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Let us now apply Euler's method again with a different step size to generate a second approximation to y(t n+1). We get a second solution, which we label with a (). Take the new step size to be one half of the original step size, and apply two steps of Euler's method. This second solution is presumably more accurate.
The first implementation of the technique at synchrotron facilities was performed in 1998 by Kleuker et al. [2] X-ray diffraction computed tomography can be divided into two main categories depending on how the XRD data are being treated, specifically the XRD data can be treated either as powder diffraction or single crystal diffraction data ...
This is a list of free and open-source software for geological data handling and interpretation. The list is split into broad categories, depending on the intended use of the software and its scope of functionality. Notice that 'free and open-source' requires that the source code is available and users are given a free software license.
It is an X-ray-diffraction [2] method and commonly used to determine a range of information about crystalline materials. The term WAXS is commonly used in polymer sciences to differentiate it from SAXS but many scientists doing "WAXS" would describe the measurements as Bragg/X-ray/powder diffraction or crystallography .
Free-electron lasers have been developed for use in X-ray diffraction and crystallography. [27] These are the brightest X-ray sources currently available; with the X-rays coming in femtosecond bursts. The intensity of the source is such that atomic resolution diffraction patterns can be resolved for crystals otherwise too small for collection.
The Scherrer equation, in X-ray diffraction and crystallography, is a formula that relates the size of sub-micrometre crystallites in a solid to the broadening of a peak in a diffraction pattern. It is often referred to, incorrectly, as a formula for particle size measurement or analysis.
Furthermore, a Patterson map of N points will have N(N − 1) peaks, excluding the central (origin) peak and any overlap. The peaks' positions in the Patterson function are the interatomic distance vectors and the peak heights are proportional to the product of the number of electrons in the atoms concerned.
Dr. Miller had done research on X-ray instrumentation at Washington University in St. Louis. Dr. Duffendack also hired Dr. Bill Parish, a well known researcher in X-ray diffraction, to head up the section of the lab on X-ray instrumental development. X-ray diffraction units were widely used in academic research departments to do crystal analysis.