research papers\(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)

Journal logoSTRUCTURAL SCIENCE
CRYSTAL ENGINEERING
MATERIALS
ISSN: 2052-5206
Volume 70| Part 2| April 2014| Pages 275-282

Structure refinement of the δ1p phase in the Fe–Zn system by single-crystal X-ray diffraction combined with scanning transmission electron microscopy

aDepartment of Materials Science and Engineering, Kyoto University, Yoshida, Sakyo-ku, Kyoto 606-8501, Japan, bCenter for Elements Strategy Initiative for Structure Materials (ESISM), Kyoto University, Yoshida, Sakyo-ku, Kyoto 606-8501, Japan, cDepartment of Mechanics, Kobe University, Rokkodai-cho, Nada-ku, Kobe, Hyogo 657-8501, Japan, and dEM Application Group, JEOL Ltd, 1-2 Musashino 3-chome, Akishima, Tokyo 196-8558, Japan
*Correspondence e-mail: okamoto.norihiko.7z@kyoto-u.ac.jp

(Received 22 October 2013; accepted 21 December 2013; online 17 March 2014)

The structure of the δ1p phase in the iron−zinc system has been refined by single-crystal synchrotron X-ray diffraction combined with scanning transmission electron microscopy. The large hexagonal unit cell of the δ1p phase with the space group of P63/mmc comprises more or less regular (normal) Zn12 icosahedra, disordered Zn12 icosahedra, Zn16 icosioctahedra and dangling Zn atoms that do not constitute any polyhedra. The unit cell contains 52 Fe and 504 Zn atoms so that the compound is expressed with the chemical formula of Fe13Zn126. All Fe atoms exclusively occupy the centre of normal and disordered icosahedra. Iron-centred normal icosahedra are linked to one another by face- and vertex-sharing forming two types of basal slabs, which are bridged with each other by face-sharing with icosioctahedra, whereas disordered icosahedra with positional disorder at their vertex sites are isolated from other polyhedra. The bonding features in the δ1p phase are discussed in comparison with those in the Γ and ζ phases in the iron−zinc system.

1. Introduction

The iron−zinc binary system has been intensively investigated in both thermodynamic and crystallographic aspects over several decades (Ghoniem & Lohberg, 1972[Ghoniem, M. A. & Lohberg, K. (1972). Metall, 26, 1026.]; Bastin et al., 1974[Bastin, G. F., Vanloo, F. J. J. & Rieck, G. D. (1974). Z. Metallkdd. 65, 656-660.]; Perrot & Dauphin, 1988[Perrot, P. & Dauphin, J. (1988). Calphad, 12, 33-40.]; Petersen et al., 1988[Petersen, S., Spencer, P. J. & Hack, K. (1988). Thermochim. Acta, 129, 77-87.]; Reumont et al., 2000[Reumont, G., Perrot, P., Fiorani, J. M. & Hertz, J. (2000). J. Phase Equilib. 21, 371-378.]; Su et al., 2001[Su, X., Tang, N. & Toguri, J. M. (2001). J. Alloys Compd. 325, 129-136.]; Nakano et al., 2005[Nakano, J., Malakhov, D. V. & Purdy, G. R. (2005). Calphad, 29, 276-288.]; Kainuma & Ishida, 2005[Kainuma, R. & Ishida, K. (2005). Tetsu Hagane, 91, 349-355.]; Johansson et al., 1968[Johansson, A., Ljung, H. & Westman, S. (1968). Acta Chem. Scand. 22, 2743-2753.]; Brandon et al., 1974[Brandon, J. K., Brizard, R. Y., Chieh, P. C., McMillan, R. K. & Pearson, W. B. (1974). Acta Cryst. B30, 1412-1417.]; Koster & Schoone, 1981[Koster, A. S. & Schoone, J. C. (1981). Acta Cryst. B37, 1905-1907.]; Brown, 1962[Brown, P. J. (1962). Acta Cryst. 15, 608-612.]; Hong & Saka, 1997[Hong, M. H. & Saka, H. (1997). Scr. Mater. 36, 1423-1429.]; Uwakweh et al., 2000[Uwakweh, O. N. C., Liu, Z., Jordan, A., Chakoumakos, B., Spooner, S. & Maziasz, P. (2000). Metall. Mater. Trans. A, 31, 2739-2745.]; Belin & Belin, 2000[Belin, C. H. E. & Belin, R. C. H. (2000). J. Solid State Chem. 151, 85-95.]; Belin et al., 2000[Belin, R., Tillard, M. & Monconduit, L. (2000). Acta Cryst. C56, 267-268.]) partly because of the enormous importance of hot dip galvannealed (GA) steels which find wide applications in exposed automobile body panels owing to its high corrosion resistance, weldability and paintability (Marder, 2000[Marder, A. R. (2000). Prog. Mater. Sci. 45, 191-271.]). The coating layer of GA steels usually consists of five intermetallic compounds, Γ (Fe3Zn10), Γ1 (Fe11Zn40), δ1k (FeZn7), δ1p (FeZn10) and ζ (FeZn13) phases, which appear in the zinc-rich domain of the iron−zinc binary phase diagram (Ghoniem & Lohberg, 1972[Ghoniem, M. A. & Lohberg, K. (1972). Metall, 26, 1026.]; Kubaschewski, 1982[Kubaschewski, O. (1982). Iron-Binary Phase Diagrams. Berlin: Springer-Verlag.]; Nakano et al., 2005[Nakano, J., Malakhov, D. V. & Purdy, G. R. (2005). Calphad, 29, 276-288.]; Kainuma & Ishida, 2005[Kainuma, R. & Ishida, K. (2005). Tetsu Hagane, 91, 349-355.]). Despite the intensive investigations of the intermetallic phases (Allen & Mackowiak, 1963[Allen, C. & Mackowiak, J. (1963). Corros. Sci. 3, 87-97.]; Ghoniem & Lohberg, 1972[Ghoniem, M. A. & Lohberg, K. (1972). Metall, 26, 1026.]; Bastin et al., 1977[Bastin, G. F., Vanloo, F. J. J. & Rieck, G. D. (1977). Z. Metallkdd. 68, 359-361.]), it is only recently that the existence of two distinct phases (δ1k and δ1p) in the δ1 region has been accepted (Kainuma & Ishida, 2005[Kainuma, R. & Ishida, K. (2005). Tetsu Hagane, 91, 349-355.]; Hong & Saka, 1997[Hong, M. H. & Saka, H. (1997). Scr. Mater. 36, 1423-1429.]). The δ1 (δ1k/δ1p) phase was long considered to be relatively ductile so as to play an important role in the deformation of the coating when GA steels are bent, stretched and drawn during the forming process, because coating failure is mitigated when the coating layer consists largely of the δ1 (δ1k/δ1p) phase (Kato et al., 1994[Kato, C., Koumura, H., Uesugi, Y. & Mochizuki, K. (1994). TMS Annual Meeting, The Physical Metallurgy of Zinc Coated Steel, edited by A. R. Marder, pp. 241-249. San Francisco, CA: TMS.]). However, we have recently revealed that both of the δ1k and δ1p phases are extremely brittle exhibiting no plastic deformation in compression tests of polycrystalline micropillar specimens (Okamoto et al., 2013[Okamoto, N. L., Kashioka, D., Inomoto, M., Inui, H., Takebayashi, H. & Yamaguchi, S. (2013). Scr. Mater. 69, 307-310.]). The structural information about the δ1k and δ1p phases is limited, although it is indispensable for understanding their plastic deformability.

Belin et al. (Belin & Belin, 2000[Belin, C. H. E. & Belin, R. C. H. (2000). J. Solid State Chem. 151, 85-95.]) performed crystal structure refinement of the δ1p phase by single-crystal X-ray diffraction with a laboratory X-ray source (Mo Kα), and the results will be described in next section. On the other hand, Hong et al. (Hong & Saka, 1997[Hong, M. H. & Saka, H. (1997). Scr. Mater. 36, 1423-1429.]) found a stark difference in selected-area electron diffraction (SAED) patterns between the δ1p and δ1k phases. Additional streaks are observed in SAED patterns of the δ1k phase at positions indicating that the a-axis dimension of the δ1k phase is three times that of the δ1p phase. Hong et al. (Hong & Saka, 1997[Hong, M. H. & Saka, H. (1997). Scr. Mater. 36, 1423-1429.]) thus concluded that the δ1k phase has a superlattice structure based on the δ1p phase. However, further refinement of the crystal structure of the δ1k phase has yet to be made. We have recently tried to perform crystal structure refinement of the δ1k phase (as well as the δ1p phase) by scanning transmission electron microscopy (STEM). In the course of our STEM investigation of the δ1p phase, however, we have found some evidence that is against the results of the crystal structure refinement of the δ1p phase by Belin et al. (Belin & Belin, 2000[Belin, C. H. E. & Belin, R. C. H. (2000). J. Solid State Chem. 151, 85-95.]), which might arise from the difficulties in unambiguously distinguishing iron from zinc with a powerless laboratory X-ray source due to the small difference in the X-ray scattering factors between iron and zinc. We have therefore decided to re-investigate the crystal structure of the δ1p phase, based on which superlattice structure of the δ1k phase is formed, paying special attention to distinguishing iron from zinc with a synchrotron X-ray source of high luminance and coherence, combining with ultra-high-resolution STEM with a correction of spherical-aberration (Cs) that permits direct observation of individual atomic columns.

