Pseudopotential in the study of phonon dynamics of Pd-based metallic glasses Aditya M. Vora * Sadhu Vaswani International School, 12/C Lilashah Nagar, Gandhidham (Kutch) 370 201 Gujarat, India Received 4 September 2005; received in revised form 11 May 2006 Available online 24 July 2006 Abstract The phonon dynamics of Pd 35 Zr 65 and Pd 80 Si 20 two non-crystalline systems have been studied in terms of the eigen frequencies of the localized collective excitations using model potential formalism. The pair potential and pair correlation function are obtained in Wills– Harrison (WH) form from the well recognized model potential of Gajjar et al. The phonon dispersion curves are computed from the three approaches proposed by Hubbard–Beeby (HB), Takeno–Goda (TG) and Bhatia–Singh (BS). Various elastic and thermodynamic properties have been studied from the elastic limit of the dispersion relations. The advanced local field correction function due to Sarkar et al. is used for the first time to include the influence of exchange and correlation on the aforesaid properties. The ratio (r 2 /r 1 ) of the position of the second peak (r 2 ) to that of the first peak (r 1 ) of g(r) for both metallic glasses is close to the c/a ratio in close-packed hex- agonal structure. Qualitatively, the phonon dispersion curves (PDC) computed from the BS approach are found to be better than HB and TG approaches. Ó 2006 Elsevier B.V. All rights reserved. PACS: 71.15.H; 63.50.+x; 65.60.+a Keywords: Acoustic properties; Phonons; Amorphous metals, metallic glasses; Thermodynamics 1. Introduction During last several years, the study of transition metallic (TM) and transition metal–metalloid (TM–M) glasses has been subject of great interest by many researchers because of their wide ranging of physical as well as technical appli- cations in the field of materials science and engineering. The pseudopotential theory is very much successful to study the simple metallic glasses [1], but applications to TM-based or TM–M type metallic glasses are very few [2–4]. This may be due to the difficulties in choicing the interatomic pair potential. Wills and Harrison (WH) [5] have overcome most of the difficulties of transition metals by a separate treatment of s- and d-states, account for the effect of s–d hybridization and arrived at a new representa- tion of the effective pair potential. Based on this, present study reports the phonon dynamics of largely unexplored two Pd-based TM–TM and TM–M glasses such as Pd 35 Zr 65 and Pd 80 Si 20 . The Pd 35 Zr 65 is a candidate of TM–TM glass system while Pd 80 Si 20 is a candidate of TM–M group. We have used HB [6], TG [7] and BS [8,9] approaches to compute the phonon frequencies of these alloys. The local field correction due to Sarkar et al. [10] is used to introduce exchange and correlation effects. The phonon dynamics of Pd 35 Zr 65 glass was reported by Pratap et al. [2]. They have used effective pair potential (EPP) and effective atom model (EAM) with HB approach. The pho- non dynamics of Pd 80 Si 20 glass has been studied by Prasad et al. [3]. They have adopted hypernetted chain approxima- tions to generate the partial pair potentials from experi- mental static structure factor with HB [6] and TG [7] approaches. Saxena [4] has reported the phonon dynamics 0022-3093/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2006.05.016 * Present address: Parmeshwari 165, Vijaynagar Area, Hospital Road, Bhuj–Kutch, 370 001 Gujarat, India. Tel.: +91 2832 256424. E-mail address: voraam@yahoo.com www.elsevier.com/locate/jnoncrysol Journal of Non-Crystalline Solids 352 (2006) 3217–3223