Temperature Dependence of the Static Distortion in Incommensurate Displacive Phases and its Effect on the Diffraction Pattern. II. Satellite Reflections

Modulated structure ofRb2ZnCl4in the soliton regime close to the lock-in phase transition

“…This important property was already pointed out in Ref. 27 Here we have shown in addition that this quotient approximately equals the quotient between the amplitudes of first-order and fifth-order harmonics which, as FIG. 7.…”

“…It is important to note that the soliton model and the resulting strong correlations between the first and fifth harmonics can be cross-checked by analyzing directly the experimental diffraction diagram. It can be demonstrated 27 that in a soliton configuration as the one described above the quotient between the structure factor of a first-order satellite H = ͑G , h 4 = ±1͒ and that of the closest fifth-order satellite HЈ = ͑GЈ , h 4 = ±5͒, so that G ± q L = GЈ ±5q L ͑where G , GЈ are vectors of the reciprocal lattice of the average structure͒, is approximately the same for all such pairs of reflections ͉F͑GЈ,h 4 = ± 5͉͒ ͉F͑G,h 4 = ± 1͉͒…”

“…Due to the limited time available at the synchrotron, we were not able to measure a complete dataset of satellites of the fifth order. Instead, we measured the intensities of selected reflections, for which, based on the predictions from theory, 25,27 we expected a relatively high signal. Preliminary studies of a comparatively small crystal of very good quality ͑as demonstrated by the extremely sharp reflection profiles of the main reflections͒ showed that satellite intensities of the fifth order were, unfortunately, extremely weak and even at the synchrotron source hardly detectable.…”

“…Unfortunately this error seems to be propagating in more recent publications. 26 The effect of a soliton regime on the diffraction diagram of Rb 2 ZnCl 4 was analyzed theoretically and simulated by Aramburu et al 27 It was shown that, if the effect of secondary modes is neglected, the ratio of the intensities of pairs of fifth-order and first-order satellites superimposing at the lock-in transition will follow a unique law, dependent only on the soliton density n s and independent of the specific reflection. A simulation showed that secondary modulations not associated with the order parameter may produce a significant dispersion of these intensity ratios, but their mean value did not change and could still be related with the theoretical value dependent only on n s .…”

An elementary introduction to superspace crystallography

“…11). Other special functions include the block-wave, a combination of segments with saw-tooth shape and segments with block-wave shape, and the soliton wave [23]. An interesting class of compounds with large, non-harmonic modulations are the hexagonal perovskites, which can be described as the stacking of two or three types of atomic layers, where the stacking sequences range from short and long periods to incommensurate order [24,25].…”