2. Crystal structure of the δ1p phase previously reported

Belin et al. (Belin & Belin, 2000[Belin, C. H. E. & Belin, R. C. H. (2000). J. Solid State Chem. 151, 85-95.]) have reported that the δ1p phase crystallizes in a hexagonal lattice with the space group P63/mmc (Hahn, 2005[Hahn, T. (2005). International Tables for Crystallography, Vol. A, Space-Group Symmetry, 5th ed. Dordrecht, The Netherlands: Springer.]) occupying 52 different crystallographic (Wyckoff) positions. The unit cell is huge including 556 atoms, of which 52 are iron, as shown in Fig. 1[link]. As can be seen in the [11[\overline 2]0] projection of the unit cell (Fig. 2[link]a), two mirror planes exist at z = [1\over 4] and [3\over 4] and an inversion centre at the origin. This means that it is sufficient to consider the atomic arrangement only in [1\over 4] of the unit cell, which is the minimum repeating unit of the [11[\overline 2]0] projection, to fully describe the crystal structure when viewed along the [11[\overline 2]0] direction.1 The structure can be considered to consist of a dense packing of zinc-centred polyhedra, which include normal icosahedra [centred at Zn(3), Zn(5), Zn(28), Zn(39), Zn(42) and Zn(44) sites],2 bicapped pentagonal prisms [centred at Zn(27) and Zn(45)], 16-atom icosioctahedra [tetracapped truncated octahedra, centred at Zn(4)], and disordered icosahedra [centred at Zn(40)] with positional disorder being at the vertex sites as shown in Fig. 1[link]. Positional disorder means that the vertex position splits into several different sites with the occupancy for each of the split sites less than unity. However, for a particular vertex position the sum of the occupancies for all the split sites is unity. An icosahedron having such positional disorder is called disordered icosahedra, while the normal icosahedron does not have any positional disorder in the vertex positions. Out of the 52 Fe atoms per unit cell, 32 atoms are located in 2/3 of the vertex sites of disordered icosahedra, while the other 20 atoms are located randomly in mixed sites with zinc throughout the rest of the structure. The vertices of the disordered icosahedron consist of Fe(41), Zn(46), Fe(47), Fe(48), Fe(49), Zn(50), Zn(51) and Fe(52) sites with the occupancies being 1 for Fe(41), 2/3 for Fe(48) and 1/3 for the other six sites. Depending on how positional disorder occurs in the vertex sites of the disordered icosahedron, three different orientations exist for the disordered icosahedron, which are related with each other by 120° rotations about a threefold axis of the hexagonal unit cell at (x,y) = ([2\over 3], [1\over 3]).

[Figure 1]
Figure 1
Structural model of the δ1p phase reported by Belin et al. (Belin & Belin, 2000[Belin, C. H. E. & Belin, R. C. H. (2000). J. Solid State Chem. 151, 85-95.]).
[Figure 2]
Figure 2
(a) [11[\overline 2]0] projection of the structural model reported by Belin et al. (Belin & Belin, 2000[Belin, C. H. E. & Belin, R. C. H. (2000). J. Solid State Chem. 151, 85-95.]). (b) Experimental HAADF image taken along the [11[\overline 2]0] zone axis by high-resolution STEM imaging. (c) HAADF image calculated based on the structural model depicted in (a). The framed area in (b) and (c) corresponds to the projection of the unit cell.

However, the reported crystal structure of the δ1p phase is questionable when referring to the fact that the atomic distance between the Zn(7) and Zn(8) sites is anomalously short (0.74 Å) when compared with the bonding distance in pure zinc (2.79 Å). On top of that, it seems very strange that most Fe atoms are concentrated on disordered icosahedra and that all normal icosahedra are centred by a Zn atom, while the 12 vertex sites are also mostly Zn atoms (actually with mixed occupancies with iron).

3. Experimental

Elements (4N purity) with a molar ratio of Zn:Fe = 97.5:2.5 were sealed in a quartz ampoule under vacuum. The ampoule was heated at 1073 K for 12 h to completely mix the elements. Subsequently, the ampoule was quickly cooled down to 943 K and then slowly cooled down to 808 K over 270 h (−2 K h−1), followed by water quenching. We obtained large hexagonal prismatic crystals terminated by pyramidal faces with an approximate size of 8 × 8 × 20 mm by dissolving the zinc matrix with concentrated hydrochloric acid. The crystals were of high quality for single-crystal X-ray diffraction. The chemical composition was measured on several crystals by energy-dispersive X-ray spectroscopy (EDS) in a scanning electron microscope. The average composition was 9.7 ± 0.4 at.%Fe. Some of the crystals were annealed in an evacuated quartz ampoule at 673 K for 168 h followed by furnace-cooling, and we found no change in microstructure and composition, indicating the high thermal stability of the crystal phase. A columnar specimen with the longitudinal axis being parallel to the crystallographic c axis was machined from one of the grown single crystals with a Jeol JIB-4000 focused ion-beam (FIB) apparatus at an operating voltage of 30 kV. The crystal size was approximately 28 µm in diameter and 24 µm in length. Synchrotron X-ray diffraction experiments were carried out at 298 K with a large cylindrical image-plate (IP) camera installed at the BL02B1 of SPring-8. The large IP camera enables high statistical data to be obtained. The wavelength of the incident X-ray used was 0.35450 Å (35.00 keV). The crystal structure was solved by direct methods (SIR97; Altomare et al., 1999[Altomare, A., Burla, M. C., Camalli, M., Cascarano, G. L., Giacovazzo, C., Guagliardi, A., Moliterni, A. G. G., Polidori, G. & Spagna, R. (1999). J. Appl. Cryst. 32, 115-119.]), and refined by full-matrix least-squares techniques on F2 (SHELXL97; Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]). All calculations were performed with the WinGX crystallographic software package (Farrugia, 1999[Farrugia, L. J. (1999). J. Appl. Cryst. 32, 837-838.], 2012[Farrugia, L. J. (2012). J. Appl. Cryst. 45, 849-854.]). High-resolution (spatial resolution: ∼ 1.3 Å) scanning transmission electron microscopy (STEM) imaging was made with a Jeol JEM-2100F STEM operated at 200 kV. The probe convergence angle and the inner/outer detector angles for high-angle annular dark-field (HAADF) imaging were 10 and 88–234 mrad, respectively. Ultra-high-resolution (spatial resolution: ≤ 0.8 Å) STEM imaging was made with a Cs-corrected Jeol JEM-ARM200 STEM operated at 200 kV. The probe convergence angle and the inner/outer detector angles for HAADF and annular bright-field (ABF) imaging were 22, 90–370 and 11–22 mrad, respectively. STEM image simulations were performed with the WinHREM software package (Ishizuka, 2002[Ishizuka, K. (2002). Ultramicroscopy, 90, 71-83.]).

4. Results

4.1. STEM imaging

Fig. 2[link](b) indicates an experimental high-resolution STEM HAADF image taken along the [11[\overline 2]0] zone-axis orientation. The framed area in Fig. 2[link](b) corresponds to the projection of the unit cell (Fig. 2[link]a) as reported by Belin et al. (Belin & Belin, 2000[Belin, C. H. E. & Belin, R. C. H. (2000). J. Solid State Chem. 151, 85-95.]). A STEM HAADF image calculated with the atomic coordinates given by Belin et al. (Belin & Belin, 2000[Belin, C. H. E. & Belin, R. C. H. (2000). J. Solid State Chem. 151, 85-95.]) is shown in Fig. 2[link](c). Some parts of the experimental image of Fig. 2[link](b) cannot be well reproduced by calculation, as indicated by A and B in Fig. 2[link](c). The intensity of bright dots in these areas in the calculated image of Fig. 2[link](c) is too weak when compared with that in the experimental image of Fig. 2[link](b). Areas A correspond to a part of the disordered icosahedron comprising mostly Fe atoms (dashed circles in Fig. 2[link]a), while areas B correspond to a part of a normal icosahedron centred at Zn(44), according to the result of structure refinement by Belin et al. (Belin & Belin, 2000[Belin, C. H. E. & Belin, R. C. H. (2000). J. Solid State Chem. 151, 85-95.]). However, we cannot deduce the correct atomic coordinates only from the STEM HAADF image of Fig. 2[link](b) because of the insufficient spatial resolution of ∼ 1.3 Å. We thus employed the Cs-corrected STEM of ultra-high resolution better than 0.8 Å to obtain more detailed information about the correct atomic coordinates. Figs. 3[link](a) and (b) show STEM HAADF and ABF images, respectively, simultaneously taken along the [11[\overline 2]0] zone-axis orientation with the Cs-corrected STEM. The areas framed with a dotted line in Figs. 3[link](a) and (b) correspond to the projection of the unit cell. In the experimental STEM HAADF image of Fig. 3[link](a), most of the atomic columns are resolved in isolation from other columns in spite of the complex crystal structure. The STEM HAADF and ABF image basically exhibit a reversed image contrast (Findlay et al., 2010[Findlay, S. D., Shibata, N., Sawada, H., Okunishi, E., Kondo, Y. & Ikuhara, Y. (2010). Ultramicroscopy, 110, 903-923.]). Figs. 3[link](c) and (d) are magnified images of the areas framed with a solid line (corresponding to 1/4 of the unit cell) in Figs. 3[link](a) and (b), respectively. STEM HAADF and ABF images calculated with the atomic coordinates given by Belin et al. (Belin & Belin, 2000[Belin, C. H. E. & Belin, R. C. H. (2000). J. Solid State Chem. 151, 85-95.]) are shown in Figs. 3[link](e) and (f), respectively. Some inconsistencies between the experimental and calculated images are evidently observed. For both STEM HAADF and ABF images, the intensity of the areas (z = ∼ 0.165 and 0.25) indicated by dashed circles in the calculated images is much weaker than that of the corresponding areas in the experimental images. The opposite is true for the areas indicated by open circles in the calculated images. These mean that the x and y coordinates of the Zn(7) and Zn(36) sites reported by Belin et al. (Belin & Belin, 2000[Belin, C. H. E. & Belin, R. C. H. (2000). J. Solid State Chem. 151, 85-95.]), see Fig. 3[link](g), are incorrect.

