In-Plane Positional Fluctuations of Zinc Atoms in Single Crystal Mg85Zn6Y9 Alloy Studied by X-ray Fluorescence Holography

Koji Kimura; Kouichi Hayashi; Koji Hagihara; Hitoshi Izuno; Naohisa Happo; Shinya Hosokawa; Motohiro Suzuki; Hiroo Tajiri

doi:10.2320/matertrans.M2016459

Abstract

We performed X-ray fluorescence holography measurements on a single crystal Mg₈₅Zn₆Y₉ alloy, having a synchronized 18R long period stacking ordered structure, and successfully obtained Zn Kα holograms. The reconstruction shows “U”-shaped atomic images in remarkable contrast to the prediction of an existing model with Zn₆Y₈ L1₂ clusters. To explain this feature we calculated holograms using a model with positional fluctuations, and fit the reconstruction to the experimental results. It was found that large rotational fluctuations of the clusters can explain the “U”-shaped images.

1. Introduction

Recently, novel Mg alloys, containing Zn and rare earth metals¹⁾, have attracted significant attention because of their excellent mechanical properties. When small amounts of Zn and Y are added to pure Mg, the mechanical properties of the alloy, such as the strength and the ductility, are remarkably improved^1,2). Furthermore, the Mg-Zn-Y alloys exhibit a non-flammable nature and high thermal stability³⁾ in contrast to pure Mg. Owing to these superior properties, the new Mg alloys are expected to serve as a next-generation light weight structural material, e.g. aircraft and subway bodies.

For clarifying the origin of such excellent properties, extensive studies on the microscopic structure of the Mg alloys have been performed^4–6), and it has been found that a long-period stacking ordered (LPSO) phase is formed in some of the Mg alloys. Until now, four poly types have been reported, that is, 10H, 14H, 18R, and 24R type LPSO structures^7–12) (according to the Ramsdell notation¹³⁾), among which the 18R type LPSO structure is formed in the Mg₈₅Zn₆Y₉ LPSO alloy, the sample investigated in this work. The 18R type LPSO structure has an 18-fold stacking periodicity of close packed layers along the stacking direction. The 18R stacking sequence is characterized by the periodical insertion of the stacking fault at every 6 hexagonal close packed stacking layers, and the remarkable feature of this atomic arrangement is that Zn and Y impurities are enriched around the stacking faults, as revealed by transmission electron microscope measurements¹⁴⁾. Thus, this structure is called synchronized LPSO structure. Furthermore, based on Z-contrast scanning transmission electron microscopy and first principle calculations, Egusa and Abe¹⁵⁾ have proposed a structural model, where Zn and Y atoms form Zn₆Y₈ L1₂ type clusters around the stacking faults.

In addition to the average atomic configurations of Zn and Y, deviations from the ideal atomic positions of these atoms were discussed with diffraction techniques^15,16). In these studies, diffuse diffraction spots were observed, which suggests an incomplete in-plane ordering of Zn and Y. However, exact features of the in-plane arrangement of Zn and Y atoms in their chemically modulated layer have not yet been sufficiently clarified. For example, information on the positional correlation between adjacent L1₂ clusters is still insufficient. Furthermore, although first principle calculation predicts that the L1₂ clusters in Mg-Zn-Y alloy undergo inward contraction¹⁷⁾, the details of the exact positional fluctuations of atoms have not been experimentally revealed. Investigation on such positional fluctuations of Zn/Y atoms in the LPSO phase must be important, since it affects the mechanical properties¹⁸⁾ and the allowable range of composition for the formation of the LPSO phase¹⁷⁾. Their characteristics are essential for obtaining insight into the strengthening mechanism and the stability of the LPSO phase, which is necessary to design practical structural materials.

X-ray fluorescence holography (XFH)¹⁹⁾ can visualize the three-dimensional atomic configurations around the selected elements and provides useful information on the local arrangements of the substitutional Zn and Y atoms in the LPSO phase. In particular, XFH is highly sensitive to positional fluctuations of atoms¹⁹⁾. Thus we can directly obtain real-space information on the positional fluctuations of the substitutional atoms.

