Hostname: page-component-74656f9884-54qdv Total loading time: 0 Render date: 2026-11-10T06:33:22.084Z Has data issue: false hasContentIssue false
  • English
  • Français

The effect of particles on the absorption factor for diffracted X-rays in single-phase powders measured at cylindrical geometry— a computational study

Published online by Cambridge University Press:  10 January 2013

J. Collazo ,
H. Hermann ,
A. Teresiak  and
K. Wetzig
J. Collazo
Affiliation:
Institute of Solid State and Materials Research Dresden, Postfach 270016, D-01171 Dresden, Germany
H. Hermann
Affiliation:
Institute of Solid State and Materials Research Dresden, Postfach 270016, D-01171 Dresden, Germany
A. Teresiak
Affiliation:
Institute of Solid State and Materials Research Dresden, Postfach 270016, D-01171 Dresden, Germany
K. Wetzig
Affiliation:
Institute of Solid State and Materials Research Dresden, Postfach 270016, D-01171 Dresden, Germany
Get access

Abstract

The results of computer simulations of the absorption of diffracted X-rays in single-phase powders measured at cylindrical (or Debye–Scherrer capillary) geometry taking into consideration the size of the powder particles are presented. The samples are simulated by random dense packings of equal spheres. The calculations are carried out for different values of the ratio, Da, of particle size to cylinder diameter, the product, κ, of linear absorption coefficient and cylinder radius and the scattering angle 2θ. Strong deviations of the absorption factor from the values for the ideal case of very fine particles are found in the region 0≤2θ≤30°, and for medium and high values of κ,(κ≥5) and Da (Da≥0.002). The consequences for the experiment are discussed.

Keywords

absorption factorcylindrical geometrydiffraction of X-rayssimulations

Information

Type
Research Article
Information
Powder Diffraction , Volume 13 , Issue 4 , December 1998 , pp. 249 - 253
Copyright
Copyright © Cambridge University Press 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Bargiel, M., and Moscinski, J. (1991). “C-language program for the irregular close packing of hard spheres,” Comput. Phys. Commun. 64, 183–192.CrossRefGoogle Scholar
Dwiggin, C. W. Jr. (1992). “Analytical solution for the X-ray absorption factor for cylinders in two special cases,” Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. Crystallogr. A28, 219–220.Google Scholar
Gradstein, I. S. and Ryshik, I. M. (1981). Tables of Series, Products and Integrals (Harri Deutsch, Thun, Frankfurt/M.), Vol. I, p. 368.Google Scholar
Hermann, H., and Collazo, J. (1995). “Microabsorption of X-ray intensity in fractal microstructures,” J. Appl. Crystallogr. 28, 786–792.CrossRefGoogle Scholar
Hermann, H., and Ermrich, M. (1987). “Microabsorption of X-ray intensity in randomly packed specimens,” Acta Crystallogr., Sect. A: Found. Crystallogr. A43, 401–405.CrossRefGoogle Scholar
Hill, R. J., and Madsen, I. C. (1995). Structure Determination from Powder Diffraction Data, International Workshop, Oxford.Google Scholar
Kasper, J. S., and Lonsdale, K. (1989). International Tables for X-Ray Crystallography (Kluwer, Dordrecht), 3rd ed., Vol. II, 292 pp.Google Scholar
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (1995). Numerical Recipes in C: The art of Scientific Computing, (Cambridge University Press, Cambridge), 2nd ed., p. 309.Google Scholar
Weber, K. (1967). “Neue Absorptionfaktortafeln für den Kreiszylinder,” Acta Crystallogr. 23, 720–725.CrossRefGoogle Scholar