[Figure 3]
Figure 3
(a) HAADF and (b) ABF images simultaneously taken along the [11[\overline 2]0] zone axis with the Cs-corrected STEM. The framed area corresponds to the projection of the unit cell. (c) and (d) Magnified images of the parts indicated by a solid frame in (a) and (b). (e) HAADF and (f) ABF images calculated with the structural parameters reported by Belin et al. (Belin & Belin, 2000[Belin, C. H. E. & Belin, R. C. H. (2000). J. Solid State Chem. 151, 85-95.]). (h) HAADF and (i) ABF images calculated with the structural parameters refined in the present study. The corresponding portion of [11[\overline 2]0] projection of the structural models (g) reported by Belin et al. (Belin & Belin, 2000[Belin, C. H. E. & Belin, R. C. H. (2000). J. Solid State Chem. 151, 85-95.]) and (j) refined in the present study.

4.2. Single-crystal synchrotron X-ray diffraction

The details of the single-crystal X-ray diffraction are given in Table 1[link]. The space group P63/mmc was assigned according to the literature by Belin et al. (Belin & Belin, 2000[Belin, C. H. E. & Belin, R. C. H. (2000). J. Solid State Chem. 151, 85-95.]), and indeed best fitted to our diffraction data. No additional reflections or streaks were observed even when the image plate was overexposed. The structural solution and subsequent refinement yielded 52 crystallographic sites. Table 1 of the supporting information3 gives the refined coordinates and isotropic displacement parameters for the δ1p phase. In the refinement we employed the following procedures. At first, all atoms were assumed to be Zn with full occupancy because of the small difference in the scattering factors for iron and zinc. Since the eight atomic sites from Zn38 to Zn45 exhibited extraordinarily large isotropic displacement parameters their occupancies were allowed to vary, but all of them eventually converged to be 1/3. Although the occupancies for all the other sites were also allowed to vary after introducing iron, all of them eventually converged to be 1, indicating the absence of positional disorder and vacancies except for the eight atomic sites from Zn38 to Zn45. This means that no sites with mixed occupations of iron and zinc atoms exist in the crystal structure. Fe atoms exclusively occupy the seven atomic sites from Fe1 to Fe7, while Zn atoms exclusively occupy the other sites. The unit cell contains 556 atoms (Pearson symbol hP556), of which 52 are Fe atoms and 504 are Zn atoms. The chemical formula for the δ1p phase is therefore Fe13Zn126, instead of FeZn10 as previously described by Ghoniem et al. and Belin et al. (Ghoniem & Lohberg, 1972[Ghoniem, M. A. & Lohberg, K. (1972). Metall, 26, 1026.]; Belin & Belin, 2000[Belin, C. H. E. & Belin, R. C. H. (2000). J. Solid State Chem. 151, 85-95.]). The composition derived from the structure refinement (9.35 at.%Fe) was in good agreement with that estimated by EDS analysis (9.7 ± 0.4 at.%Fe). Finally, anisotropic displacement parameters for all sites were refined. In Table 1 of the supporting information , the atomic sites are arranged in increasing order of the magnitude of the c-axis coordinate for iron and zinc with full occupancy and then zinc with one-third occupancy.

Table 1
Summary of crystallographic data and structure refinement for δ1p

Crystal data
Chemical formula Fe13Zn126
Mr 8963.89
Crystal system, space group Hexagonal, P63/mmc
Temperature (K) 300
a, c (Å) 12.8297 (2), 57.286 (1)
V3) 8166.0 (3)
Z 4
Radiation type Synchrotron, λ = 0.35450 Å
μ (mm−1) 20.094
Crystal size (mm) 0.028 × 0.028 × 0.024
   
Data collection
Diffractometer HUBER 4-circle
Absorption correction
No. of measured, independent and observed [I > 2σ(I)] reflections 203 263, 16 996, 14 411
Rint 0.028
(sin θ/λ)max−1) 1.111
Completeness to θ = 23.19° 99.9%
 
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.031, 0.127, 1.03
No. of reflections 16 996
No. of parameters 308
Δρmax, Δρmin (e Å−3) 5.91, −4.16
Computer programs: CrystalClear (Rigaku, 2006[Rigaku (2006). CrystalClear. Rigaku Corporation, Tokyo, Japan.]), SORTAV (Blessing, 1995[Blessing, R. H. (1995). Acta Cryst. A51, 33-38.]), SIR92 (Altomare et al., 1999[Altomare, A., Burla, M. C., Camalli, M., Cascarano, G. L., Giacovazzo, C., Guagliardi, A., Moliterni, A. G. G., Polidori, G. & Spagna, R. (1999). J. Appl. Cryst. 32, 115-119.]), SHELXL97 (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]), WinGX publication routines (Farrugia, 1999[Farrugia, L. J. (1999). J. Appl. Cryst. 32, 837-838.]).

4.3. Comparison of X-ray diffraction data with Cs-corrected STEM images

The Cs-corrected STEM observation has revealed that the atomic coordinates of the two atomic sites [Zn(7) and Zn(36)] reported in the literature by Belin et al. (Belin & Belin, 2000[Belin, C. H. E. & Belin, R. C. H. (2000). J. Solid State Chem. 151, 85-95.]) are incorrect, as shown in Figs. 3[link](c)–(g). Instead, the two sites have been refined as Zn24 and Zn36 sites by single-crystal X-ray diffraction in the present study (see Table 1 of the supporting information ). Figs. 3[link](h) and (i) show STEM HAADF and ABF images, respectively, calculated based on the structural model obtained by single-crystal X-ray diffraction in the present study, as schematically illustrated in Fig. 3[link](j). The calculated images of Figs. 3[link](h) and (i) are in good agreement with the corresponding experimental images (Figs. 3[link]c and d), supporting the validity of the structural model refined in the present study.

5. Discussion

The crystal structure of the δ1p phase is best understood by considering the packing of coordination polyhedra including normal Zn12 icosahedra, disordered Zn12 icosahedra and Zn16 icosioctahedra, as illustrated in Fig. 4[link]. All Fe atoms in the seven Wyckoff positions (Fe1–Fe7) exclusively occupy the centre of normal icosahedra (Fe1/Fe2/Fe3 and Fe5/Fe6/Fe7) and disordered icosahedron (Fe4). This is completely different from the structural model reported by Belin et al. (Belin & Belin, 2000[Belin, C. H. E. & Belin, R. C. H. (2000). J. Solid State Chem. 151, 85-95.]), who allocated most Fe atoms to the vertex sites of disordered icosahedra and Zn atoms in the centre of all other constituting polyhedra. In addition to the iron-centred normal and disordered icosahedra, Zn21-centred icosahedra and Zn15-centred icosioctahedra appear in our structural model. The latter also appear in the structural model by Belin et al. (Belin & Belin, 2000[Belin, C. H. E. & Belin, R. C. H. (2000). J. Solid State Chem. 151, 85-95.]; Fig. 1[link]). The bicapped pentagonal prism (Fig. 1[link]) described by Belin et al. (Belin & Belin, 2000[Belin, C. H. E. & Belin, R. C. H. (2000). J. Solid State Chem. 151, 85-95.]) does not exist in our structural model. Normal icosahedra, in which Fe1, Fe2 and Fe3 reside at the centre, are connected with each other forming a slab parallel to the c plane (Fig. 5[link]). In the slab, three Fe2-centred icosahedra are connected with one another by face-sharing, whereas Fe1-, Fe2- and Fe3-centred icosahedra are interconnected with each other by sharing Zn atoms at vertices. This is also the case for the Fe5-, Fe6- and Fe7-centred icosahedra. They are connected with each other forming another slab parallel to the c plane (Fig. 5[link]). Three Fe6-centred icosahedra are connected with one another by face-sharing, whereas Fe5-, Fe6- and Fe7-centred icosahedra are interconnected by sharing Zn atoms at vertices. No edge-sharing is observed in the connection among iron-centred icosahedra. The Zn15-centred icosioctahedron is connected with Fe3- and Fe5-centred normal icosahedra by face-sharing so as to bridge two slabs of normal icosahedra. The Zn21-centred icosahedron is connected with Fe6-centred normal icosahedra by face-sharing. On the other hand, the Fe4-centred disordered icosahedron is isolated from all other polyhedra. Out of the 504 Zn atoms, 52 are dangling Zn atoms (Zn13/Zn20/Zn28/Zn34) as indicated by dark grey spheres (dark green in the colour version) in Figs. 4[link] and 5[link]. As the δ1p phase can be regarded as a Frank–Kasper phase, the dangling Zn atoms actually reside at the centre of interpenetrating polyhedra. However, it is difficult to accurately define those interpenetrating polyhedra because they consist partly of the partially occupied sites with positional disorder (Zn38–Zn45). The dangling Zn atoms in Zn20 sites are on the same height level as the Fe4-centred disordered icosahedron (with respect to the c axis), while dangling Zn atoms in Zn13 sites are located at a level between disordered icosahedra and a slab of normal icosahedra centred by Fe1/Fe2/Fe3 and those in Zn28/Zn34 sites are located at a level between disordered icosahedra and a slab of normal icosahedra centred by Fe5/Fe6/Fe7.

[Figure 4]
Figure 4
Structural model of the δ1p phase refined in the present study, featuring the coordination polyhedra including the iron-centred normal and disordered Zn12 icosahedra, the zinc-centred Zn12 icosahedra and the Zn16 icosioctahedra.
[Figure 5]
Figure 5
[2[\overline 1][\overline 1]0] projection of the crystal structure of the δ1p phase which describes alternate stacking of two types of slabs comprising iron-centred normal Zn12 icosahedra (Fe1/Fe2/Fe3-centred and Fe5/Fe6/Fe7-centred). Between the two types of slabs are the iron-centred disordered Zn12 icosahedra, zinc-centred icosahedra, zinc-centred icosioctahedra, and dangling Zn atoms that do not constitute any polyhedra. The atoms constituting the vertices of the polyhedra are not depicted in the figure.

