X-ray scattering from amorphous solids Ruixing Feng a , Z.H. Stachurski a, ⁎, M.D. Rodriguez b , P. Kluth b , L.L. Araujo b , D. Bulla b , M.C. Ridgway b a Research School of Engineering, The Australian National University, Canberra ACT 0200, Australia b Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200, Australia abstract article info Article history: Received 15 January 2013 Received in revised form 15 March 2013 Available online xxxx Keywords: X-ray scattering; Metallic glasses; Covalent glasses; Chalcogenide glasses The main objective of this work is to verify the proposed models by comparing computed outcomes with ex- perimental results. For metallic glasses the novel ideal amorphous solid model is used to simulate the struc- ture and the atomic positions which are input into the Debye equation. Computations predict structure factor or scattered intensity which agree well with the experimentally obtained data. For covalent materials, such as amorphous silica or amorphous polyethylene with short range order the Warren approach offers a simple method to predict X-ray scattering in good agreement with experimental data. Neither of the two above methods works well for chalcogenide glasses which require calculations involving spherical harmonics. © 2013 Elsevier B.V. All rights reserved. 1. Introduction The pioneering findings of von Laue and Braggs on X-ray diffrac- tion led rapidly to the determination of precise locations of atoms in crystalline minerals and materials. Studies of space group sym- metry provided theoretical basis for definition and description of crystal structures, corroborated by the diffraction methods. For amorphous solids the geometrical methods are less well developed. The positions of atoms are usually not known a priori and the vision of atomic arrangements is difficult to perceive clearly [1]. However, if the positions of atoms are known, say, at r 0 ,r 1 ,r 2 ,…r N with their corresponding atomic scattering factors, f 1 ,f 2 ,…f N , then the scattered intensity emanating from such a solid can be predicted by the Debye equation [2]: Is ðÞ¼ ∑ i ∑ j f i s ðÞf j s ðÞ sin 2πsr ij   ; 2πsr ij for i and j from 0 to N; ð1Þ where: r ij =|r j − r i | is the distance between scattering centers, and s = |(S − S 0 )|/λ is the magnitude of the scattering vector. The phase difference between any two scattered rays is δ =2πsr ij , determined only by r ij for a fixed angle of scattering, with an equal probability of phase difference having any value between 0 and 2π. It is assumed that a model for the atomic-scale arrangements ex- ists. Then, the main objective is to verify the proposed model by a trial-and-error method [3]. A crucial test is to compare the predicted scattering trace with experimentally derived data. Then there are three possible outcomes: (i) the agreement is good in which case the model is accepted, (ii) the agreement is not good, in which case it is rejected, or (iii) the model is modified to improve the agreement until case (i) is reached. The final acceptance of the atomic arrange- ment is achieved only in corroboration with other complementary methods. 2. Experimental methods 2.1. Preparations of samples 2.1.1. Metallic glasses The range of samples covered in this study is listed in Table 1. The Fe–B alloy samples were between 25 and 30 μm in thickness, the Ni– Si–B were 35 μm, and the Ti–Cu–Zr were ∼ 30 μm, respectively. All the ribbon-like samples were made by melt spinning technique with no further annealing. All the other metallic glasses were made in bulk. Ingots of the alloys were prepared by arc melting a mixture of pure metal elements in a titanium-gettered argon atmosphere, followed by suction casting into copper molds to form bulk metallic glass (BMG) solid samples [4]. For each metallic glass an IAS Round Cell model of 10 6 spheres has been generated, and the coordinates of the sphere centers have been used to predict X-ray scattering by a program based on Eq. (1). 2.1.2. Covalent glasses Plate glass or powder samples from pure silica have been prepared by grinding. Amorphous polyethylene has been researched extensive- ly in the past and some relevant data from published literature has been used in this work. Journal of Non-Crystalline Solids xxx (2013) xxx–xxx ⁎ Corresponding author. E-mail address: zbigniew.stachurski@anu.edu.au (Z.H. Stachurski). NOC-16560; No of Pages 7 0022-3093/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jnoncrysol.2013.04.070 Contents lists available at SciVerse ScienceDirect Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/ locate/ jnoncrysol Please cite this article as: R. Feng, et al., X-ray scattering from amorphous solids, J. Non-Cryst. Solids (2013), http://dx.doi.org/10.1016/ j.jnoncrysol.2013.04.070