Refinement parameters

Unresolved issues may show up in the refinement parameters. In general, the value of wR2 should not be much larger than twice the value of / 1. The second parameter in the expression for the weight should not be much larger than 1.0. The value of the S (goodness of fit) value when refined with SHELXL should be around 1.0. The final difference map should be essentially featureless with negative and positive excursions of the same order.  

---

Fig. 3.4 Permeability profiles for (a) warfarin (acid), (b) propranolol (base) and (c) morphine (ampholyte) based on a BBB PAMPA model (plON) composed of animal brain extract of lipids. The data (unpublished) were analyzed with the pCEL-X program (plON), with the refined parameters indicated in the three frames. In all three cases, there was evidence for the permeation of charged...

Table 1. YCo5 refined parameters for the atomic magnetic model.

Using the refinement parameters, electron density maps were calculated. Figure 1 shows an example derived from CU96. According to all refinement results the intensities of the strong reflections were too low. Therefore, they were omitted for the electron density studies. The problem is currently under study. Additionally, low-temperature measurements are planned for the near future. 

Danforth DN (1986) Effect of refining parameters on paper properties. Proceedings of the International Conference on New Technologies in Refining, 2, PIRA, Birmingham, England, UK... 

Table 1. Experimental and refinement parameters for Na- ECR1 and NH4- ECR1 at selected temperatures. The data of the RT refinements are taken from Gualtieri et al. (5)...

Derivative of intensity against structure parameters and thickness can be obtained using the first order perturbation method [31]. The finite difference method can also be used to evaluate the derivatives. Estimates of errors in refined parameters can also be obtained by repeating the measurement. In case of CBED, this can also be done by using different... 

Accurate measurements of low order structure factors are based on the refinement technique described in section 4. Using the small electron probe, a region of perfect crystal is selected for study. The measurements are made by comparing experimental intensity profiles across CBED disks (rocking curves) with calculations, as illustrated in fig. 5. The intensity was calculated using the Bloch wave method, with structure factors, absorption coefficients, the beam direction and thickness treated as refinement parameters. 

The final refinement was done with Ce, Cu and P on the positions as discussed above. All atom positions and B s, including the crystal orientation and thickness of each data set were refined. The final atomic parameters are given in Table 3. The refined parameters of each diffraction set and the individual R values are given in Table 4. 

The variances and covariances of the deformation density result both from the errors in the observations, and from the uncertainties in the refined parameters,... 

In the system Ba(Pb1.xBix)Os, the compound with x = 0.25 must be considered the first discovered ceramic material showing high-temperature superconductivity (7). Structure determinations have been carried out over the entire range of composition (8)-(ll) and the refined parameters are presented in Table 2. Superconductivity in this system exists only for values of x between 0.05 and 0.35. The value of the critical temperature increases with x, reaches a maximum value Tc 13K for x = 0.25, and then decreases. For x > 0.35, the material becomes a semiconductor. 

The compound NCu02 (N = Ca0 86Sr014) is an insulator, but its structure, which is a simple defect perovskite made of layers (CuOa) sandwiched between layers (N), can be considered as the parent structure of a large family of superconductors. The sequence. ..(Cu0 )OiC(N)e o(Cu02)OjC. .. is in fact one of the building blocks of many compounds considered in this review. The refined parameters for NCu02 are given in Table 3. 

Compounds with n 2 have never been prepared, however. The refined parameters of BaYM2Og are given in Table 4, and the structure of Ba2YCu3Ox will be discussed in a separate section. 

Space group P2X, 2 independent molecules, Cu-Ka radiation, 1890 reflections, 250 refined parameters R values 0.0718 for (D)-configuration, 0.0730 for (L)-configuration. 

Table I. Crystal Data Collection and Refinement Parameters...

The approximate nature of a model of this kind, the large number of parameters needed for its description, and the likely occurrence of many overlapping interactions, can make the results ambiguous and lead to systematic errors in the refined parameter values. Usually, therefore, diffraction data for a single solution are not sufficient for a complete and unbiased derivation of the structure of a specific complex. If iso-structural substitution can be used to eliminate some of the pair interactions, then much more precise and detailed information about the... 

Toraya s Method. The WPPD as implemented by Toraya et al.11 decomposes the peak profiles and background functions to obtain the best fit to the experimental powder pattern of the individual pure phase data by least-squares refinement. The integrated intensities of the pure phases are then stored with the other refined parameters, such as the profile parameters and the unit-cell parameters of the phases to be quantified. During quantification step, the integrated intensity of the phase being quantified is scaled, as defined in Eq. (12.4), such that the total of the scale factors for the component phases sum to unity. The scale factors of the individual components are then refined by least-squares methods until a best fit is observed with respect to the pattern of unknown composition. 

Toraya s WPPD approach is quite similar to the Rietveld method it requires knowledge of the chemical composition of the individual phases (mass absorption coefficients of phases of the sample), and their unit cell parameters from indexing. The benefit of this method is that it does not require the structural model required by the Rietveld method. Furthermore, if the quality of the crystallographic structure is poor and contains disordered pharmaceutical or poorly refined solvent molecules, quantification by the WPPD approach will be unbiased by an inadequate structural model, in contrast to the Rietveld method. If an appropriate internal standard of known quantity is introduced to the sample, the method can be applied to determine the amorphous phase composition as well as the crystalline components.9 The Rietveld method uses structural-based parameters such as atomic coordinates and atomic site occupancies are required for the calculation of the structure factor, in addition to the parameters refined by the WPPD method of Toraya. The additional complexity of the Rietveld method affords a greater amount of information to be extracted from the data set, due to the increased number of refinable parameters. Furthermore, the method is commonly referred to as a standardless method, since the structural model serves the role of a standard crystalline phase. It is generally best to minimize the effect of preferred orientation through sample preparation. In certain instances models of its influence on the powder pattern can be used to improve the refinement.12... 

Table 1. Crystal Data and Structure Refinement Parameters for I—V ...

Table 2. Crystal Data and Struciure Refinement Parameters for the 1,3-CHDCs, I-IV...

Table 2 Crystal data and structure refinement parameters for I...

One question that arises is if one uses multiscale simulation to predict systems behavior from first principles, then why does one need to carry out parameter estimation from experimental data The fact is that model predictions using even the most accurate QM techniques have errors. In the foreseeable future, one would have to refine parameters from experiments to create a fully quantitative multiscale model. Furthermore, for complex systems, QM techniques may be too expensive to carry out in a reasonable time frame. As a result, one may rely on estimating parameters from experimental data. Finally, an important, new class of problems arises when one has to estimate parameters of... 

Figure 21. Electrostatic potential in the peptide plane of AcPhe calculated from the kappa refinement parameters (a) and fitted potential (b). Contours 0.05 e A-1.

The occasional large deviation of a j, from its population mean can have a large effect on the refined parameters Oj because the quantity [j, -/(.... .., x)] enters 2A as the... 

---