Multiple Coulomb phase in the fluoride pyrochlore CsNiCrF6

The Coulomb phase is an idealized state of matter whose properties are determined by factors beyond conventional considerations of symmetry, including global topology, conservation laws and emergent order. Theoretically, Coulomb phases occur in ice-type systems such as water ice and spin ice; in dimer models; and in certain spin liquids. However, apart from ice-type systems, more general experimental examples are very scarce. Here we study the partly disordered material CsNiCrF6 and show that this material is a multiple Coulomb phase with signature correlations in three degrees of freedom: charge configurations, atom displacements and spin configurations. We use neutron and X-ray scattering to separate these correlations and to determine the magnetic excitation spectrum. Our results show how the structural and magnetic properties of apparently disordered materials may inherit, and be dictated by, a hidden symmetry—the local gauge symmetry of an underlying Coulomb phase

A Paracrystalline Description of Defect Distributions in Wüstite, Fe1-xO

Diffuse X-ray scattering data from a crystal of wüstite, Fe0.943O, are presented. Satellite reflections corresponding to an incommensurate repeat distance of ∼2.7a in all three cubic directions were observed (the P′ phase). The satellites were diffuse, anisotropically elongated, interconnected by weaker continuous streaks, and negligible in intensity beyond first order. Monte Carlo computer simulations have been carried out which demonstrate that this diffraction behavior is consistent with defect clusters forming a paracrystalline (or highly distorted) lattice. The paracrystalline distribution which best fits the observations is such that the spacing between defects tends to be maintained fairly constant, but relative lateral translations may occur more variably. When these lateral translations are suppressed, additional superlattice peaks appear which are consistent with the P″ phase diffraction patterns. The diffuse satellites are systematically more intense on the low-angle side of a Bragg reflection than on the high-angle side. This behavior may be understood in terms of the well-known atomic size effect and is consistent with a local contraction of the structure around regions of low scattering power (defect clusters) and compensating expansion in other parts of the structure

Diffuse scattering and partial disorder in complex structures

The study of single-crystal diffuse scattering (SCDS) goes back almost to the beginnings of X-ray crystallography. Because SCDS arises from two-body correlations, it contains information about local (short-range) ordering in the sample, information which is often crucial in the attempt to relate structure to function. This review discusses the state of the field, including detectors and data collection and the modelling of SCDS using Monte Carlo and ab initio techniques. High-quality, three-dimensional volumes of SCDS data can now be collected at synchrotron light sources, allowing ever more detailed and quantitative analyses to be undertaken, and opening the way to approaches such as three-dimensional pair distribution function studies (3D-PDF) and automated refinement of a disorder model, powerful techniques that require large volumes of low-noise data

Chemical origin of nanoscale polar domains in PbZn_1/3Nb_2/3O<sub>3

We describe the development of an atom-based Monte Carlo simulation model which gives rise to a nanoscale polar domain structure as envisaged to occur in Pb (Zn1 3 Nb2 3) O3 (PZN) and similar relaxor ferroelectric materials. Individual domains are essentially thin platelike domains normal to each of the six 110 directions. Calculated diffuse scattering patterns have been obtained from the simulations, and these are in good agreement with observed neutron scattering data. Nanoscale domain formation is driven by the need for the Pb atoms to satisfy their valence requirements; within a planar domain, the Pb atoms are displaced in a concerted fashion away from the center of their 12-fold coordination polyhedra with an in-plane displacement along 110 towards one of the coordinating O atoms. The B -site cations Zn and Nb display a strong tendency to alternate in the 100 directions but complete order is frustrated by the 2:1 stoichiometry. No diffraction evidence has been found that this B -site ordering is directly linked to the nanoscale polar domain ordering. Such a linkage cannot be completely ruled out, but if it does exist, its effect on the diffraction pattern must be quite subtle. The B -site ordering does play an indirect role in establishing the average cell dimension, which in turn dictates the magnitude of the Pb displacements. The effect of applying an external electric field is modeled, and the results are found to be consistent with experiment

The effect of low intra-sublattice repulsion on phase diagram of YBa2Cu3O6+x: A Monte Carlo simulation study

We report the results of Monte Carlo simulation of the phase diagram and oxygen ordering in YBa2Cu3O6+x for low intra-sublattice repulsion. At low temperatures, apart from tetragonal (T), orthorhombic (OI) and 'double cell' ortho II phases, there is evidence for two additional orthorhombic phases labelled here as OIBAR and OIII. At high temperatures, there was no evidence for the decomposition of the OI phase into the T and OI phases. We find qualitative agreement with experimental observations and cluster-variation method results