The disordered icosahedron in our structural model is different from that described in the model by Belin et al. (Belin & Belin, 2000[Belin, C. H. E. & Belin, R. C. H. (2000). J. Solid State Chem. 151, 85-95.]) in two aspects: (i) the occupation behaviour at the centre and vertices, and (ii) positional disorder at the vertices. Belin et al. (Belin & Belin, 2000[Belin, C. H. E. & Belin, R. C. H. (2000). J. Solid State Chem. 151, 85-95.]) have reported that the centre of the disordered icosahedron is occupied by zinc [Zn(40)] and 2/3 of the vertex sites are occupied by Fe atoms (Fig. 6[link]a). They have further reported that while the occupancy is unity for the bottom vertex site [Fe(41)], those for the Fe(48) site and all other vertex sites with positional disorder are 2/3 and 1/3, respectively. In our structural model, however, the centre of disordered icosahedra is occupied exclusively by iron (Fe4) with all vertices being occupied by Zn atoms (Zn38–Zn45) with an occupancy of 1/3 (Fig. 6[link]b). The fact that all Fe atoms occupy the centre of normal and disordered Zn12 icosahedra indicates that the atomic bonding is stronger for the Fe—Zn bond than for the Zn—Zn bond. This is evident from the shorter average bonding distances for the Fe—Zn bond seen in the histogram of Fig. 7[link], in which the bonding distances for the Fe—Zn and Zn—Zn bonds (only for those shorter than 3.2 Å) in the δ1p phase are plotted. The same tendency in the bonding characteristics is also observed for the Γ and ζ phases in the iron–zinc system as seen in Fig. 7[link] (Belin & Belin, 2000[Belin, C. H. E. & Belin, R. C. H. (2000). J. Solid State Chem. 151, 85-95.]; Belin et al., 2000[Belin, R., Tillard, M. & Monconduit, L. (2000). Acta Cryst. C56, 267-268.]). In fact, there is also a strong tendency for these two phases to form iron-centred Zn12 icosahedra. In the Γ phase, four iron-centred Zn12 icosahedra are connected with one another in a tetrahedrally close-packed arrangement by face-sharing (Belin & Belin, 2000[Belin, C. H. E. & Belin, R. C. H. (2000). J. Solid State Chem. 151, 85-95.]), and these tetrahedrally arranged Zn12 icosahedra are connected with one another by sharing Zn atoms at vertices. In the ζ phase, on the other hand, iron-centred Zn12 icosahedra are linked to one another by vertex-sharing to form a chain of Zn12 icosahedra along the c axis (Belin et al., 2000[Belin, R., Tillard, M. & Monconduit, L. (2000). Acta Cryst. C56, 267-268.]), and dangling Zn atoms are located between the chains as if they act as glue among the chains (Okamoto et al., 2014[Okamoto, N. L., Inomoto, M., Adachi, H., Takebayashi, H. & Inui, H. (2014). Acta Mater. 65, 229-239.]). In the δ1p phase, however, both types of connection (face- and vertex-sharing) of iron-centred icosahedra and dangling Zn atoms are observed as described above. In view of the fact that the δ1p phase exists between the Γ and ζ phases composition-wise in the iron–zinc binary phase diagram (Ghoniem & Lohberg, 1972[Ghoniem, M. A. & Lohberg, K. (1972). Metall, 26, 1026.]; Kubaschewski, 1982[Kubaschewski, O. (1982). Iron-Binary Phase Diagrams. Berlin: Springer-Verlag.]; Nakano et al., 2005[Nakano, J., Malakhov, D. V. & Purdy, G. R. (2005). Calphad, 29, 276-288.]; Kainuma & Ishida, 2005[Kainuma, R. & Ishida, K. (2005). Tetsu Hagane, 91, 349-355.]), the bonding characteristic of the δ1p phase also seems to be intermediate. One point to be noted here is that there is a common characteristic for all these intermetallic phases in the iron–zinc system that Zn12 icosahedra are usually formed with an Fe atom occupying the centre, most probably due to the fact that the atomic bonding is stronger for the Fe—Zn bond than for the Zn—Zn bond. From this point of view, it seems very unfavourable for Fe atoms to occupy 2/3 the vertex sites of a zinc-centred disordered icosahedron, as reported by Belin et al. (Belin & Belin, 2000[Belin, C. H. E. & Belin, R. C. H. (2000). J. Solid State Chem. 151, 85-95.]).

[Figure 6]
Figure 6
Disordered icosahedron in the structural model (a) reported by Belin et al. (Belin & Belin, 2000[Belin, C. H. E. & Belin, R. C. H. (2000). J. Solid State Chem. 151, 85-95.]) and (b) refined in the present study.
[Figure 7]
Figure 7
Histogram of the bonding distances for the Fe—Zn and Zn—Zn bonds (shorter than 3.2 Å) in the δ1p, Γ and ζ phases (Belin & Belin, 2000[Belin, C. H. E. & Belin, R. C. H. (2000). J. Solid State Chem. 151, 85-95.]; Belin et al., 2000[Belin, R., Tillard, M. & Monconduit, L. (2000). Acta Cryst. C56, 267-268.]).

6. Conclusions

The crystal structure of the δ1p phase in the iron–zinc system has been refined by single-crystal synchrotron X-ray diffraction combined with Cs-corrected STEM. The large hexagonal unit cell of the δ1p phase with the space group of P63/mmc is best described by considering the packing of coordination polyhedra including normal Zn12 icosahedra, disordered Zn12 icosahedra and Zn16 icosioctahedra. All Fe atoms exclusively occupy the centre of normal and disordered icosahedra. Normal icosahedra constitute two types of slabs stacked alternately along the c-axis, being bridged with each other by face-sharing with icosioctahedra. Disordered icosahedra are isolated from all other polyhedra. The unit cell contains 556 atoms (Pearson symbol hP556), of which 52 are Fe atoms and 504 are Zn atoms so that the chemical formula for the δ1p phase is expressed as Fe13Zn126 rather than FeZn10. The connecting features of the iron-centred Zn12 icosahedra in the δ1p phase are intermediate between those in the Γ and ζ phases. It is the high statistical precision stemming from the X-ray source of high luminance as well as the image plate of a wide dynamic range that makes it possible to distinguish iron from zinc in the present study. Cs-corrected ultra-high-resolution STEM imaging is also powerful to directly detect discrepancies between the real structure and structural models through direct observations of individual atomic columns even when the crystal structure is considerably complicated.

Supporting information


Computing details top

Data collection: CrystalClear (Rigaku/MSC Inc., 2006); cell refinement: CrystalClear (Rigaku/MSC Inc., 2006); data reduction: CrystalClear (Rigaku/MSC Inc., 2006), SORTAV (Blessing, 1995); program(s) used to solve structure: SIR92 (Giacovazzo et al., 1993); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: ORTEP-3 for Windows (Farrugia, 1997); software used to prepare material for publication: WinGX publication routines (Farrugia, 1999).

Figures top
[Figure 1]
[Figure 2]
[Figure 3]
[Figure 4]
[Figure 5]
[Figure 6]
[Figure 7]
(I) top
Crystal data top
Fe13Zn126Dx = 7.290 Mg m3
Mr = 8963.89Synchrotron radiation, λ = 0.35450 Å
Hexagonal, P63/mmcCell parameters from 301081 reflections
Hall symbol: -P 6c 2cθ = 0.4–23.2°
a = 12.8297 (2) ŵ = 20.09 mm1
c = 57.286 (1) ÅT = 300 K
V = 8166.0 (3) Å3, metallic silver
Z = 40.03 × 0.03 × 0.03 mm
F(000) = 16472
Data collection top
HUBER 4-circle
diffractometer
14411 reflections with I > 2σ(I)
Radiation source: SPring-8 BL02B1Rint = 0.028
Si(111) double crystal monochromatorθmax = 23.2°, θmin = 0.4°
ω scanh = 2828
203263 measured reflectionsk = 2828
16996 independent reflectionsl = 99127
Refinement top
Refinement on F20 restraints
Least-squares matrix: fullPrimary atom site location: structure-invariant direct methods
R[F2 > 2σ(F2)] = 0.031Secondary atom site location: difference Fourier map
wR(F2) = 0.127 w = 1/[σ2(Fo2) + (0.1P)2]
where P = (Fo2 + 2Fc2)/3
S = 1.03(Δ/σ)max = 0.003
16996 reflectionsΔρmax = 5.91 e Å3
308 parametersΔρmin = 4.16 e Å3
Crystal data top
Fe13Zn126Z = 4
Mr = 8963.89Synchrotron radiation, λ = 0.35450 Å
Hexagonal, P63/mmcµ = 20.09 mm1
a = 12.8297 (2) ÅT = 300 K
c = 57.286 (1) Å0.03 × 0.03 × 0.03 mm
V = 8166.0 (3) Å3
Data collection top
HUBER 4-circle
diffractometer
14411 reflections with I > 2σ(I)
203263 measured reflectionsRint = 0.028
16996 independent reflections
Refinement top
R[F2 > 2σ(F2)] = 0.031308 parameters
wR(F2) = 0.1270 restraints
S = 1.03Δρmax = 5.91 e Å3
16996 reflectionsΔρmin = 4.16 e Å3
Special details top

Geometry. All s.u.'s (except the s.u. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell s.u.'s are taken into account individually in the estimation of s.u.'s in distances, angles and torsion angles; correlations between s.u.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell s.u.'s is used for estimating s.u.'s involving l.s. planes.

Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > 2σ(F2) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Fe10.00000.00000.00000.00527 (7)
Fe20.778964 (12)0.55793 (2)0.016364 (5)0.00803 (4)
Fe30.135983 (12)0.27197 (2)0.068947 (5)0.00691 (3)
Fe40.66670.33330.140259 (8)0.00727 (6)
Fe50.33330.66670.176805 (8)0.00649 (5)
Fe60.112908 (12)0.22582 (2)0.203999 (5)0.00797 (4)
Fe70.467086 (16)0.93417 (3)0.25000.00644 (4)
Zn10.36258 (2)0.00000.00000.01322 (4)
Zn20.886968 (11)0.77394 (2)0.008273 (5)0.01032 (4)
Zn30.409779 (17)0.81956 (3)0.013189 (7)0.01796 (5)
Zn40.66670.33330.024338 (11)0.01412 (7)
Zn50.195007 (15)0.39001 (3)0.027654 (5)0.01408 (4)
Zn60.547279 (16)0.09456 (3)0.031300 (6)0.01631 (5)
Zn70.070702 (12)0.14140 (2)0.034645 (5)0.01019 (4)
Zn80.31463 (2)0.043982 (19)0.045093 (4)0.01400 (3)
Zn90.33330.66670.049028 (10)0.01445 (7)
Zn100.748900 (18)0.49780 (4)0.061364 (7)0.01972 (6)
Zn110.12927 (2)0.46834 (2)0.065150 (5)0.01773 (4)
Zn120.926395 (14)0.85279 (3)0.072510 (6)0.01366 (4)
Zn130.539021 (15)0.07804 (3)0.078016 (7)0.01707 (5)
Zn140.31767 (2)0.03900 (3)0.092485 (5)0.01927 (4)
Zn150.33330.66670.095657 (12)0.01959 (9)
Zn160.203460 (18)0.40692 (4)0.104581 (7)0.01982 (6)
Zn170.08343 (2)0.16685 (4)0.109300 (6)0.02174 (6)
Zn180.450604 (15)0.90121 (3)0.110691 (6)0.01602 (5)
Zn190.880762 (18)0.76152 (4)0.133888 (9)0.02284 (7)
Zn200.02467 (3)0.35593 (2)0.137760 (5)0.02100 (5)
Zn210.00000.00000.140576 (9)0.01196 (6)
Zn220.263172 (19)0.52634 (4)0.141423 (7)0.02070 (6)
Zn230.115585 (16)0.23117 (3)0.156940 (7)0.01743 (5)
Zn240.450812 (16)0.90162 (3)0.167752 (7)0.01706 (5)
Zn250.929536 (17)0.85907 (3)0.180384 (6)0.01646 (5)
Zn260.32347 (2)0.02481 (2)0.183150 (5)0.01877 (4)
Zn270.217903 (13)0.43581 (3)0.185444 (7)0.01594 (5)
Zn280.77367 (2)0.54734 (4)0.206781 (7)0.02064 (6)
Zn290.530806 (16)0.06161 (3)0.209540 (6)0.01621 (5)
Zn300.406225 (13)0.81245 (3)0.211558 (5)0.01256 (4)
Zn310.00000.00000.219762 (10)0.01400 (7)
Zn320.883244 (18)0.76649 (4)0.224248 (9)0.02180 (6)
Zn330.06262 (2)0.36123 (2)0.226383 (4)0.01521 (4)
Zn340.66670.33330.228077 (10)0.01658 (8)
Zn350.26171 (2)0.52342 (4)0.25000.01364 (6)
Zn360.09541 (2)0.19081 (4)0.25000.01414 (6)
Zn370.45884 (4)0.13192 (3)0.25000.01935 (6)
Zn380.67731 (5)0.35463 (10)0.094695 (15)0.0182 (3)0.3333333
Zn390.48205 (8)0.18194 (9)0.115304 (17)0.02807 (19)0.3333333
Zn400.53703 (7)0.12796 (7)0.121980 (14)0.02086 (13)0.3333333
Zn410.77424 (5)0.54849 (10)0.12343 (3)0.0256 (2)0.3333333
Zn420.55462 (5)0.10925 (10)0.15604 (3)0.0246 (2)0.3333333
Zn430.44959 (6)0.20792 (6)0.158150 (13)0.01907 (16)0.3333333
Zn440.52508 (9)0.14852 (9)0.165183 (16)0.0316 (2)0.3333333
Zn450.65079 (5)0.30157 (10)0.184156 (16)0.01928 (17)0.333333
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Fe10.00559 (10)0.00559 (10)0.00464 (16)0.00279 (5)0.0000.000
Fe20.00865 (6)0.00665 (7)0.00813 (8)0.00332 (4)0.00016 (3)0.00033 (6)
Fe30.00783 (6)0.00679 (7)0.00577 (7)0.00339 (4)0.00041 (3)0.00082 (6)
Fe40.00813 (8)0.00813 (8)0.00556 (13)0.00406 (4)0.0000.000
Fe50.00718 (8)0.00718 (8)0.00512 (12)0.00359 (4)0.0000.000
Fe60.00863 (6)0.00750 (7)0.00740 (8)0.00375 (4)0.00049 (3)0.00097 (6)
Fe70.00655 (7)0.00692 (10)0.00597 (10)0.00346 (5)0.0000.000
Zn10.01400 (7)0.01178 (8)0.01313 (10)0.00589 (4)0.00100 (4)0.00201 (7)
Zn20.01154 (6)0.00759 (7)0.01052 (8)0.00379 (3)0.00049 (3)0.00097 (6)
Zn30.01632 (8)0.01993 (12)0.01883 (13)0.00997 (6)0.00272 (5)0.00544 (10)
Zn40.01003 (9)0.01003 (9)0.0223 (2)0.00502 (4)0.0000.000
Zn50.01615 (7)0.01639 (10)0.00978 (9)0.00820 (5)0.00080 (4)0.00160 (7)
Zn60.01533 (7)0.01951 (12)0.01547 (11)0.00976 (6)0.00003 (5)0.00007 (9)
Zn70.01185 (6)0.01105 (8)0.00738 (8)0.00553 (4)0.00105 (3)0.00209 (6)
Zn80.01382 (7)0.01340 (7)0.01250 (7)0.00508 (5)0.00195 (5)0.00251 (5)
Zn90.01587 (11)0.01587 (11)0.01161 (16)0.00793 (5)0.0000.000
Zn100.01738 (8)0.02126 (13)0.02182 (14)0.01063 (7)0.00352 (6)0.00703 (11)
Zn110.01838 (8)0.01114 (7)0.02527 (11)0.00858 (6)0.00398 (7)0.00051 (6)
Zn120.01111 (6)0.01594 (10)0.01555 (11)0.00797 (5)0.00130 (4)0.00261 (8)
Zn130.01732 (8)0.01432 (10)0.01855 (12)0.00716 (5)0.00086 (4)0.00173 (9)
Zn140.01899 (9)0.02672 (11)0.01409 (8)0.01291 (8)0.00032 (6)0.00097 (7)
Zn150.02108 (14)0.02108 (14)0.0166 (2)0.01054 (7)0.0000.000
Zn160.02053 (9)0.02451 (14)0.01576 (12)0.01226 (7)0.00583 (5)0.01166 (11)
Zn170.02383 (10)0.03253 (18)0.01175 (11)0.01627 (9)0.00424 (6)0.00847 (11)
Zn180.01562 (8)0.01676 (11)0.01608 (12)0.00838 (5)0.00033 (4)0.00065 (9)
Zn190.01635 (9)0.01836 (13)0.0345 (2)0.00918 (6)0.00266 (7)0.00532 (13)
Zn200.02702 (12)0.01589 (8)0.01462 (8)0.00662 (8)0.00085 (8)0.00026 (6)
Zn210.01255 (9)0.01255 (9)0.01077 (15)0.00627 (5)0.0000.000
Zn220.02202 (10)0.02606 (15)0.01537 (12)0.01303 (8)0.00571 (5)0.01142 (11)
Zn230.01808 (9)0.01704 (11)0.01682 (12)0.00852 (6)0.00063 (5)0.00126 (9)
Zn240.01656 (8)0.01976 (12)0.01594 (12)0.00988 (6)0.00162 (5)0.00323 (9)
Zn250.01397 (7)0.02328 (13)0.01524 (11)0.01164 (7)0.00036 (5)0.00072 (9)
Zn260.01781 (8)0.01644 (8)0.01620 (9)0.00416 (7)0.00151 (7)0.00063 (7)
Zn270.01382 (7)0.00974 (8)0.02292 (14)0.00487 (4)0.00044 (4)0.00087 (8)
Zn280.01937 (9)0.02702 (16)0.01808 (13)0.01351 (8)0.00383 (6)0.00767 (12)
Zn290.01552 (8)0.01673 (11)0.01677 (11)0.00837 (5)0.00067 (4)0.00134 (9)
Zn300.01496 (7)0.01314 (9)0.00897 (8)0.00657 (4)0.00137 (3)0.00274 (7)
Zn310.01353 (10)0.01353 (10)0.01493 (18)0.00676 (5)0.0000.000
Zn320.02069 (10)0.01739 (12)0.02621 (17)0.00870 (6)0.00097 (6)0.00195 (11)
Zn330.02374 (9)0.01338 (7)0.01128 (7)0.01136 (7)0.00049 (6)0.00218 (5)
Zn340.02027 (13)0.02027 (13)0.00918 (15)0.01014 (6)0.0000.000
Zn350.01159 (8)0.01877 (15)0.01296 (13)0.00938 (8)0.0000.000
Zn360.01658 (11)0.01497 (14)0.01034 (12)0.00748 (7)0.0000.000
Zn370.02906 (16)0.01195 (10)0.01872 (13)0.01150 (10)0.0000.000
Zn380.0199 (3)0.0289 (7)0.0089 (2)0.0145 (3)0.00181 (12)0.0036 (2)
Zn390.0187 (3)0.0255 (4)0.0216 (3)0.0028 (3)0.0016 (2)0.0102 (3)
Zn400.0227 (3)0.0137 (2)0.0188 (3)0.00360 (19)0.0007 (2)0.00444 (19)
Zn410.0200 (3)0.0108 (3)0.0428 (7)0.00541 (15)0.00227 (19)0.0045 (4)
Zn420.0180 (3)0.0112 (3)0.0423 (7)0.00561 (15)0.00239 (18)0.0048 (4)
Zn430.01563 (19)0.0177 (3)0.0146 (2)0.00137 (18)0.00391 (16)0.00104 (17)
Zn440.0271 (4)0.0230 (3)0.0187 (3)0.0069 (3)0.0087 (3)0.0007 (3)
Zn450.0228 (3)0.0275 (4)0.0091 (2)0.0137 (2)0.00096 (12)0.0019 (2)
