I. INTRODUCTION
Previously (Maki et al., Reference Maki, Morgan and Suzuki2016), the authors illustrated how, for a powder X-ray diffraction (PXRD) pattern of a complex, very large face-centered cubic (FCC) unit cell (a = 39.277(3) Å) oxide, M8, it becomes mandatory to investigate weak, low-angle 2θ lines (≲2% of the maximum intensity line) to determine the correct space group(s) (SG). Originally, the authors did this with ordinary, but profligate, long scans on a typical laboratory X-ray unit. The result implied that any improvement in data could only come from an intense X-ray source such as a synchrotron (sync), as very well described in Boultif and Louër (Reference Boultif and Louër2004) and citations therein to earlier papers. Here the authors present the efficacious result from a sync, confirming the earlier proposed need for a changed SG.
II. EXPERIMENTAL
The specimen was prepared and characterized exactly as described in the earlier paper (Maki et al., Reference Maki, Morgan and Suzuki2016).
The synchrotron radiation experiment was performed at the BL19B2 of SPring-8 in accord with Proposal No. 2016A1782 to the Japan Synchrotron Radiation Research Institute (JASRI). The pulverized sample was placed in a Lindemann capillary tube for X-ray diffraction analysis; of outside diameter 0.30 mm and wall thickness of 0.01 mm (Hilgenberg GmbH, TOHO, Japan). The X-ray wavelength was nominally λ = 1.0 Å. The synchrotron (synchrotron powder X-ray diffraction, SPXRD) rotating transmission measurement was performed for 1 h at room temperature. The optics use a standard double-crystal Si (1 1 1) monochromator, parallel-reflected beam with an imaging plate (IP) detector. Powder Tools ver. 3.2 was used as a plug-in of ImageJ software for the purpose of integrating the diffraction data of the IP measured with BL19B2.
III. RESULTS AND DISCUSSION
The complete SPXRD, showing all the peak tops, is illustrated in Figure 1. The beam wavelength of 0.9997 Å was accurately measured using a CeO2 standard sample collected under the same conditions. The strongest peak is the supercell (8 8 8) peak [corresponding to the (1 1 1) of the sub-cell] with a peak height ~170 000 counts s−1, which is ~62 times higher, and more monochromatic, than that from a typical laboratory X-ray source. Every strong peak is from 8 × (h k l) of the FCC sub-cell. The indexing of the new data firmly establishes a very large FCC unit cell, a = 39.277 Å (Maki et al., Reference Maki, Morgan and Suzuki2016).
Figure 1. Complete SPXRD pattern of M8 murataite.
To assign the correct SG, one needs to be sure of the (h k l) of the extremely weak supercell peaks at the low angles. These peaks are <2000 counts s−1 and are shown in detail in Figures 2 and 3; the Supplemental material contains plots for the whole 2θ range as illustrated in Figure S1.
Figure 2. (Colour online) Expanded SPXRD pattern of the all-important low 2θ section of M8, with impurities: P, pseudobrookite and Z, zirconolite.
Figure 3. (Colour online) Expanded SPXRD pattern of the low 2θ section of M8, with impurities: P, pseudobrookite and Z, zirconolite.
There are no visible lines belonging to other members of murataite family (e.g. M7, M5, or M3) or coherent intergrowths, which leads to a singularly sharp (8 8 8) peak.
Contrasting with the conventional laboratory PXRD technique (Maki et al., Reference Maki, Morgan and Suzuki2016), a very weak (1 1 1) line might be present. With the synchrotron capability, the peaks are extremely sharp and highly resolved, which greatly benefits indexing especially with increasing 2θ.
As to the assignment of a SG: – for the lower angle (h k 0), including (h 0 0) lines, it can be found that the first five (2 0 0), (4 2 0), (6 4 0), (8 6 0), and (10 0 0) lines where h + k = 2n are completely absent. However, six lines with h + k = 4n, having no overlap problems, are definitely present: – (4 0 0), (8 0 0), (8 4 0), (14 6 0), (24 4 0), and (24 16 0). Tables I and II have more details including overlap considerations. It can now be considered that the appropriate SG is most probably Fd
$\bar 3$
m (227).
Table I. Lines with (h k 0) h + k = 2n (≠4n), including (h 0 0).
Table II. Lines with (h k 0) h + k = 4n, including (h 0 0).
This SG differs from the previously proposed F
$\bar 4$
3m (216) (Pakhomova et al., Reference Pakhomova, Krivovichev, Yudintsev and Stefanovsky2016). Because of the immense size of this unit cell (the authors believe the largest volume unit-cell oxide ever studied), such small differing opinions are not surprising.
Three possible SGs, Fd
$\bar 3$
(203), Fd
$\bar 3$
m (227), and Fd3c (228) are allowed with these characteristics; of these, Fd
$\bar 3$
m (227) is the most likely based on occupancies, e.g. see: Urusov and Nadezhina (Reference Urusov and Nadezhina2009). In PDF-4+ (2015), there are 14 032 inorganic entries with atomic coordinates for Fd
$\bar 3$
m (227), while the rarer SG Fd
$\bar 3$
(203) has merely 166 entries and Fd3c (228) has only 41 entries.
IV. CONCLUSION
SPXRD data are shown to be much better resolved than laboratory PXRD data, which strongly suggest that M8 belongs to the Fd
$\bar 3$
m (227) SG.
More extensive work, e.g. single-crystal XRD, is now in order for further investigation.
SUPPLEMENTARY MATERIAL
The supplementary material for this article can be found at https://doi.org/10.1017/S0885715617000525.
ACKNOWLEDGEMENTS
The authors acknowledge Dr. Keiichi Osaka for his help on the synchrotron radiation experiments performed at the BL19B2 of SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposal No. 2016A1782). The authors very much appreciate the environment for collaborative international work, physical and intellectual, provided by Associate Professor Yoshikazu Suzuki at the University of Tsukuba, which allowed this work to so favorably progress to this conclusion. This paper has been improved by the comments of two anonymous reviewers, e.g. one reviewer pointed out the PDF-4+ data.
