Studies on the Radial Distribution Analysis in Diffraction Methods I. Errors due to the Approximation of Integration by Summation

1957 ◽  
Vol 12 (5) ◽  
pp. 495-499 ◽  
Author(s):  
Tadashi Ino
Keyword(s):  
Radial Distribution ◽  
Distribution Analysis

scholarly journals On the Use of a Modified Radial Distribution Analysis for Indexing Powder Patterns

1962 ◽  
Vol 6 ◽  
pp. 18-24
Author(s):  
A. F. Berndt
Keyword(s):  
Radial Distribution ◽  
Unit Cell ◽  
Powder Pattern ◽  
Distribution Analysis ◽  
Trial And Error ◽  
Orthorhombic Unit Cell ◽  
X Ray ◽  
Tetragonal Unit Cell ◽  
Cell Dimensions ◽  
Unit Cell Dimensions

AbstractA modification of the theory of X-ray radial distribution analysis is presented. This modification can serve as a guide to the values of the unit cell dimensions and may be useful in indexing powder patterns of unknown structures, although the use of trial and error methods is not eliminated. This technique is shown to give consistent results with known structures and is applied to the indexing of powder patterns of Pu3Ru and Pu5Ru3. The powder pattern of Pu3Ru can be indexed on the basis of an orthorhombic unit cell with a0 = 6.216 Å, b0 = 6.924 Å, and c0 = 8.093 Å, and Pu5Ru3 on the basis of a tetragonal unit cell with a0 = 8.092 Å and c0 - 10.023 Å.

Characterization of the Structure of a Novel Refractory Alloy Glass – Ni60Nb37Sn3

2002 ◽  
Vol 754 ◽  
Author(s):  
Michelle L. Tokarz ◽  
Matt Daniels ◽  
John C. Bilello ◽  
Zofia Rek
Keyword(s):  
Radial Distribution ◽  
Metallic Glasses ◽  
Hard Sphere ◽  
Nearest Neighbor ◽  
Refractory Alloy ◽  
Scattering Data ◽  
Distribution Analysis ◽  
X Ray ◽  
Nearest Neighbor Distances

ABSTRACTBulk forms of Refractory Alloy Glasses (RAGs) of the composition Ni60Nb37Sn3 have recently been synthesized as part of a larger project for potential use in structural applications. Modeling efforts of such metallic glasses have traditionally involved the use of hard sphere models without regard to potential electron density fluctuations of individual components. X-ray characterization of these materials (in both reflection and transmission modes) provided scattering data necessary for subsequent radial distribution analysis, which gives structural information such as nearest neighbor distances and packing characteristics. A model radial distribution function (RDF) was constructed based upon a hard sphere space filling assumption and compared to the RDFs obtained from experimental scattering data. The experimental RDFs showed no difference from the model RDF within the limit of experimental error, with regard to nearest neighbor distances and coordination numbers of the first two nearest neighbors.Additionally, transmission mode scattering experiments from a white beam x-ray source (E = 2 to 40 keV) demonstrated a through thickness amorphous structure of 2mm thick samples. Converted line profiles from the two-dimensional diffraction patterns from this experiment also showed agreement with reflection mode experiments. Samples of Vitreloy-106 (Zr57Nb5Cu15.4Ni12.6Al10) of similar thicknesses were used as standards due to the well-known behavior of this particular class of metallic glasses.

On the Structural Characterization of a Series of Novel Ni-Nb-Sn Refractory Alloy Glasses

2003 ◽  
Vol 806 ◽  
Author(s):  
Michelle L. Tokarz ◽  
John C. Bilello
Keyword(s):  
Radial Distribution ◽  
Hard Sphere ◽  
Alloy Composition ◽  
Distribution Functions ◽  
Refractory Alloy ◽  
Distribution Analysis ◽  
X Ray Diffraction ◽  
Characterization Methods ◽  
X Ray ◽  
Hard Sphere Models

ABSTRACTRecently refractory alloy glasses of varying Ni, Nb and Sn concentrations were prepared and studied via several characterization methods, including x-ray diffraction via standard lab and synchrotron radiation sources, SEM, and other complementary techniques. A comparison between x-ray diffraction results obtained from synchrotron sources vs. standard lab sources shows the necessity of a low-divergence source in order to distinguish nanoscale crystallites present within an amorphous matrix. The divergence of both sources was determined by comparing the diffraction patterns of a LaB6standard and noting the deviation from ideal or theoretical Bragg peaks. The crystallites in these glasses comprised between 0 and 7.5 percent by volume, depending upon the specific composition. The results presented here also show a very good sample-to-sample consistency for any given alloy composition. While x-ray diffraction results give information about the average structure, SEM was also performed to understand aspects of individual crystallite size and distribution. By studying results of varying alloy concentrations, it is seen that a very small composition range exists for near-perfect glass formers (as defined by a near zero percentage crystallinity). Radial distribution analysis was also performed for each composition and compared to hard sphere models for each alloy composition. This analysis indicated the presence of intermediate range order beyond the first nearest neighbors as indicated by the divergence of the experimental reduced radial distribution functions from that predicted by the accompanying hard sphere models.

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