : RCOST p.56 (Online Publication: Dec., 2016) TM = melting temperature and 𝛼p = volume coefficient at constant temperature Then the expression for free energy of mixing is given by GM = ⁡RT⁡[c⁡ln⁡c + (1 − c)ln(1 − c) + ⁡c⁡ln(1⁡– ⁡β) − ⁡ln(1⁡– ⁡βc)] + 𝜔𝑐(1−𝑐)⁡ (1−𝛽𝑐) (7) 2.1.2 Chemical activity (a) The activity (aA) of the element A in the binary liquid alloy is given as 𝑅𝑇𝑙𝑛𝑎𝐴 = 𝐺𝑀 + (1 − 𝑐) 𝜕𝐺𝑀 𝜕𝑐 (8) From equation (1) and (8), we get 𝑙𝑛𝑎𝐴 ⁡⁡= ⁡𝑙𝑛⁡[𝑐⁡(1 − 𝛽)⁡𝜂(𝑐)] ⁡⁡+ 𝛽(1 − 𝑐)⁡𝜂(𝑐) ⁡+⁡(1 − 𝑐)2𝜂2(𝑐)𝜔/𝑅𝑇 (9) where, 𝜂(𝑐) = 1 (1 − 𝛽𝑐)⁄ 2.1.3 Entropy of mixing (SM) The temperature derivative of GM provides an expression for integral entropy of mixing 𝑆𝑀 = −𝑅𝐺(𝑖𝑑) − 𝑅𝐺(𝑠𝑖𝑧𝑒) − 𝑐(1 − 𝑐)𝜂(𝑐)𝜕𝜔 𝜕𝑇 + 𝑅𝑇𝑐(1 − 𝑐)𝜂(𝑐) ⁡⁡×⁡ [𝛽/(1 − 𝛽) − 𝑐𝜂(𝑐)𝜔/𝑅𝑇] ∂𝛽/ ∂𝑇 (10) where, 𝜕β/𝜕T =(𝛼B –𝛼A).𝜗𝐴/𝜗𝐵and𝜂(𝑐) = 1 (1 − 𝛽𝑐)⁄ where, 𝛼A and 𝛼B are the coefficients of thermal expansion of pure species A and B respectively. 2.1.4 Heat of mixing (HM) The heat of mixing can be obtained from equation (1) and (10) from standard thermodynamic relation, 𝐻𝑀 𝑅𝑇 = 𝑆𝑀 𝑅 + 𝐺𝑀 𝑅𝑇 (11) 𝐻𝑀 𝑅𝑇 = ⁡cln⁡c⁡ +⁡(1 − c)ln⁡(1 − c) + ⁡c⁡ln(1⁡– ⁡β) − ⁡ln(1⁡– ⁡βc) +⁡ 𝑐(1−𝑐)⁡ (1−𝛽𝑐) ⁡ . 𝜔 𝑅𝑇⁡ ⁡⁡− ⁡α(c)⁡– ⁡Φ⁡(c) − ⁡⁡ 1 𝑅⁡⁡ 𝑐(1−𝑐)⁡ (1−𝛽𝑐) . 𝜕𝜔 𝜕𝑇 +⁡ 𝑇𝑐(1−𝑐)⁡ (1−𝛽𝑐) . [⁡⁡ 𝛽 (1−𝛽) ⁡− ⁡ 𝑐 (1−𝛽𝑐) 𝜔 𝑅𝑇⁡ ]⁡. 𝜕𝛽 𝜕𝑇 (12) where, 𝛼(𝑐) = [𝑐𝑙𝑛𝑐 + (1 − 𝑐)ln⁡(1 − 𝑐)]andф(𝑐) = [𝑐𝑙𝑛(1 − 𝛽) − ln⁡(1 − 𝛽𝑐)] 2.2 Microscopic functions 2.2.1 Concentration fluctuation in the long wavelength limit (Scc(0)) To study the atomic order of binary liquid alloy it is important to understand the behavior of the long wavelength limit of the concentration- concentration structure factor (Scc(0)) and is given as [10,17,18] 𝑆𝐶𝐶(0) = 𝑅𝑇 ( 𝜕2𝐺𝑀 𝜕𝑐2 )T,P,N (13) The expression for concentration fluctuation in the long wavelength limit is obtained using equation (1) and (13) and is expressed as K. K. Mishra et al./ BIBECHANA 14 (2017) 54-65 : RCOST p.57 (Online Publication: Dec., 2016) 𝑆𝑐𝑐(0) = 𝑐𝐴𝑐𝐵 [1− 𝑐𝐴𝑐𝐵 (1−𝛽𝑐)3 ⁡{2(1−𝛽) 𝜔 𝑅𝑇 −𝛽2(1−𝛽𝑐)}] (14) The experimental values of concentration fluctuation in the long wavelength limit Scc(0) derived from experimental data of the activities of the constituent species of the binary liquid alloys from the relation 1 ,, 1 ,, )1()0(                   NPT B B NPT A A c a ca c a acScc where aA and aB are the activities of the component of A and B respectively. 2.2.2 Short range order parameter (α1) The Warren-Cowley short range order parameter 𝛼1 can be estimated from the knowledge of Scc(0) as 𝛼1 = 𝑠−1 𝑠(𝑍−1)+1 (15) where Z= coordination number and 𝑆 = 𝑆𝑐𝑐(0) 𝑆𝑐𝑐 𝑖𝑑(0) 2.3 Surface tension Buttler assumed the existence of surface monolayer at the surface of a liquid as a separate phase that is in thermodynamic equilibrium with the bulk phase and derived an equation, known as Buttler equation [7, 21, 22]. Buttler equation for the surface tension, σ of a binary A-B solution at temperature T reads as [7, 21, 22] 𝛤 = 𝛤1 + 1 𝐴1 (𝐺1 𝐸,𝑠 − 𝐺1 𝐸,𝑏) + 𝑅𝑇 𝐴1 [ln(1 − 𝑋2 𝑠) − ln(1 − 𝑋2 𝑏)] = ⁡𝛤2 + 1 𝐴2 (𝐺2 𝐸,𝑠 − 𝐺2 𝐸,𝑏) +⁡⁡⁡⁡ 𝑅𝑇 𝐴2 [ln(𝑋2 𝑠) − ln(𝑋2 𝑏)] (16) where, Γ1 and Γ2 are the surface tension of the pure component 1 and 2 respectively. 