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Pair Distribution Function (pair + distribution_function)
Selected AbstractsPair distribution functions calculated from interatomic potential models using the General Utility Lattice ProgramJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 3 2007Elizabeth R. Cope A new module has been developed for the widely used General Utility Lattice Program (GULP). The phonon-based theory developed by Chung & Thorpe [Phys. Rev. B (1999), 59, 4807,4812] to calculate pair distribution function (PDF) peak widths has been utilized to give a selection of commonly used correlation functions. A numerical library of neutron scattering information is now available within GULP, and is used to produce results that can be compared with neutron scattering experimental data. The influence of different phonon modes on the PDF can be assessed by excluding modes above or below a cut-off frequency. Results are presented for sample crystallographic systems, MgO, SrTiO3 and ,-cristobalite, as well as CaxSr1,xTiO3 at x = 0.5, which makes use of the capability to handle partial occupancies to compare different Ca/Sr ordering arrangements with a disordered model in which every Ca/Sr site has 50% occupancy of both species. [source] Local 3D real space atomic structure of the simple icosahedral Ho11Mg15Zn74 quasicrystal from PDF dataCRYSTAL RESEARCH AND TECHNOLOGY, Issue 12 2003S. Brühne Abstract We present a new complementary strategy to quasicrystalline structure determination: The local atomic structure of simple icosahedral (si) Ho11Mg15Zn74 [a(6D) = 5.144(3)Å in a sphere of up to r = 17Å was refined using the atomic pair distribution function (PDF) from in-house X-ray powder diffraction data (MoK,1, Qmax = 13.5Å,1; R = 20.4%). The basic building block is a 105-atom Bergman-Cluster {Ho8Mg12Zn85}. Its center is occupied by a Zn atom , in contrast to a void in face centred icosahedral (fci) Ho9Mg26Zn65. The center is then surrounded by another 12 Zn atoms, forming an icosahedron (1st shell). The 2nd shell is made up of 8 Ho atoms arranged on the vertices of a cube which in turn is completed to a pentagon dodecahedron by 12 Mg atoms, the dodecahedron then being capped by 12 Zn atoms. The 3rd shell is a distorted soccer ball of 60 Zn atoms, reflecting the higher Zn content of the si phase compared to the fci phase. In our model, 7% of all atoms are situated in between the clusters. The model corresponds to a hypothetical 1/1-approximant of the icosahedral (i) phase. The local coordinations of the single atoms are of a much distorted Frank-Kasper type and call to mind those present in 0/1-Mg2Zn11. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] H2xMnxSn3-xS6 (x,=,0.11,0.25): A Novel Reusable Sorbent for Highly Specific Mercury Capture Under Extreme pH ConditionsADVANCED FUNCTIONAL MATERIALS, Issue 7 2009Manolis J. Manos Abstract The H2xMnxSn3-xS6 (x,=,0.11,0.25) is a new solid acid with a layered hydrogen metal sulfide (LHMS). It derives from K2xMnxSn3,xS6 (x,=,0.5,0.95) (KMS-1) upon treating it with highly acidic solutions. We demonstrate that LHMS-1 has enormous affinity for the very soft metal ions such as Hg2+ and Ag+ which occurs via a rapid ion exchange process. The tremendous affinity of LHMS-1 for Hg2+ is reflected in very high distribution coefficient KdHg values (>106,mL g,1). The large affinity and selectivity of LHMS-1 for Hg2+ persists in a very wide pH range (from less than zero to nine) and even in the presence of highly concentrated HCl and HNO3 acids. LHMS-1 is significantly more selective for Hg2+ and Ag+ than for the less soft cations Pb2+ and Cd2+. The Hg2+ ions are immobilized in octahedral sites between the sulfide layers of the materials via Hg,S bonds as suggested by pair distribution function (PDF) analysis. LHMS-1 could decrease trace concentrations of Hg2+ (e.g. <100,ppb) to well below the acceptable limits for the drinking water in less than two min. Hg-laden LHMS-1 shows a remarkable hydrothermal stability and resistance in 6,M HCl solutions. LHMS-1 could be regenerated by treating Hg-loaded samples with 12,M HCl and re-used without loss of its initial exchange capacity. [source] Pair distribution functions calculated from interatomic potential models using the General Utility Lattice ProgramJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 3 2007Elizabeth R. Cope A new module has been developed for the widely used General Utility Lattice Program (GULP). The phonon-based theory developed by Chung & Thorpe [Phys. Rev. B (1999), 59, 4807,4812] to calculate pair distribution function (PDF) peak widths has been utilized to give a selection of commonly used correlation functions. A numerical library of neutron scattering information is now available within GULP, and is used to produce results that can be compared with neutron scattering experimental data. The influence of different phonon modes on the PDF can be assessed by excluding modes above or below a cut-off frequency. Results are presented