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Only Fe3+ ions occupy the tetrahedral A site, while Fe2+ and
Fe3+ ions equally occupy the octahedral B site. Various
physical properties of magnetite such as metallic behaviour,
mixed valence and electron hopping are subject to the cation
distribution between ferrous and ferric ions in the two kinds of
site. The key to understanding these phenomena is 3d electrons. It is known in X-ray absorption experiments that
magnetite has a pre-edge structure at the Fe K edge
(Maruyama et al., 1995). Since the electric dipole 1s–3d transition is generally prohibited for octahedral sites, the pre-edge
peak of magnetite at the K absorption edge has been discussed
to relate the Fe3+ ions at tetrahedral A sites, where the site
symmetry of the sites is Td (4 3m). Another possibility has also
been proposed for magnetite in the electronic structure
calculation by the local-spin density approximation (LSDA),
where an A–O–B super-exchange interaction exists among the
sites (Anisimov et al., 1996).
The electric transition from 1s orbitals causes the X-ray
resonant scattering (XRS) at the K absorption edge. Since the
XRS reflects the electronic state well, it would be the best way
to use the photon energy related to the specific electronic
transition near the pre-edge. The XRS is defined by the
anomalous scattering factor, and a site-independent determination is helpful in interpreting the origin of the pre-edge
peak. The photon energy for the pre-edge study can be
selected based on information from spectra of XANES as well
as X-ray magnetic circular dichroism (XMCD). Most diffraction experiments to pinpoint photon energies with synchrotron radiation would require the anomalous scattering terms
of the atomic scattering factor. The real part of the anomalous
scattering factor f 0 can be suitably calculated based on relativistic wavefunctions and agrees considerably with experimental values at energies far from an absorption edge
(Cromer & Liberman, 1970). Since the theoretical values are
calculated for an isolated atom, they are not accurate enough
in the energy region close to an absorption edge. There is a
discrepancy due to a chemical shift by the oxidation state of
the atom and the local chemical environment. Many attempts
have been made near an absorption edge to measure anomalous scattering factors for relatively simple materials using
various X-ray techniques, such as using an X-ray interferometer (Bonse & Materlik, 1976), the intensity ratio of
Friedel-pair reflections (Fukamachi & Hosoya, 1975), total
reflection measurement (Fukamachi et al., 1978), the index of
refraction through a prism (Fontaine et al., 1985) and integrated intensity measurement (Templeton et al., 1980). A
realistic determination of f 0 may be to use the dispersion
relation of the Kramers–Kronig integral because of its easy
access to the data. Based on the X-ray absorption spectra
measured with synchrotron radiation, f 0 values for GaAs, Ti,
Ni and Cu were determined at the K edge from the imaginary
part f 00 (e.g. Fukamachi et al., 1977; Hoyt et al., 1984).
However, once two or more crystallographic sites exist in
the crystal structure, most of the above methods would be
powerless for reasons of the requirement of a site-independent f 0 . In this study the integrated intensity method is
adopted to observe the anomalous scattering effect for A and


Okube, Yasue and Sasaki

Fe K pre-edge peak of magnetite

B sites in the magnetite structure. Similar approaches, sitespecific studies on the diffraction anomalous fine structure and
resonant magnetic Bragg scattering, have been reported for
magnetite (Kobayashi et al., 1998).
It is possible using X-ray diffraction techniques to pinpoint
a specific atom by extracting resonantly scattered electrons.
For example, the difference-Fourier synthesis emphasizing a
difference in XRS intensity gives the residual electron density
on a targeted atom. An analytical approach of using the shell
structure factor has been proposed (Sasaki & Tsukimura,
1987). In the study of (Co,Ni,Zn)SiO3, 1s core electrons are
extracted from the total electrons to distinguish three kinds
of transition-metal elements simultaneously occupying two
crystallographic sites. Recently, the extraction analyses were
extended to observe magnetic electron orbitals, by using the
intensity difference in resonant X-ray magnetic scattering
between left-handed and right-handed circular polarizations
(Kaneko et al., 2010). Applying the above technique to the
electrons causing the pre-edge peak becomes important to
confirm the origin of the pre-edge peak for magnetite.
In this study the origin of the pre-edge peak of magnetite
will be discussed to determine the anomalous scattering
factors and to make comparisons in residual electron-density
maps between the A and B sites. The Fourier-synthesis technique, described as the electron-density difference (r) =
(r)on (r)off , is one such candidate in the use of the XRS
intensity data measured at selective energies ‘on’ and ‘off’ the
Fe K pre-edge peak.

2. Experimental
The magnetite used in this study was a highly stoichiometric
sample which was grown from Fe3O4 powder in a Pt–10% Rh
crucible by the Bridgman method in a CO–CO2 atmosphere
˚ and the
(Todo et al., 2001). The cell dimension a = 8.4000 (3) A

space group is Fd3m (No. 227). A spherical single crystal of
diameter 0.13 mm was mounted on a glass fiber for X-ray
diffraction study.
The conventional measurements of integrated intensity
were made using a Rigaku AFC7 four-circle diffractometer
with a graphite (002) monochromator for Mo K radiation
˚ ). The intensity data were collected up to
( = 0.71069 A
sin / = 1.36, in the range 18 h1, h2, h3 18 for reflection
indices. The scan width and speed in ! were 1.5 + 0.3 tan ( )
and 1.0 ( min 1), respectively. The intensity variation of the
three standard reflections was kept to less than 1.5%
throughout the data collection. Lorentz, polarization and
spherical absorption effects were corrected for. The linear
absorption coefficient was = 146.44 cm 1. The transmission
factors ranged from 0.289 to 0.333. In a total of 6228 reflections measured, 3016 reflections with F > 3 (F) were used for
simultaneous refinements of a scale factor, an isotropic
extinction parameter (Becker & Coppens, 1974), atomic
coordinates and temperature factors. The function wi(|Fobs|
k|Fcalc|)2 was minimized, with wi = 1/ 2(F) and k = a scale
factor, by the full-matrix least-squares program RADY
(Sasaki, 1987). Atomic scattering factors for Fe2+ and Fe3+
J. Synchrotron Rad. (2012). 19, 759–767