Conference-Atomic Holography 2010-Applications of X-ray Fluorescence Holography to Materials Sciences

In this review article, we demonstrate the feasibility of x-ray fluorescence holography (XFH) technique by introducing our several recent applications to materials sciences, such as a diluted magnetic semiconductor Zn1−xMnxTe mixed crystal, a DVD-RAM material Ge2Sb2Te5, and a shape memorial alloy Ti50Ni44Fe4. The interests are concentrated to the intermediate-range atomic arrangements and their spatial fluctuations. [DOI: 10.1380/ejssnt.2011.265]


I. INTRODUCTION
Needless to say, it is very important to know atomic structure of materials for understanding their nature.If the sample is a perfect single crystal, the single crystal structure analysis using x-ray or neutron diffraction (XD or ND) is the perfect method, which detects periodicity of single crystal.Even if a single crystal has an extremely large size of the unit cell, such as protein crystals, difficulties can nowadays be solved using intense synchrotron radiation sources.Powder diffraction method is also a powerful tool to determine the crystal system and its lattice parameters even for polycrystalline materials.Although a proper model is required, it is possible to determine detailed positions of the individual atoms in its unit cell.
If the sample is not a perfect crystal, e.g., modified by mixing of other elements, the above methods cannot determine the positions of the elements perfectly, because the perfect periodicity of the atomic structure is broken and it comprises a randomness in the atomic positions.As a result, the unit cell size of the crystal becomes in principle infinite.In recent days, most of functional materials are made up of mixing of many elements, which are categorized as such imperfect crystals.Thus, one should recognize that the diffraction is not the perfect method for investigating their atomic structures.
An alternative method for obtaining atomic structures is x-ray absorption fine structure (XAFS), which is widely used for investigating local atomic structure around a specific element, and can be adopted to even disordered materials.From this method, however, one can obtain only one-dimensional information, i.e., directionally averaged pair distribution functions.Moreover, the obtained information is usually limited to the second or third neighboring atoms due to the short mean-free path of x-ray excited photoelectrons.
Thus, it is very important to find a new method that can bridge the farsighted XD and nearsighted XAFS for investigating the structure of imperfect crystals.For this, we think that x-ray fluorescence holography (XFH) is a good tool, which was developed by Tegze and Faigel [1,2] as a reliable method of structure characterization.There are several advantages as a structural characterization method compared to the XD or XAFS as follows.
1) It allows one to obtain a three-dimensional (3D) atomic image without any special models.
2) Local atomic image can be obtained around a specific element emitting fluorescent x-rays up to about fifteenth neighboring atoms at present.
3) Structural information around an impurity atom or a low-dimensional sample is measurable with no special experimental constraints.
4) Fluctuations of atomic positions can be clarified for each individual neighboring atom.
5) Single phase is not necessary for the sample crystal.
On the other hand, this technique has some disadvantages as follows.
a) The sample should be single crystalline phase.
b) It has still an insufficient spatial resolution of about 0.05 nm.
c) It needs a wide flat surface with more than 5 × 5 mm 2 at present.
d) It takes a long time for the measurement, i.e., one or two days per one fluorescent x-ray of one sample even using an intense third-generation synchrotron light source.
By taking these advantages and disadvantages into account, we have carried out the XFH experiments for studying the structure of several crystals, such as diluted magnetic semiconductor Zn 1−x Mn x Te, a DVD material Ge 2 Sb 2 Te 5 , and a shape memorial alloy Ti 50 Ni 42 Fe 6 .In this paper, we review recent applications of the XFH technique to structural properties of these functional materials.In Sec.II, the principle of the XFH technique is briefly introduced.Then, the experimental method and data analysis procedure are given in Sec.III Our recent applications to materials science are shortly presented using three subsections in Sec.IV.And we summarize this review article in the last section.

