Photon Factory Activity Report 2014 #32 (2015) B

BL-6C/2014G691

Anisotropic thermal expansion in Invar alloys
Shinya Hosokawa1,*, Yuuki Ideguchi1, Kenji Kamimura1, Koji Kimura1, Naohisa Happo2,Kunio Yubuta3, and Kouichi Hayashi3,†1
Department of Physics, Kumamoto University, Kumamoto 860-8555, Japan
2
Graduate School of Information Sciences, Hiroshima City University, Hiroshima 731-3194, Japan
3
Institute of Materials Research, Tohoku University, Sendai 980-8577, JapanFe and Ni Kα x-ray fluorescence holography measurements were employed for drawing three-dimensional atomic imagesof a Fe66Ni34 Invar alloy around the Fe and Ni central atoms, respectively. The obtained atomic images around the Ni
central atom show the usual fcc atomic arrangement as predicted with x-ray diffraction. However, those around the Fe
central atom exhibit a bcc-like atomic arrangement in the near region. This result suggests that the Invar effect shown inthe Fe66Ni34 alloy would be explained by a gradual structural change in the local structure from sparse bcc to dense fcc
with increasing temperature, and the spin transformation may be a phenomenon accompanied by such a structural change.
1 Introduction
In 1897, Guillaume [1] discovered an Invar alloy of
Fe66Ni34, which has anomalously small thermal expansion
over a wide temperature range. This effect has beenutilized in various kinds of industrial products. It has beenrecognized for a long time that the Invar effect originatesfrom magnetism, i.e., there are two types of electronic
states in Fe, typically high-spin (HS) and low-spin (LS)states [2]. In this two-states model, the equilibrium
potential energy is lower in the HS state than that in theLS one, while the atomic radius is larger in the former.
These assumptions result in the competition of thermal
expansion due to the increase of density in the LS state athigh temperatures.
Recently, Yokoyama and Eguchi [3] discussed theirXAFS results on Fe64.6Ni35.4 by comparing with those of
x-ray diffraction (XD). It was found that the local bonddistance around the Fe atom and the lattice constantremain almost unchanged with varying temperature as themacroscopic thermal expansion indicates, while the local
bond distance around the Ni atoms shows a usual thermal
expansion
withincreasing
temperature.
These
experimental results imply a curious local atomic
arrangement in this Invar alloy that with increasing
temperature, the Ni atoms having an elongatedinteratomic bonds should squeeze into the same size ofthe crystal lattice, suggesting large lattice distortions
around the minority Ni atoms and also the fundamental
lattice of majority Fe atoms.
X-ray fluorescence holography (XFH) is a newly
developed technique for atom-resolved structuralcharacterizations of materials, and enables one to draw
three-dimensional (3D) atomic images around a specificelement emitting fluorescent x-rays [4]. Owing to aninterference between direct incident x-rays and thosescattered by surrounding atoms, the fluorescent x-ray
intensity from the emitter slightly modulates with incident
x-ray angles by about 0.1 %, from which 3D images ofneighboring toms can be obtained by simple Fouriertransforms without any special atomic models. This
technique has, in particular, an excellent potential forinvestigating local structures around minority atoms [5].

