‘Soft’ phonon modes,structured diffuse scattering and the crystal chemistry of Fe-bearing sphalerites

Electron diffraction has been used to carefully investigate the reciprocal lattices of a range of iron-bearing sphalerites looking for evidence of Fe clustering and/or Fe/Zn ordering in the form of either additional satellite reflections or a structured diffuse intensity distribution accompanying the strong Bragg reflections of the underlying sphalerite-type average structure. While a highly structured diffuse intensity distribution in the form of transverse polarized f110g sheets of diffuse intensity has been detected and found to be characteristic of all compositions,it does not appear to arise from Fe clustering and/or Fe/Zn ordering. Rather inherently low frequency,and therefore strongly thermally excited,phonon modes propagating along reciprocal space directions perpendicular to each of the six /110S real space directions of the average structure are suggested to be responsible for these f110g sheets of diffuse intensity. Monte Carlo simulation (for a range of Zn–S,Zn–Zn and S–S interaction strengths) and subsequent Fourier transformation is used to confirm the existence of these low-frequency phonon modes of distortion as well as to show that they are an intrinsic,predictable property of the corner-connected tetrahedral structure of sphalerite. The low-frequency phonon modes involve coupled (Zn,Fe) and S motion in one-dimensional strings along /110S real space directions

Deformed Penrose tilings

Monte Carlo (MC) simulation of a model quasicrystal (2D Penrose rhomb tiling) shows that the kinds of local distortions that result from size-effect-like relaxations are in fact very similar to mathematical constructions called deformed model sets. Of particular interest is the fact that these deformed model sets are pure point-diffractive, i.e. they give diffraction patterns that have sharp Bragg peaks and no diffuse scattering. Although the aforementioned MC simulations give diffraction patterns displaying some diffuse scattering, this can be attributed to the fact that the simulations include a certain amount of unavoidable randomness. Examples of simple deformed model sets have been constructed by simple prescription and hence contain no randomness. In this case the diffraction patterns show no diffuse scattering. It is demonstrated that simple deformed model sets can be constructed, based on the 2D Penrose rhomb tiling, by using deformations which are defined in terms of the local environment of each vertex. The resulting model sets are all topologically equivalent to the Penrose tiling (same connectedness), are perfectly quasicrystalline but show an enormous variation in the Bragg peak intensities. For the examples described, which are based on nearest-neighbour environments, 12 deformation parameters may be chosen independently. If more distant neighbours are taken into account further sets of parameters may be defined. One example of these simple deformed tilings, which shows great similarity to the size-effect-distorted tiling, is discussed in detail

Diffuse Scattering and Monte Carlo Studies or Relaxor Ferroelectrics

A renewed interest in the field of ferroelectricity has taken place in recent years since the finding of exceptional piezoelectric properties in the lead-oxide class of relaxor ferroelectric materials typified by the disordered perovskite PbZn1/3Nb2/3O3 (PZN). Although PZN and numerous related materials have been extensively studied over a long period, a detailed understanding of the exact nature of their polar nanostructure has still not emerged. In this article, we describe the development of Monte Carlo computer models, which seek to account for the detailed three-dimensional (3-D) diffuse neutron scattering data that have been recorded from a single crystal of PZN. It has been established that the observed diffuse patterns are due to planar nanodomains oriented normal to the six 〈110〉 directions, but there is still some uncertainty concerning the direction of the local Pb ionic shifts, which remains an area of controversy. It is argued that further detailed analysis and experiments in which data are recorded with the crystal in an applied field should allow these remaining issues to be resolved

Approaches to modeling diffuse scattering from molecular crystals : Para-Terphenyl (C18H14)

Diffuse scattering is a probe of the local correlations in a crystal, whereas Bragg peaks are descriptive of the average long-range ordering. The long-range average is the result of numerous local configurations the population of which cannot be determined from the Bragg peaks. Diffuse scattering can examine this population. This is particularly the case when making use of the three-dimensional distribution of diffuse scattering from single crystals. However, diffuse scattering is very weak and broad and is often of similar intensity to the experimental background, which makes data collection demanding. Disorder can also take many forms and local configurations are not constrained by the average crystallographic symmetry. Here, three approaches to the modeling of diffuse scattering from molecular crystals will be discussed. All three approaches are based on a Monte Carlo (MC) simulation. As an example, the modeling of neutron diffuse scattering from para-terphenyl (PTP, C 18H14) will be described