BL04B2: Disordered structure probed by high-energy x-ray diffraction techniqueIn this practice, we measure diffraction pattern of amorphous silica (SiO2) using the two-axis
diffractometer dedicated for disordered materials (see Fig. 1, [1]). The energy of incident x-rays
is 113 keV obtained by a Si 111 monochromator with the 3rd harmonic reflection. The scattered
x-rays from the sample are collected by a Ge detector using a conventional θ - 2θ step scanmethod. We analyze the diffraction pattern and obtain Faber-Ziman total structure factor S(Q)[2] by the following equation,
S(Q) =I(Q) − f (Q)f (Q)= ∑ c ic j

2+1

2

[Re f i (Q) f j ∗ (Q)
f (Q)

ij

2]S (Q) = ∑ w (Q)S (Q),
ij

ij

ij

(1)

ij

where S(Q) can be obtained by a normalization of the corrected x-ray scattering intensity I(Q).
The pair distribution function g(r) is obtained by a Fourier transformation of S(Q),g(r) = 1+= 1+∫2π ρr 0
1

Q max

2∞

Q[S(Q) −1]sin(Qr)dQ∑ π1r ∫−∞ ∫ 0

Q max

r′[gij ( r′) −1]⋅ wij (Q)cos[Q(r − r′)]dr′dQ,(2)ijwhere Q is the absolute value of wave number (Q =⏐Q⏐= (4 π/λ) sinθ, 2θ: scattering angle, λ:wavelength of incident x-rays) and < > means the average per one atom, and ci and fi(Q)represents atomic fraction of i and atomic form factor of i, respectively. wij(Q), Sij(Q), and gij (r)is weighting factor of i-j correlation for x-rays, partial structure factor for i-j correlation, andpartial pair distribution function for i-j correlation, respectively. ρ is an atomic number density.
We can assign atomic correlation peaks and derive the coordination number with integrating
peak area in the real-space function.
One may realize after the experiment that diffraction data yield only one-dimensional structural
information. In order to reveal the complicated structure in disordered materials, it is necessary
to construct 3-dimensional atomic configuration on the basis of diffraction data. The RMC
method [3,4] has been shown to be a useful tool to construct a three-dimensional structuralmodel of disordered materials using mainly experimental diffraction data. In the RMC
simulation technique the atoms of an initial configuration are moved so as to minimize thedeviation from the experimental diffraction data, using a standard Metropolis Monte Carloalgorithm [5]. In this practice, we try to model 3-dimensional atomic configuration ofamorphous silica, which is in consistent with the diffraction data. We hope everybody can findout “order within disorder [6]” in the amorphous materials, since the structure of disorderedmaterials can be understood to exhibit an unique atomic order.

Fig. 1 Photograph of two-axis diffractometer for disordered materials.
(a) incident slit, (b) ionization chamber, (c) CCD camera, (d) vacuum chamber,(e) receiving slits, (f) fully automatic attenuators (g) Ge detector, (h) 2θ arm.
Beam stop is hidden behind the receiving slits.
References[1] S. Kohara, M. Itou, K. Suzuya, Y. Inamura, Y. Sakurai, Y. Ohishi, and M. Takata, J. Phys.:Condens. Matter, 19, 506101 (2007).
[2] T.E. Faber and J.M. Ziman, Phil. Mag. 11, 153 (1965).
[3] R. McGreevy and L. Pusztai, Mol. Simul. 1, 359 (1988).
[4] R. McGreevy, J. Phys.: Condens. Matter 13, R877 (2001).
[5] N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, and E. Teller, J. Phys.
Chem. 21, 1087 (1953).
[6] P.S. Salmon, Nature Materials 1, 87 (2002).