Use of radial symmetry for the calculation of cylindrical absorption coefficients and optimal capillary loadings
Abstract
The problem of numerically evaluating absorption correction factors for cylindrical samples has been revisited using a treatment that fully takes advantage of the sample symmetry. It is shown that the path lengths for all points within the sample at all possible diffraction angles can be trivially determined once the angledependent distance distribution for a single line of points is calculated. This provides advantages both in computational efficiency and in gaining an intuitive understanding of the effects of absorption on the diffraction data. A matrix of absorption coefficients calculated for μRproducts between 0 and 20 for diffraction angles θ _{D}of 0–90° were used to examine the influence of (1) capillary diameter and (2) sample density on the overall scattered intensity as a function of diffraction angle, where μ is the linear absorption coefficient for the sample andRis the capillary radius. On the basis of this analysis, the optimal sample loading for a capillary experiment to maximize diffraction at angles of 0–50° is in general expected to be achieved when the maximum radius capillary compatible with the beam is used and when the sample density is adjusted to be 3/(4μR) of its original density.
 Authors:
 Publication Date:
 Research Org.:
 Argonne National Lab. (ANL), Argonne, IL (United States). Advanced Photon Source (APS)
 Sponsoring Org.:
 National Science Foundation (NSF)
 OSTI Identifier:
 1324787
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Applied Crystallography (Online); Journal Volume: 48; Journal Issue: 1
 Country of Publication:
 United States
 Language:
 ENGLISH
Citation Formats
Khalifah, Peter. Use of radial symmetry for the calculation of cylindrical absorption coefficients and optimal capillary loadings. United States: N. p., 2015.
Web. doi:10.1107/S1600576714026569.
Khalifah, Peter. Use of radial symmetry for the calculation of cylindrical absorption coefficients and optimal capillary loadings. United States. doi:10.1107/S1600576714026569.
Khalifah, Peter. Fri .
"Use of radial symmetry for the calculation of cylindrical absorption coefficients and optimal capillary loadings". United States.
doi:10.1107/S1600576714026569.
@article{osti_1324787,
title = {Use of radial symmetry for the calculation of cylindrical absorption coefficients and optimal capillary loadings},
author = {Khalifah, Peter},
abstractNote = {The problem of numerically evaluating absorption correction factors for cylindrical samples has been revisited using a treatment that fully takes advantage of the sample symmetry. It is shown that the path lengths for all points within the sample at all possible diffraction angles can be trivially determined once the angledependent distance distribution for a single line of points is calculated. This provides advantages both in computational efficiency and in gaining an intuitive understanding of the effects of absorption on the diffraction data. A matrix of absorption coefficients calculated for μRproducts between 0 and 20 for diffraction angles θDof 0–90° were used to examine the influence of (1) capillary diameter and (2) sample density on the overall scattered intensity as a function of diffraction angle, where μ is the linear absorption coefficient for the sample andRis the capillary radius. On the basis of this analysis, the optimal sample loading for a capillary experiment to maximize diffraction at angles of 0–50° is in general expected to be achieved when the maximum radius capillary compatible with the beam is used and when the sample density is adjusted to be 3/(4μR) of its original density.},
doi = {10.1107/S1600576714026569},
journal = {Journal of Applied Crystallography (Online)},
number = 1,
volume = 48,
place = {United States},
year = {Fri Jan 30 00:00:00 EST 2015},
month = {Fri Jan 30 00:00:00 EST 2015}
}

The problem of numerically evaluating absorption correction factors for cylindrical samples has been revisited using a treatment that fully takes advantage of the sample symmetry. It is shown that the path lengths for all points within the sample at all possible diffraction angles can be trivially determined once the angledependent distance distribution for a single line of points is calculated. This provides advantages in both computational efficiency and in gaining an intuitive understanding of the effects of absorption on diffraction data. A matrix of absorption coefficients calculated for µR products between 0 and 20 for diffraction angles θ _{D} ofmore »

Bohmcriterion approximation versus optimal matched solution for a cylindrical probe in radialmotion theory
The theory of positiveion collection by a probe immersed in a lowpressure plasma was reviewed and extended by Allen et al. [Proc. Phys. Soc. 70, 297 (1957)]. The numerical computations for cylindrical and spherical probes in a sheath region were presented by F. F. Chen [J. Nucl. Energy C 7, 41 (1965)]. Here, in this paper, the sheath and presheath solutions for a cylindrical probe are matched through a numerical matching procedure to yield “matched” potential profile or “M solution.” The solution based on the Bohm criterion approach “B solution” is discussed for this particular problem. The comparison of cylindricalmore »