BGMN Models
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This page explains some of the special features in the BGMN software.

Peak model

Base of the BGMN program is the modeling of the peak profiles (fig. 1) through deconvolution of wavelength distribution, instrumental profile and real structure (crystallite size and micro strain broadening, see fig. 1). For this purpose, the instrumental profile is simulated on different angular points 2 Theta in accordance with the geometrical conditions by using a raytracing algorithm. Some examples of resulting instrumental profiles which can not be fitted by simple asymmetric functions like Pearson VII, are presented here. In BGMN this complex profiles are described by several Lorentzian functions (fig. 1). The parameters of these functions are interpolated over the whole angular range. These profiles are convolutable with wavelength distribution (experimentally determined, also described by sum of 4 Lorentzian functions) and the sample profiles to be determined.

Fig. 1: Peak model in the BGMN program

Numerical algorithm

A special optimization algorithm permits the use of fixed upper and lower limits for the most parameters so that physically meaningless values can be prevented.

Modeling of preferred orientation

As preferred orientation models, spherical harmonicssurface functions of even order which can also describe multiple preferred orientation depending on Laue group with up to 66 parameters stand in addition to a simple ellipsoidal model. The determined texture correction factor is computed for every reflex. As a result, a judgement of success and meaning is possible for the texture correction.

Anisotropic peak broadening

Crystallite size and micro strain broadening can be refined anisotropic in a simple manner. The program determines automatically the main axes of the broadening ellipsoides.

Automatic refinement

It is the most important program feature that there is no necessity for a refinement strategy influenced by the user. All parameters to be refined are unlocked in the starting model, good initial values are only required for the lattice constants. A solution is always found without intervention of the user. The error calculation for the parameters and possible shift of a parameter to a limit defined in the starting model allow a judgement whether the starting model was sufficient or not.

Reference