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Correct interpretation of diffraction properties of quartz crystals for X-ray optics applications. Corrigendum

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aAdvanced Photon Source, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA, and bInstituto de Ciencias da Vida e da Natureza, Universidade Federal da Integracao Latino-Americana, 2044 Foz do Iguacu, Parana, 85867-970, Brazil
*Correspondence e-mail: xiahuang@aps.anl.gov

(Received 27 February 2018; accepted 14 March 2018; online 27 April 2018)

Errors about left-handed (laevorotatory) quartz and right-handed (dextro­rotatory) quartz in the paper by Huang, Gog, Kim, Kasman, Said, Casa, Wieczorek, Hönnicke & Assoufid [J. Appl. Cryst. (2016), 51, 140–147] are corrected.

In the paper by Huang et al. (2016[Huang, X.-R., Gog, T., Kim, J., Kasman, E., Said, A. H., Casa, D. M., Wieczorek, M., Hönnicke, M. G. & Assoufid, L. (2018). J. Appl. Cryst. 51, 140-147.]), the authors erroneously stated that the helical arrangement of the Si atoms in quartz is the same as the `optical handedness'. The authors are grateful to Professor A. M. Glazer at Physics Department, University of Oxford, for pointing out that this statement is incorrect (see also Glazer, 2018[Glazer, A. M. (2018). J. Appl. Cryst. 51, 915-918.]). In fact, the two types of handedness are opposite to each other (Glazer & Stadnicka, 1986[Glazer, A. M. & Stadnicka, K. (1986). J. Appl. Cryst. 19, 108-122.]). Therefore, in the right-handed hexagonal coordinate system, the unit cell with the three Si atoms located at (u, 0, 0), (−u, −u, 1/3) and (0, u, 2/3) and the six O atoms at (x, y, z), (y, x, 2/3 − z), (−y, x − y, 2/3 + z), (−x, yx, 1/3 − z), (yx, −x, 1/3 + z) and (x − y, −y, −z) corresponds to right-handed quartz (space group P3221) with right-handed optical rotation (dextrototation), although here the three Si atoms form a left-handed helix (or left-handed screw, LS). Accordingly, still in the right-handed hexagonal coordinate system, the unit cell with the Si atoms located at (u, u, −1/3), (−u, 0, 0) and (0, −u, 1/3) (forming a right-handed screw, RS) and the O atoms at (x, xy, z − 1/3), (y, yx, 1/3 − z), (−y, −x, 1/3 + z), (−x, −y, −z), (yx, y, z) and (xy, x, 2/3 − z) corresponds to left-handed quartz (space group P3121) with left-handed optical rotation (laevorotation). Since the authors have adopted u = 0.4699, x = 0.4141, y = 0.2681 and z = 0.1188, right-handed quartz (P3221) corresponds to the z(+) setting in the right-handed hexagonal coordinate system of Donnay & Le Page (1978[Donnay, J. D. H. & Le Page, Y. (1978). Acta Cryst. A34, 584-594.]), and left-handed quartz (P3121) corresponds to the z(−) setting in the right-handed hexagonal coordinate system. These settings correspond to the `reverse settings' (widely adopted in the X-ray community) so that reflection [10\overline 1\overline 1] is stronger than [10\overline 1 1], and [30\overline 3\overline 1] is much stronger than [30\overline 31].

In summary, except for the words `right- or left-handed hexagonal coordinate systems' and `left-handed helix', all the other words `left-handed' should be `right-handed' and the words `right-handed' should be `left-handed' in the original paper and the original supporting information. A revised version of the paper and the supporting information with all the corrections has been deposited as new supporting information to this paper.

Supporting information


References

First citationDonnay, J. D. H. & Le Page, Y. (1978). Acta Cryst. A34, 584–594.  CrossRef CAS IUCr Journals Web of Science Google Scholar
First citationGlazer, A. M. (2018). J. Appl. Cryst. 51, 915–918.  CrossRef IUCr Journals Google Scholar
First citationGlazer, A. M. & Stadnicka, K. (1986). J. Appl. Cryst. 19, 108–122.  CrossRef CAS Web of Science IUCr Journals Google Scholar
First citationHuang, X.-R., Gog, T., Kim, J., Kasman, E., Said, A. H., Casa, D. M., Wieczorek, M., Hönnicke, M. G. & Assoufid, L. (2018). J. Appl. Cryst. 51, 140–147.  CrossRef CAS IUCr Journals Google Scholar

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