Assessment of Surface Tension and Viscosity of In-Zn melt

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1 The Himalayan Phyic Vol. 6 & 7, pril 2017 (15-19) ement of Surface Tenion and Vicoity of In-Zn melt ISSN R. P. Koirala 1, 2*, S.K. Yadav 2, 3, 4,. P. Singh 1, I. S. Jha 2, D. dhikari 2 1 Univerity Department of Phyic, T.. hagalpur Univerity, hagalpur, ihar, India 2 Department of Phyic,... Campu, Tribhuvan Univerity, iratnagar, Nepal 3 Central Department of Phyic, Tribhuvan Univerity, Kirtipur, Nepal 4 PUSET, Purwanchal Univerity, iratnagar, Nepal *Correponding author: rpphyic@gmail.com btract: comparative tudy of the concentration dependence of urface tenion and vicoity of molten In-Zn alloy at 700 K ha been performed uing energetic, obtained from thermodynamic analyi in the framework of elf-aociation model. The urface tenion of the alloy ha been calculated from the two method, layered tructure approach and elf aociating mixture method, and vicoity from oelwyn-hughe equation and Kaptay equation. The theoretically computed reult for the thermodynamic propertie of the alloy are found in excellent agreement with the correponding experimental reult howing that the alloy i egregating in nature. oth urface tenion and vicoity of the In-Zn alloy are found to increae with the addition of Zn atom. Keyword: Enthalpy of mixing; Self aociation; Surface tenion; Vicoity. 1. Introduction Indium, relatively rare but veratile metal, can be alloyed to many metal uch a bimuth, lead, gold, platinum, gallium, tellurium, thallium, ilver, tin and ha been called vitamin in alloy. It can form fuible alloy with gallium, zinc etc. and are ued for older. Of many indium baed alloy, In- Zn alloy in the liquid tate, in particular poe everal intereting feature. It i reported that In-Zn alloy i eutectic in the range from 2.06 to 3.80 atomic percent of zinc having a eutectic temperature of o C [1]. The oberved data of the free energy of mixing and the entropy of mixing of In-Zn alloy at 700 K [2] how remarkable deviation from the ideal value. lo the concentration fluctuation in long range limit, S CC (0) computed from oberved activity data [2] how aymmetrical behaviour about the equi-atomic compoition. With thee feature a uch the In-Zn alloy i drawing attention of the reearcher [1, 3] toward the invetigation of it alloying nature. The olubility in a binary alloy can be dicued in term of the atomic volume ratio, valence ratio and electronegativity difference of the component metal and but thee factor are not explicitly available in any imple way. In order to undertand the alloying behaviour of binary liquid alloy in detail, thermo-phyical propertie uch a thermodynamic, urface and tranport propertie of mixing are taken into account. The energetic in a liquid alloy i comprehended from the etimation of the free energy of mixing, heat of 15 mixing and entropy of mixing. The nature of atomic bonding reulting in a particular kind of arrangement of atom in the alloy, either ordering or egregating, i judged from the analyi of the tructural propertie, the concentration fluctuation in long range limit and hort range order parameter. The mechanim behind variou phenomena uch a mechanical behaviour, kinetic of phae tranformation and catalytic activity can be undertood from the knowledge of urface concentration and urface tenion. Vicoity i one of the tranport propertie, which i required to undertand the high temperature dynamic in the liquid alloy. In the preent work, we intend to carry out a theoretical tudy of mixing behaviour of In-Zn alloy at 700 K by computing the energetic in it from thermodynamic analyi baed on elf aociation model, and the urface tenion and vicoity from the method baed on tatitical thermodynamic. We employ elf aociation model for the tudy of the thermodynamic propertie of the alloy becaue the value of experimental S cc (0) are found to be greater than the ideal S cc (0) at all compoition. In computation of both urface tenion and vicoity in thi work, we employ the energetic like interaction energy, enthalpy of mixing etc. computed from elf-aociation model [4-6]. Due to canty of experimental data of urface tenion and vicoity a function of compoition, we intend to carry out comparative analye for both of thee propertie. The urface tenion i computed from layered tructure approach [7-10] and

