Pair Distribution Function Method Research Articles

PDF Analysis of Bi0.9−xLa0.1TbxFeO3

Bi 0.9− x La 0.1 Tb x FeO 3 with x = 0.0 and 0.075 were synthesized by the solid-state reaction. Although it was difficult to obtain pure BiFeO 3 with single phase, the La-substituted Bi 0.9 La 0.1 FeO 3 can be obtained easily without any impurity phase. The Tb-substituted Bi 0.825 La 0.1 Tb 0.075 FeO 3 showed a well-saturated ferromagnetism. The average and local structures of the Bi 0.9 La 0.1 FeO 3 and Bi 0.825 La 0.1 Tb 0.075 FeO 3 crystals were analyzed by Rietveld refinement and pair-distribution function (PDF) method, respectively. The La and Tb atoms were completely substituted for the Bi, and lattice strain owing to different ionic radii was relaxed only by the bond distribution between the A-site atoms and the oxygen atoms.

Localversusaverage structure: a study of neighborite (NaMgF3) utilizing the pair distribution function method for structure determination

The temperature-dependent local structure (< 2 nm) of neighborite (NaMgF3) is probed through least-squares refinement of structure models fit to the pair distribution function [G(r)] derived from the total high-energy X-ray scattering of sample powders. In contrast to previous temperature-dependent structure models obtained through Rietveld refinement and statistical modelling of powder diffraction data, it is found that the average Mg—F bond length, corresponding to a ∼2 Å peak in theG(r), increases between 323 and 1123 K. At each temperature, asymmetry in this peak is consistent with an orthorhombic (Pbnm) perovskite local structure, allowing three unique Mg—F values and deformation of MgF6octahedra. Defined by the three orthogonal Mg—Mg distances, the pseudo-cubic unit cell of local structure models becomes metrically tetragonal and cubic at temperatures greater than ∼623 and 1038 K, respectively. A discontinuity in the temperature dependence of the fluorine atomic displacement parameters at 1038 K suggests thermal activation of new vibrational modes in NaMgF3at high temperature, consistent with transverse vibration of the bridging fluorine atoms (Mg—F—Mg).

Understanding the Insulating Phase in Colossal Magnetoresistance Manganites: Shortening of the Jahn-Teller Long-Bond across the Phase Diagram ofLa1−xCaxMnO3

The detailed evolution of the magnitude of the local Jahn-Teller (JT) distortion in La(1-x)Ca(x)MnO3 is obtained across the phase diagram for 0< or =x< or =0.5 from high-quality neutron diffraction data using the atomic pair distribution function method. A local JT distortion is observed in the insulating phase for all Ca concentrations studied. However, in contrast with earlier local structure studies, its magnitude is not constant, but decreases continuously with increasing Ca content. This observation is at odds with a simple small-polaron picture for the insulating state.

Analysis of Disordered Materials Using Total Scattering and the Atomic Pair Distribution Function

Without a doubt, our ability to determine the atomic structure of complex materials has revolutionized our understanding of these materials over the last decades. Neutron scattering with its unique abilities has contributed greatly to this success. The range of applications of neutron scattering in geosciences are apparent when reading through this volume of Reviews in Mineralogy & Geochemistry. Usual structure determination, the realm of crystallography, is based on the analysis of Bragg intensities. In this article we want to look beyond or underneath the Bragg peaks and discuss the atomic pair distribution function (PDF) method as an approach to more fully understand the atomic structure of complex materials, from the local to the medium range all the way to the long range structure of the material. As mentioned above, structure determination is commonly based on the analysis of Bragg peaks either using single crystal diffraction (Ross and Hoffman 2006, this volume) or powder diffraction (Harrison 2006, this volume). However, one needs to keep in mind, that the structure resulting from Bragg scattering is only the long range average structure of the material. Many materials owe their interesting properties to defects within the material and obviously a complete structural picture and understanding of the properties will require knowledge of the “true” atomic structure. Geological samples are no exception and in fact are among the most complex systems known. Deviations from the average structure, e.g., in form of defects, manifest themselves as diffuse scattering. This is illustrated in an example shown in Figure 1⇓. Two 2D structures have been simulated; both have the same lattice parameters, contain one atomic site in the unit cell as well as contain a total of 30% vacant sites. The difference is the vacancy ordering. Figure 1a⇓ shows the structure with a …

Atomic pair distribution function analysis of materials containing crystalline and amorphous phases

Abstract The atomic pair distribution function (PDF) approach has been used to study the local structure of liquids, glasses and disordered crystalline materials. In this paper, we demonstrate the use of the PDF method to investigate systems containing a crystalline and an amorphous structural phase. We present two examples: Bulk metallic glass with crystalline reinforcements and Fontainebleau sandstone, where an unexpected glassy phase was discovered. In this paper we also discuss the refinement methods used in detail.

Nanoscale clusters in the high performance thermoelectricAgPbmSbTem+2

The local structure of the $\mathrm{Ag}{\mathrm{Pb}}_{m}\mathrm{Sb}{\mathrm{Te}}_{m+2}$ series of thermoelectric materials has been studied using the atomic pair distribution function (PDF) method. Three candidate-models were attempted for the structure of this class of materials using either a one- or a two-phase modeling procedure. Combining modeling the PDF with HRTEM data we show that $\mathrm{Ag}{\mathrm{Pb}}_{m}\mathrm{Sb}{\mathrm{Te}}_{m+2}$ contains nanoscale inclusions with composition close to $\mathrm{Ag}{\mathrm{Pb}}_{3}\mathrm{Sb}{\mathrm{Te}}_{5}$ randomly embedded in a PbTe matrix.

