Full profile refinement

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... 

Full profile refinement by derivative difference minimization,... 

Structural details for representative samples were also determined by full profile refinements of powder X-ray and neutron diffraction data. Quantitative relationships between the magnetic and superconducting properties and the composition and structure are presented. The relative contributions of the Cu-0 chains and layers to the superconducting transition temperature are discussed. 

FIGURE 20 X-ray diffraction spectra of Eu from 4 to 35 GPa with Rietveld full-profile refinements (red lines) for bcc and hep phases. Pt pressure marker peaks are identified by asterisks in all spectra (Bi et al., 2011). 

The least squares refinement of structural parameters employing full profile powder diffraction data is discussed in Chapter 7. 

The background should never be subtracted prior to full pattern decomposition and full profile-based Rietveld refinement. In these cases it is approximated using various analjdical functions with coefficients, which are refined along with other parameters. Thus computed background is then added to the intensity calculated as a function of Bragg angle. 

At this point, it is useful to calculate a Fourier map to verify that no other weakly scattering atoms (i.e. Si) have been missed. The electron density distribution has been calculated and it confirms that there are no additional atoms in the unit cell of GdsSi4. Proceeding with the refinement of all relevant parameters in the order indicated in Table 7.30, the full profile least squares fit converges easily. Data file Ch7Exllb.inp is found on the CD. 

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. 

Full profile fitting can be useful for various tasks including unit cell refinement involving peak overlap, space group assignment, extracting intensities prior to structure solution, and pre-structure refinement fitting of the powder pattern. The two main methods are listed below. 

VMRIA VMRIA a program for a full profile analysis of powder multiphase, neutron diffraction time of ffight (direct and Fourier) spectra, V. B. Zlokazov, V. V. Chernyshev, J. Appl. Crystallogr., 1992, 25, 447 451 and DELPHI based visual object oriented programming for the analysis of experimental data in low energy physics, V. B. Zlokazov, Nucl. Instrum. Methods Rhys. Res. A, 2003, 502(2 3), 723 724 Rietveld refinement of TOF data... 

Full profile Rietveld method was used for the refinement of the lattice parameters, positional and displacement parameters of atoms. Data evaluation was performed by using the WrnCSD program package [5]. 

Proffen T, Billinge SJL (1999) PDFFIT, a program for full profile structural refinement of the atomic pair distribution function. J Appl Crystallogr 32 572-575... 

T. Proffen, and S. J. L. Billinge, "PDFFIT, A Program for Full Profile Structural Refinement of the Atomic Pair Distribution Function," / Appl. Crystallogr., 32,572-75 (1999). 

The X-ray structure of a-4T single crystals grown from the vapor phase has been solved simultaneously by two groups during the course of this review [61, 62]. Nevertheless, data had been previously predicted on the basis of calculations by Gavezzotti and Filippini [52] and further refined by Porzio et al. from X-ray powder diffraetion data using the Rietveld full-profile analysis [53, 63]. 

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. 

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