II. PRINCIPLES OF X-RAY FLUORESCENCE HOLOGRAPHY
The XFH is a noble technique, which is recently developed remarkably by using synchrotron radiation.Figure 1 shows schematic views of the principles of XFH process.The process (a) is called normal mode.When x-rays with an energy higher than an absorption edge of a constituent element, are irradiated onto the sample, the corresponding fluorescent x-rays are emitted from the sample.If they directly enter the detector, they are the reference waves.On the other hand, they are sometimes scattered by the neighboring atoms, after which they enter the detector.In this case, they are the object waves.The reference and object waves interfere with each other.Therefore, when the angle dependence of the fluorescent x-rays is measured, a contrast can be detected in intensity, which is called hologram.
The process (b) is called inverse mode, which is based on the idea of the optical reciprocity of the normal XFH.The atoms emitting fluorescent x-rays serve as the detector of the field originating from the interference between the incident and scattered x-rays, which give the reference and object waves, respectively.In this mode, therefore, the position of the detector is fixed with respect to the sample crystal, and the angles of the incident x-rays vary.
In either mode, the observed fluorescent x-ray intensity, I(k), is given as where I 0 is the incident x-ray intensity, R the distance between the sample and detector, and a j the contribution of scattering by a neighboring j-atom.The first term in [ ] is the background, the second one corresponds to the hologram signal, and the third one is a negligibly small value of the interference between the object waves.The hologram signal is in general very weak in intensity, i.e., about one thousandth of the background, and thus, a synchrotron radiation source with an intense x-ray flux is necessary to carry out the XFH experiments.

III. EXPERIMENTAL METHOD AND DATA ANALYSIS
The XFH experiments were mainly carried out at the beamline BL6C of the Photon Factory in High Energy Accelerator Research Organization (PF-KEK) at Tsukuba, Japan.The measurements were performed in inverse mode.The schematic diagram and photograph of the experimental setup are depicted in Fig. 2(a) and (b), respectively.
A single crystal sample with a flat surface was fixed at the center of a three-axes goniometer.Monochromatized x-ray beam from the bending magnet source was irradiated onto the sample.The measurements were performed by rotating the two axes of the sample, 0 • ≤ θ ≤ 70 • in steps of 1 • and 0 • ≤ ϕ ≤ 360 • in steps of about 0.35 • , and detecting small variations in fluorescent x-ray intensity with angles.The fluorescent x-rays were collected using an avalanche photodiode (APD) detector with a cylindrical graphite-crystal energy analyzer.Typically, each scan took 6-11 h.Details of the experimental setup were given elsewhere [3,4].
The holograms were recorded at about ten incident xray energies above the absorption edge in steps of 0.5 keV.The hologram oscillation data were obtained by subtracting the background from the normalized intensities.An extension of the hologram data to the 4π sphere was carried out using crystal symmetry and the measured x-ray standing waves (XSW) lines.Figure 3 shows an example of the Zn Kα hologram measured at the incident x-ray energy of 11.5 keV for Zn 0.4 Mn 0.6 Te diluted magnetic semiconductor [5] Since a Fourier transform of the XFH data at a single incident x-ray energy produces false twin images, a 3D atomic image was constructed using Barton's algorithm [6] by superimposing the holograms with the different incident x-ray energies, which can highly suppress the false images.

IV. APPLICATIONS TO MATERIALS SCIENCE A. Mixed crystal
Due to the difference of spatial scales surveyed by the XD (or ND) and XAFS measurements, different results were reported even in the first nearest neighbor distances of mixed crystal.For example, mixed crystals of diluted magnetic semiconductors Zn 1−x Mn x Te, being taken up in this subsection, have such different reports between them.
The ternary mixture Zn 1−x Mn x Te is one of the socalled diluted magnetic semiconductors which have attracted much attention due to their striking magnetic or magneto-optical properties [7].Various properties of this intermediate phase between magnetic and semiconducting materials can be controlled by a change of concentration.The structure of Zn 1−x Mn x Te has been believed that Zn 2+ cations are randomly replaced by Mn 2+ magnetic ions in its zinc-blend structure.
Figure 4 shows the concentration dependence of the nearest neighbor distance obtained from XD [8] and XAFS [9] for Zn 1−x Mn x Te.From the lattice constants, a, obtained from XD results showing sharp Bragg peaks even for the mixtures [8], the bond lengths were calculated for their zinc-blende structure, √ 3a/4, which are given by the triangles in Fig. 4. As clearly seen in the figure, the XD results show the Vegard's law behavior, i.e., it linearly changes with x.On the contrary, results from the XAFS experiments given by the circles indicate that the nearest neighbor distance changes very little with x; it looks largely keeping the Pauling's bond lengths of Zn-Te and Mn-Te different by 0.0078 nm.Recently, we have clarified where Pauling's bond length interconnects with Vegard's law in a mixed crystal by measuring Zn Kα XFH for the Zn 0.4 Mn 0.6 Te mixed crystal [5].
Figures 5(a small circles Zn or Mn atoms.The thick circles locate on a (001) plane, and correspond to the atomic images in (a) and (b).
A careful comparison of the images between the Zn 0.4 Mn 0.6 Te and ZnTe crystals reveals that the images of the first and fifth neighboring Te atoms (one and three bonds, respectively) in the Zn 0.4 Mn 0.6 Te mixed crystal are much weaker than those in the ZnTe perfect crystal.However, the most important result of the present XFH experiment is that the images of the thirteenth neighboring atoms (five bonds) come back to be much stronger.Moreover, the further distant Te atoms also show clear images.In order to show them clearer, the image intensities of Te atoms in Zn 0.4 Mn 0.6 Te and ZnTe are given in Fig. 7. Their intensity ratios are also given below the marks in the figure .Although the ratio values are rather scattered, those for near neighbor Te atoms below 0.8 nm range about 0.5-0.6.On the contrary, those for the distant Te atoms beyond 0.8 nm approach a large value of 0.7-0.8.Thus, the Te sublattice keeps the long-range periodicity.
From the above experimental results by the XFH measurement, it is qualitatively clarified that the lattice distortions caused by keeping the Pauling's bond length with the nearest-neighboring Te atoms in Zn 0.4 Mn 0.6 Te diluted magnetic semiconductor vanish within about five chemical bonds, and interconnect with the Vegard's law.Further detailed quantitative discussion on the spatial fluctuations in this mixed crystal is given in our previous paper [5] by using a model named a locomotive wheel atomic configuration model.
Similar results were obtained in another diluted magnetic semiconductor Cd 1−x Mn x Te [10], and a mixed crystal In 1−x Ga x Sb [11].A different result was, however, observed in Cd 1−x Zn x Te γ-ray detector material [12], where only the first neighboring shell is distorted.

