A Guide to Discriminating the Rhombohedral Cell from the Face-Centred Pseudo Cubic Cell

Nobuo Ishizawa † and Yumi Inagaki ¶

† Ceramics Research Laboratory, Nagoya Institute of Technology, Asahigaoka 10-6-29, Tajimi, Gifu 507-0071 JAPAN

¶ Graduate School of Nagoya Institute of Technology, Gokiso-cho, Nagoya, Aichi 466-8555


Abstract

The crystal in cubic system contains four 3-fold axes with different orientations, whereas the rhombohedral modification with the face-centred pseudo cubic cell contains only one ‘true’ 3-fold axis. The discrimination of the ‘true’ 3-fold axis from the other three ‘pseudo’ 3-fold axes is not difficult when the rhombohedral distortion is large. However, the difficulty increases as the distortion becomes small and the cell dimensions become very close to values of ‘metrically cubic’. This note first summarizes the geometrical relation among the face-centred pseudo cubic, primitive rhombohedral, and triple-hexagonal cells. Then it provides a procedure to choose the ‘true’ 3-fold axis, and accordingly the ‘true’ rhombohedral cell, from the experimentally-obtained face-centred pseudo cubic cell. In the description of this guide, a special attention has been paid for the Smart Apex II single-crystal X-ray diffractometer users.

http://www.crl.nitech.ac.jp/ar/2008/3549_crl_ar2008_review.pdf