𝐺𝑖 𝐸,𝑠 and𝐺𝑖 𝐸,𝑏 (i = 1,2) are partial excess free energy of component i in the surface and the bulk respectively. The molar surface area of the component i can be computed by using the relation 𝐴𝑖 = 𝐾.𝑁𝐴 1/3 . 𝑉𝑖 2/3 (17) where, K (= 1.091) is geometrical factor for the liquid alloy [23, 24] NA is Avogadro’s number and Vi is the molar volume of the component I. For binary mixture𝑋1 𝑏 + 𝑋2 𝑏 = 𝑋1 𝑠 + 𝑋2 𝑠 = 1, where 𝑋𝑖 𝑠⁡𝑎𝑛𝑑⁡𝑋𝑖 𝑏 are mole fractions of component i in the surface and bulk respectively. R is universal gas constant and T stands for absolute temperature. 2.4 Viscosity To study the atomic transport behavior in Zn-Cd alloys, we have computed its viscosity at 800 K by using Kaptay equation and BBK model [24, 25]. 2.4.1 Kaptay equation Kaptay [24] equation for the viscosity of the binary liquid alloys at temperature T is given as 𝜂 = ℎ𝑁𝐴 ∑ 𝐶𝐾Ω𝐾+Ω 𝐸 𝐾 ⁡⁡exp⁡[ ∑ 𝐶𝐾𝐺𝐾 ∗ ⁡−⁡𝜃.𝐻𝑀𝐾 𝑅𝑇 ] (18) K. K. Mishra et al./ BIBECHANA 14 (2017) 54-65 : RCOST p.58 (Online Publication: Dec., 2016) where, h = Plank’s constant, NA is Avogadro’s number, R is the ideal gas constant, ΩEis the excess molar volume upon alloy formation, HM is enthalpy of mixing of the alloy, CK (=A,B) represents concentration,ΩK represents the molar volume and 𝐺𝐾 ∗ is the Gibb’s energy of activation of the viscous flow in pure component K and 𝜃 is a constant whose value is taken to be 0.155±0.015 [25]. 𝐺𝐾 ∗of component K can be calculated from the equation [25] 𝐺𝐾 ∗ = 𝑅𝑇 ln ( 𝜂𝐾Ω𝐾 ℎ𝑁𝐴 ) (19) where, 𝜂K is the viscosity of pure component K; is the planks constant. 𝜂K at temperature T can be evaluated by 𝜂𝐾 =⁡𝜂𝑂𝐾⁡ exp [ 𝐸𝑛 𝑅𝑇 ] (20) where, 𝜂𝑂𝐾⁡ is constant (in unit of viscosity) and En is the energy of activation of viscous flow for pure metal (in unit of energy per mole). 2.4.2 Budai-Benko- Kaptay (BBK) model The expression for estimation of the viscosity of a multi- component alloy from BBK model is given by [25] 𝜂 = 𝐴(𝑇∑ 𝑐𝐾𝑀𝐾⁡𝐾 )1/2. (∑ 𝑐𝐾Ω𝐾 +Ω𝐸 ⁡)⁡𝐾 − 2 3 . exp[(∑ 𝑐𝐾𝑇𝑚,𝑘 − 𝐻𝑀 𝑞𝑅𝐾 ) . 𝐵 𝑇 ]⁡ (21) where, A and B are fitting parameter equal to (1.80±0.39)x10-8 (J-Kmol-1/3)1/2 and (2.34±0.20) respectively; cK is the concentration , and MK is the atomic mass of the given component K, q is the semi – empirical parameter equal to q≡25.4±2; ΩK is the molar volume of the alloy, and Tm,kis the effective melting temperature of the component K given by 𝑇𝑚,𝑘 =⁡ 𝑇 𝐵 ⁡𝑙𝑛 ( 𝜂𝐾Ω𝐾 2 3 𝐴𝑀𝐾 1 2𝑇 1 2 ) (22) where ,𝜂K is viscosity of the pure component K. 3. Result and discussion 3.1 Free energy of mixing To compute the free energy of mixing GM/RT of molten Zn-Cd as a function of concentration at 800 K, size factor (ф) and energy parameter are required. The interchange energy ω has been calculated from equation (7) with the help of experimental values of GM [26] in the concentration range of cZn=0.1 to 0.9 by the method of successive approximation and the value of size factor ф is evaluated by equation (5) and (6) in alloying temperature. In the present work the best fit value of ordering energy (ω) has been found to be 1.085RT. The size ratio (i.e. ф = VCd/VZn) where V stands for atomic volume for the constituent atom in Zn-Cd alloys at 800K is determined by using equation (5). The value of size ratio is found to be 1.43. Using these two input parameters the free energy of mixing GM of Zn-Cd liquid alloys at 800 