Structure refinement by Rietveld method (Rietveld, 1969) is available in EXPO2014. Graphical and computing tools are available in the program in order to attain a successful automatic or user-defined Rietveld refinement.
The refined variables include peak shape parameters, unit cell dimensions, coordinates of atoms in the structure model, background coefficients, scale factor, isotropic displacement parameters. Atomic displacement parameters can be refined individually or in a group of atoms with the same atomic type or the same environment. Correction for the preferred orientation can be achieved by the March-Dollase approach. The background is described using empirical functions: classical polynomial function, Chebyshev polynomial function, cosine Fourier series. The background can also modeled by mouse-click selection of pattern points. The available peak shape functions are: Pseudo-Voigt, Pearson VII, Thompson-Cox-Hastings pseudo-Voigt.
The non-linear least squares are carried out by employing the damped Gauss-Newton method. The refinement convergence condition is reached when the increments on parameters become smaller with respect to their standard deviations or when the relative gradient of χ2 minimized function is less then a tolerance value. Tolerance value and the maximum number of cycles could be suitably modified by the user.
The Le Bail technique can be adopted to perform a full pattern decomposition prior to Rietveld refinement in order to determine starting values of parameters (background, peak shape, zero shift and unit cell dimensions) to refine. This strategy is suggested especially if the available structure model is not completed (McCusker et al., 1999) or when the starting model is too different from the target model.
The refinement can be carried out by following two alternative approaches: 1) the user can decide the refinement strategy via graphic interface; 2) an automatic refinement schedule can be applied. In the automatic mode, groups of parameters are refined according to a fixed sequence as established in the Rietveld guidelines (Young, 1995). In the last step of refinement all parameters are refined simultaneously.
The knowledge of molecular geometry can be exploited in the refinement in form of restraints on bond distances, angles and planes. To simplify the setting of restraints, the program is able to extract from the connectivity of the initial model the possible restraints providing a list of current and target values. The user can select the restraints to be included in the refinement procedure and eventually modify the target value.
Some figures of merit are available in order to follow the progress and evaluate the quality of refinement: the weighted profile R-factor and the unweighted profile R-factor calculated for the full pattern (Rwp, Rp); the corresponding figures background-subtracted (Rwp', Rp'); the statistically expected R value (Rexp); the goodness-of-fit (Rwp/Rexp); the Durbin-Watson d-statistic. R values similar to those used in case of single crystal data are also available: RF and the Bragg-intensity R (Rb)which use the structure factor moduli extracted from the experimental profile. In addition, graphical tools are available for visualizing: 1) the observed, calculated and difference pattern and the cumulative χ2 value; 2) the evolution of the structure model during the refinement in real time.
where:
N is the total number of counts in the pattern and P is the number of refined parameters.
Preparing Input file for Rietveld Refinement |
To run EXPO2014 for Rietveld refinement, first you need to create the input file. This is an example of the typical input file:
%Structure paracetamol |
It is supposed that the cell parameters and the space group have been determined before and a structure model is available and imported by using the command %fragment followed by the file name containing the structure. %rietveld is a command to access to the Rietveld Refinement graphical interface.
Alternatively, when a structure model is available, you can access directly to the graphic interface from menu "Refine" > "Rietveld"
For suggestions and bugs contact:
annagrazia.moliterni@ic.cnr.it
References |
Rietveld, H.M.: A profile refinement method for nuclear and magnetic structures. J. Appl. Cryst. 2 (1969) 65–71.
McCusker, L.B.; Von Dreele, R.B.; Cox, D.E.; Louër, D.; Scardi, P.: Rietveld refinement guidelines. J. Appl. Cryst. (1999). 32, 36-50
The Rietveld Method. Edited by R. A. Young, Oxford University Press, Oxford (1995)
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