In this study, we performed XFH measurements on a single crystal Mg₈₅Zn₆Y₉ alloy. We report the local atomic image around Zn, showing widely distributed features. The atomic images are compared with those obtained from a simulation, taking into account the fluctuation of the Zn atoms, from which we discuss how the obtained images can be explained.

2. Experimental Procedure

Master alloy ingots of Mg₈₅Zn₆Y₉ were prepared using high frequency induction melting of pure metals in carbon crucibles²⁰⁾. The directionally solidified (DS) Mg₈₅Zn₆Y₉ alloy composed almost entirely of the 18 R LPSO phase was grown with the Bridgman method under an Ar atmosphere²⁰⁾. Figure 1(b) shows a photograph of the DS sample used for the present XFH measurement. The measurements were performed for the single crystal region, indicated in the figure. The size of the single crystal area is approximately 1 × 3 mm².

Fig. 1

(a) Experimental setup for XFH measurements on the single crystal LPSO alloy. (b) Photograph of the present Mg₈₅Zn₆Y₉ sample. The single crystal area is enclosed with the solid lines.

The XFH experiment was performed at BL39XU in SPring-8. The beamline achieves a well-focused beam with a high beam intensity stability²¹⁾, which enables us to obtain high-quality holograms from the small-sized sample. The experimental set up is illustrated in Fig. 1(a). Using a focusing mirror, the incident beam was vertically focused to 20 μm on the sample. The horizontal width of the beam was adjusted to 20 μm using the slit in front of the sample. For extracting the Zn Kα fluorescence X-rays, we used the cylindrical graphite analyzer. The signal was collected with the avalanche photodiode detector. The incident beam intensity was monitored with an ion chamber. We set the energy of the incident X-rays to be 10 keV–13.5 keV above the Zn K-edge energy of 9.66 keV. The energy step was set to be 0.25 keV. The ranges of the exit and azimuthal angles, θ and φ (see Fig. 1), were θ = 0–70° and φ = 0–360° in steps of 1° and 0.25°, respectively. The photon flux of the incident X-ray was 1.6 × 10¹¹ photons/s at 12 keV.

The alignment of the sample position was performed as follows. First, the incident beam position was confirmed by X-ray sensitive films on the sample holder. The area around the beam spot was magnified using a telescopic camera, and the position of the goniometer was precisely adjusted so that the incident beam can go through the rotational axes of θ and φ. Then, we put the sample on the holder and set θ = 90°, where the sample surface is aligned parallel to the incident beam. In this alignment, we horizontally moved the sample position in the direction perpendicular to the beam path and determined the on-axis position, where the sample cut the beam and the intensity monitored behind the sample is reduced by half. Also, we adjusted the center of the single crystal area to the incident beam position using the telescopic camera. Because of such a precise adjustment and the well-focused beam, the incident beam was well within the single crystal area for the whole solid angle range measured and we successfully obtained the holograms.

3. Results and Discussions

Figure 2(a) shows the Zn Kα hologram obtained at the incident X-ray energy of 11.00 keV. Here, the three-fold symmetric manipulation was performed. We can weakly observe standing wave lines in this hologram (indicated with dashed curves).

Fig. 2

Zn Kα X-ray fluorescence hologram of Mg₈₅Zn₆Y₉ at 11.00 keV. (a), (b) Experimentally obtained holograms. (c), (d) Calculated holograms obtained from the structural model proposed by Egusa and Abe¹⁵⁾. Threefold and sixfold symmetric manipulations were carried out for (a), (c) and (b), (d), respectively.

