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Experimental: Rietveld Refinement Details

The description of the Rietveld refinement process should contain the following points:-

  1. Raw Data Refined
    State:
    1. the data range used in refinement.
    2. whether any regions of data were omitted, for example, due to the presence of impurity peaks or asymmetric peaks, and what 2q ranges these regions cover.
  2. Scale Factors and Phase Fractions
    State:
    1. if the scale factor was refined
    2. when more than one phase is present, what combination of scale factor and phase fractions was refined.
  3. Background
    State:
    1. if the background was fit manually by linear interpolation
    2. if a function was used to fit the background - state which function and how many terms were used to fit it.
  4. Peak Position Parameters
    1. specify if lattice parameters and/ or a zero point were refined and where their starting values were obtained from (was the unit cell from prior indexing or a related structure).
  5. Reflection Peak Shape Representation
    Include:
    1. the name and formula for the function used to represent the peak shape (Gaussian, Lorentzian, pseudo-Voigt, Pearson VII), the formula for the 2q dependence of the function and the parameters refined.
    2. additional information if other variables that effect the peak shape were included, such as, asymmetry, strain or particle size anisotropy, sample displacement etc - for each, include the model, formula, corresponding reference and the parameters refined.
  6. Structural Model
    1. state from where the starting structural model arose - earlier solution or reference the article it was taken from.
    2. give the chemical formula of the model and Z (the number of formula units in one unit cell).
    3. state the adjustable parameters that were refined including:
      atomic coordinates
      site occupancies
      temperature factors (overall temperature factor, isotropic or anisotropic)
    4. state if any values of adjustable parameters were fixed - if so, at what value, why this value was used, and why was the parameter fixed?
    5. state if any constraints were applied, for example, whether certain types of atom were constrained to have the same value for the isotropic temperature factors during refinement or if the occupancy of one crystallographic site was constrained to be occupied by two different types of atoms whose total occupancy is 100 %.
    6. state if any restraints were applied, for example, to certain bond lengths or angles in the structure; what weights were applied to these restraints and if they were kept constant or lowered during refinement.
    7. state if any atoms, typically hydrogen, were not included in the structural model or if they were placed in positions expected for a particular molecular fragment such as a -CH2- group.
  7. Additional Effects
    1. include information on any other effects that needed to be applied to the data , such as, preferred orientation, extinction, absorption and micro-absorption.
    2. for each effect specify the function used to model it, its reference, and the parameters refined.
  8. General details:
    1. computer program used for refinement and its reference.
    2. specify how the weights were calculated for each observation.
    3. the atomic scattering factors used and their source.
    4. the size of the last-cycle shifts relative to the errors.
    5. the total number of parameters refined.
    6. state and give the magnitude of the correlation matrix element for the largest correlations involving any structural parameter.
Interpretation

Again when reading sections in a paper concerning the details of the Rietveld refinement look out for the points listed above. Check that the description is consistent with the values given for the refined parameters. For example, if it is stated that the isotropic temperature factors for a certain element type were constrained to have the same value, look at the refinement results tables to make sure that the parameters in question do indeed have equal values. Look for the reasons given for applying certain corrections in the refinement procedure. Ideally, these should be based on results from other experimental techniques. For example, if a correction to the peak shape function was applied to allow for the peak broadening resulting from the particle size along a specific crystallographic direction being particularly short, then see if there is any mention of this conclusion having been verified using electron diffraction and electron microscopy (i.e. by showing that the broadening direction chosen in the refinement and the shortest dimension of the particles coincided). As another example, if a correction for preferred orientation was applied in the refinement, see if any mention is made of verification of the implied correspondence between the habit of the crystallites and the crystallographic direction specified for the correction.

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© Copyright 1997-2006.  Birkbeck College, University of London. Author(s): Martin Attfield