CPD News Index

Fundamental Parameters Workshop - EPDIC 6, August 1998

The Bruker-AXS GmbH cordially invites you to the following workshop, which will be held as a satellite meeting accompanying the 6th EPDIC conference in Budapest:

"A New Fundamental Parameters Approach in Profile Analysis of Powder Data"

Line profile shapes are a convolution of (i) the emission profile, (ii) an instrument component and (iii) specimen aberrations. This approach to line profile analysis is well known latest since the pioneering work of Klug & Alexander in 1974. Nevertheless, until today current profile fit routines still apply empirical models to the peaks which do not distinguish between these contributions and are often inadequate in modeling observed peak shapes in X-ray data.

A common problem is the description of peak asymmetry which is mainly a result of axial divergence effects. In addition, the extraction of sample effects, such as crystal size/strain broadening relies on the (time consuming) measurement of a large crystal size, strain free 'standard' sample under the same instrumental conditions as the 'unknown' sample.

The problem with an empirical/standard approach is that a large number of refinable parameters are required to accurately describe line profiles over the whole 2Theta range. This parametrization as well as the insufficient description of instrumental contributions (such as asymmetry) performed by recent profile fit routines result either in inadequate fits or in erroneous interpretation of the specimen contributions.

The new fundamental parameters approach presented in this workshop uses a convolution based method to synthesize line profiles. Instrumental and specimen aberrations are convoluted with the emission profile to form the final line profile. Peak position, shape and asymmetry are described by the instrument and sample contributions resulting in accurate estimates of Bragg angle and profile shape. Sample related effects, such as specimen absorption, crystallite size and strain broadening, are entered as refinable values. The physical parameters of the diffractometer, such as the receiving slit length, horizontal divergence, and the primary and secondary Soller slit angles, are measurable quantities and are not usually refined but can be if required. This theoretical modeling of line profiles provides information on diffractometer misalignment and/or geometric irregularities. Significantly the fundamental parameters approach reduces the number of refined parameters and thus decreases parameter correlation in general.

Computationally demanding numerical convolutions, indicative of the fundamental parameters approach, have in the past made it an unlikely approach for routine line profile or Rietveld analysis (e.g. Howard & Snyder, 1989), but this has been overcome with the inclusion of a number of fast algorithms and by using a direct convolution-interpolation procedure. Efficiencies in the refinement procedure together with extremely fast algorithms has resulted in an approach that is at least three to ten times faster than conventional profile fit programs - even for non-convolution based fit routines.

The procedures presented at the workshop are expected to overcome the recent, empirical profile fitting methods.

The topics to be discussed are:

1. Possibilities and limits of recent profile analysis
2. Fundamental parameter approach vs. conventional fitting techniques
   • a) Principles & core mathematics
   • b) Generation of line profiles
   • c) Emission profile, instrument characterisation, sample contributions
3. STANDARDLESS real structure analysis (crystallite size, microstrain, absorption, ...)
4. Instrument characterisation (axial divergence, horizontal divergence or flat specimen, slit dimensions, ...)
5. Use of any parameter couplings and of any constraints (linear and non-linear)
6. "How many peaks are there?"
7. Instrument alignment aspects
8. Software

Preliminary date: Monday, 24. August, 16:30 - 18:30. The final schedule will be provided in the 2nd announcement and at the EPDIC registration desc.

Workshop language is ENGLISH. Participation is free.

For further information please contact:

Dr. Arnt Kern
Bruker-AXS GmbH
Oestliche Rheinbrueckenstr. 50
D-76181 Karlsruhe, Germany.
Fax:      ++49-721-595-6693
E-mail:   Arnt.Kern@bruker-axs.de