K has been computed using equation (7) for concentration range cZn =0.1 to 0.9. The experimental values of free energy of mixing are taken from the ref. [26]. K. K. Mishra et al./ BIBECHANA 14 (2017) 54-65 : RCOST p.59 (Online Publication: Dec., 2016) The plot of computed and experimental values of free energy of mixing with respect to concentration is depicted in fig 3.1. The computed and experimental values of free energy of mixing are in good agreement in entire concentration range. The disagreement between the computed and experimental values is within 6%. The theoretical values is minimum around cZn = 0.4 (i.e. GM/RT = -0.3919) while the experimental values is minimum around cZn = 0.5 (i.e. GM/RT = -0.3927). The minimum value suggests that Zn-Cd alloy in liquid state at 800 K is weekly interacting system. 3.2 Activity By putting the input parameters interchange energy (ω) and size factor (ф) in equation (8) and (9), we have computed the activity of Zn and Cd of Zn-Cd alloys in molten state at 800 Fig. 3. 1: Free energy of mixing of Zn-Cd liquid alloys at 800 K. The solid line represents theoretical values and circle represents experimental values Fig.3. 2: Activities aZn and aCd of Zn-Cd liquid alloys at 800 K. The solid line represents theoretical values and circle represents experimental values. The computed values of activity of both the components of Zn-Cd alloys at 800 K are in good agreement with the experimental values for whole range of concentration with some discrepancies. For zinc the maximum departure from experimental value [26] of lnaZn from experimental value is 9.4% around cZn = 0.4 as shown in figure 3.2. 3.3 Heat of mixing The heat of mixing of Zn-Cd liquid alloy at 800 K has been determined by using equation (10). Both of the computed and experimental values of heat of mixing are positive in whole range of concentrations. The computed and experimental values of heat of mixing are in reasonable agreement in all compositions. K. K. Mishra et al./ BIBECHANA 14 (2017) 54-65 : RCOST p.60 (Online Publication: Dec., 2016) There is small negative deviation of computed values from experimental values in the region CZn>0.4 whereas small positive deviation has been observed in the region CZn<0.4 at CZn=0.4. The computed and experimental values are almost same. The graphical comparison between computed and experimental values [26] of heat of mixing with respect to concentration is displayed in fig 3.3. 3.4 Entropy of mixing Following equation (11) the entropy of mixing of Zn-Cd alloy in molten state at 800 K has computed. For the computation of entropy of mixing the basic input parameters are interchange energy (ω), size factor (ф) and temperature derivative of ordering energy (dω/dT). For the consistency we have used the same values of these parameters as used in the calculation of free energy of mixing, activity and heat of mixing. The computed and experimental values are found to be in excellent agreement. The disagreement between computed and experimental values is within 1%. The computed entropy of mixing is minimum (i.e.SM/R = 0.7050) at CZn =0.5. The computed values of entropy of mixing together with experimental values are plotted as a function of concentration as shown in fig 3.4. Fig. 3. 