Hanna Lind

A general structure model for Bi–Se phases using a superspace formalism

Solid-state synthesis in the Bi-Se system produced both commensurate and incommensurate phases of compositions ranging from Bi2Se3 to Bi4Se3, all crystallising in rhombohedral or trigonal layer structures. The a parameters are very similar for all phases but the c parameters vary irregularly between 10 and 100 A. A general model for all these phases was developed, using single crystal X-ray diffraction and a four-dimensional superspace formalism. The 4D superspace group is P: R3: m11, with approximate cell parameters of a ≈ 4.2 A and c ≈ 5.7 A valid for all phases. The q vector value in this model, ranging from 1.70[001]* to 1.80[001]* is the only parameter that varies with the composition. Two different modelling options were developed for the structures. One of them was a single-atom refinement model consisting of harmonic modulation waves and the other was a two-atom model based on a displacive sawtooth modulation of the Se atom. Both models converged to low R-values (Rall < 0.07) and small residual electron density values for all phases. The q vector may be physically interpreted as arising from the average distance between homoatomic layers in the structures. (Less)

On the question of commensurability : the Nowotny chimney-ladder structures revisited

A composite approach was used for the structure solution and refinement of two new Nowotny chimney-ladder phases, (Mo/Rh)11Ge18 and (Mo/Rh)13Ge22, found during investigations in the Mo/Rh/Ge system. The descriptions of the phases with conventional models (in I¯42d(No. 122) with a=5.885(2) Å, c=52.62(2) Å for (Mo/Rh)11Ge18 and a=5.922(1) Å, c=62.88(4) Å for (Mo/Rh)13Ge22) led to high numbers of unobserved reflections, high parameter/reflection ratios and an unstable refinement in the case of (Mo/Rh)13Ge22. Microscopy studies showed that the phases were in fact incommensurately modulated. Therefore, a composite model consisting of a rather stable diamond-like transition-metal substructure and a helical main-group-metal arrangement was developed. For the refinement of both phases, (Mo/Rh)11Ge18 as well as (Mo/Rh)13Ge22, the same model – same space group pair (W: P4/nnc:q¯1q1 P: I41/amd: 1¯1ss), same atom positions and modulation waves – was used. The refinements converged rapidly, showing that the presented structure model is very general, and may well be applicable to any Nowotny chimney-ladder phase.

Structure of δ1-CoZn7.8, an example of a phason pinning-unpinning transformation?

The novel structure of the δ1 phase in the cobalt-zinc system was determined by single-crystal X-ray diffraction. The structure features fused double icosahedra linked by edge-and face-sharing. The δ1-CoZn7.8 structure is incommensurately modulated along the columnar b direction. The extent of the linear pentagonal antiprismatic intergrowth is limited to a maximum of two overlapping icosahedra because of geometric demands and radii relations. Even this limited fusion of icosahedra leads to strain that is believed to be the origin of the structural modulation. The compound was synthesized using a centrifugation-aided filtration method which yielded single crystals grown on cobalt pieces in a zinc-rich melt. The (3 + 1)-dimensional superspace group is F2/m(0β0)s0 and the modulation wavevector was determined to q = 0.234b*. The partial amorphization of the sample when subjected to mechanical grinding is an indication of a metastable structure. The incommensurability of the structure may be seen as an ordered pinning of phasons. (Less)

Incommensurately modulated Nowotny chimney-ladder phases : Cr1-xMoxGe~1.75 with x=0.65 and 0.84

Abstract The crystal structures of two new ternary, incommensurately modulated phases in the Cr/Mo/Ge system, Cr1-xMoxGe∼1.75 with x = 0.65 and 0.84, have been refined using the same composite approach as for the earlier reported compounds, (Mo/Rh)11Ge18 and (Mo/Rh)13Ge22, from the Mo/Rh/Ge system. The composite model consists of a rather stable diamond-like transition metal substructure and a helical main group element arrangement. The same super space group pair, W:P4/nnc: q1̅q1 P:I41/amd: 11̅ss, the same positions and modulation waves were used. The refinements of the new phases in the Cr/Mo/Ge system converged rapidly to R-values below 5% with GOF of 2.53 and 3.71, respectively. Each structure is built by two sub lattices with the parameters - a, cx and the modulation vector qx - for Ge and a, cT and qT for the transition metals. The refined data for x = 0.65 are found to be a = 5.935(2), cx = 2.770(1), cT = 4.839(1), qx = 0.428 [001]*, qT = 0.253 [001]* and for x = 0.84, a = 5.963(1), cx = 2.786(1), cT = 4.875(1), qx = 0.430 [001]*, qT = 0.264 [001]*. It is clearly shown the composite approach is applicable to different chimney-ladder compounds, even though they have quite different compositions and hence q-vectors.

Re-determining the nowotny chimney-ladder structure VGe1.82 from powder diffraction data

This thesis is based on a study of five distinct intermetallic systems with the aim of expanding the general knowledge of aperiodically modulated crystal structures. Families of compounds that contain a variety of superstructures together with incommensurately modulated structures have been investigated mainly by means of single crystal X-ray diffraction and higher dimensional structure models.A uniform (3+1)-dimensional structure for Bi-Se phases was developed with the composition as a single variable. The structure description is based on a cubic NaCl type structure with homoatomic layer stackings. It is shown by computational modelling that the formation energies of bismuth selenides with more than 40 at. % Bi are close to zero, a result that supports the idea of a continuous series of stackings corresponding to an ordered solid solution of Bi in Bi2Se3.The Nowotny chimney-ladder structures are described with a (3+1)-dimensional composite structure, valid for all such compounds regardless of the included elements, the composition or the valence electron concentration. A new member is added to this family by the ZrBi1.62 compound. The modulation is believed to arise as a secondary effect of the criteria of a fixed electron count.A symmetry analysis is presented for the RE1+e(MB)4 (RE = rare earth elements, M = iron metal elements) family of compounds and a uniform (3+1)-dimensional composite structure description has been developed. The modulation may be due to the presence of unusually short contacts between the RE channel atoms, giving rise to a rotational modulation of the (MB)4 tetraederstern chains.A (3+1)-dimensional incommensurate structure has been determined for the novel δ1 – CoZn compound. The structure displays a unique assembly of fused icosahedra and the modulation is induced by geometric strain.The structure of the K(PtSi)4 compound was re-determined. Despite a close kinship with the RE1+e(MB)4 compounds, this structure is not modulated.