Another advantage of this technique is that positionalfluctuations of individual neighboring atoms can beevaluated in the radial and angular directions separately
by comparing with theoretical calculation and XAFSresults [5].
We have recently measured Fe and Ni Kα XFH on
Fe66Ni34 single crystal Invar alloy at room temperature,and obtained an unexpected and interesting result, which
will be reported in this paper in detail.
2 Experiment
The single crystal of Fe66Ni34 Invar alloy was grown at
Cooperative Research and Development Center for
Advanced Materials, Institute for Materials Research,Tohoku University. The crystal was cut and polished soas to have a flat (111) surface of about 10 mmφ. The
crystallinity was examined by taking a Laue photograph,and the concentration and homogeneity were confirmed
over the sample within the experimental errors by anelectron-probe micro-analysis.
Fe and Ni Kα XFH measurements on Fe65Ni35 Invar
alloy were carried out at room temperature at BL-6C ofthe Photon Factory in the High Energy Accelerator
Research Organization (PF-KEK), Tsukuba, Japan. The
sample was placed on a two-axes table of adiffractometer. The measurements were performed ininverse mode by changing two axes, the exit angle of 0° ≤θ ≤ 75° in steps of 1.00° and the azimuthal angle of 0° ≤ φ≤ 360° in steps of about 0.35°. Incident x-rays werefocused onto the (111) surface of the sample. Fe or Ni Kα
fluorescent x-rays were collected using an avalanche
photodiode detector with a toroidal graphite crystal
energy analyzer. The XFH signals were recorded at eight
different incident x-ray energies from 7.5 to 11.0 keV forFe and from 8.5 to 12.0 keV for Ni in steps of 0.5 keV.
Details of the experimental setup are given elsewhere [4].
Holographic oscillation data were obtained bysubtracting the background from the fluorescent x-rayintensities. An extension of the hologram data was carriedout using the crystal symmetries of the fcc structure [3]and the measured x-ray standing wave lines. From thePhoton Factory Activity Report 2014 #32 (2015) B

hologram patterns, 3D atomic configuration images werereconstructed using Barton’s algorithm [6] bysuperimposing the holograms with eight different incident
x-ray energies, which can highly suppress the appearanceof twin images.
3 Results and Discussion
Figure 1(a) shows atomic images around the Ni central
atom on the (001) plane obtained from Ni Kα XFH
measurement. The dashed lines indicate unit cells of thefcc structure for the Fe66Ni34 Invar alloy obtained fromXD measurement [3]. The characteristic image for the fcc
structure is located at the center of the squares in addition
to those at the intersections of the unit cells. Althoughlarge lattice distortions were expected from previous
XAFS and XD measurements [3], such distortions are
hardly seen in the XFH images.

(a)Figure 1(b) shows atomic images around the Fe central
atom on the (001) plane obtained from Fe Kα XFH
measurement. The dashed lines also indicate unit cells. Afeature very different from Fig. 1(a) is that the images atthe center of the squares are very weak, indicating that thelocal atomic configurations around the Fe atom would bea bcc-like structure, the same as that in pure Fe crystal.
Note that such a bcc-like structure is limited in the firstcell, and the fcc-like structures look to be recovered in thedistant unit cells.
From the present XFH experiments, a new idea issuggested for the Invar effect in the Fe66Ni34 Invar alloythat with increasing temperature, local structures aroundthe Fe atoms gradually change from sparse bcc-like todense fcc-like, and the change of the HS-LS spin states
may be accompanied by the gradual structural changewith temperature. Detailed discussion is necessary byobtaining further structural investigations using
Mössbauer spectroscopy and XAFS measurements, which
are now in progress.
Acknowledgement
The authors thank Professor S. Sasaki and Dr. M.
Okube for the support of the XFH experiments. The
experiments were performed at BL-6C (No. 2014G691).
This work was supported by Grant-in-Aid for Scientific
Research on Innovative Areas “3D Active-Site Science”(No. 26105006).

(b)

References[1] C. E. Guillaume, C. R. Hebd. Seanes Acad. Sci. 125,235 (1897).
[2] R. J. Weiss, Proc. Phys. Soc. London, 82, 281 (1963).
[3] T. Yokoyama and K. Eguchi, Phys. Rev. Lett. 107,065901 (2011).
[4] K. Hayashi et al., J. Phys.: Condens. Matter 24,093201 (2012).
[5] S. Hosokawa et al., Phys. Rev. B 87, 094104 (2013).
[6] J. J. Barton, Phys. Rev. Lett. 67, 3106 (1991). *hosokawa@sci.kumamoto-u.ac.jp. †Present address:Department of Materials Science and Engineering,
Graduate School of Engineering, Nagoya Institute ofTechnology, Nagoya 466-8555, Japan.

Fig. 1: Atomic images of Fe66Ni34 Invar alloy around the(a) Ni and (b) Fe central atoms on the (001) planeobtained from Ni and Fe Kα XFH measurements,
respectively.