The theoretical calculation of the holograms was also performed using 3D-AIR-IMAGE²²⁾, developed for analyzing and simulating X-ray fluorescence and photoelectron holograms. The calculation was based on the structural model proposed by Egusa and Abe¹⁵⁾, where the Zn and Y atoms form Zn₆Y₈ L1₂ clusters around the stacking faults. We chose Zn as the emitter. The incident x-ray energy was chosen according to the experiment. As mentioned above, the range of θ in the experiment was 0–70°. Because the LPSO crystal has only two-fold rotational symmetry with respect to the a and b axes, the range of θ in the experimental data is limited to 0–70° and 110–180°, even after the symmetric procedure. By taking this into account, we simulated the holograms in the same θ range as the experiment. Figure 2(c) shows an example of simulated Zn hologram at the incident x-ray energy of 11.00 keV. The standing wave line originating from the (4 −2 8) Bragg reflection is indicated with the dashed curve.

Figures 3(a) and (b) show the experimental and calculated images, respectively. The Barton algorithm²³⁾ was used for the reconstruction. Figure 3(c) shows the atomic configurations in a Zn plane located on the stacking fault based on the model proposed by Egusa and Abe¹⁵⁾. The emitter Zn atom is located at the center. Since the Zn atoms have three atomic sites, the hologram measurements observe the superposition of these different configurations, which possesses sixfold rotational symmetry. Thus, sixfold symmetric manipulation was performed for the experimental and calculated holograms (Figs. 2(b) and (d)), from which atomic images are reconstructed (Figs. 3(a) and (b)).

Fig. 3

Reconstructed in-plane atomic images obtained from (a) experiment and (b) calculation. (c) Zn layer around the stacking fault based on the model proposed by Egusa and Abe¹⁵⁾.

The remarkable feature observed in the experimental result is the presence of U-shaped images around the central Zn atom (Fig. 3(a)). When we compare the experimental image with the calculated one (Fig. 3(b)), we find that the 1st and 2nd nearest neighboring Zn atoms are located near these U-shaped images (solid circles). As shown in Fig. 3(c), the 1st nearest Zn atoms belong to the same cluster as the emitter. The 2nd nearest ones belong to the neighboring clusters. The distances from the emitter to the 1st and 2nd nearest Zn atoms are 4.5 Å and 7.6 Å, respectively. We interpret that these neighboring Zn atoms contribute to the formation of the U-shaped images. However, the experimental result cannot be explained without any positional fluctuations.

We calculated the atomic image of Zn layers, including the positional fluctuations indicated in Fig. 4(c). Figure 4(c) shows the regular triangle of Zn atoms in the L1₂ cluster formed along the stacking layer. The rotational in-plane fluctuations of this triangle are introduced to the calculation. The rotational shifts are denoted as δΘ. In addition, we considered a shrinking of the triangle, δr, because we observe the atomic images closer to the central atom than the original position of the 1st nearest neighbor in the experimental results as in Fig. 3(a). Such a contraction is conceivable by considering large accumulations of electrons inside the Zn₆Y₈ L1₂ clusters reported by Kimizuka et al.¹⁷⁾ If δΘ and δr are independent of each other, the atomic images only broaden around the original position, which cannot explain the experimental results; thus, there should be some relation between these fluctuations. Here, we assume the relation, δr ∝ −|δΘ|.

Fig. 4

(a) Calculated atomic image of the Zn layer, where positional fluctuations are introduced. (b) Enlargement of the dashed square in (a). (c) Description of the fluctuation introduced in the calculation. (d), (e) Residual sum of squares (RSS) as a function of δr_max and |δΘ|_max. Here, the RSS is derived by taking the difference between the calculated and experimental atomic images in the range of 3.25 Å–9.0 Å from the center.