Investigation of the Negative Thermal Expansion Mechanism of Zeolite Chabazite Using the Pair Distribution Function Method

We have used the pair distribution function (PDF) method to gain insight into the mechanism of contraction of zeolite chabazite. Using this method we followed how the interatomic distances of the local structure changed with temperature. By optimization of the structure by free energy minimization and using the Reverse Monte Carlo technique we were able to find structural models at low and at high temperatures that agreed quantitatively with our experimental PDFs. From these models we conclude that the mechanism of contraction with temperature cannot involve rocking of the tetrahedra as rigid unit modes as there are distortions of the tetrahedra with temperature (indicating internal vibrations) and also that the mechanism of contraction probably involves a mode that translates along the Si-O3-Si-O4-Si linkages inside of the D6R of zeolite chabazite.

A pair distribution function analysis of zeolite beta

We describe the structural refinement of zeolite beta using the local structure obtained with the pair distribution function (PDF) method. A high quality synchrotron and two neutron scattering datasets were obtained on two samples of siliceous zeolite beta. The two polytypes that make up zeolite beta have the same local structure; therefore refinement of the two structures was possible using the same experimental PDF. Optimized structures of polytypes A and B were used to refine the structures using the program PDFfit. Refinements using only the synchrotron or the neutron datasets gave results inconsistent with each other but a cyclic refinement with the two datasets gave a good fit to both PDFs. The results show that the PDF method is a viable technique to analyze the local structure of disordered zeolites. However, given the complexity of most zeolite frameworks, the use of both X-ray and neutron radiation and high-resolution patterns is essential to obtain reliable refinements.

High pressure study of a Zr-based bulk metallic glass and its composite

Abstract Energy dispersive X-ray diffraction was used to study the structural evolution of a bulk metallic glass (BMG) alloy and its composite with W particles under hydrostatic pressure. The diffraction data, especially the pair distribution function (PDF) of the BMG allowed the direct measurement of its elastic strain. The results suggest that PDF patterns of BMGs can be used to deducetheir strain evolution in composites as well as in monolithic form. Although the PDF method of strain measurement in amorphous alloys offers lower resolution compared to the analysis of Bragg reflections from crystalline materials, the PDF techique yields valuable information about the deformation of BMGs.

Role of framework sodium versus local framework structure in determining the hydrothermal stability of MCM-41 mesostructures.

Two mesostructured MCM-41 silicas that differ dramatically in hydrothermal stability have been examined by (29)Si MAS NMR spectroscopy and pair distribution function (PDF) analysis of synchrotron X-ray scattering data. The less stable mesostructure assembled from sodium silicate and the substantially more stable derivative made from fumed silica possess equivalent local framework wall structures, as judged by NMR and PDF methods. Approximately 80% of the SiO(4) tetrahedra are fully cross-linked as Q(4) (Si(OSi)(4)) units in both calcined samples. Additionally, the structural correlation distances for the two materials are nearly identical, having values of 1.62(1), approximately 2.60, and 3.09(1) A for the Si-O, O-O, and nearest neighbor Si-Si distances in the framework. Sodium ions in the framework play a crucial role in limiting the hydrothermal stability of the mesostructure. Residual sodium ( approximately 0.05-0.10% Na(2)O) is retained in the MCM-41 made from sodium silicate, even after two ion exchange reactions with ammonium ions in more than 300 - fold excess. The entrapped framework sodium ions catalyze the collapse of the mesopores upon exposure to 20% steam at 800 degrees C for 5 h. The sodium - free mesostructure assembled from fumed silica retains an open framework under the same hydrothermal conditions. The stability of the fumed silica derivative, however, is greatly compromised when doped with as little as 0.10% Na(2)O, thus confirming the deleterious effect of sodium on hydrothermal stability.

Molecular Dynamics Simulations of the Variation of Structure and Energy in the Solidification of Liquid Au

Bymeans of molecular dynamics simulation technique,the solidification processes of Au under different cooling velocity has been studied.It has been concluded that the cooling velocity is critical to the structure of Au.With pair distribution function and pairsanalysis method,the local symmetry of molecular-cluster has been analyzed.The variations of potential energy with the temperature and the relationship between the energy and the structure of molecular-cluster have also been studied.From the eye of the variation of energy,the conclusion has been discussed.

Probing the short-range order and dynamics of phase transitions using neutron powder diffraction

We report evidence that the local structure of the perovskite based material, La 2 − x Ba x CuO 4, is disordered. The disorder takes the form of inhomogeneous octahedral tilts. The average crystal structure is a superposition of the local tilting environments. The local symmetry is different from the average, long-range order, and local bond lengths deviate from those obtained from the crystallographic coordinates. This has implications for band structure calculations based on the crystallographic coordinates. We discuss the implications of the local structure for understanding the microscopic origin for the phase transitions in this material. The evidence presented is from neutron powder diffraction data analyzed using the pair distribution function method. We describe this method and mention possible extensions to this method for extracting local dynamics at phase transitions.

Determining medium range order by powder diffraction

The method of atomic pair-distribution function (PDF) analysis of powder diffraction data, applied to the study of short-to-medium range atomic order in crystalline solids, is described. In real crystalline materials local atomic order is sometimes significantly different from the long range crystallographic lattice structure, due to lattice defects or some other local effects. While various physical properties are affected by such short and intermediate range order, there is not a wealth of experimental methods that can effectively characterize the local atomic order. We suggest that the PDF method coupled with the real space analysis is one of the most effective tools for this purpose.