## 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 angle-dependent 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} of 0° to 90° were used to examine the influence of (1) capillary diameter and of (2) sample density on the overall scattered intensity as a function of diffraction angle, where µ is the linear absorption coefficient for the sample and R is the capillary radius. Based on 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:

- Stony Brook Univ., NY (United States); Brookhaven National Lab., Upton, NY (United States)

- Publication Date:

- Research Org.:
- Brookhaven National Laboratory (BNL), Upton, NY (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1183834

- Report Number(s):
- BNL-107865-2015-JA

Journal ID: ISSN 1600-5767; JACGAR; R&D Project: CO009; KC0302010

- Grant/Contract Number:
- SC00112704

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Applied Crystallography (Online)

- Additional Journal Information:
- Journal Name: Journal of Applied Crystallography (Online); Journal Volume: 48; Journal Issue: 1; Journal ID: ISSN 1600-5767

- Publisher:
- International Union of Crystallography

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

### 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. Sun .
"Use of radial symmetry for the calculation of cylindrical absorption coefficients and optimal capillary loadings". United States. doi:10.1107/S1600576714026569. https://www.osti.gov/servlets/purl/1183834.
```

```
@article{osti_1183834,
```

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 angle-dependent 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 θD of 0° to 90° were used to examine the influence of (1) capillary diameter and of (2) sample density on the overall scattered intensity as a function of diffraction angle, where µ is the linear absorption coefficient for the sample and R is the capillary radius. Based on 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 = {2015},

month = {2}

}