Structural and energetic anomaly in liquid Na–Sn alloys D. Adhikari a, b, ⁎, B.P. Singh a , I.S. Jha b a Univ. Dept. of Physics, T. M. Bhag. University, Bhagalpur, Bihar, India b Dept. of Physics, M.M.A.M. Campus (Tribhuvan University), Biratnagar, Nepal abstract article info Article history: Received 28 September 2011 Received in revised form 14 November 2011 Accepted 23 December 2011 Available online 9 January 2012 Keywords: Binary alloy Na–Sn alloy Complexes Interaction energies The alloying behaviour of Na–Sn liquid alloys at 773K has been studied by using regular associated solution model. This model has been utilized to determine the complex concentration in a regular associated solution of Na and Sn. We have then used the complex concentration to calculate the free energy of mixing (G M ), enthal- py of mixing (H M ), entropy of mixing (S M ), concentration fluctuations in long wavelength limit (S CC (0)), the Warren Crowley short-range parameter (α 1 ) and ratio of mutual and intrinsic diffusion coefficients (D M /D id ). The analysis suggests that heterocoordination leading to the formation of complex Na 3 Sn is likely to exist in the liquid and is of a strongly interacting nature. The theoretical analysis reveals that the pairwise interaction energies between the species depend considerably on temperature and the alloys are more ordered towards in- termediate region. © 2012 Elsevier B.V. All rights reserved. 1. Introduction The study of the mixing behaviour of liquid alloys is of immense importance for physicists, chemists and engineers for designing and exploring new materials. Thus determination of different properties of liquid alloys, such as thermodynamic, surface, structural, electrical, magnetic properties has been the subjects of active research in metal- lurgical science for many years. But understanding the properties of liquid alloys is much more difficult than that of crystals due to the presence of strong interactions among the particles and their state of disorder in liquid state. Several theoretical models [1–12] have long been employed to solve the complexities of obtaining different properties of binary liquid alloys. In this work we have studied the thermodynamic and structural properties of Na–Sn liquid alloy at 773K on the basis of regular associated solution model. In regular associated solution model, strong associations among the constituent species are assumed to exist in the liquid phase of binary al- loys close to the melting temperature. Due to the strong associations present in the solution, complexes are formed. Thus the binary alloys in a liquid phase can be considered as a ternary mixture of unassociated atoms of components and complexes, all in chemical equilibrium. But the interactions between both the unassociated atoms and the complex are considered no longer equal and hence unassociated atoms do not in- teract equally with the complex. Several workers [13–21] have theoretically and experimentally tried to understand different properties of Na–Sn system in liquid state. Asymmetry in various properties of mixing of molten Na–Sn al- loys is noticed around equiatomic composition. The size factor (Ω Na / Ω Sn = 1.45; Ω being the atomic volume) and electronegativity differ- ence ( E Sn -E Na = 1.03) are not large enough to account for the anomalous behaviour of mixing properties. The phase diagram shows the existence of several intermediate phases in the liquid state of Na–Sn alloys which has been confirmed by several workers [19,22,23]. Several pieces of experimental evidence clearly demon- strate that the asymmetric behaviour for a large number of liquid al- loys occur at or near the stoichiometric composition where stable intermetallic compound exist in the solid phase. It is, therefore, natu- ral to propose that the ‘chemical complexes’ or psedomolecules' exist in the liquid phase near the melting temperature. From the Na–Sn phase diagram (see refs. suggested above), the Na 9 Sn 4 intermetallic compound exists up to 478 °C, and it melts congruently at that tem- perature. The curve of the enthalpy of mixing of Na–Sn solutions at 500 °C exhibits the minimum value at 43 at.% Sn [22,23]. These find- ings are corroborated by neutron diffraction measurements [18].Tak- ing into account that in the liquid phase the irregularities (due to strong interactions in the system in questions) on the property- curves sometimes are often shifted with respect to the exact compo- sition of an energetically favoured intermetallic compound, the Na 9 Sn 4 (31 at.%Sn) can be approximated by A 3 B stoichiometry (Na 3 Sn, with 25 at.%Sn), because none of the models used takes into account the stoichiometry A 9 B 4 (always the stoichiometric coeffi- cients are small integers). Thus we consider Na 3 Sn phase to describe the thermodynamic and structural properties of Na–Sn liquid alloy at 773K. The layout of the paper is as follows. In Section 2, the theoretical basis of our work is presented. Section 3 gives the results and discus- sion of this work. Finally, the conclusions are outlined in Section 4. Journal of Molecular Liquids 167 (2012) 52–56 ⁎ Corresponding author at: Univ. Dept. of Physics, T. M. Bhag. University, Bhagalpur, Bihar, India. E-mail address: adksbdev@yahoo.com (D. Adhikari). 0167-7322/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2011.12.010 Contents lists available at SciVerse ScienceDirect Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq