Tests of the empirical potential structure refinement method and a new method of application to neutron diffraction data on water

Empirical potential structure refinement (EPSR) is a method for developing a structural model of a liquid for which diffraction measurements are available. The EPSR technique involves refining a starting interatomic potential energy function in a way that produces the best possible agreement between the simulated and measured site-site partial structure factors. Here a series of test simulations are performed to establish how well the EPSR method can recover the interatomic potential for a single component fluid of Lennard-Jones particles, and for a binary fluid consisting of charged atoms interacting at short range by a Lennard-Jones potential. Special attention is given to the problem of developing an accurate interatomic potential for water using these procedures. An alternative method for perturbing the starting potential is used to obtain the best possible fit to the diffraction data. The resulting parametrization of the water potential is in contrast to many existing effective potentials for water, and indicates that water molecules in the liquid at ambient conditions are highly polarized, as has been suggested in recent ‘first-principles’ simulations of water. Three-body correlation functions and spatial density functions derived from the EPSR simulations show excellent agreement with those obtained with the model potential simulations. However, the potentials extracted by EPSR are found to depend on the constraints applied to the hardness of the core potential and the energy and pressure of the simulation, even when the fits to the data are equally good. It is concluded that performing EPSR on diffraction data can be used as a good test for interatomic potentials and to derive reliable many-body structures in the liquid state, but cannot on its own be used to derive a reliable set of site-site pair potentials for a particular system.     

Combined Rietveld refinement of BaMgAl10O17:Eu using X-ray and neutron powder diffraction data

The phosphor, BaMgAl₁₀O₁₇:Eu²⁺, showing a blue emission band at about 450 nm was prepared by a normal solid-state reaction using BaCO₃, Al₂O₃, MgO and Eu₂O₃ as starting materials with AlF₃ as a flux. The study of combined Rietveld refinement and photoluminescence spectra was carried out to determine the structural parameters, such as lattice constants, the valence state of Eu, the site preference of Mg and site fractions of Mg and Eu. The occupancies of Eu and Mg were 0.022 and 0.526, respectively. The valence state of Eu was the divalent state because there was only one broad line at about 450 nm in the photoluminescence spectrum. The site preference of Mg atoms was the tetrahedral site of Al atoms surrounded by oxygen atoms in the spinel block. Lattice parameters decreased due to the difference of two ionic radii, Eu²⁺(1.09 Å) and Ba²⁺(1.34 Å), compared with those of BaMgAl₁₀O₁₇.     

Crystal structure refinement at high pressures using angle-dispersive powder diffraction techniques

Abstract

The development of area detectors such as the imaging plate (IP) allows the use of angle-dispersive techniques for powder diffraction studies at high pressure. Integration of the 2-d pattern greatly improves the powder averaging and signal-to-noise ratio, making it possible to carry out full Rietveld refinements of crystal structures in high-pressure phases. An IP system is being developed at the Synchrotron Radiation Source (SRS), Daresbury, and the current status of this system -hardware and software -is described. Recent results on La₂CuO₄ and lnSb demonstrate the effectiveness and advantages of the techniques.     

Normalisation and assessment of neutron diffraction data from liquids

A couple of normalisation criteria have been proposed to assess liquid structure data over the past decade. In this paper, a critical examination of these and other plausible criteria is made. Neutron diffraction data from liquid krypton measured by Clayton and Heaton is used to study these criteria. It is shown that if the structure factorS (Q)=1+γ (Q) satisfies the Krogh-Moe relation, namely whereQ is the wavevector transfer andρ ₀ the mean atomic number density,S (Q) is properly normalised. Subjecting such data to the other criteria would reveal, however, the quality of data in so far as systematic errors and/or termination errors are concerned. If the data is measured with reasonable accuracy to sufficiently large values of the wavevector transfer all these criteria would assess the quality of the data to almost the same extent. This is established in this paper by improving and extending the liquid krypton data by procedures similar to that of Kaplow, Strong and Averbach and subjecting this revised data to the various criteria. It is concluded, thereby, that (i) one can study the neutron diffraction data from liquids using any of the criteria mentioned in the paper to improve the quality of the data and (ii) for normalisation purposes the simple relation {ie328-2} would suffice.     

CO2–water supercritical mixtures: Test of a potential model against neutron diffraction data

A neutron diffraction experiment on supercritical mixtures of water and CO₂ at two concentrations is presented. Data are analyzed within the EPSR framework and the water–water and water–CO₂ radial distribution functions are compared with those calculated by a Molecular Dynamics simulation performed by using the TIPS2 and EPM-M potential models for water and CO₂ respectively. It is found that the Molecular Dynamics simulation reproduces the overall shape of the site–site radial distribution functions, although missing a few subtle changes brought along when the CO₂ concentration is increased.     