Bond lengths (Å) top
Fe1—Zn72.5313 (3)Zn19—Zn412.4417 (13)
Fe1—Zn7i2.5312 (3)Zn19—Zn20xxxiv2.6595 (3)
Fe1—Zn7ii2.5312 (3)Zn19—Zn20xxxi2.6595 (3)
Fe1—Zn7iii2.5313 (3)Zn19—Zn21xxx2.6772 (4)
Fe1—Zn7iv2.5313 (3)Zn19—Zn43xii2.7351 (8)
Fe1—Zn7v2.5313 (3)Zn19—Zn43viii2.7351 (8)
Fe1—Zn2vi2.5561 (2)Zn19—Zn17xxxi2.7440 (4)
Fe1—Zn2vii2.5561 (2)Zn19—Zn17viii2.7440 (4)
Fe1—Zn2viii2.5561 (2)Zn19—Zn252.8756 (6)
Fe1—Zn2ix2.5561 (2)Zn19—Zn23xxxi2.9251 (4)
Fe1—Zn2x2.5561 (2)Zn19—Zn23viii2.9251 (4)
Fe1—Zn2xi2.5561 (2)Zn19—Zn14xii2.9603 (5)
Fe2—Zn22.4444 (4)Zn20—Zn40xv2.5399 (9)
Fe2—Zn42.5369 (3)Zn20—Zn232.6452 (4)
Fe2—Zn5vii2.5871 (4)Zn20—Zn19xi2.6595 (3)
Fe2—Zn8viii2.6130 (3)Zn20—Zn18viii2.6663 (4)
Fe2—Zn8xii2.6130 (3)Zn20—Zn26xv2.6903 (4)
Fe2—Zn1xiii2.6587 (2)Zn20—Zn39xv2.7010 (10)
Fe2—Zn1viii2.6587 (2)Zn20—Zn42xxxv2.7087 (10)
Fe2—Zn102.6630 (5)Zn20—Zn222.7381 (4)
Fe2—Zn6viii2.7161 (3)Zn20—Zn14xv2.7508 (4)
Fe2—Zn6ii2.7161 (3)Zn20—Zn24viii2.7657 (4)
Fe2—Zn3iv2.7821 (4)Zn20—Zn43xv2.8361 (8)
Fe2—Zn3ix2.7821 (4)Zn21—Zn17i2.5782 (5)
Fe3—Zn72.4425 (4)Zn21—Zn17ii2.5782 (5)
Fe3—Zn162.5329 (4)Zn21—Zn19x2.6772 (4)
Fe3—Zn11xiv2.5727 (3)Zn21—Zn19xi2.6772 (4)
Fe3—Zn112.5727 (3)Zn21—Zn19viii2.6772 (4)
Fe3—Zn172.5899 (4)Zn21—Zn232.7342 (4)
Fe3—Zn12viii2.6278 (2)Zn21—Zn23i2.7342 (4)
Fe3—Zn12xi2.6278 (2)Zn21—Zn23ii2.7342 (4)
Fe3—Zn14ii2.6568 (3)Zn21—Zn25viii2.7663 (5)
Fe3—Zn14xv2.6568 (3)Zn21—Zn25xi2.7663 (5)
Fe3—Zn8xv2.6757 (2)Zn21—Zn25x2.7663 (5)
Fe3—Zn8ii2.6757 (3)Zn22—Zn22viii2.7004 (7)
Fe3—Zn52.7048 (4)Zn22—Zn22xviii2.7004 (7)
Fe4—Zn40xvi2.5343 (7)Zn22—Zn272.7151 (6)
Fe4—Zn402.5343 (7)Zn22—Zn24viii2.7296 (4)
Fe4—Zn40xvii2.5343 (7)Zn22—Zn24xviii2.7296 (4)
Fe4—Zn40viii2.5343 (7)Zn22—Zn20xiv2.7381 (4)
Fe4—Zn40ii2.5343 (7)Zn22—Zn18viii2.8737 (4)
Fe4—Zn40xii2.5343 (7)Zn22—Zn18xviii2.8737 (4)
Fe4—Zn45viii2.5393 (10)Zn23—Zn25xi2.6136 (4)
Fe4—Zn452.5393 (10)Zn23—Zn25viii2.6136 (4)
Fe4—Zn45ii2.5393 (10)Zn23—Zn20xiv2.6452 (4)
Fe4—Zn41ii2.5776 (11)Zn23—Zn26ii2.7943 (3)
Fe4—Zn41viii2.5776 (11)Zn23—Zn26xv2.7943 (3)
Fe4—Zn412.5776 (11)Zn23—Zn272.7993 (5)
Fe5—Zn22xviii2.5572 (5)Zn23—Zn19xi2.9251 (4)
Fe5—Zn222.5572 (5)Zn23—Zn19viii2.9251 (4)
Fe5—Zn22viii2.5572 (5)Zn24—Zn42xxv2.4024 (11)
Fe5—Zn302.5666 (4)Zn24—Zn302.6980 (5)
Fe5—Zn30viii2.5666 (4)Zn24—Zn22viii2.7296 (4)
Fe5—Zn30xviii2.5666 (4)Zn24—Zn22xviii2.7296 (4)
Fe5—Zn27xviii2.6124 (3)Zn24—Zn20viii2.7657 (4)
Fe5—Zn27viii2.6124 (3)Zn24—Zn20xix2.7657 (4)
Fe5—Zn272.6124 (3)Zn24—Zn27viii2.7795 (3)
Fe5—Zn24viii2.6616 (4)Zn24—Zn27xviii2.7795 (3)
Fe5—Zn242.6616 (4)Zn24—Zn44xxiv2.8187 (12)
Fe5—Zn24xviii2.6616 (4)Zn24—Zn44xxv2.8187 (11)
Fe6—Zn33xiv2.4899 (3)Zn24—Zn26xxiv2.9201 (4)
Fe6—Zn332.4899 (3)Zn25—Fe6viii2.5784 (3)
Fe6—Zn272.5639 (4)Zn25—Fe6xxxi2.5784 (3)
Fe6—Zn25viii2.5784 (3)Zn25—Zn23viii2.6136 (4)
Fe6—Zn25xi2.5784 (3)Zn25—Zn23xxxi2.6136 (4)
Fe6—Zn26ii2.6595 (3)Zn25—Zn26xii2.6878 (4)
Fe6—Zn26xv2.6595 (3)Zn25—Zn26viii2.6878 (4)
Fe6—Zn362.6638 (3)Zn25—Zn25xxxvi2.7121 (7)
Fe6—Zn312.6665 (3)Zn25—Zn25xviii2.7121 (6)
Fe6—Zn232.6965 (5)Zn25—Zn322.7152 (6)
Fe6—Zn32viii2.8040 (3)Zn25—Zn31xxx2.7460 (6)
Fe6—Zn32xi2.8040 (3)Zn25—Zn21xxx2.7663 (5)
Fe7—Zn33xix2.5677 (2)Zn26—Zn442.4827 (9)
Fe7—Zn33xx2.5677 (2)Zn26—Zn432.5273 (7)
Fe7—Zn33xxi2.5677 (2)Zn26—Zn28viii2.6418 (4)
Fe7—Zn33viii2.5677 (2)Zn26—Fe6ii2.6595 (3)
Fe7—Zn35xxii2.5762 (3)Zn26—Zn33xxxiii2.6713 (3)
Fe7—Zn35xxi2.5762 (3)Zn26—Zn25viii2.6878 (4)
Fe7—Zn30xxiii2.5843 (3)Zn26—Zn20xxxiii2.6903 (4)
Fe7—Zn302.5843 (3)Zn26—Zn27ii2.7075 (3)
Fe7—Zn37xxiv2.5916 (5)Zn26—Zn23ii2.7943 (3)
Fe7—Zn37xxv2.5916 (4)Zn26—Zn43ii2.8122 (8)
Fe7—Zn29xxvi2.7161 (4)Zn26—Zn292.8859 (3)
Fe7—Zn29xxv2.7161 (4)Zn26—Zn24xxviii2.9201 (4)
Zn1—Fe2viii2.6587 (2)Zn27—Zn30viii2.6993 (3)
Zn1—Fe2ix2.6587 (2)Zn27—Zn30xviii2.6993 (3)
Zn1—Zn62.7253 (3)Zn27—Zn26xv2.7075 (3)
Zn1—Zn6xxvii2.7253 (3)Zn27—Zn26ii2.7075 (3)
Zn1—Zn3vii2.7746 (3)Zn27—Zn24viii2.7795 (3)
Zn1—Zn3xxviii2.7746 (3)Zn27—Zn24xviii2.7795 (3)
Zn1—Zn82.7780 (3)Zn27—Zn332.9118 (4)
Zn1—Zn8xxix2.7780 (3)Zn27—Zn33xiv2.9118 (4)
Zn1—Zn2ix2.8170 (3)Zn28—Zn45ii2.5728 (7)
Zn1—Zn2viii2.8170 (3)Zn28—Zn45viii2.5728 (7)
Zn1—Zn5ii2.8306 (2)Zn28—Zn322.6325 (6)
Zn1—Zn5iv2.8306 (2)Zn28—Zn26viii2.6418 (4)
Zn2—Fe1xxx2.5561 (2)Zn28—Zn26xii2.6418 (4)
Zn2—Zn7vii2.6324 (4)Zn28—Zn342.6725 (5)
Zn2—Zn7xxxi2.6671 (3)Zn28—Zn29ii2.7595 (3)
Zn2—Zn7viii2.6671 (3)Zn28—Zn29viii2.7595 (3)
Zn2—Zn2iv2.6847 (3)Zn28—Zn37xxi2.7747 (4)
Zn2—Zn2xxxii2.6847 (3)Zn28—Zn37xxxviii2.7747 (4)
Zn2—Zn8xii2.7444 (3)Zn28—Zn43xii2.7945 (8)
Zn2—Zn8viii2.7444 (3)Zn28—Zn43viii2.7945 (8)
Zn2—Zn5vii2.7485 (4)Zn29—Fe7xxviii2.7161 (4)
Zn2—Zn1xiii2.8170 (3)Zn29—Zn33xxxiii2.7564 (3)
Zn2—Zn1viii2.8170 (3)Zn29—Zn33xxxvii2.7564 (3)
Zn3—Zn92.6648 (5)Zn29—Zn28ii2.7595 (3)
Zn3—Zn6vii2.7214 (5)Zn29—Zn28viii2.7595 (3)
Zn3—Zn4vii2.7400 (6)Zn29—Zn30xxviii2.7708 (5)
Zn3—Zn1vii2.7746 (3)Zn29—Zn44xvi2.7906 (11)
Zn3—Zn1xxv2.7746 (3)Zn29—Zn442.7906 (11)
Zn3—Fe2iv2.7821 (4)Zn29—Zn37xvi2.8056 (4)
Zn3—Fe2xiii2.7821 (4)Zn29—Zn372.8056 (4)
Zn3—Zn5viii2.7927 (3)Zn29—Zn26xvi2.8859 (3)
Zn3—Zn5xviii2.7927 (3)Zn30—Zn27viii2.6993 (3)
Zn3—Zn3xviii2.9423 (7)Zn30—Zn27xviii2.6993 (3)
Zn3—Zn3viii2.9423 (7)Zn30—Zn33viii2.7221 (3)
Zn4—Fe2ii2.5369 (3)Zn30—Zn33xix2.7220 (3)
Zn4—Fe2viii2.5369 (3)Zn30—Zn35xxi2.7255 (3)
Zn4—Zn6viii2.6828 (4)Zn30—Zn35xxii2.7255 (3)
Zn4—Zn62.6828 (4)Zn30—Zn29xxv2.7708 (5)
Zn4—Zn6ii2.6828 (4)Zn30—Zn30viii2.8055 (5)
Zn4—Zn3vii2.7400 (6)Zn30—Zn30xviii2.8055 (5)
Zn4—Zn3iv2.7400 (6)Zn31—Zn32viii2.6072 (4)
Zn4—Zn3ix2.7400 (6)Zn31—Zn32x2.6072 (4)
Zn4—Zn10ii2.7997 (7)Zn31—Zn32xi2.6072 (4)
Zn4—Zn102.7997 (7)Zn31—Fe6i2.6665 (3)
Zn4—Zn10viii2.7997 (7)Zn31—Fe6ii2.6665 (3)
Zn5—Fe2vii2.5871 (4)Zn31—Zn362.7378 (5)
Zn5—Zn11xiv2.6800 (4)Zn31—Zn36xxxix2.7378 (5)
Zn5—Zn112.6800 (4)Zn31—Zn36xl2.7378 (5)
Zn5—Zn2vii2.7485 (4)Zn31—Zn25x2.7460 (6)
Zn5—Zn72.7912 (4)Zn31—Zn25xi2.7460 (6)
Zn5—Zn3viii2.7927 (3)Zn31—Zn25viii2.7460 (6)
Zn5—Zn3xviii2.7927 (3)Zn32—Zn31xxx2.6072 (4)
Zn5—Zn1ii2.8306 (2)Zn32—Fe6viii2.8040 (3)
Zn5—Zn1iv2.8306 (2)Zn32—Fe6xxxi2.8040 (3)
Zn5—Zn8ii2.8371 (3)Zn32—Zn36xxi2.8110 (4)
Zn5—Zn8xv2.8371 (3)Zn32—Zn36xli2.8110 (4)
Zn6—Zn132.6824 (5)Zn32—Zn33xxxiv2.8161 (3)
Zn6—Fe2viii2.7161 (3)Zn32—Zn33xxxi2.8161 (3)
Zn6—Fe2ii2.7161 (3)Zn32—Zn32xxiii2.9504 (10)
Zn6—Zn3vii2.7214 (5)Zn32—Zn26xii3.1029 (5)
Zn6—Zn1xxvii2.7253 (3)Zn32—Zn26viii3.1029 (5)
Zn6—Zn82.8315 (3)Zn33—Fe7xxi2.5677 (2)
