Crystal structure superstructure, determination

In principle, any modification of the intra- or intermolecular relationships that break the averaged crystal symmetry on a macroscopic scale corresponds to a structural phase transition. Diffraction techniques (X-ray or neutron) are thus of primary importance to characterize the different phases. From the Bragg peaks that measure the long-range order of the mean crystal structure, the space groups, atomic positions and thermal parameters can be determined in each phases (Fig. 1). Moreover, in the most favorable cases, these methods can directly measure information on the order parameter and pretransitional ordering by following the superstructure at 7< Tc,... 

The crystal structure of vitusite-(Ce) was determined by Karpov et al. (1980). They reported two structural models (fig. 23), which are mutually related by displacement along a quarter of the a-axis. They also reported that the presence of a superstructure was indicated by very weak reflections having pseudo-intervals along the h-axis, but the cell dimension of the superstructure could not be determined. They pointed out... 

The structure was determined on a single crystal. Superstructure reflections have been found a =4a, c = c. There exists a phase with a hexagonal lattice a = 10.264, c = 5.744, space group P63 (ref. [20])... 

In the paramagnetic regime, the evolution of the EPR line width and g value show the presence of two transitions, observed at 142 and 61 K in the Mo salt, and at 222 and 46 K in the W salt. Based on detailed X-ray diffraction experiments performed on the Mo salt, the high temperature transition has been attributed to a structural second-order phase transition to a triclinic unit cell with apparition of a superstructure with a modulation vector q = (0,1/2, 1/2). Because of a twinning of the crystals at this transition, it has not been possible to determine the microscopic features of the transition, which is probably associated to an ordering of the anions, which are disordered at room temperature, an original feature for such centrosymmetric anions. This superstructure remains present down to the Neel... 

For A3MF6 compounds with larger alkali cations, only a few single-crystal investigations are known. It seems to be clear that K3M0F6 and KsWFe crystallize in the cubic elpasolite-type structure, as well as most of the (NH4)3M F6 compounds at room temperature. For (NH4)3ScF6, a monoclinic structure variant has been reported recently. Very complicated superstructures with five-fold axes have been fonnd in different laboratories for some K and Rb componnds (see citation in Ref 33). However, no stracture determinations are known to date. 

Structure (i) was originally assigned to all three compounds, but as the result of later studies the following structures have been proposed CoAsS, (ii), NiAsS, (iii), and NiSbS, (i). It would seem that the greatest reliance may be placed on the later work on CoAsS, which shows that the apparently cubic structure is a polysynthetic twin of a monoclinic structure, and it is not impossible that other structures in this family are in fact superstructures of lower symmetry. As a result of the difference between Ni-Sb, 2-57 A, and Ni-S, 2-34 A, the symmetry of NiSbS has dropped to the enantiomorphic crystal class 23 the absolute structure has been determined. ... 

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