B. DVD material
In recent years, rewritable optical media such as digital versatile disk random access memory (DVD-RAM) have been widely used for recording large amounts of data.It is well known that this recording process is governed by a laser-induced crystalline-amorphous phase transition of the thin film media material, such as Ge 2 Sb 2 Te 5 in the case of DVD-RAM.It has been, however, difficult to understand the mechanism behind the very fast recording and erasing achieved in phase change materials based on the conventional idea of laser-induced melting and recrystallizing processes; the real mechanism was mysterious for about two decades.
The structure of polycrystalline Ge 2 Sb 2 Te 5 in thin film has been intensively investigated using powder XD [13,14].They found that the structure of the thin film is not hexagonal as is stable in the equilibrium phase of Ge 2 Sb 2 Te 5 , but rather a metastable face-centered cubic (fcc) structure.Based on this experimental result, they proposed a rocksalt-type structural model in which the anion site is fully occupied by Te atoms and the cation site is randomly occupied by Ge, Sb, and about 20% vacancies.
Kolobov et al. carried out an x-ray absorption study of laser-crystallized and laser-amorphized Ge 2 Sb 2 Te 5 thin films [15] to clarify the details of the local structure.From the results, they proposed a unique structure model named an umbrella flip model as shown in Fig. 8.The red balls indicate the Ge atoms, and the others the Te atoms.They found that the metastable phase was, in fact, a distorted rocksalt structure as shown in Fig. 8(a), in which the six Ge(Sb)-Te equal-length bonds split into two groups of three shorter and three longer bonds as is in GeTe.
They also concluded that the laser-induced amorphization is triggered by an umbrella-flip motion of the Ge atoms from an octahedral position in the distorted rocksalt crystal into a tetrahedral position in the amorphous phase as shown in Fig. 8(b).They pointed out that this phase transition occurs without rupture of strong covalent bonds upon the transformation to the amorphous state, allowing the transition to be both fast and reversible.During the crystallization process, however, one of the covalent bonds is broken and replaced by three weak resonant bonds in the crystalline state.As mentioned in the introductory section, the XFH technique can directly be adopted to clarify the local-and intermediate-range atomic structures even in thin films, and we have chosen XFH to obtain a deeper insight into the structure of this fascinating material.In this subsection, we present a 3D atomic image of Ge 2 Sb 2 Te 5 epitaxial layers around the Ge atoms, and discuss the implications of these measurements on the phase transition mechanism in DVD-RAM materials [16].
Ge 2 Sb 2 Te 5 epitaxial layers with a thickness of about 2 µm were grown by helicon sputtering of a Ge 2 Sb 2 Te 5 target onto a (100) GaSb single-crystal substrate containing no Ge at a substrate temperature of 200 • C. XD measurements confirmed that the film had a fcc structure with a lattice constant of 0.60751 (5) nm.This value is slightly larger than the previous powder XD result [14], and is likely the result of heteroepitaxial strain effects from the slightly larger lattice constant 0.6096 nm of the substrate.The incident x-rays were focused onto the (001) surface of the sample, and the Ge Kα fluorescent x-rays were collected.The XFH was recorded at six incident x-ray energies of 11.5-14.0keV in steps of 0.5 keV.To suppress the thermal agitation of the atoms, the sample was cooled down to 100 K using a cryostream apparatus.
The obtained atomic image on the (001) plane is shown in Fig. 9(a).The cross at the center of the figure indicates the central Ge atom.A clear, fourfold atomic structure is visible.This image clearly reveals that the Ge 2 Sb 2 Te 5 single crystal film does not have hexagonal point symmetry around the Ge atoms.The distance from the central atom to the neighboring atoms is about 0.45 nm, which is much larger than the Ge-Te nearest-neighbor distance of 0.283 nm obtained from the previous EXAFS experiment [15].Thus, these atomic images should correspond to the second-nearest-neighbor Ge or Sb atoms.Other fourfold symmetric atomic images are visible at the symmetric positions of the central Ge atom with respect to each edge of the square made by four second-neighbor Ge(Sb) atoms.These images correspond to the fourth-nearest-neighbor Ge(Sb) atoms.From these results it is reasonable to assign a cubic structure to the Ge(Sb) sublattice.In this figure, however, the Te atoms cannot be observed.If the structure were a perfect rocksalt structure, the Te atoms would be located near the dashed circles.The difference between the distorted rocksalt structure reported previously and the structure reported here with Ge atoms in a tetrahedral symmetry positions is likely to be due to the different sample preparation conditions; the presence of heteroepitaxial strain arising from lattice mismatch may have resulted in the stabilization of a different metastable phase, which also manifests a larger lattice constant compared to that observed for the unstrained distorted rocksalt phase.On the contrary, commercially available DVD disks are prepared in the form of a polycrystalline thin film on a polycarbonate substrate.In films prepared this way, the strain may relax due to the small grain size of polycrystal Ge 2 Sb 2 Te 5 , resulting in the stabilization of the distorted rocksalt phase.Laser irradiation of this commercial DVD material, however, locally raises the temperature, which increases the lattice constant as confirmed by an XD measurement [18].As was demonstrated in a theoretical paper [19], the total energy of the rocksalt structure is slightly lower than that of the spinel structure, but becomes similar at an increased lattice parameter.Since the lattice parameter in the present film is about 0.8% larger than usually reported for Ge 2 Sb 2 Te 5 , this may be the reason why the Ge atoms switch to the tetrahedral symmetry sites.This movement of the Ge atoms seems to be similar to the umbrella-flip proposed earlier for the laser-induced phase transition [15].In conclusion, the structure found by this XFH experiment may provide support for the previously suggested umbrella-flip switching of the Ge atoms during the laser-induced phase transition widely utilized in rewritable optical media.

