Residual profile

A profile residual based on the weighted intensities of the profite at each point is defined as... 

In this example, lattice parameters and the zero shift correction have a substantial impact on the quality of the fit and the weighted profile residual, Rwp, decreases nearly two-fold (from 24 to 12 %), while the refinement of peak shape parameters decreases R p by only 4 %. Therefore, in this case lattice parameters should have been refined first. However, it is not always obvious which parameters are more important and should be released at a particular stage of the least squares refinement. Because of this, in complex cases a trial-and-error approach is often employed. ... 

Rp and profile residuals (Eqs. 6.18 to 6.22) can be easily lowered by increasing the number of adjustable parameters in a completely unreasonable structural model. Thus, relevant residuals should be employed to gauge the fit between the observed and experimental data rather than as an exclusive measure of the rationality of the underlying crystal structure. 

As expected, adding the contribution from the impurity phase (again as Le Bail s approximation) results in further reduction of the profile residuals, see row six in Table 7.7. The final model of this crystal structure, as determined using the combined Rietveld refinement in the two-phase approximation, is found in the data file Ch7Ex01k.inp on the CD. Structural parameters are listed in Table 7.8. 

Hence, similar to the previous example, the range below 20 = 15° was excluded from further refinement. It is certainly worthwhile to note that this exclusion eliminates 400 points ( 9 %) from the profile, which contains more than 4,600 data points total, but it leaves out only 3 ( 0.3 %) of about 1000 possible Bragg reflections. As far as the structural model is of concern, such truncation of the experimental data is indeed valid, and is often employed in structure determination from powder diffraction. With this modification, followed by several least squares minimization steps, profile residuals decrease but Rb is slightly increased. 

Case 4. The two bands are separated, there is no mixed zone left, but there is still a plateau on the top of the second band profile, residual of the interaction between the two bands. This is the beginning of the "touching bands" situation (Eqs. in Table 8.4). 

The process is cyclic the procedure stops when all anions have been positioned. For each feasible model the profile residual is calculated and those corresponding to the best agreement factors are selected for Rietveld refinement. 

Functional parameters FP of a sensor include the sensitivity S, cross sensitivities, temperature coefficient TC, temperature coefficient of sensitivity TCS, offset O, and corresponding TCO. Nonhnearities of TCS and TCO are NLTCS and NLTCO. And we also have hysteresis, burst pressure, hermeticity, and other parameters. These functional parameters need to be described by model parameters MPj, j= l...n, which are appropriate for the processes used to fabricate the device (layer thickness, etching profiles, residual layer stress, etc.). 

By this point, the engineer wdl have developed a business risk profile of the organization. In the business risk profile, residual business risks are classified as either strategic or process risks. Also, interactions among risks are identified, and the risk classifications and identified interactions are cross-matched with related business performance attributes. 

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