Zn6—Zn8xvi2.8315 (3)Zn33—Zn26xv2.6713 (3)
Zn6—Zn10ii2.9147 (4)Zn33—Zn37xv2.6749 (4)
Zn6—Zn10viii2.9147 (4)Zn33—Zn33xxiii2.7059 (4)
Zn7—Zn2vii2.6324 (4)Zn33—Zn352.7147 (4)
Zn7—Zn2xi2.6671 (3)Zn33—Zn30viii2.7220 (3)
Zn7—Zn2viii2.6671 (3)Zn33—Zn29xxxv2.7564 (3)
Zn7—Zn12viii2.6980 (4)Zn33—Zn362.7762 (4)
Zn7—Zn12xi2.6980 (4)Zn33—Zn32xi2.8161 (3)
Zn7—Zn7i2.7212 (5)Zn33—Zn33xiv3.0277 (5)
Zn7—Zn7ii2.7212 (5)Zn34—Zn34xxiii2.5118 (11)
Zn7—Zn8xv2.7772 (3)Zn34—Zn452.5406 (11)
Zn7—Zn8ii2.7772 (3)Zn34—Zn45viii2.5406 (11)
Zn8—Fe2viii2.6130 (3)Zn34—Zn45ii2.5406 (11)
Zn8—Zn11xxxiii2.6563 (3)Zn34—Zn28ii2.6725 (5)
Zn8—Fe3ii2.6757 (2)Zn34—Zn28viii2.6725 (5)
Zn8—Zn10viii2.7067 (4)Zn34—Zn37xvii2.9110 (4)
Zn8—Zn142.7164 (3)Zn34—Zn37xvi2.9110 (4)
Zn8—Zn2viii2.7444 (3)Zn34—Zn37xxi2.9110 (4)
Zn8—Zn7ii2.7772 (3)Zn34—Zn372.9110 (4)
Zn8—Zn12viii2.8357 (4)Zn34—Zn37xxxviii2.9110 (4)
Zn8—Zn5ii2.8371 (3)Zn35—Fe7xxi2.5762 (3)
Zn8—Zn8ii2.9081 (5)Zn35—Fe7xxii2.5762 (3)
Zn9—Zn3viii2.6648 (5)Zn35—Zn33xiv2.7147 (4)
Zn9—Zn3xviii2.6648 (5)Zn35—Zn33xxiii2.7147 (4)
Zn9—Zn152.6712 (9)Zn35—Zn33xlii2.7147 (4)
Zn9—Zn11xviii2.7422 (3)Zn35—Zn30xxii2.7255 (3)
Zn9—Zn11xix2.7422 (3)Zn35—Zn30xxi2.7255 (3)
Zn9—Zn11viii2.7422 (3)Zn35—Zn30viii2.7255 (3)
Zn9—Zn112.7422 (3)Zn35—Zn30xviii2.7255 (3)
Zn9—Zn11xxxiv2.7422 (3)Zn35—Zn35xxi2.7568 (8)
Zn9—Zn11xiv2.7422 (3)Zn35—Zn35xxii2.7568 (8)
Zn10—Zn382.4853 (10)Zn36—Fe6xxiii2.6638 (3)
Zn10—Zn13ii2.6668 (3)Zn36—Zn31xxiii2.7378 (5)
Zn10—Zn13viii2.6668 (3)Zn36—Zn33xlii2.7762 (4)
Zn10—Zn8xii2.7067 (4)Zn36—Zn33xxiii2.7762 (4)
Zn10—Zn8viii2.7067 (4)Zn36—Zn33xiv2.7762 (4)
Zn10—Zn38viii2.7338 (9)Zn36—Zn32xxi2.8110 (4)
Zn10—Zn38ii2.7338 (9)Zn36—Zn32viii2.8110 (4)
Zn10—Zn6ii2.9147 (4)Zn36—Zn32xi2.8110 (4)
Zn10—Zn6viii2.9147 (4)Zn36—Zn32xliii2.8110 (4)
Zn10—Zn14xii3.1218 (5)Zn37—Zn37xxxix2.5016 (6)
Zn11—Zn11xviii2.4710 (4)Zn37—Fe7xxviii2.5916 (4)
Zn11—Zn8xv2.6563 (3)Zn37—Zn33xxxiii2.6749 (4)
Zn11—Zn11xiv2.6915 (5)Zn37—Zn33xliv2.6749 (4)
Zn11—Zn13xxxv2.7158 (4)Zn37—Zn37xvi2.7488 (8)
Zn11—Zn162.7165 (5)Zn37—Zn28xxi2.7747 (4)
Zn11—Zn14xv2.7895 (4)Zn37—Zn28viii2.7747 (4)
Zn11—Zn18viii2.9064 (4)Zn37—Zn29xxiii2.8056 (4)
Zn11—Zn153.1179 (5)Zn37—Zn34xxiii2.9110 (4)
Zn12—Fe3viii2.6278 (2)Zn38—Zn38ii0.4098 (19)
Zn12—Fe3xxxi2.6278 (2)Zn38—Zn38viii0.4098 (19)
Zn12—Zn14xii2.6944 (4)Zn38—Zn39viii2.2938 (13)
Zn12—Zn14viii2.6944 (4)Zn38—Zn39xii2.2938 (13)
Zn12—Zn7viii2.6980 (4)Zn38—Zn39xvii2.5312 (10)
Zn12—Zn7xxxi2.6980 (4)Zn38—Zn39ii2.5312 (10)
Zn12—Zn17viii2.7426 (4)Zn38—Zn392.6511 (12)
Zn12—Zn17xxxi2.7426 (4)Zn38—Zn39xvi2.6511 (12)
Zn12—Zn12xviii2.8330 (6)Zn38—Zn40viii2.6728 (11)
Zn12—Zn12xxxvi2.8330 (6)Zn38—Zn40xii2.6728 (11)
Zn12—Zn8xii2.8357 (4)Zn39—Zn41viii0.9521 (14)
Zn12—Zn8viii2.8357 (4)Zn39—Zn401.2695 (15)
Zn13—Zn40xvi2.6020 (9)Zn39—Zn39ii1.516 (2)
Zn13—Zn402.6020 (9)Zn39—Zn40xvi1.8827 (15)
Zn13—Zn10ii2.6668 (3)Zn39—Zn38viii2.2938 (13)
Zn13—Zn10viii2.6668 (3)Zn39—Zn38ii2.5312 (10)
Zn13—Zn18xxviii2.7137 (5)Zn39—Zn432.5393 (11)
Zn13—Zn11xxxvii2.7158 (4)Zn39—Zn40ii2.6607 (14)
Zn13—Zn11xxxiii2.7158 (4)Zn39—Zn43ii2.6654 (12)
Zn13—Zn14xvi2.7533 (3)Zn40—Zn40xvi0.6916 (18)
Zn13—Zn142.7533 (3)Zn40—Zn39xvi1.8827 (15)
Zn13—Zn39xvi2.8014 (10)Zn40—Zn421.9924 (19)
Zn13—Zn392.8014 (10)Zn40—Zn41viii2.0399 (10)
Zn14—Zn392.3774 (8)Zn40—Zn442.5018 (12)
Zn14—Fe3ii2.6568 (3)Zn40—Zn20xxxiii2.5399 (9)
Zn14—Zn12viii2.6944 (4)Zn40—Zn18xxviii2.6240 (8)
Zn14—Zn20xxxiii2.7508 (4)Zn40—Zn41ii2.6505 (11)
Zn14—Zn17ii2.7760 (4)Zn40—Zn39ii2.6607 (14)
Zn14—Zn41viii2.7781 (12)Zn41—Zn39xii0.9521 (14)
Zn14—Zn16ii2.7831 (4)Zn41—Zn39viii0.9521 (14)
Zn14—Zn11xxxiii2.7895 (4)Zn41—Zn43viii2.0007 (19)
Zn14—Zn19viii2.9603 (5)Zn41—Zn43xii2.0007 (19)
Zn14—Zn402.9776 (9)Zn41—Zn40xii2.0399 (10)
Zn15—Zn182.7446 (4)Zn41—Zn40viii2.0399 (10)
Zn15—Zn18viii2.7446 (4)Zn41—Zn40ii2.6505 (11)
Zn15—Zn18xviii2.7446 (4)Zn41—Zn40xvii2.6505 (11)
Zn15—Zn16xviii2.9309 (4)Zn41—Zn14xii2.7781 (12)
Zn15—Zn16viii2.9309 (5)Zn42—Zn440.9289 (16)
Zn15—Zn162.9309 (5)Zn42—Zn44xvi0.9289 (16)
Zn15—Zn22xviii3.0503 (7)Zn42—Zn40xvi1.9924 (19)
Zn15—Zn22viii3.0503 (7)Zn42—Zn43xvi2.2670 (10)
Zn15—Zn223.0503 (7)Zn42—Zn432.2670 (10)
Zn15—Zn11xviii3.1179 (5)Zn42—Zn24xxviii2.4024 (11)
Zn16—Zn222.4930 (5)Zn42—Zn43xvii2.6469 (10)
Zn16—Zn172.6810 (6)Zn42—Zn43ii2.6469 (10)
Zn16—Zn11xiv2.7165 (5)Zn42—Zn452.6760 (18)
Zn16—Zn18viii2.7788 (3)Zn42—Zn20xxxiii2.7087 (10)
Zn16—Zn18xviii2.7788 (3)Zn43—Zn43ii0.4329 (16)
Zn16—Zn14xv2.7831 (4)Zn43—Zn441.5554 (17)
Zn16—Zn14ii2.7831 (4)Zn43—Zn44ii1.9199 (16)
Zn16—Zn202.7931 (4)Zn43—Zn41viii2.0007 (19)
Zn16—Zn20xiv2.7931 (4)Zn43—Zn42ii2.6469 (10)
Zn17—Zn212.5782 (5)Zn43—Zn39ii2.6654 (12)
Zn17—Zn12viii2.7426 (4)Zn43—Zn452.6879 (10)
Zn17—Zn12xi2.7426 (4)Zn43—Zn44xvi2.7235 (14)
Zn17—Zn19xi2.7440 (4)Zn44—Zn44xvi1.262 (3)
Zn17—Zn19viii2.7440 (4)Zn44—Zn43ii1.9199 (16)
Zn17—Zn14ii2.7760 (4)Zn44—Zn452.1145 (14)
Zn17—Zn14xv2.7760 (4)Zn44—Zn45ii2.5019 (10)
Zn17—Zn232.8211 (6)Zn44—Zn45viii2.6515 (12)
Zn18—Zn40xxiv2.6240 (8)Zn44—Zn40xvi2.6705 (12)
Zn18—Zn40xxv2.6240 (8)Zn44—Zn43xvi2.7235 (14)
Zn18—Zn20viii2.6663 (4)Zn45—Zn45viii0.6112 (19)
Zn18—Zn20xix2.6663 (4)Zn45—Zn45ii0.6112 (19)
Zn18—Zn13xxv2.7137 (5)Zn45—Zn44xvi2.1145 (14)
Zn18—Zn16viii2.7788 (3)Zn45—Zn44xvii2.5019 (10)
Zn18—Zn16xviii2.7788 (3)Zn45—Zn44ii2.5019 (10)
Zn18—Zn22viii2.8737 (4)Zn45—Zn28ii2.5728 (7)
Zn18—Zn22xviii2.8737 (4)Zn45—Zn28viii2.5728 (7)
Zn18—Zn11viii2.9064 (4)Zn45—Zn44viii2.6515 (12)
Zn18—Zn11xix2.9064 (4)Zn45—Zn44xii2.6515 (12)
Symmetry codes: (i) y, x, z; (ii) x, xy, z; (iii) x, y, z; (iv) y, x, z; (v) x, x+y, z; (vi) y1, x1, z; (vii) x+1, y+1, z; (viii) y+1, x+1, z; (ix) x+1, x+y, z; (x) x1, y1, z; (xi) x1, xy, z; (xii) x+y+1, x+1, z; (xiii) x+1, x+y+1, z; (xiv) x+y, y, z; (xv) y, xy, z; (xvi) x+y+1, y, z; (xvii) y+1, xy, z; (xviii) x, xy+1, z; (xix) x+y, x+1, z; (xx) x+y, x+1, z+1/2; (xxi) y+1, x+1, z+1/2; (xxii) x, xy+1, z+1/2; (xxiii) x, y, z+1/2; (xxiv) x+y+1, y+1, z; (xxv) x, y+1, z; (xxvi) x, y+1, z+1/2; (xxvii) x+1, y, z; (xxviii) x, y1, z; (xxix) xy, y, z; (xxx) x+1, y+1, z; (xxxi) x+1, xy+1, z; (xxxii) x+2, x+y+1, z; (xxxiii) x+y, x, z; (xxxiv) y+1, xy+1, z; (xxxv) y, x+1, z; (xxxvi) y+2, x+2, z; (xxxvii) y+1, x, z; (xxxviii) x+y+1, x+1, z+1/2; (xxxix) x, xy, z+1/2; (xl) y, x, z+1/2; (xli) x+1, xy+1, z+1/2; (xlii) x+y, y, z+1/2; (xliii) x1, xy, z+1/2; (xliv) x+y, x, z+1/2.