C. Shape memorial alloy
Shape memory alloys (SMA) are promising materials for actuators because they exhibit large reversible strain and strong recovery forces upon repeated heating and cooling.These features of SMAs are due to a reversible phase transition, i.e., the martensitic transition, between the parent and martensite phases.Ti-Ni alloys, which are the most practical SMAs, exhibit two kinds of martensitic transitions.One is a direct first-order phase transition from the B2 parent phase (P phase) to the B19' martensite phase, and the other is a sequence of firstorder phase transitions from the B2 phase to the R phase and from the R phase to the B19' phase.It was found that the first-order phase transition in Ti 50 Ni 50−x Fe x are suppressed with increasing Fe content, and only the precursor phenomena are observed when more than 6 at.% of Fe atoms are substituted for Ni [20].This precursor phenomena of Ti 50 Ni 50−x Fe x are recognized as a second-orderlike transition from the P phase to the incommensurate phase (IC phase).Particularly for Ti 50 Ni 44 Fe 6 , a commensurate phase (C phase) appears upon further cooling.The R and C phases have a similarity that superlattice diffraction spots, such as 1 3 1 3 0 diffraction, are observed in selected-area electron diffraction patterns.Therefore, Ti 50 Ni 44 Fe 6 is a suitable sample for investigating the lattice modulation accompanied by the appearance of the superlattice structure.The XFH experiments were performed on Ti 50 Ni 44 Fe 6 for the P phase at 225 K and the C phases at 100 K, which show different local environments at the P and C phases, and the atomic dynamics related to the phase transition is discussed [21].
The single-crystal Ti 50 Ni 44 Fe 6 alloy was grown by a floating-zone method.The sample was about 6 mm in diameter with a surface orientation of (110).The incident x-ray energies were 8.0-12.0keV in 0.5 keV steps.Using the toroidally bent graphite crystal, Fe Kα fluorescent xrays from the sample were analyzed and focused onto the detector.10(a).In contrast, the far atomic images in Fig. 10(b), such as those located at 300, 310, and 320 positions, in the C phase are weaker than those in the P phase in Fig. 10(a).
In order to clarify the intensity changes upon the phase transition, each intensity ratio of the atomic images in the C and P phases was calculated.Figures 11(a Figures 10(c) and (d) exhibit the atomic images of the Ti planes at z = 1.5 Å in the P and C phases, respectively.From the comparison of these two figures, only the images of the first neighbor Ti atoms have a large difference; these images are very weak for the P phase but markedly clear for the C phase.The radial distribution functions around Fe were obtained from the XAFS data.However, such a large difference of the first neighbor Ti peak intensity was not observed between the C and P phases.Thus, spatial fluctuations should occur in the angular direction.From a simple calculation, it is suggested that the large intensity difference between the first neighbor Ti atoms of the C (100K) and P (225 K) phases can be realized only when the angular fluctuations in the C phase is a very small value lower than 0.1 Å, similar to the radial value, and that in the P phase is larger than 0.4 Å [21].We believe that our findings provide an important hint to understanding the mechanism of the martensite phase transition of the TiNi series.