3: Heat of mixing of Zn-Cd liquid alloys at 800 K. The solid line represents theoretical values and circle represents experimental values. Fig. 3. 4: Entropy of mixing of Zn-Cd liquid alloys at 800 K. The solid line represents theoretical values and circle represents experimental values. 3.5 Concentration – Concentration structure factor in long wavelength limit Scc(0) The theoretical value of Scc(0) of Zn-Cd liquid alloys at 800 K computed from equation (12) using the same energy parameter ω and size factor ф for the full range of concentration (i.e. CZn= 0.1 to 0.9) as used for the computation of free energy of mixing, activity, heat of mixing and entropy of mixing. K. K. Mishra et al./ BIBECHANA 14 (2017) 54-65 : RCOST p.61 (Online Publication: Dec., 2016) Both the computed and experimental values of Scc(0)>Scc id(0). The plot of computed and experimental values of Scc(0) along with the ideal values with respect to concentration are also depicted in figure 3.5. The computed values of Scc(0) are in good agreement with the experimental values in entire range. The disagreement between the computed and experimental values is within 12%. The theoretical value is maximum at CZn= 0.6 (=0.6407), but the experimental value is maximum at CZn = 0.5 (=0.5522). The Scc(0) is used to understand the nature of atomic order in binary alloys. Any deviation of Scc(0) from ideal value is of interest in reflecting the extent of interactions in the mixture. At the given composition if Scc(0)Scc id(0), there is tendency of segregation or phase separation. In present case Scc(0)>Scc id(0) which indicates that Zn-Cd liquid alloys is segregating in nature. 3.6 Chemical short range order parameter (α1) The chemical short range parameter has been computed by using equation (13) as a function of concentration of Zn-Cd liquid alloys at 800 K for full range of concentrations. In our present work we have computed the value of short range order parameters for different values of coordination numbers (i.e. Z= 7,8,10). Fig. 3. 5: Concentration fluctuation of Zn-Cd liquid alloys at 800 K. The solid line represents theoretical values, dotted line represents ideal values and circle represents experimental values. Fig.3 . 6: Chemical short range parameter (𝛼1) of Zn-Cd liquid alloys at 800 K for different co- ordination number Z= 7, 8 and 10. Dotted line represents ideal Scc(0). The values of short range order parameter have been found positive in all concentration ranges. The value of short range order parameter has been found maximum at CZn = 0.6 in all three coordination numbers. The plot of computed values of Zn-Cd liquid alloy at 800 K is depicted in fig3.6. K. K. Mishra et al./ BIBECHANA 14 (2017) 54-65 : RCOST p.62 (Online Publication: Dec., 2016) The knowledge of short range order parameter (α1) provides an immediate insight into the nature of the local arrangement of atoms in the mixture. The minimum possible value of α1 is -1 and it implies complete ordering of unlike atoms pairing at nearest atoms. On the other hand the maximum value of α1 is +1 which implies complete segregation leading to the phase separation and α1=0 corresponding to the random distribution of atoms. Figure 3.6 shows that α1 is positive in the entire concentration range (i.e. CZn= 0.1 to 0.9) showing that α1 in Zn-Cd is segregating system of like atoms pairing (i.e. Zn-Zn and Cd- Cd ) as nearest neighbours. 