Probing the local structure of liquid binary mixtures by x-ray absorption spectroscopy Angela Trapananti 1, * and Andrea Di Cicco 1,2 1 Istituto Nazionale per la Fisica della Materia (INFM) and Dipartimento di Fisica, Università degli Studi di Camerino, Via Madonna delle Carceri, I-62032 Camerino (MC), Italy 2 Istituto Nazionale di Fisica Nucleare (INFN), Laboratori Nazionali di Frascati, Via E. Fermi, 40, I-00044 Frascati (Roma), Italy (Received 12 November 2003; revised manuscript received 23 March 2004; published 6 July 2004) Local structure of binary mixtures has been usually determined by diffraction techniques. In the past few years the analysis of x-ray absorption spectroscopy data has been proved to be a powerful tool for an accurate determination of the structure of solid and liquid systems, complementary to x-ray or neutron scattering methods. In this paper we report about a procedure to extract pair correlation functions of liquid and disordered binary mixtures from x-ray absorption fine structure (XAFS) data, satisfying both long-distance behavior and long wavelength limit of Bhatia-Thornton structure factors. An application to accurate XAFS data collected on a CuSn binary metal alloy Cu6Sn5 is reported and compared with existing models. DOI: 10.1103/PhysRevB.70.014101 PACS number(s): 61.10.Ht, 61.25.Mv I. INTRODUCTION Binary metal alloys are a wide class of materials, with a variety of structural and electronic properties determined by the different solubility of the individual components. While solid metal alloys are relevant to numerous technological applications (coils for hybrid magnets, electrodes, lifting contacts, dental materials), molten alloys are especially inter- esting from the point of view of basic physics. Indeed a detailed knowledge of their structural properties and in par- ticular an accurate investigation of their short-range correla- tions could be essential to understand interactions between different chemical species under thermodynamic equilibrium conditions and for the development of interatomic potentials. In spite of their interest, very few experimental studies have been devoted to reveal the type of short-range order in binary alloys. A typical question to be answered is whether these systems will phase separate (like atom nearest neigh- bors) or order (unlike atom nearest neighbors). In a binary mixture, the set of three pair distribution func- tions g  r necessary for a complete description of two- body correlations has been usually determined by diffraction techniques (see Ref. 1 for a review). Neutron diffraction pro- vides information on both short-range and long-range g  r properties, but its application is limited to systems for which a complete set of contrasting isotopes is available. Moreover, these experiments are expensive and time consuming hinder- ing the performance of systematic studies on the evolution of structural properties as a function of thermodynamic vari- ables (pressure and/or temperature) or concentration. In the past decades the x-ray absorption spectroscopy (XAS) has been proved to be a powerful tool for an accurate determination of the structure of liquid and highly disordered materials 2 even under extreme high-pressure 3 and/or high temperature conditions (see Ref. 4 and references therein). Modulations of the absorption cross section above a deep core level excitation edge allow one to investigate the envi- ronment of the photoabsorber in a range limited by the pho- toelectron mean free path. One of the most appealing fea- tures of the XAS technique is the possibility to determine the atomic environment of a selected atomic species simply by tuning the energy of the incoming beam around its K-edge. However determining pair distribution functions from a set of XAS data is a challenging problem especially for mul- ticomponent systems. The current strategy for the structural refinement from XAS data requires modeling of the distribu- tions as a superposition of distinct peaks whose parameters are fitted to the experimental spectrum. This strategy is adopted by the GNXAS multiple-scattering data-analysis method 5,6 and has been extended to include multiedge struc- tural refinements 7 in multicomponent systems for an accurate determination of the local environment of the different atomic species. In highly disordered systems, peaks overlap in a continu- ous broadened distribution showing usually a distinct first peak corresponding to closest-neighbors distance. While the application of a peak-fitting strategy, limited to the first peak is still reasonable, it has been shown that a strong correlation between coordination numbers and shape parameters of the model distribution can lead to misleading results if the fit is performed without constraints. 4,8 A simple but rigorous method overcoming this limitation using physical constraints into a still model dependent peak- fitting approach has been introduced for monoatomic systems 8 and extended to ionic binary liquids. 9 The purpose of this paper is to report a new scheme to refine partial distribution functions, starting from a set of realistic pair distributions provided by computer simulations or diffraction experiments, which fully generalize this suc- cessful approach to liquid and disordered binary systems. This method allows us to refine the short-range peaks of a set of model partial distribution functions with constraints de- rived from long-range properties of the mixture, as the long- wavelength limits of Bhatia-Thornton structure factors. 10 This approach is not limited to melts of metal alloys, but it can be applied to all binary liquids and possibly extended to their disordered solid phases (amorphous, glasses, etc.) for which experiments are feasible, but a valid data-analysis method is still missing. Here, the method is applied to determine the local struc- ture of a liquid Cu6Sn5 alloy, for which accurate XAS spec- PHYSICAL REVIEW B 70, 014101 (2004) 0163-1829/2004/70(1)/014101(7)/$22.50 ©2004 The American Physical Society 70 014101-1