Study of the atomic structure and dynamics of Cu-Fe nanocomposites by X-ray diffraction and inelastic neutron scattering

The atomic structure and the dynamics of Cu_{1 ? x} Fe _x samples (x = 0.15, 0.5, and 0.85) obtained by melt spinning from the elements that are immiscible under standard conditions has been investigated. The change in the physical properties of the system obtained in this way is due to the formation of nanocrystallites.     

Liquid metal pair potentials from structure data

In linear screening theory, the zeroth order result is the equality of the potential of mean force and the pair potential. The Kirkwood superposition approximation holds to the same order.The next order yields an equation for the pair potential identical with the first order iteration of Johnson and March from the Born-Green equation.     

Magnetic ordering in Mn<Subscript>3</Subscript>Sb determined by neutron diffraction data

The magnetic structure of a new Mn₃Sb compound in the Mn-Sb system being characterized by the ferromagnetic ordering of Mn I and Mn II magnetoactive atoms with magnetic moments differing in magnitude is determined by the neutron diffraction technique. The proposed model of magnetic structure is in agreement with the magnetometry data, Mössbauer spectroscopy, and principles of symmetry analysis.     

Magnetic structure of ErCo10Mo2 and TbCo10Mo2 determined by time-of-flight neutron powder diffraction

The crystal and magnetic structures of tetragonal compounds ErCo₁₀Mo₂ and TbCo₁₀Mo₂ (space group I₄/mmm) have been investigated by time-of-flight neutron powder diffraction at 5 K. The compound ErCo₁₀Mo₂ is planar at 5 K whilst TbCo₁₀Mo₂ remains axial even at low temperatures. The magnetic moments of the three Co sublattices have been determined, with moments of 1.0(0.2)μ _B , 0.8(0.2)μ _B and 0.8(0.2)μ _B for 8i, 8j and 8f sites respectively. The Er and Tb moments are reduced by approximately 7% from their free-ion values by the action of the tetragonal crystal field.     

Warble in carillon bells: An investigation using neutron diffraction

It is speculated that warble in carillon bells can be caused by mode splitting as a result of internal strains produced by non-uniform cooling during casting. The neutron diffraction technique makes possible the measurement of internal strain and is here applied to a in (166 mm) carillon bell with a pronounced 3 Hz warble. Internal strain variations with a 180° periodicity about the bell circumference were detected. From symmetry considerations this periodicity requires that all partials (other than m = 0) should have their doublets split. Measurements of the bell partials confirmed this splitting. The metallographic phases present in the bell metal were also determined and found to agree with expectations.     

Electronic structure of GdP as determined from optical data

The growth of large single crystals of GdP of various stoichiometry has permitted for the first time accurate measurements of the reflectivity for photon energies from 0.03 to 12 eV. By means of a Kramers-Kronig analysis it was possible to separate intra- and interband transitions. The latter ones have provided valuable information about the structure of the 5d conduction band, its crystal field splitting and the position in energy of the 4f levels of Gd³⁺. The variation of the plasma resonance with deviations from stoichio-iometry does not exclude a semimetallic behavior of GdP.     

Magnetic structure of LaCrO3 perovskite under high pressure from in situ neutron diffraction

The temperature-pressure phase diagram for both the crystal and magnetic structures of LaCrO(3) perovskite has been mapped out by in situ neutron-diffraction experiments under pressure. The system offers the opportunity to study the evolution of magnetic order, spin direction, and magnetic moment on crossing the orthorhombic-rhombohedral phase boundary. Moreover, a microscopic model of the superexchange interaction has been developed on the basis of the crystal structure obtained in this work to account for the behavior of T(N) under high pressure.     

CO2 motion in carbon dioxide deuterohydrate determined by applying maximum entropy method to neutron powder diffraction data

Crystal structures of carbon dioxide deuterohydrate were studied by neutron powder diffraction at temperatures from 10 to 200 K. Maps of scattering length density distribution were obtained using a maximum entropy method (MEM), which clarified the motion of CO₂ molecules in the hydrate. In small cages, the carbon atom of the CO₂ molecule is at the center of the cage, and the oxygen atoms of CO₂ revolve freely around the carbon atom. In large cages, the carbon atom also is at the center of the cage, but the oxygen atoms tend to revolve around the carbon atom along the plane parallel to the hexagonal facets of the cage.