3.7 Surface tension The surface tension of the liquid alloys can be computed using equation (14). The ratio of partial excess Gibbs energy in the bulk and that in the surface can be expressed as 𝛽 =⁡ 𝐺𝑖 𝐸,𝑠 𝐺𝑖 𝐸,𝑏 where⁡𝐺𝑖 𝐸,𝑠 and 𝐺𝑖 𝐸,𝑏 are the partial excess free energy in the surface and that in the bulk. The values of excess mixing of the pure componenst are taken from ref. [26]. The value of parameter β has been taken as 0.83 as suggested by different researchers to compute surface tension of liquid alloys [27-29]. We have taken the surface tension of Zn-Cd and temperature coefficients for pure Zn and Cd components from the ref. [30]. The surface tension of the pure component at the temperature of study have been computed by the equation 𝛤(𝑇) = ⁡𝛤𝑚 + 𝜕𝛤 𝜕𝑇 (𝑇 − 𝑇𝑚) T=800 K; Tm= melting temperature (Tm= 692.5 K for Zn, and 594 K for Cd); 𝜕𝛤 𝜕𝑇 (= -0.17mNm-1K-1 for Zn, and -0.26 mNm-1K-1 for cadmium) is the temperature coefficient of surface tension. Fig 3. 7: Surface tension of Zn-Cd liquid alloy at 800 K. Solid line is calculated surface tension and dotted line is ideal surface tension. Fig 3. 8 : Viscosity (𝜂) of Zn-Cd liquid alloy at 800K versus concentration of Zn. Dotted line represents ideal viscosity, solid line represents BBK and solid with circle represents Kaptay. K. K. Mishra et al./ BIBECHANA 14 (2017) 54-65 : RCOST p.63 (Online Publication: Dec., 2016) The graph shows that the computed surface tension for Zn-Cd system at 800 K is less than ideal value (= C1Γ1 + C2Γ2) at all the concentration of Zn as shown in figure 3.7 i.e. there is negative departure of surface tension from ideality. It is found that surface tension of Zn in Zn-Cd alloy is increased on increasing the bulk concentration of Zn. 3.8 Viscosity To compute viscosity of Zn-Cd alloy at 800 K, the viscosities of the pure components Zn and Cd at 800 K are required. The viscosity of pure component can be obtained with the help of constants 𝜂ok and E for the metals [31]. We have used Kaptay equation (15) and BBK model (16) to evaluate viscosity of the alloy and compared the results as shown in figure 3.8. To calculate the viscosity by Kaptay equation enthalpy of mixing (HM), the Gibbs free energy of activation of various viscous flow of the pure components (G*) and excess molar volume of the alloy (ΩE) are required. The enthalpy of mixing is taken from Flory’s model calculations. The value of G* for each component was calculated from equation (17) with knowing the viscosity and molar volumes of pure components. Due to lack of experimental data we have taken the volume of ΩE to be zero in our calculations for simplicity. Viscosity from BBK model requires heat of mixing (HM), excess molar volume of the component (ΩE) and effective melting temperature of the component (Tm,k). Heat of mixing is calculated from Flory’s model calculation and ΩE is taken as zero in our calculation for simplicity. 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