Physica B 390 (2007) 377–385 Energy of formation for Ag x In 1x and Ag x Sn 1x liquid binary alloys G.M. Bhuiyan à , A.Z. Ziauddin Ahmed Department of Physics, University of Dhaka, Dhaka-1000, Bangladesh Received 27 May 2006; received in revised form 24 August 2006; accepted 25 August 2006 Abstract We have investigated the free energy of formation for Ag x In 1x and Ag x Sn 1x liquid binary alloys at temperatures 1173 and 1250 K, respectively. A microscopic theory based on the first order perturbation has been applied. The interionic interaction and a reference liquid are the fundamental components of the theory. The interionic interaction is described by a local pseudopotential. A liquid of hard spheres (HS) of two different effective diametres and charges is used to describe the reference system. The results of the calculations for energy of formation agree very well with the available experimental data. Our calculations also reveal that a simple perturbative approach along with appropriate effective pair potentials can produce nearly quantitative results for the concerned alloys. r 2006 Elsevier B.V. All rights reserved. PACS: 05.70.Ce; 05.70.a Keywords: Free energy; Energy of formation; Liquid binary alloys; Perturbation theory; Hard sphere; General microscopic theory of metals; Pseudopotential; sp-d hybridization 1. Introduction We have systematically investigated the free energy of formation for Ag x In 1x and Ag x Sn 1x liquid less simple binary alloys at 1173 and 1250 K, respectively. To under- stand the mixing behaviour of two elemental systems forming a binary alloy has been a subject of considerable interest to physicists, chemists and metallurgist. This is due to the fact that the interionic interaction in an alloy largely differs from those of the constituent elemental systems and consequently the physical properties of alloys deviate from those of the parent elements. The study of energy of formation is important not only to understand this property alone but also to understand other characteristic properties such as compound formation, phase separation or segregation etc. of binary alloys. Recently an increasing attraction toward the study of different physical properties of binary alloys is observed [1–6]. Among these alloys Ag x In 1x has drawn a special attention due to some of its characteristic properties, for example the presence of pseudogap in the density of states and deviation of its magnetic susceptibility from the linearity at some concentration [6]. In addition, recent X-ray diffraction measurement of total and partial static structure factors [7] arouse further attention to it. Ag x In 1x and Ag x Sn 1x liquid binary alloys are con- stituted from three different elemental systems Ag, In and Sn. These elements have completely filled d-bands. None- theless, there physical properties are significantly influ- enced by the d-band via sd (or sp-d) hybridization (sometimes refereed to as sd mixing) [7,8]. The effect of sd-hybridization is also effective in the alloy state and, there are evidences that in some alloys this effect changes with relative alloy concentrations [9]. It is therefore important to take the hybridization effect into account for the study of both elemental metals and their alloys. In order to take this effect into account precisely any concrete theoretical expression has not been developed yet. So this effect is accounted for approximately by changing the relative occupancy of the s and d bands. In doing this there is no restriction as such to use suitable values for Z the effective s-electron occupancy number provided the self- consistent calculations of charge transfer support it. For example, Wills–Harrison [10] used Z ¼ 1:5 for all elements of the 3d, 4d and 5d series except for Au for which they ARTICLE IN PRESS www.elsevier.com/locate/physb 0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.08.041 à Corresponding author. Tel.: +880 2 9671257; fax: +880 2 8615583. E-mail address: gbhuiyan@univdhaka.edu (G.M. Bhuiyan).