Journal Articles Journal of Applied Crystallography Year : 2024

Duality of spaces and the origin of integral reflection conditions

Abstract

The dualism between direct and reciprocal space is at the origin of well-known relations between basis vectors in the two spaces. We show that when a coordinate system corresponding to a non-primitive unit cell is adopted, this dualism has to be handled with care. In particular, the reciprocal of a non-primitive unit cell is not a unit cell but a region in reciprocal space that does not represent a unit of repetition by translation. The basis vectors do not correspond to reciprocal-space cell lengths, contrary to what is stated even in the CIF core dictionary. The corresponding unit cell is a multiple of this region. The broken correspondence between basis vectors and unit cell is at the origin of the integral reflection conditions.

Domains

Cristallography
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Dates and versions

hal-04675926 , version 1 (28-11-2024)

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Massimo Nespolo. Duality of spaces and the origin of integral reflection conditions. Journal of Applied Crystallography, 2024, 57 (6), pp.1733-1746. ⟨10.1107/S1600576724008367⟩. ⟨hal-04675926⟩
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