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 61.5 keV obtained by a Si 220 monochromator. The scattered x-rays from the sample

are collected by a Ge detector using a conventional ! - 2! step scan method. We analyze thediffraction pattern and obtain Faber-Ziman total structure factor S(Q) [2] by the following

equation,S(Q) =I(Q) " f (Q)
2f (Q)= # c ic j

2+1

Re f i (Q) f j (Q)[ij$f (Q)2] S (Q) = # w (Q)S (Q),
ij

ij

ij

ij

(1)

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),
Q max
1
Q[ S(Q) $1]sin(Qr)dQ
2
2" #r 01 ( Q max
r'[gij ( r') $1]) wij (Q)cos[Q(r $ r')]dr'dQ,= 1+"r $( 0g(r) = 1+
%

& % %ij(2)

where Q is the absolute value of wave number (Q =!Q!= (4 "/#) sin!, 2!: scattering angle, #: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,and partial pair distribution function for i-j correlation, respectively. " is an atomic numberdensity. We can assign atomic correlation peaks and derive the coordination number withintegrating peak area in the real-space function.

One may realize after the experiment that diffraction data yield only one-dimensional

structural information. To reveal the complicated structure in disordered materials, it isnecessary 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

structural model of disordered materials using mainly experimental diffraction data. In theRMC simulation technique the atoms of an initial conﬁguration are moved so as to minimize
the deviation 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 ﬁnd

out “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) 2! 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).