for sample crystallographic systems, MgO, SrTiO3 and ,-cristobalite, as well as CaxSr1,xTiO3 at x = 0.5, which makes use of the capability to handle partial occupancies to compare different Ca/Sr ordering arrangements with a disordered model in which every Ca/Sr site has 50% occupancy of both species. [source] The Effects of Temperature on the Local Structure of Metakaolin-Based Geopolymer Binder: A Neutron Pair Distribution Function InvestigationJOURNAL OF THE AMERICAN CERAMIC SOCIETY, Issue 10 2010Claire E. White Neutron pair distribution function (PDF) analysis is utilized to advance the understanding of the local atomic structural characteristics of geopolymer binders derived from metakaolin, specifically the nature and amount of the water associated with these materials. Samples were heated in air to temperatures up to 1200°C, then analyzed ex situ by high momentum transfer neutron total scattering and PDF analysis. Water contained in large pores, along with water associated with hydration of potassium cations in the geopolymer framework structure, comprise the majority of water in this material. The remaining water is situated in small pores and as terminal hydroxyl groups attached to the Si,Al framework. The Si,Al framework structure undergoes only subtle rearrangement upon heating, but maintains a tetrahedral aluminosilicate framework environment. After crystallization with heating beyond 1000°C, the geopolymer gel is predominantly converted to leucite, with small amounts of amorphous mullite and glassy silica, which have never before been observed in heated geopolymers. This demonstrates the value of neutron PDF analysis to probe the local structure of these important geopolymeric materials. [source] Temperature and Pressure Effects on Local Structure and Chain Packing in cis -1,4-Polybutadiene from Detailed Molecular Dynamics SimulationsMACROMOLECULAR THEORY AND SIMULATIONS, Issue 5 2006Georgia Tsolou Abstract Summary: We present results for the temperature and pressure dependence of local structure and chain packing in cis -1,4-polybutadiene (cis -1,4-PB) from detailed molecular dynamics (MD) simulations with a united-atom model. The simulations have been executed in the NPT statistical ensemble with a parallel, multiple time step MD algorithm, which allowed us to access simulation times up to 1 µs. Because of this, a 32 chain C128cis -1,4-PB system was successfully simulated over a wide range of temperature (from 430 to 195 K) and pressure (from 1 atm to 3 kbar) conditions. Simulation predictions are reported for the temperature and pressure dependence of the: (a) density; (b) chain characteristic ratio, Cn; (c) intermolecular pair distribution function, g(r), static structure factor, S(q), and first peak position, Qmax, in the S(q) pattern; (d) free volume around each monomer unit along a chain for the simulated polymer system. These were thoroughly compared against available experimental data. One of the most important findings of this work is that the component of the S(q) vs. q plot representing intramolecular contributions in a fully deuterated cis -1,4-PB sample exhibits a monotonic decrease with q which remains completely unaffected by the pressure. In contrast, the intermolecular contribution exhibits a distinct peak (at around 1.4 Å,1) whose position shifts towards higher q values as the pressure is raised, accompanied by a decrease in its intensity. 3D view of the simulation box containing 32 chains of C128cis -1,4-polybutadiene at density ,,=,0.849 g,·,cm,3 and the conformation of a single C128cis -1,4-PB chain fully unwrapped in space. [source] Relationship between the atomic pair distribution function and small-angle scattering: implications for modeling of nanoparticlesACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2009Christopher L. Farrow The relationship between the equations used in the atomic pair distribution function (PDF) method and those commonly used in small-angle-scattering (SAS) analyses is explicitly shown. The origin of the sloping baseline, ,4,r,0, in PDFs of bulk materials is identified as originating from the SAS intensity that is neglected in PDF measurements. The nonlinear baseline in nanoparticles has the same origin, and contains information about the shape and size of the nanoparticles. [source] Equation of State of Strongly Coupled Quark,Gluon Plasma , Path Integral Monte Carlo ResultsCONTRIBUTIONS TO PLASMA PHYSICS, Issue 7-8 2009V.S. Filinov Abstract A strongly coupled plasma of quark and gluon quasiparticles at temperatures from 1.1Tc to 3Tc is studied by path integral Monte Carlo simulations. This method extends previous classical nonrelativistic simulations based on a color Coulomb interaction to the quantum regime. We present the equation of state and find good agreement with lattice results. Further, pair distribution functions and color correlation functions are computed indicating strong correlations and liquid-like behavior (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Necessary