2 R. P. Koirala et al elf aociating mixture method [11]. For the calculation of vicoity of the alloy, we employ oelwyn-hughe (-H) equation [12] and Kaptay equation [12]. In the following ection, the expreion required for the calculation are preented. Section 3 outline the reult and dicuion of the work, and concluion i given in ection THEORETICL SIS 2.1 Thermodynamic propertie The elf-aociation model [4, 5] i a tatitical mechanical formulation for tudying phae egregating binary liquid alloy. ccording to thi model, one mole of a binary liquid alloy - i aumed to conit of N (=Nc ) atom of elemental metal and N (=Nc ) atom of elemental metal ituated at equivalent ite, N being the total number of atom, and c and c the mole fraction concentration of and repectively. There i hort ranged atomic interaction between the nearet neighbour that form a polyatomic matrix leading to the formation of like atom cluter or elfaociate of the type i and j, where i and j are the number of atom in the cluter of element and repectively [5]. In the framework of elf aociation model, the following expreion are ued in computing the thermodynamic function of binary liquid alloy [5]: (i) Free energy of mixing, G The free energy of mixing, G i given by G = RT [ c lnϕ+ c ln( 1 ϕ)] + c ( 1 ϕ) W (1) with φ = c /( c n c ) (2) + Here, R i molar ga contant; T i the temperature; W i ordering energy parameter and n = j / i i the ratio of elfaociate formed by like atom pair. (ii) Entropy of mixing, S The entropy of mixing, S i obtained by the temperature derivative of the free energy of mixing and can be put in the form W (3) S = R [ clnϕ+ c ln( 1 ϕ)] c( 1 ϕ) (iii) Enthalpy of mixing, H The enthalpy of mixing, H i related to the free energy of mixing, G and the entropy of mixing, S by the tandard thermodynamic relation H = G + T S W or H = c (1 φ) [ W T ] (4) 2.2. Surface Propertie (i) The firt approach [7, 8] link urface tenion of a binary liquid alloy, to it bulk thermodynamic propertie through the urface tenion and, and activity coefficient γ and γ of the component and of the alloy, which can be expreed a: S c S 2 2 W σ= σ + Yln + [p(c ) + q(c) ] (5a) γ c a S c S 2 2 W σ = σ + Y ln + [p(c) + q(c) ] (5b) γ c a with Y = k T / a, where k i oltzmann contant; p and q are urface coordination fraction which are taken a p = 0. 5 and q = 0.25 for cloed packed tructure; c and c are urface concentration of and component repectively. W i the order energy parameter which, in thi analyi, i taken from thermodynamic calculation done in the framework of elf-aociation model. a i the mean atomic urface area of the alloy which i calculated a: a = c k ak ; k =, (6) where the atomic area of hypothetical urface for each component i calculated a: 2 / 3 a k = (Vk / N) (7) where N i vogadro number and V k i the molar volume of the component k at the temperature of invetigation, T, which i calculated from denity of the metal at that temperature. (ii) The econd approach for computing urface propertie i elf-aociating mixture method developed for egregating alloy. In thi method the urface concentration i computed by imultaneouly olving the following pair of equation [9] at all bulk concentration and then the urface tenion of the alloy i computed from either of the equation: ( σ = σ + k T / a)[ln c / c ) + p{ln(c φ / c φ) + (c φ c φ ) / c c } + q{ln(c / φ) + ( φ c ) / c } + iω kt p ϕ + q ϕ (8a) 2 2 / { ( 1 ) ( 1)( 1 ) }] The Himalayan Phyic Vol. 6 & 7, pril

