Parameters occupancy

Site Localized moment Spin proportion Occupation parameter ... 

The two special (a) and (b) Wyckoff positions have no free coordinate parameter. The two occupancy parameters are 100%. The Pearson symbol is cP2. 

No free parameters in the atomic positions of Mg and Ge. In this case the two occupancy parameters have been found to be 100%. The Pearson symbol is cF12 (CaF2 is considered the prototype of this structure). 

The occupancy parameter of N is 75% that is three atoms are statistically distributed in the four positions. The real stoichiometry corresponds to Mo2N0.75 and in the unit cell there are 11 atoms instead of the ideal value of 12. The Mo position has the free parameterz for which, in this particular case the value 0.258 has been determined. The Pearson symbol is tI12 (11). 

I Site-occupatioH parameters. A complete description of a system requires detailed knowledge about the occupancy of all available sites by all die participating species. However, with K constituents and N sites, this leads to different configurations, which is computationally unrealistic. A usefid approximation is to use average site-occupation parameters, for equivalent crystallographic sites. 

To complete the picture it is useful to define distribution variables, Xj, which are atomic fiactions normalised to a mole of atoms as related to site-occupation parameters. The x and y variables are related geometrically through the equation ... 

Extinction parameters isotropic or anisotropic Occupancy parameters ... 

Fig. 15 Occupancy parameter (12) and deviation parameter (0) as a function of spin speed (a) and concentration (b) of TMV solution for spin-assisted assembly of TMV particles on wrinkled surfaces [85]...

Figure3.19 Schematic representation ofthe bulk radius Rmax, the solid angle Qmax, and the sphere occupation parameter Socc.

Table 9.5a. Intramolecular interglucose hydrogen bonds of the flip-flop type 0-( )D D( )-0 observed in, 8-eyclodextrin at room temperature (neutron diffraction). The occupational parameters of the oxygen atoms are 1.0, those of the deuterium atoms vary between 0.344 and 0.654. (For atom numbering scheme see Chapter 18 [454].)... 

A special case of static disorder occurs when an atom is present in only a fraction of the unit cells in the crystals. For instance, a ligand might be present in only half of the unit cells, or a side chain might have two or more possible conformations. This type of disorder can be modeled with an occupancy parameter 0, ranging from one (fully present) to zero (absent). It is simply the fraction of unit cells where the atom in question is present. Low occupancy is, however, difficult to distinguish from high B-factor. Indeed B-factors and occupancies are statistically correlated. Therefore, occupancies are normally used only when there are sufficient data (i.e., high resolution) to justify a more complicated disorder model. 

We have not considered modulations of the displacement (thermal) parameters and occupation parameters. The explicit consideration of these terms, together with 3 + d-dimensional symmetry operators, in the structure factors gives rise to more complex expressions than those written in this section. The reader interested in a deeper knowledge of this subject is invited to check the specialized articles in the existing literature. An excellent review of the different structure factor formalisms is provided by Van Smaalen. ... 

These were largely due to inappropriate use of the method being applied. For the Rietveld based techniques, these errors included (i) entry of incorrect crystal structure information, including atom coordinates and thermal vibration parameters, (ii) incorrect space group notation, (iii) incorrect atom site occupation parameters, (iv) allowing structure parameters (especially thermal parameters) to refine to physically unrealistic values, and (v) not completing the refinement. 

All adjustments to the least-squares occupancies have been of 3a or less correlations between thermal and occupancy parameters have therefore not been a serious problem. 

Isotrope displacement parameters Bj Occupation parameters Oj Anisotropic displacement paramters 6/y Preferred orientation T Absorption A... 

The occupancy parameters for ultrastable Y, Structure III, show the absence of the same 15.4 aluminum ions as in Structure I, but 25.0 0(3)... 

The summation is over all the p atoms in the unit cell vvdth atomic scattering factor The modulation describes the individual atomic displacement relative to its basic position r. The integration variable t is related to the fourth dimension by the expression X4 = q. r -1- r (see Fig. 2). The first line of this expression corresponds to the structure factor of a conventional crystal (/i4 is equal to zero, and thus H = h). The second line of the expression is specific to aperiodic structures and contains the information related to the atomic modulation function in superspace. In addition to a displacement parameter, the modulation can also be affected by a variable occupation parameter p. ... 

Yak] Yakel, H.L., Brynestad, J., Non-random Site-occupation Parameters in (Cr,Fe)23Ce Phases , Scr. Metall, 16(4), 453-454 (1982) (Crys. Structure, Thermodyn., Calculation, Experimental, 6)... 

The output from the Le Bail/Rietveld refinements were combined to show the variation of several important structure-property indicators (unit cell, thermal, phase fraction and occupancy parameters) versus time/temperature profiles (Fig. 4.3). Given the fact that thermal B-factors and site occupancy parameters are... 

The density of lattice vacancies can be determined, usually accurately, by the site occupation parameter. Thus if the local atomic potential is bifurcated and atoms are locally displaced, it may appear that partial occupation of the displaced site describes the system quite well. However, in such cases there is usually strong coupling between the occupation parameter and the DW factor during the process of refinement. Also, local displacement of an atom is usually accompanied by a lattice relaxation around the displaced atom and a much increased DW factor of the displaced site. Thus, in practice, it is very difficult to describe anharmonic local displacements through partial occupation of two closely spaced sites. 

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