Photon Factory Activity Report 2022 #40 (2023)

BL-6C/2019G635

Three-dimensional atomic configurations in a ZnFe2O4 single crystal
by X-ray fluorescence holography

Shinya HOSOKAWA1,*, Naohisa HAPPO2, Koichi HAYASHI3, and Tomohiro
MATSUSHITA4
1 Institute of Industrial Nanomaterials, Kumamoto University, Kumamoto 860-8555, Japan
2 Graduate School of Information Sciences, Hiroshima City University, Hiroshima 731-3194,
Japan
3 Department of Physical Science and Engineering, Nagoya Institute of Technology, Nagoya
466-8555, Japan
4 Division of Materials Science, Nara Institute of Science and Technology, Ikoma 630-0192,
JapanThree dimensional atomic structures of a zinc ferrite Franklinite ZnFe2O4 crystal was investigated by X-ray
fluorescence holography with an atom-solved and element-selected functions. The obtained holograms wereanalyzed using a sparse modeling approach of a L1-regression. From the present analysis, it was found that Zn
and Fe atoms are perfectly located at tetrahedral A sites and octahedral B sites, respectively. This conclusion
contradicts results of a neutron diffraction experiment, where site exchanges occurred between Zn and Fe atoms
for fine particles by about 10–15% (T. Kamiyama et al., Solid State Commun. 81, 563 (1992)).
1 Introduction
A zinc ferrite crystal of Franklinite ZnFe2O4 has anormal spinel structure [1]. This material achieved
interests of only basic geology and crystallography
sciences for a long time; however, it has recently
attracted applicational interests as a cathode material
for Li ion batteries since 2004 [2,3].
In the crystal, the O2- anions form a cubic close
packed structure, and the Zn2+ and Fe3+ cations
preferentially occupy tetrahedral A and octahedral B
sites, respectively. Note that the bond length in the Asite is 0.1959 nm, which is slightly shorter than that in
the B site of 0.2037 nm and would be affected by thecation radius with valencies, coordination numbers,and spin states.
There were several arguments on the occupationsof cation atoms whether the Zn2+ and Fe3+ cations
selectively enter the A and B sites, respectively, in thecrystal or not. Kamiyama et al. [4] discussed thecation distributions in ZnFe2O4 fine particles byneutron powder diffraction. They reported a large size
dependence of the Fe3+ occupancy at the tetrahedral
A site of 10.8 (14.2) % with the crystal size of 0.960(0.290) nm. The cation occupations in ZnFe2O4 werealso studied by Jeyadevan et al. [5] with Fe and Zn K
X-ray
absorption
finestructure(XAFS)
measurements. The samples were manufactured bysome different methods of usual sintering,
coprecipitation (particle size of about 8 nm), and thatannealed after the coprecipitated one. From theXAFS data as well as a remarkable increase ofmagnetization, it was concluded that Zn ions in thecoprecipitated ZnFe2O4 are occupied both in A and B
sites. On the other hand, it was not examined
experimentally so far whether such an anomaly incation distributions intrinsically exist even in large
ZnFe2O4 crystal or not.
X-ray fluorescence holography (XFH) is a novel
method for atom-resolved and element-selective
structural characterizations and enables to draw
three-dimensional (3D) atomic images around a
specific element emitting fluorescent X-rays [6]. For
reconstructing atomic images from measured
holographic data, Barton’s multi-wavelength method[7] based on the Fourier transform is typically used.
However, atomic images reconstructed by this direct
problem method frequently contain considerable
artifacts, although a fundamental twin image problem
is mostly solved. Since the intensities of the artifact
reach about 30% of the maximum of the atomic
images and unphysical negative signals remain by
Barton’s algorithm, however, a more sophisticatedalgorithm is necessary to clarify the present
judgement for wrong distributions of Zn and Fe cationof about 10%.
Recently, we have utilized a new algorithm basedon an inverse problem and representing sparsemodeling approach [8] and applied it to somefunctional materials [9]. By using this algorithm,
particularly, have succeeded in drawing weak imageof less than 20% of the maximum value in a Mndoped Bi2Te3 topological insulator [10]. In this paper,
we report the results of Zn and Fe Kα XFH data ofZnFe2O4 single crystal analyzed by the new algorithmand discussed the cation distributions in this bulk
spinel crystal.
2 Experiment and analysis
A single crystal of natural ZnFe2O4 was purchased
at Crystal Base Co., Ltd. in Osaka, Japan, which wasimported from SurfaceNet GmbH at Rheine,Photon Factory Activity Report 2022 #40 (2023)

