Profile refinement

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. 

All of these hexafluorides are dimorphic, with a high-temperature, cubic form and an orthorhombic form, stable below the transition temperature (92). The cubic form corresponds to a body-centered arrangement of the spherical units, with very high thermal disorder of the molecules in the lattice, leading to a better approximation to a sphere. Recently, the structures of the cubic forms of molybdenum (93) and tungsten (94) hexafluorides have been studied using neutron powder data, with the profile-refinement method and Kubic Harmonic analysis. In both compounds the fluorine density is nonuniformly distributed in a spherical shell of radius equal to the M—F distance. Thus, rotation is not completely free, and there is some preferential orientation of fluorine atoms along the axial directions. The M—F distances are the same as in the gas phase and in the orthorhombic form. 

These revolutionary ideas lead to further neutron measurements of the structure of zeolite A, which have confirmed the correctness of the traditional 4 0 ordering scheme.58 59 Neutron diffraction traces for several samples of a dehydrated Na zeolite A with Si to A1 ratios of 1.03, 1.09 and 1.12 failed to show any rhombohedral distortions similar to those reported in ref. 57, and in each case the data was consistent with a cubic structure.58 Neutron diffraction experiments on a T1 exchanged sample of the same Na zeolite that had shown the rhombohedral distortion in ref. 57 showed that the crystals now had cubic symmetry59 60 and therefore the distortion that had been measured for the Na zeolite A must be very sensitive to the identity of the exchangeable cations. Profile refinement of this neutron data56 57 also showed a pronounced bimodal distribution of the bond lengths as would be predicted by the 4 0 model. In conclusion it appears that the chemical shifts observed in the n.m.r. experiments can be influenced by factors such as local strain, as well as by the local environment of each Si atom. 

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. 

The fundamental simplicity of the powder diffraction experiment coupled with the sophistication of the available numerical data processing techniques and unsurpassed visual elegance, with which the results of the full profile refinement are represented, have transformed the powder diffraction technique into a modem and exceptionally important experimental tool in structure determination. Without a doubt, the powder method is poised to play a role in stmcture determinations with ever-increasing complexity. A recent example of the successful refinement of the sperm whale Physeter catodon) metmyoglobin stmcture from synchrotron powder diffraction data is an excellent illustration of how far the technique has been already advanced. ... 

The DDM algorithm can be readily adapted to any full-profile refinement routine. It was included into the computer program DDM, which is based on a modified and corrected code of BDWS-9006PC. A variant of DDM has recently been implemented in the BGMN program. 

First preliminary variants of DDM were applied in the full-profile X-ray diffraction structure analysis of a series of new silica mesoporous materials and ordered nanopipe mesostructured carbons. DDM allowed stable back-ground-independent full-profile refinement of the structure parameters of these advanced nanomaterials, a result that was unattainable by any other method. To date, DDM has been applied to many various mesoporous and mesostructured substances. The structural parameters of a series of face-centred cubic (Fm3m), body-centred cubic Im3m), and two-dimensional hexagonal (pGmm) mesoporous silicates were determined by DDM from synchrotron XRD. A comprehensive structural analysis of mesoporous silicates SBA-16 (cage-type cubic Irriim), their carbon replicas, and silica/carbon composites was performed by applying DDM. The structure of MCM-48 mesoporous silicate materials was analysed in detail by DDM from different laboratory and synchrotron XRD data. The pore wall thickness of both as-made and... 

J. C. Taylor and C. E. Matulis, Absorption contrast effects in the quantitative XRD analysis of powders by full multi-phase profile refinement, J. Appl. Crystallogr., 1991, 24, 14-17. 

Simpro Simultaneous structure refinement of neutron, synchrotron and X ray powder diffraction patterns, J. K. Maichle, J. Ihringer and W. Prandl, J. Appl. Crystallogr., 1988, 21, 22 27 and A quantitative measure for the goodness of fit in profile refinements with more than 20 degrees of freedom, J. Ihringer, J. Appl. Crystallogr., 1995, 28, 618 619... 

Full profile refinement by derivative difference minimization,... 

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