conditions for the N -representability of pair distribution functionsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 7 2006Paul W. Ayers Abstract A necessary condition for the N -representability of the electron pair density proposed by one of the authors (E. R. D.) is generalized. This shows a link between this necessary condition and other, more widely known, N -representability conditions for the second-order density matrix. The extension to spin-resolved electron pair densities is considered, as is the extension to higher-order distribution functions. Although quantum mechanical systems are our primary focus, the results are also applicable to classical systems, where they reduce to an inequality originally derived by Garrod and Percus. As a simple application, bounds to the average angle between an electron pair are derived. It is shown that computational methods based on variational minimization of the energy with respect to the electron pair density can give extremely poor results unless robust N -representability constraints are considered. For reference, constraints for the N -representability of the pair density are summarized. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [source] Characterization of amorphous API:Polymer mixtures using X-ray powder diffractionJOURNAL OF PHARMACEUTICAL SCIENCES, Issue 11 2008Ann Newman Abstract Recognizing limitations with the standard method of determining whether an amorphous API,polymer mixture is miscible based on the number of glass transition temperatures (Tg) using differential scanning calorimetry (DSC) measurements, we have developed an X-ray powder diffraction (XRPD) method coupled with computation of pair distribution functions (PDF), to more fully assess miscibility in such systems. The mixtures chosen were: dextran,poly(vinylpyrrolidone) (PVP) and trehalose,dextran, both prepared by lyophilization; and indomethacin,PVP, prepared by evaporation from organic solvent. Immiscibility is detected when the PDF profiles of each individual component taken in proportion to their compositions in the mixture agree with the PDF of the mixture, indicating phase separation into independent amorphous phases. A lack of agreement of the PDF profiles indicates that the mixture with a unique PDF is miscible. In agreement with DSC measurements that detected two independent Tg values for the dextran,PVP mixture, the PDF profiles of the mixture matched very well indicating a phase separated system. From the PDF analysis, indomethacin,PVP was shown to be completely miscible in agreement with the single Tg value measured for the mixture. In the case of the trehalose,dextran mixture, where only one Tg value was detected, however, PDF analysis clearly revealed phase separation. Since DSC can not detect two Tg values when phase separation produces amorphous domains with sizes less than approximately 30 nm, it is concluded that the trehalose,dextran system is a phase separated mixture with a structure equivalent to a solid nanosuspension having nanosize domains. Such systems would be expected to have properties intermediate to those observed for miscible and macroscopically phase separated amorphous dispersions. However, since phase separation has occurred, the solid nanosuspensions would be expected to exhibit a greater tendency for physical instability under a given stress, that is, crystallization, than would a miscible system. © 2008 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 97:4840,4856, 2008 [source] A new approach to calculating powder diffraction patterns based on the Debye scattering equationACTA CRYSTALLOGRAPHICA SECTION A, Issue 1 2010Noel William Thomas A new method is defined for the calculation of X-ray and neutron powder diffraction patterns from the Debye scattering equation (DSE). Pairwise atomic interactions are split into two contributions, the first from lattice-pair vectors and the second from cell-pair vectors. Since the frequencies of lattice-pair vectors can be directly related to crystallite size, application of the DSE is thereby extended to crystallites of lengths up to ~200,nm. The input data correspond to unit-cell parameters, atomic coordinates and displacement factors. The calculated diffraction patterns are characterized by full backgrounds as well as complete reflection profiles. Four illustrative systems are considered: sodium chloride (NaCl), ,-quartz, monoclinic lead zirconate titanate (PZT) and kaolinite. The effects of varying crystallite size on diffraction patterns are calculated for NaCl, quartz and kaolinite, and a method of modelling static structural disorder is defined for kaolinite. The idea of partial diffraction patterns is introduced and a treatment of atomic displacement parameters is included. Although the method uses pair distribution functions as an intermediate stage, it is anticipated that further progress in reducing computational times will be made by proceeding directly from crystal structure to diffraction pattern. [source] | ||||||||||||||||