Rietveld refinement using GSAS

Table 7.23. Final atomic parameters and interatomic distances (in A) of ma2Mo 022 obtained from Rietveld refinement using GSAS. The refined unit cell parameters are a = 23.0707(3), b = 5.51522(7), c = 19.5669(2) A, P = 122.930(1) , V = 2089.68(5) A space group C2/c. All crystallographic data can be also found on the CD in the files Ch7Ex07c.exp and Ch7Ex07c.cif.

Just as in the case of full pattern decomposition, we will use two freely available software codes (LHPM-Rietica and GSAS ) to carry out Rietveld refinements using either or both x-ray and neutron diffraction data. Many... 

All computations described in the following five sections have been performed using GSAS (General Structure Analysis System), one of the most advanced implementations of the Rietveld refinement approach... 

All samples were single phase without detectable impurities. The crystal structure was refined by the Rietveld method (Rietveld, 1959) from X-ray powder diffraction data using GSAS software package (Larson Von Dreele, 1994). 

XRD powder patterns of fresh and used catalysts, measured at room temperature on a Bruker D8 Advance diffractometer equipped with Sol-X detector, were subjected to Rietveld structure refinement in Immm space group using the GSAS package (Larson and Von Dreele, 1994). 

These two relationships can be easily programmed in GSAS and in the majority of Rietveld software codes by using a constraint apparatus, which was briefly discussed above (see section 7.3.3 and Eq. 7.9). Since the constraints affect only the shifts that are determined during every least squares refinement cycle but not the values of the related parameters, the latter should be synchronized manually prior to imposing constraints. For example, in our case when the computed shift for g-v2a is 0.02, then the new values of the constrained parameters (Eqs. 7.9, 7.11 and 7.12) will be calculated as follows ... 

Later Von Dreele implemented the general description of texture by spherical harmonics in GSAS. Von Dreele proved that, by using this description, beside the robustness of the texture correction in the Rietveld method it is also possible to perform a reliable quantitative texture analysis. He measured by neutron time-of-flight diffraction a standard calcite sample previously used for a texture round robin. The patterns from different detector banks and sample orientations were processed by GSAS, refining the harmonic coefficients simultaneously with the structural and other parameters. Six pole distributions calculated from the refined harmonic coefficients and used as input in the... 

Consequently, if the peak shifts for one or more peaks are measured as a function of T in the range (0, ujl) at y and y + re for three fixed values of y e.g., 0, 71/4 and nj2) the stress tensor elements 5, can be determined from the intercept and the slopes of these lines. It is presumed that the single-crystal elastic constants are known and the diffraction elastic constants in Equations (109) and (110) can be calculated following one of the models presented before. This is the conventional sin T method. Alternatively Equation (107) can be used in a least-square analysis or implemented in the Rietveld codes. If diffraction patterns measured in several points (T, y) are available the stress tensor elements 5,- can be refined together with the structural and other parameters. The implementation in GSAS is the Voigt formula Equation (90) and not Equation (107). In this case refinable parameters are the strain tensor elements e,. 

The Rietveld method is a refinement technique in which the whole powder pattern is fitted by varying a number of instrumental and stmctural-model parameters. The successful use of the method is directly related to the quality of both the diffraction data and the structural model being refined. The Rietveld method is widely available for the structure refinement of powder data through such programs such as GSAS, FullProf, and Rietan. ... 

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