Experimental details

Crystal data
Chemical formulaFe13Zn126
Mr8963.89
Crystal system, space groupHexagonal, P63/mmc
Temperature (K)300
a, c (Å)12.8297 (2), 57.286 (1)
V3)8166.0 (3)
Z4
Radiation typeSynchrotron, λ = 0.35450 Å
µ (mm1)20.09
Crystal size (mm)0.03 × 0.03 × 0.03
Data collection
DiffractometerHUBER 4-circle
diffractometer
Absorption correction
No. of measured, independent and
observed [I > 2σ(I)] reflections
203263, 16996, 14411
Rint0.028
(sin θ/λ)max1)1.111
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.031, 0.127, 1.03
No. of reflections16996
No. of parameters308
Δρmax, Δρmin (e Å3)5.91, 4.16

Computer programs: , CrystalClear (Rigaku/MSC Inc., 2006), SORTAV (Blessing, 1995), SIR92 (Giacovazzo et al., 1993), SHELXL97 (Sheldrick, 2008), ORTEP-3 for Windows (Farrugia, 1997), WinGX publication routines (Farrugia, 1999).

 

Footnotes

1The asymmetric unit of the space group P63/mmc has a volume of 1/12 of the unit cell.

2Atom labels with and without parentheses correspond to those reported by Belin et al. (Belin & Belin, 2000[Belin, C. H. E. & Belin, R. C. H. (2000). J. Solid State Chem. 151, 85-95.]) and determined in the present study, respectively.

3Supporting information for this paper is available from the IUCr electronic archives (Reference: DK5020 ).

Acknowledgements

This work was supported by JSPS KAKENHI grant numbers 24246113 and 25709066, and the Elements Strategy Initiative for Structural Materials (ESISM) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan, and in part by Advanced Low Carbon Technology Research and Development Program (ALCA) from the Japan Science and Technology Agency (JST). This work was also supported by Research Promotion Grant from ISIJ and Grants for Technical Research from JFE 21st Century Foundation. The synchrotron radiation experiments were performed at the BL02B1 of SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposal Nos. 2012B1145 and 2013A1394). We wish to thank Dr K. Sugimoto and Dr N. Yasuda for their assistance at the BL02B1 of SPring-8.

References

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Volume 70| Part 2| April 2014| Pages 275-282
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