3 ement of Surface Tenion and Vicoity of In-Zn melt σ =σ + (kt / a)[lnc / c) + p{ln(c(1 φ )/c(1 φ) 3. RESULTS ND DISCUSSION + ( i j)( ϕ ϕ)/ i} q{ln((1 φ) / c) + φ(i j) /i} 3.1. Thermodynamic propertie jω / k T{p( φ ) + (q 1) φ }] (8b) with φ = ic /( ic + jc ) and φ = ic /( ic + jc ) (9) where i atom of element (=In) are aumed to be aociated with j atom of element (=Zn) and all other ymbol have the ame meaning a thoe in the firt approach Vicoity (i) The firt equation we employ for the computation of vicoity of liquid In-Zn alloy i oelwyn-hughe (-H) equation which i baed on fact that the vicou flow become more difficult when the coheion energy of the alloy i increaed and at a temperature T, it i given a [12]: η= ( c η+ c η )( 1 2c c. H / RT ) (10) where η and η k repreent repectively the vicoity of the alloy and of pure metal k ( k =, ) ; c k the mole fraction of component k, H the heat of mixing of the alloy and R i the univeral ga contant. For mot metal the variation of vicoity, η k with temperature T may be expreed a [13]: ηk = ηok exp( E / RT ) (11) where, η and E are contant for pure metal and are ok expreed in unit of vicoity and energy per mole repectively. (ii) The econd equation that we employ to compute the vicoity of the alloy i the Kaptay equation [12]. Thi equation preent the theoretical relationhip between the coheion energy of the alloy and the activation energy of vicou flow. It i expreed a: * * h N c + a G c2g.h η = exp (12) E c V + c V + V R T * where G i the Gibb energy of activation of the vicou k flow in pure component k, given by * ηkv k Gk = RT ln( ) ( k =, ) (13) hn t a given temperature mixing propertie of a binary liquid alloy vary with the compoition of the alloy. The ratio of elfaociate, n and the ordering energy, W of elf aociation model have been etimated a model fit parameter for the liquid In-Zn alloy at 700 K by uing the experimental value of the free energy of mixing, G [2] in Eq. (1). We have obtained the bet fit value of the parameter to be n = and W = RT. The poitive ign of W indicate a tendency of like atom pairing in the liquid In-Zn alloy. Next we have computed the entropy of mixing, S from Eq. (3) by etimating the temperature dependence of the energy W parameter to be given a, = R. The non-zero value of thi term indicate that the interaction energy i temperature dependent. Uing the calculated value of the free energy of mixing and the entropy of mixing, we have next computed the enthalpy of mixing, H of the alloy throughout the whole range of bulk concentration from Eq. (4). The enthalpy of mixing contain information about the nature of binding in the liquid alloy. Similarly, entropy of mixing help to draw important tructural information of binary liquid alloy. It repreent the haring of energy between the pecie in the alloy and determine the equilibrium tate of the mixture. Here, H i enthalpy of mixing of the alloy; N i vogadro number; V k repreent the molar volume of the component k; E V i the exce molar volume which can be neglected for implicity [12]. Figure 1- Free energy of mixing (G ), entropy of mixing (S ) and enthalpy of mixing (H ) of In-Zn alloy at 700K veru concentration of Zn: olid curve-theory; circle-experimental [2]. Theoretically computed reult for G, S and H are compared with the correponding experimental reult [2] 17 The Himalayan Phyic Vol. 6 & 7, pril 2017

4 in Fig. 1. The plot how that the computed reult for G and S are in well agreement with the experimental reult but a light departure i oberved in H. Thi diparity may be due to entropic contribution. The elf aociation model thu well explain the oberved thermodynamic propertie of liquid In-Zn alloy at 700 K. Poitive ign of the enthalpy of mixing along with the parameter W indicate that the liquid In-Zn alloy at 700 K i egregating in nature Surface tenion Following the reference [13], the molar volume and urface tenion of In and Zn metal at 700 K are computed. Uing the value of W and the activity coefficient of the metal [2] a input, the urface