Atomic occupancy determinative methods

The analytical determination of the derivative dEtotldrir of the total energy Etot with respect to population n, of the r-th molecular orbital is a very complicated task in the case of methods like the BMV one for three reasons (a), those methods assume that the atomic orbital (AO) basis is non-orthogonal (b), they involve nonlinear expressions in the AO populations (c) the latter may have to be determined as Mulliken or Lbwdin population, if they must have a physical significance [6]. The rest of this paper is devoted to the presentation of that derivation on a scheme having the essential features of the BMV scheme, but simplified to keep control of the relation between the symbols introduced and their physical significance. Before devoting ourselves to that derivation, however, we with to mention the reason why the MO occupation should be treated in certain problems as a continuous variable. 

With small molecules, it is usually possible to obtain anisotropic temperature factors during refinement, giving a picture of the preferred directions of vibration for each atom. But a description of anisotropic vibration requires six parameters per atom, vastly increasing the computational task. In many cases, the total number of parameters sought, including three atomic coordinates, one occupancy, and six thermal parameters per atom, approaches or exceeds the number of measured reflections. As mentioned earlier, for refinement to succeed, observations (measured reflections and constraints such as bond lengths) must outnumber the desired parameters, so that least-squares solutions are adequately overdetermined. For this reason, anisotropic temperature factors for proteins have not usually been obtained. The increased resolution possible with synchrotron sources and cryocrystallography will make their determination more common. With this development, it will become possible to obtain better estimates of uncertainties in atom positions than those provided by the Luzzati method. 

Cation Site Distribution, Thin-film EDS analysis can also be used to quantitatively determine the site occupancy of atoms in a known crystal structure. Atom Location by Channeling Enhanced Microanalysis (ALCHEMI) is a technique which utilises electronchanneling enhanced X-ray emission for specific atoms in a crystal when appropriately oriented relative to the incident beam [43]. The method involves no adjustable parameters, can be used on relatively small areas of sample and provides fractional occupancies of atom positions [44] Unlike X-ray diffraction which has had limited success with adjacent elements in the periodic table [e.g. 45], ALCHEMI can provide site occupancies for adjacent elements and is relatively insensitive to sample thickness or the precise electron beam orientation [44] ... 

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... 

The technique of channeling-enhanced X-ray emission (CHEXE) has enabled cation site occupancies to be determined in various minerals, including transition metal ions in spinels and ferromagnesian silicates (Taftp, 1982 Taftp and Spence, 1982 Smyth and Taftp, 1982 McCormick etal., 1987). The method, which is based on relative intensities of X-ray peaks measured on crystals with diameters as small as 50 nm under the electron microscope, is particularly useful for determining site occupancies of minor elements with concentrations as low as 0.05 atom per cent in a structure. The most important criterion for the determination of element distribution in a mineral by this technique is that the cation sites should lie on alternating crystallographic planes. In order to make quantitative site population estimates, additional information is required, particularly the occupancy of at least one element in one of the sites or in another site that lines up with one of the sites of interest (McCormick et al., 1987). For example, cation site occupancies by CHEXE measurements have been determined from X-ray peak intensity ratios of Si to Ni, Mn, Cr and Fe in forsterite, as well as thermal disordering of these cations in heated olivines (Smyth and Taftp, 1982). 

Although HRTEM has atomic resolution, most images of oxides show only metal atoms, as oxygen s contribution to the image contrast is not significant. As a result of the development of Cs-corrected TEM, it has become possible to see directly oxygen atoms [13]. Even then, determination of the positions and occupation factors of oxygen in oxides still has to be rely on diffraction methods. 

Maneb or mancozeb. Headley (1996) used an inductively coupled plasma-atomic emission spectrometry (ICP-AES) method for occupational exposure estimations that measures mancozeb by determining the elemental manganese portion of the pesticide in a sample. The method was successful in analyzing urine (0.02 mg/L), wash water (0.02 mg/L), tank mixes (0.02 mg/L), cellulose acetate filters (0.5 pg), and fabric from patches and clothing (0.5 pg), with detection limits in parentheses. However, ICP-AES methods cannot differentiate among various forms of manganese, so it is important that background... 

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