Germany. The crystal had a flat (001) surface with asize of 10 × 10 mm2 and a thickness of 0.5 mm. The
crystallinity of the sample was confirmed by taking a
Laue photograph.
Zn and Fe Kα XFH experiments on the ZnFe2O4
crystal were carried out at the beamline BL-6C of thePhoton Factory located in the High Energy
Accelerator Research Organization (PF-KEK) inTsukuba, Japan. X-rays were focused onto thesample with a size of about 0.5 × 0.5 mm2 by asagittal cylindrical mirror. The sample was placed ona rotatable table for the incident angle θ and theazimuthal angle φ. The incident X-rays were focusedwith a size of 0.3 × 0.3 mm2 on a (001) surface of thesample. The measurements were performed ininverse mode by changing 0° ≤ θ ≤ 75° in steps of 1°
and 0° ≤ φ ≤ 360° in steps of ∼ 0.35° of the sample.
The Zn (8.638 keV) and Fe (6.403 keV) Kα
fluorescent X-rays were collected by an avalanche
photodiode detector via a cylindrical graphite crystal
energy-analyzer. The XFH signals were recorded at13 different incident X-ray energies from 13.0 to 16.5
keV in steps of 0.25-0.50 keV for Zn Kα and at 15
different incident X-ray energies from 13.5 to 17.0
keV in steps of 0.25-0.50 keV for Fe Kα. Details of theexperimental setup are given elsewhere [6].
The holographic oscillation data were obtained bynormalizing the fluorescent X-ray intensities to theincident X-ray intensities measured with an ion
chamber, and then, subtracting the backgrounds.
Extensions of the holographic data to the 4π solid
angles were carried out by the measured X-ray
standing wave (XSW) lines in the holographic datawith fourfold rotational symmetries around all theaxes and three mirror symmetries in both the Zn andFe Kα holograms.
To perfectly reconstruct atomic images, an infinite
number of holograms are necessary for varying kfrom 0 to ∞. In Barton’s algorithm, the Fourier integral
is replaced by a sum of a limited number of hologramswith different k values, which is the main reason for
the appearance of artifacts in the reconstructedatomic images. To solve this problem, Matsushita
developed a new algorithm, SPEA- L1 [8], based on
an inverse problem and a sparse modeling. The
details of this algorithm and excellent improvementsof the atomic images by the L1-regularized linear
regression were clearly given in our research papers[10-13] and review papers [9, 14].
3 Results and Discussion
Figure 1 shows atomic images on the (001) planearound the Zn (upper) and Fe (lower) atoms. Idealneighboring cation positions are indicated by large
and small circles when the central atoms at thecenters of the figures are located at the A and B sites,respectively. As seen in the figures, most of theneighboring atomic images are located at the ideal
cation positions although small artifacts are mainly
seen near the central atoms. A large difference isobserved between the atomic images around the Zn
and Fe atoms, i.e., atomic images are not seen at theB site around the Zn atom while distinct images areseen there around the Fe atom.
To quantitatively observe the cation occupancies,
image intensities are exhibited in Fig. 2 along thedashed lines in Fig. 1 around the (a) Zn and (b) Featoms. For clarity, the curve around Zn is displaced
by 0.6. As seen in Fig. 2(a), no atomic images aredetected at the B site around the Zn atom. On theother hand, as seen in Fig. 2(b), distinct atomic
images are observed at the B site around the Fe atom.
4 Conclusion
From the present analysis for the Zn and Fe Kα
XFH, it was concluded that Zn and Fe atoms are
perfectly located at tetrahedral A sites and octahedral
B sites, respectively, in the ZnFe2O4 bulk crystal. Thisconclusion contradicts results of a neutron diffraction
experiment, where site exchanges occurred between
Zn and Fe atoms for fine particles by about 10–15%[4].

Fig. 1: Atomic images on the (001) plane around theZn (upper) and Fe (lower) atoms.

Photon Factory Activity Report 2022 #40 (2023)* shhosokawa@kumamoto-u.ac.jp

Fig. 2: Atomic distributions along the dashed lines inFig. 1 around (a) Zn and (b) Fe atoms. For clarity,
the curve around Zn is displaced by 0.6.
Acknowledgement
XFH measurements were carried out at BL6C in
the PF-KEK (No. 2019G635). Financial supports by
JSPS Grant-in-Aid for Transformative Research
Areas (A) ‘Hyper-Ordered Structures Science’ areacknowledged (Nos. 21H05569 and 23H04117 forSH, No. 20H05881 for KH, and 20H05884 for TM).
SH is also supported by JSPS Grant-in- Aid for
Scientific Research (C) (No. 22K12662) and theJapan Science and Technology Agency (JST)CREST (No. JPMJCR1861).
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