Equivalence of superspace groups

Abstract

The standard settings of (3 + d)-dimensional superspace groups are determined for a series of modulated compounds, especially concentrating on d = 2 and 3. The coordinate transformation in superspace is discussed in view of its implications in physical space.

Spin-Peierls distortions in TiPO4

“…63.1.13.8 with standard setting Amam(00σ 3 )0s0]. 31,32 In the description of the lock-in phase as commensurately modulated structure, different sections t = t 0 of superspace lead to different symmetries of the fourfold, 2a × b × c superstructure. 33 The best fit to the diffraction data was obtained for t 0 = 1 8 , which corresponds to space group P bnm for the superstructure [see Fig.…”

KEu(MoO4)2: Polymorphism, Structures, and Luminescent Properties

“…The reflection conditions hklm: h + k + l = 2n and hk0m: h, k = 2n correspond to the (3+1)D superspace group I2/b(αβ0)00 (unique axis c) (15.1.4.1 in Stokes-Campbell-van Smaalen notations, B2/b(αβ0)00 in a standard setting). 45 The [11̅ 0]* pattern shows hk00: h, k = 2n+1 reflections that are forbidden by the I2/b symmetry. However, on tilting the sample around the [hk00] direction, these reflections become weaker and finally disappear in the [001]* pattern.…”

Standard and non-standard settings of superspace groups

“…66 41 . On the other hand, our electron diffraction study of "chain-ladder" compounds reveals that it is only the amplitude of displacive modulation of basic crystal structure that is slightly affected by charge and spin ordering [4]. [1] Milat O., Van Tendeloo G., Amelinckx S., Mebhod M., Deltour R. (1992), Acta.…”

“…We discuss the need for non-standard settings in some cases and the desirability of employing standard settings of superspace groups in other cases [4]. These features are illustrated by the analysis of the symmetries of a series of compounds, comparing published and standard settings and the transformations between them.…”