Microsoft Word - main.doc 18 B.P. Singh et.al FREE ENERGY OF MIXING AND ACTIVITY OF HgK LIQUID ALLOY B.P. Singh1, I.S. Jha2 and D. Adhikari2 1University Department of Physics, T.M. Bhagalpur University, India 2M.M.A.M. Campus, Biratnagar, Tribhuvan University, Nepal Abstract The large asymmetry observed in free energy of mixing of HgK liquid alloy is discussed on basis of Flory’s model. The concentration dependence of the free energy of mixing and activity of mercury has got special attention in the discussion. Key words: liquid alloy, Flory’s model, Free energy of mixing, activity. 1. Introduction The free energy of mixing and activity of HgK liquid alloy show large deviation from the ideal values [1,5]. The observed values of free energy of mixing (GM) are quite asymmetrical around the equi-atomic composition (c=0.5) and they show large minima near 60% of Hg [1]. In the present work, Flory’s expression for the free energy of mixing has been used to explain the alloying behavour of HgK liquid alloys. Working expressions and the results for free energy of mixing and activity are given in Section 2 and 3 receptively. Conclusion of the work is given in section 4. 2. General Formalism Flory’s expression for the free energy of mixing of a binary mixture consisting of Nc mole of species A(=Hg) and N(1-c) mole of species B(=K) is given by [2]. M 1 cG RT[c ln c (1 c) In (1 c) c ln(1 ) In(1 c)] c , ..............(i) 1 c − = + − − + −β − −β +ω −β where 0 A B V1 V β = − 0 AV and 0 BV being the atomic volumes of species A and B respectively 0 0 B AV / V 3.3 at 600 K.(Simoji 1977) . =  [4] Activity is a very important thermodynamic function because it is one of the fortunate functions which are obtained directly from experiment. The activity (a) of an element in a binary liquid is given by BK T Ina ZFE= − Where Z = valency of carrier ions of the element F = Faraday’s constant KB = Boltzmann constant E = Electromotive force which is observed directly from the experiment In order to obtain the expression for ‘a’ let us recall the standard thermodynamic relation: 19 BIBECHANA Vol. 6, March 2010 M M GRT In a G (1 c) . ................(ii) c ∂ = + − ∂ Differentiating equation (i) partially with respect to ‘c’ M 2 G 1 2c (1 c)cRT In c ln(1 c) In (1 ) ...........(iii) c c 1 c (1 c)   ∂ β − β − = − − + −β + +ω +  ∂ β −β −β    Using equations (i) and (iii) in equation (ii), we get 2 2 c(1 ) (1 c) (1 c)In a ln ............(iv) 1 c 1 c RT (1 c) −β β − ω − = + + −β −β −β 3. Result and Discussion The value of interchange energy is determined form the observed data of GM in the concentration range from 0.1 to 0.9 [1]. The value of / RTω used in the present work is -5.51. The computed values of MG / RT from equation (i) are furnished in Table -1 and plotted in Fig. – 1 with its observed values at 600 K. as a function of cHg. The computed and observed values of the free energy of mixing are in well agreement. It may be noted that the free energy of mixing of HgK liquid alloys exhibits asymmetry around equi-atomic composition. Our computed values of GM do not differ from the experimental values by more than 7.6% at any concentration. Equation (iv) has been used to compute In aHg, which is tabulated in Table-2 and plotted in Fig.-2 along with the experimental values of ln aHg at 600K, [3]. The computed and observed values of activity are in reasonable agreement/ it is observed that the activity of Hg in the HgK liquid alloys remains quite a small value for most of the concentrations i.e. Hgc 0.7≤ and then it rises very fast. There is slightly disagreement between the theoretical and experimental values of ln aHg for small concentrations of mercury but this disagreement reduces considerably at the Hg-rich end. 4. Conclusion Flory’s, model has been considered to study the concentration dependence of free energy of mixing and activity of HgK liquid alloy. Our theoretical investigation explains the asymmetry in the free energy of mixing to a great extent. The activity has been successfully explained. References 1. T.E Faber, Introduction to the theory of Liquid Metals, Cambridge University Pres, U.K. (1972). 2. P.J. Flory, J. Chem. Phys. 10, (1942) 51. 3. R. Hultgren, O.D Desai,, D.T. Hawkins, M. Gleiser, and K.K., Kelley, Selected Values of the Thermodynamics Properties of Binary Alloys, A.S.M., U.S.A. (1973). 4. M. Simoji, Liquid Metals, London Acad., U.K. (1977). 5. R.N. Singh, and A.B. Bhatia, J. Phys., F14, (1984) 2309. 20 G M /R T cHg B.P. Singh et. al TABLES & GRAPHS Table – 1 Free energy of mixing of HgK liquid at 600 K GM/RT cHg Theoretical Experimental* 0.1 -0.9053 -0.8181 0.2 -1.6135 -1.4835 0.3 -2.1975 -2.0927 0.4 -2.6573 -2.6491 0.5 -2.9759 -3.0963 0.6 -3.1206 -3.3464 0.7 -3.0368 -3.2809 0.8 -2.6327 -2.7800 0.9 -1.7432 -1.7218 • Hultgen et al, 1973 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Theoretical Experimental* Fig.-1. GM/RT – cHg curve for HgK liquid alloy at 600 K 21 In a H g cHg BIBECHANA Vol. 6, March 2010 Table – 2 Activity of Hg in liquid alloys at 600 K . In aHg cHg Theoretical Experimental* 0.1 -7.9069 -6.9078 0.2 -6.7666 -6.9078 0.3 -5.8626 -6.2146 0.4 -5.0171 -5.8091 0.5 -4.1689 -4.9618 0.6 -3.2883 -3.8167 0.7 -2.3639 -2.4889 0.8 -1.4125 -1.2483 0.9 -0.5220 -0.3538 *Hultgren et al, 1973 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Theoretical Experimental* Fig.-2. In aHg-cHg curve for liquid alloy at 600 K.