concentration and urface tenion of the liquid In-Zn alloy at 700 K have been computed by olving the pair of equation (5a) and (5b) in the full range of bulk concentration. Next, Eq. (7a) and (7b) are olved together for the urface concentration by auming the liquid In-Zn alloy at 700 K to be a elf-aociating mixture with i=1.68 (In) and j= 1(Zn) in the ratio of elf-aociate and the urface tenion of the alloy i computed at all bulk concentration from either equation Vicoity R. P. Koirala et al Uing vicoitie of the component from reference [13] and enthalpy of mixing computed from elf aociation model, the vicoity of the In-Zn alloy at 700 K i calculated from Eq. (10) and (12) a function of bulk concentration of Zn atom. The contribution of exce volume of the alloy, V E i too mall to be neglected and it i not taken in thi work. The vicoity of the In-Zn alloy in our analyi ha been found to increae with the addition of the Zn atom. reaonably good agreement i noticed in the et vicoity value [Fig. 3] computed from two method. Figure 3- Vicoity of In-Zn alloy at 700K veru concentration of Zn: olid curve- oelwyn-hughe equation; circle- Kaptay equation. Figure 2- Surface tenion of In-Zn alloy at 700K veru concentration of Zn: olid curve-layered tructure approach; circle-elf-aociating mixture method. The urface tenion iotherm ha been depicted in Figure (2). The plot how that there i good agreement in the two et of the reult having noticeable deviation from the ideal value. The urface tenion iotherm how that the urface tenion of the alloy increae with increae in concentration of Zn atom lowly and almot linearly up to the compoition In 0.4 Zn 0.6. bove that compoition, i.e. toward the Zn-rich end of the compoition, a rapid increae in urface tenion i noticed. 4. Concluion Our theoretical invetigation for the thermodynamic propertie of mixing of In-Zn alloy at 700 K well explain the aymmetry oberved in the propertie and reveal that homo-coordination of atom i preferred over heterocoordination in the liquid alloy. The two et of urface tenion value obtained from the two approache are found in excellent agreement while there i only atifactory agreement between the two et of reult for the vicoity. oth urface tenion and vicoity are found to increae with the addition of Zn atom howing marked deviation from ideality. The Himalayan Phyic Vol. 6 & 7, pril

5 ement of Surface Tenion and Vicoity of In-Zn melt cknowledgment One of the author (R.P. Koirala) extend hi incere gratitude to Prof. Dr. Pradeep Raj Pradhan and Prof. Dr. hok Kumar (Pot Graduate Department of Phyic,... Campu, Tribhuvan Univerity, iratnagar, Nepal), and Prof. Dr. L.N. Jha (Former Head, Central Department of Phyic, Tribhuvan Univerity, Kirtipur, Nepal) for their fruitful uggetion and encouraging dicuion. REFERENCES [1] J. Dutkiewicz and W. Zakulki, ulletin of lloy Phae Diagram, 5, 284 (1984) [2] R. Hultgren, P. D. Deai, D. T. Hawkin,. Gleier and K.K. Kelly, Selected value of the thermodynamic propertie of binary alloy, S, etal Park, OH (1973) [3] C. L. Wilon and E.. Peretti, Ind. Eng. Chem., 28, 204 (1936) [4] R. N. Singh and F. Sommer, Rep. Prog. Phy. 60, 57 (1997) [5]. C. nuionwu, C.. adu and C. E. Orji, PRN- J. Phyic, 72, 951 (2009) [6] R. P. Koirala, J. Kumar,. P. Singh and D. dhikari, J. Non-Cryt. Solid , 9 (2014) [7]. C. nuionwu and G.. debayo, The bdu Salam International Centre for Theoretical Phyic, IC/2008/065. [8] L. C. Praad, R. N. Singh and G. P. Singh, Phy. Chem. Liq. 27, 179 (1994) [9] R. Novakovic, D. Giuranno, E. Ricci, S. Delante, D. Li and G. orzone, Surf. Sci. 605, 248 (2011) [10] I. Koirala,. P. Singh and I. S. Jha, The Himalayan Phyic, 4, 40 (2013) [11] L. C. Praad and R. K. Jha, phy. tat. ol. (a) 202, 2709 (2005) [12] I. udai,. Z. enko, G. Kaptay, aterial Science Forum, , 489 (2007) [13] E.. rande and G.. rook, Smithell etal Reference ook, Seventh edition 14-7, (1992) 19 The Himalayan Phyic Vol. 6 & 7, pril 2017