In the calculation, 1600 Zn triangles are considered, each of which randomly takes δr and δΘ values within the ranges of δr < δr_max and |δΘ| < |δΘ|_max. In addition, the relation, δr = −(δr_max/|δΘ|_max) |δΘ| + δr_max is assumed, where the coefficient δr_max/|δΘ|_max is selected taking into account the condition δr > 0. We obtained δr_max = 0.6 Å and |δΘ|_max = 18.2° as follows. From the difference between the simulated and the experimental images, we calculated the residual sum of square (RSS) as a function of δr_max and |δΘ|_max, as shown in Figs. 4(d) and (e). When we calculated the RSS, we chose the range of 3.25–9.0 Å from the center for extracting the U-shaped images. As Fig. 4(d) shows, the RSS is minimized at δr_max = 0.6 Å when we set |δΘ|_max = 20°. Under the condition in which δr_max = 0.6 Å, RSS is minimized at |δΘ|_max = 18.2°, derived from the polynomial fit to the data point (solid curve). In fact, RSS = 1.358 × 10⁻⁴ at |δΘ|_max = 18.2°, which is the smallest value of any calculated RSS.

Figure 4(a) shows the calculated atomic image. The original atomic positions are indicated with solid circles. As indicated with the dashed square, the U-like shape is observed. Figure 4(b) shows the enlargement of the region enclosed by the dashed square. The U-like shape is composed of the distributed images of the 1st and 2nd neighboring atoms. The atomic image at approximately x = 0 and y = 3.3–4.5 Å corresponds to the 1st nearest neighbor. Because of shrinking,δr, the position of the atomic image shifts closer to the central atom from the original position (solid circle). The relation δr = −(δr_max/|δΘ|_max) |δΘ| + δr_max, that is, |δΘ| = −(|δΘ|_max/δr_max)δr + |δΘ|_max is also reflected in this image. The image becomes broader in the tangential direction as the distance from the center increases and bifurcates at approximately y = 4 Å. The broad atomic images at approximately y = 5–9 Å correspond to the 2nd nearest neighbors, which belong to the neighboring clusters. The images are distributed in the direction indicated with an arrow in Fig. 4(b), which is caused by the rotation and shrinking of the neighboring clusters. These distributed images of the 1st and 2nd neighboring atoms are connected at approximately y ～ 5 Å, and consequently the U-like shape is formed.

The sixfold images observed at approximately 11 Å from the center indicated by dashed circles in Fig. 4(a) correspond to the Zn atoms separated by the lattice constant. In the experimental results, the corresponding broad images are observed as indicated by dashed circles in Fig. 3(a). Since the experimental images are distributed more widely than the calculated ones, it is suggested that the real inter-cluster correlation is weaker than the calculated results.

Although there are some deviations from the experimental results, such as the intensity and the detailed shape of the atomic images, the model described above at least qualitatively explains the U-shaped images observed in the experiment. The translational fluctuation of the cluster and a more elaborate correlation between δr and δΘ may be necessary for improving the agreement with the experimental results.

4. Conclusion

In summary, we have performed Zn Kα XFH experiments on a single crystal Mg₈₅Zn₆Y₉ LPSO alloy and successfully obtained the holograms. The reconstruction shows the U-shaped atomic images, which are not reproduced with a model of ordered Zn₆Y₈ L1₂ clusters. These images are qualitatively explained by the simulation including the shrinking and the large rotation of the L1₂ clusters. Our finding suggests that the main reason which prevent the formation of the ordered and stable in-plane structure in the Mg₈₅Zn₆Y₉ LPSO alloy is the rotation of the L1₂ cluster. In the near future, we will perform XFH measurements on a Mg₇₅Zn₁₀Y₁₅ alloy with highly ordered L1₂ clusters²⁴⁾ for comparison, which will be useful for clarifying the formation process of the LPSO phase.

Acknowledgments

This study was supported by grant-in-aid for Scientific Research on Innovative Areas (“3D Active Site Science” and “Materials Science on Synchronized LPSO Structure”) from the Ministry of Education, Culture, Sports, Science, and Technology of Japan (Nos. 2605006 and No. 24109505, respectively). This work was performed with the approval of SPring-8 (Proposal Nos. 2014A1172, 2014B1289, 2014B1296, and 2015A0116).

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