Error bars in powder diffraction

Roman Pielaszek ,  Witold Łojkowski 

Polish Academy of Sciences, Institute of High Pressure Physics (UNIPRESS), Sokolowska 29/37, Warszawa 01-142, Poland

Abstract

Imaging of atomic-scale phenomena in macroscopic world (e.g. on photographic film) made X-ray diffraction one of the most powerful experimental techniques in the history of science. This success came real in large extent due to elegant simplicity of fundamental diffraction formulas, such as Laue or Bragg equations.

Both, the diffraction phenomena and the simplicity of original theory have their sources in phase relations establishing the method. Phase-related math is extremely simple in binary (black&white) considerations that constitute the fundamental formulas. However, in any intermediate (gray) case, where φ≠n·2π, the math becomes less elegant and not that simple anymore.

Obviously, the preferred solution of this problem is to tag all φ≠n·2π photons as "noise" or "parasitic intensity" and cut them off. However, in the present paper we would like to use them to determine some basic error estimates for selected quantities being used n X-ray diffraction. This will help to draw error bars around readings of crystallite size, dispersion of sizes, lattice parameter or phase concentration.

 

Auxiliary resources (full texts, presentations, posters, etc.)
  1. FULLTEXT: Error bars in powder diffraction, Microsoft Office Document, 3MB
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Presentation: Poster at 11th European Powder Diffraction Conference, Poster session, by Roman Pielaszek
See On-line Journal of 11th European Powder Diffraction Conference

Submitted: 2008-02-29 00:37
Revised:   2009-06-07 00:48