Volume 230, Issue 1 - Special Issue: Aperiodic order and disorder / Guest Editors: Sander van Smaalen and Hans Boysen

n -Dodecane/urea is a member of the prototype series of n -alkane/urea inclusion compounds. At room temperature, it presents a quasi-one dimensional liquid-like state for the confined guest molecules within the rigid, hexagonal framework of the urea host. At lower temperatures, we report the existence of two other phases. Below T c =248 K there appears a phase with rank four superspace group P6 1 22(00 γ ), the one typically observed at room temperature in n -alkane/urea compounds with longer guest molecules. A misfit parameter, defined by the ratio γ= c h / c g ( c host / c guest ), is found to be 0.632±0.005. Below T c1 =123 K, a monoclinic modulated phase is created with a constant shift along c of the guest molecules in adjacent channels. The maximal monoclinic space group for this structure is P12 1 1(α0 γ ). Analogies and differences with n -heptane/urea, which also presents a monoclinic, modulated low-temperature phase, are discussed.

This article presents a brief overview of our recent work on the nature of long period modulation in the premartensite and martensite phases of Ni 2 MnGa ferromagnetic shape memory alloy using high resolution synchrotron x-ray powder diffraction patterns. The commensurate structure model using the Pnnm space group is unable to account for the peak positions of the satellite reflections that appear due to modulations correctly. LeBail and Rietveld refinements using the (3+1)-D super space group Immm(00γ)s00 show that the peak positions of all the reflections, including the satellites, can be explained satisfactorily using incommensurate modulations for both the premartensite and martensite phases. The incommensurate modulation vectors are found to be q =0.33761(5) c* =(1/3+δ 1 ) c* and 0.43160(3) c* =(3/7+δ 2 ) c* , where δ 1 and δ 2 are the degrees of incommensuration for the premartensite and martensite phases, respectively. The periodicity of the closest rational approximant of the premartensite and martensite phases are confirmed to be 3 M and 7 M, respectively, in agreement with single crystal diffraction results.

The crystal structure of labradorite is characterized by two modulation waves with largely different periods of about 1500 Å and 50 Å, giving rise to s- and e-satellites, respectively. The problems to determine the true structure by diffraction methods are discussed. Since each s-lamella has its own e-modulation, common experiments are not sufficient. Using only s-satellites around main reflections assumes e-averaged structures of the s-lamellae. On the other hand, using only averaged e-satellites and main reflections integrated over the s-satellites leads to a hypothetical, idealised structure such as if there were no s-modulation. For this reason the analysis of an extensive data set, including e-satellites up to third order, cannot resolve the Ca/Na modulation unambiguously, although the Si/Al modulation can be determined consistently from directly refined occupancies and T-O bond lengths.

The problems occurring in structure analyses of modulated surfaces by LEED or X-ray diffraction are briefly discussed. In previous LEED studies of modulated surfaces a commensurate unit cell and Fourier coefficients to describe the modulation function has been used. The wave length of the modulation and the size of the supercell are limited in this way by the computational effort of the multiple scattering calculations. To overcome this problem an approximation is proposed allowing the analysis of commensurate or incommensurate surface modulations with long wave lengths.

X-ray diffraction and transmission electron microscopy were used to probe the structure of the misfit compound [(SnSe) 1.15 ] 1 (VSe 2 ) 1 grown using an elementally modulated precursor. The specular X-ray diffraction pattern contained only 00 l reflections, which yielded a c lattice parameter of 1.203(1) nm. Cross-section STEM revealed alternating layers of SnSe and VSe 2 , in agreement with the structure model refined from the X-ray diffraction pattern using Rietveld refinement. Plan-view transmission electron microscopy revealed the in-plane grain structure of the films, yielding grain sizes in agreement with previously reported in plane X-ray diffraction studies and the cross-section STEM images. The plan view images also contained Moiré fringes resulting from grains with different relative tilting on both sides of interfaces as well as Moiré fringes resulting from different relative rotations between domains. An energy-filtered nano-beam electron diffraction pattern obtained from at least one domain in the [(SnSe) 1.15 ] 1 (VSe 2 ) 1 sample investigated in cross section contained a series of resolvable supercell reflections along the c axis that indicated that the supercell c-axis lattice parameter was a multiple of three times that determined using X-ray diffraction. Energy filtered NBED of plan-view samples showed diffraction patterns from select regions with 12-fold symmetry, indicating that the arrangement of the layers is not rotationally random from layer to layer. This suggests that during the self-assembly of the amorphous modulated elemental precursor, the SnSe and VSe 2 constituent layers must nucleate off the adjacent interfaces of the growing crystal, yielding layers that are locally rotationally aligned with growing crystal. Different processing conditions during the precursor to crystal self-assembly might enable the domain size and/or the extent of order to be controlled.

The term “high-entropy alloys (HEAs)” first appeared about 10 years ago defining alloys composed of n =5–13 principal elements with concentrations of approximately 100/ n at.% each. Since then many equiatomic (or near equiatomic) single- and multi-phase multicomponent alloys were developed, which are reported for a combination of tunable properties: high hardness, strength and ductility, oxidation and wear resistance, magnetism, etc. In our paper, we focus on probably single-phase HEAs (solid solutions) out of all HEAs studied so far, discuss ways of their prediction, mechanical properties. In contrast to classical multielement/multiphase alloys, only single-phase multielement alloys (solid solutions) represent the basic concept underlying HEAs as mixing-entropy stabilized homogenous materials. The literature overview is complemented by own studies demonstrating that the alloys CrFeCoNi, CrFeCoNiAl 0.3 and PdFeCoNi homogenized at 1300 and 1100°C, respectively, for 1 week are not single-phase HEAs, but a coherent mixture of two solid solutions.

Spatially interacting Gaussian random variables arranged on a hexagonal lattice are used to construct examples of hexagonal paracrystals. As for previously described paracrystals on a square lattice the distributions may be specified by a variance, σL2,$\sigma _L^2,$ defining the magnitude of the displacement away from the underlying perfect lattice together with parameters defining transverse and longitudinal correlations ( ρ T and ρ L ) between neighbouring displacements. A strong longitudinal correlation indicates a small variation from cell to cell in the length of the cell edge whereas a strong transverse correlation indicates a small variation in the cell edge direction. For values of σ L >∼0.30 of the unit cell spacing the diffraction patterns contain diffuse peaks only with no evidence of Bragg peaks arising from the underlying regular lattice.

Different descriptions of the stacking disorder of the so-called “cubic” phase “ice I c ” and stacking-faulted hexagonal ice I h exist. We present an overview of the effect of different stacking disorder interaction ranges s from s = 2 to s = 4 after Jagodzinski on the (neutron) powder diffraction patterns of stacking-disordered ice I, which we propose to name ice I ch . We fit in a systematic approach simulated diffraction data of ice I ch for s up to 4 with a multi-peak approach. In this way we allow for estimating the relative proportion of cubic sequences in the stacking sequences by using readily accessible observables of a diffraction pattern.