Rietveld profile refinements

Figure 6.6. Effects of calcination at 1273 K on two Ceo.5Zro.5O2 samples (A. commercial, B ex-citrate) and Rietveld profile refinement of the XRD pattern of Ceo sZro.sOi (sample B calciend for 5 h at 1273 K) (1) fresh samples, (2) calcined at 1273 K for 5 h, (3) calcined at 1273 K for 100 h and (4) Rietveld analysis (Courtesy of Dr. Di Monte University of Trieste).

RVP Rietveld Profile Refinement Chemical abstracts registry number (if available)... 

H.M. Rietveld, A profile refinement method for nuclear and magnetic structures, J. Appl. Crystallogr. 2 (1969) 65-71. 

The ID diffraction profiles are also ideally suited to profile refinement, as illustrated in Figs. 9 and 13 in Sect. 4, from which atomic coordinates can be obtained using standard Rietveld methods. 

A survey of the usovite phases obtained up to now [5,15,18] shows that Al3+, Ga3+ and all the 3D tervalent ions from V3+ to Fe3+ readily occupy the M"3+ site all the 3D divalent ions from Mn2+ to Cu2+ can be used as M 2+ as for M2+, it may be Ca2+, Cd2+ or Mn2+ almost every combination of choices in these three series of possibilities will allow to obtain an usovite for the stoichiometry Ba2MM M"2F14 (with however some exceptions as BaMnFeF7 [19]). The correctness of the original structure determination has now been confirmed by several full X-ray structure refinements on single crystals and by Rietveld profile analyses on powder neutron diffractograms, so that this structural type is now firmly established and may be seen as rather common among fluorides. 

Rietveld, H.M. Profile refinement method for nuclear and magnetic structures. J. Appl. Crystallogr. 1969, 2, 65-71. Iyengar, S.S. Phadnis, N.V. Suryanarayanan, R. Quantitative analyses of complex pharmaceutical mixtures by the rietveld method. Powder Diffr. In press. 

Rietveld, H.M., A Profile Refinement Method for Nuclear and Magnetic Structures, J. 

Reddy M, Reddy G, Manorama SV (2001) Preparation, characterization, and spectral studies on nanociystalline anatase Ti02. J Solid State Chem 158 180-186 Rieker T, Hanprasopwattana A, Datye A, Hubbard P (1999) Particle size distribution inferred from small-angle X-ray scattering and transmission electron microscopy. Langmnir 15 638-641 Rietveld HM (1969) A profile refinement method for nuclear and magnetic stractnres. J Appl Crystallogr 2 65-71... 

To a certain extent, the Rietveld method (also known as the full pattern or the full profile refinement) is similar to the full pattern decomposition using Pawley and/or Le Bail algorithms, except that the values of the integrated... 

Full profile refinement is computationally intense and employs the nonlinear least squares method (section 6.6), which requires a reasonable initial approximation of many fi ee variables. These usually include peak shape parameters, unit cell dimensions and coordinates of all atoms in the model of the crystal structure. Other unknowns (e.g. constant background, scale factor, overall atomic displacement parameter, etc.) may be simply guessed at the beginning and then effectively refined, as the least squares fit converges to a global minimum. When either Le Bail s or Pawley s techniques were employed to perform a full pattern decomposition prior to Rietveld refinement, it only makes sense to use suitably determined relevant parameters (background, peak shape, zero shift or sample displacement, and unit cell dimensions) as the initial approximation. 

It is worth noting that parameters identical to those listed in our examples can be expected only when the same computer codes are used to perform full profile refinement due to small but detectable differences in the implementation of the Rietveld method by various software developers. Furthermore, even when the same version of an identical computer program is employed to treat the same set of experimental data, small deviations may occur due to subjective decisions, such as when to terminate the refinement. In the latter case, however, the differences should be within a few least squares standard deviations. 

---