TY - JOUR

T1 - Appropriate zone-axis orientations for the determination of crystal polarity by convergent-beam electron diffraction

AU - Tanaka, Katsushi

AU - Okamoto, Norihiko L.

AU - Fujio, Satoshi

AU - Sakamoto, Hiroki

AU - Inui, Haruyuki

N1 - Publisher Copyright:
© 2015 International Union of Crystallography.

PY - 2015/6/1

Y1 - 2015/6/1

N2 - A convergent-beam electron diffraction (CBED) method is proposed for polarity determination, in which polarity is determined from the intensity asymmetry of any of the hkl- Friedel pairs appearing in a zone-axis CBED pattern with a symmetric arrangement of Bijvoet pairs of reflections. The intensity asymmetry occurs as a result of multiple scattering among Bijvoet pairs of reflections in the CBED pattern. The appropriate zone-axis orientations for polarity determination are deduced for 19 of the 25 polar point groups from symmetry considerations so as to observe Bijvoet pairs of reflections symmetrically in a single CBED pattern. These appropriate zone-axis orientations deduced for the 19 polar point groups coincide with nonpolar directions. This is because the nonpolar directions for these point groups are perpendicular to an even-fold rotation axis, which guarantees the symmetric arrangement of Bijvoet pairs of reflections with respect to the symmetry (m-m′) line in a CBED pattern taken along any of the appropriate zone-axis orientations. The m-m′ line in the CBED pattern is proved to be perpendicular to the trace of the even-fold rotation axis. On the other hand, if the nonpolar direction is either perpendicular to a mirror plane or parallel to a roto-inversion axis as in the four point groups m, 3m1, 31m, , the nonpolar direction cannot be used as the appropriate zone-axis orientation for polarity determination because the Bijvoet pairs of reflections are not arranged symmetrically in the CBED pattern. The validity of the CBED method is confirmed both by experiment and by calculation of CBED patterns.

AB - A convergent-beam electron diffraction (CBED) method is proposed for polarity determination, in which polarity is determined from the intensity asymmetry of any of the hkl- Friedel pairs appearing in a zone-axis CBED pattern with a symmetric arrangement of Bijvoet pairs of reflections. The intensity asymmetry occurs as a result of multiple scattering among Bijvoet pairs of reflections in the CBED pattern. The appropriate zone-axis orientations for polarity determination are deduced for 19 of the 25 polar point groups from symmetry considerations so as to observe Bijvoet pairs of reflections symmetrically in a single CBED pattern. These appropriate zone-axis orientations deduced for the 19 polar point groups coincide with nonpolar directions. This is because the nonpolar directions for these point groups are perpendicular to an even-fold rotation axis, which guarantees the symmetric arrangement of Bijvoet pairs of reflections with respect to the symmetry (m-m′) line in a CBED pattern taken along any of the appropriate zone-axis orientations. The m-m′ line in the CBED pattern is proved to be perpendicular to the trace of the even-fold rotation axis. On the other hand, if the nonpolar direction is either perpendicular to a mirror plane or parallel to a roto-inversion axis as in the four point groups m, 3m1, 31m, , the nonpolar direction cannot be used as the appropriate zone-axis orientation for polarity determination because the Bijvoet pairs of reflections are not arranged symmetrically in the CBED pattern. The validity of the CBED method is confirmed both by experiment and by calculation of CBED patterns.

KW - Bijvoet pairs

KW - convergent-beam electron diffraction

KW - enantiomorphs

KW - nonpolar axes

KW - polarity

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U2 - 10.1107/S1600576715004884

DO - 10.1107/S1600576715004884

M3 - Article

AN - SCOPUS:84930641775

SN - 0021-8898

VL - 48

SP - 736

EP - 746

JO - Journal of Applied Crystallography

JF - Journal of Applied Crystallography

ER -