V. SUMMARY
In summary, we demonstrate the feasibility of x-ray fluorescence holography (XFH) technique in this article by introducing our several recent applications to materials sciences, such as a diluted magnetic semiconductor Zn 1−x Mn x Te mixed crystal, a DVD-RAM material Ge 2 Sb 2 Te 5 , and a shape memorial alloy Ti 50 Ni 44 Fe 4 .The interests are concentrated to the intermediate-range atomic arrangements and their spatial fluctuations.The direct 3D structural information obtained by XFH is building an effective bridge between XD investigating long-range periodicity of crystals and XAFS having large advantages to obtain local structures.

FIG. 1 :
FIG. 1: The principle of x-ray fluorescence holography in (a) normal and (b) inverse modes.

FIG. 8 :
FIG. 8: The umbrella flip model proposed by Kolobov et al. [15] to explain the (a) crystal − (b) amorphous phase change of Ge2Sb2Te5.The red balls indicate the Ge atoms, and the others the Te atoms.

FIG. 9 :
FIG. 9: Atomic images around the central Ge atoms on the (a) (001) and (b) (110) planes.The contrasts in the right and left panels are different to optimize the images.After Ref. [16].

Figure 9 (
Figure 9(b) shows an atomic image on the (110) plane.As indicated by the green circles, two atomic images are located near the shoulder of the central Ge atom.The distance from the central Ge atom is 0.27±0.01nm.Thus, these atomic images correspond to the nearest-neighbor Te atoms.The bond angle of Te-Ge-Te is near the tetrahedral value of about 110 • .The third-nearest-neighbor Te atoms are also seen in the lower part of the figure, as indicated by the green circles.The observed image is very similar to the previously studied case of zinc-blende structure[17] with Ge atoms located in tetrahedral symmetry sites.

FIG. 10 :
FIG. 10: Atomic images on the (001) lattice plane at z=0 Å(upper) and z=1.5 Å(lower) in the P (left) and C phases (right).The intersections of the dotted lines indicate the ideal positions of the Ni/Fe atoms in (a) and (b) and the Ti atoms in (c) and (d).After Ref. [21].

FIG. 11 :
FIG. 11: Atomic arrangements of Ni/Fe planes with intensity ratios of C and P phases at (a) z = 0 Å and (b) z = 3.0 Å.The dashed circles with the radius of 8 Å indicate the area of a cluster-like structure in the C phase at 100 K.The gray bar indicates the intensity ratios of the C and P phases.The lightness shows the atomic image enhancement due to phase transition to C phase.After Ref. [21].
) and (b) show the intensity ratios given on the Ni/Fe atomic plane at z = 0 Å and at z = 3.0 Å, respectively.The ratios are converted to the lightness of the spots.The images of neighboring Ni/Fe atoms within the radius of about 8 Å indicated by dashed circle are enhanced in the C phase.Thus, it is clarified that the formation of the cluster with a size of 8 Å in the C phase.