Site occupancy factors

Fig. 11.3 Mutual orientations of azulene molecules in the layered structure shown on Fig. 11.2, at two levels of z coordinate z = 0 corresponds to the layer with blue color, z = 0.25 to the red one. A, B, and C stand for different orientations at respective levels, numbers indicate site occupation factors for each of the particular orientations...

B stands for the isotopic thermal factor, q for the site occupancy factor, and R for the residuals. ax/al x 104. 

The crystal structure of 4(5)-nitro-5(4)-methoxyimidazole contains a 1 1 mixture of two tautomers, 4-nitro-5-methoxy- and 5-nitro-4-methoxyimidazole [55], This is one of the very few cases of 4,5-disubstituted imidazoles for which there are two annular tautomers in the crystal. The molecular structure is the superposition of these tautomer forms. The structure is centrosymmetric and the N-H hydrogen atoms are disordered over two ring N atoms. Owing to the hydrogen-bond pattern, the values of their site occupation factors have to be exactly equal to 1/2. The molecules are connected into a three-dimensional network by means of N-H... N and C-H... 0 hydrogen bonds [55],... 

With alloys and substitutional solid solutions, it is possible that a mixture of atoms (of similar size, valence, etc.) may reside at a general or special position and all its equivalent coordinates. The fraction of atoms of one type residing at that position is given by the site occupancy, or site occupation factor. The sum of the site occupation factors for that site must equal unity. The distribution of two or more types of atoms over a single site is completely random. Where two atoms are distributed over all the equivalent coordinates of different sites with similar local coordination environments (but not identical site symmetry), electronic, or other, effects can result in partial site preferences. That is, there can be a nonstatistical distribution over the two sites. 

Figure 6. Integrated pattern obtained from the plate shown in Figure 5 and showing the time evolution as a K-rich phase, with peaks shifted to lower 20, replaces the Na -faujasitic phase. Selected powder diffraction patterns obtained from these data are suitable for Rietveld analysis and the derived stmctural models allow determination of individual site-occupancy factors within the stmcture as a function of time. These reveal the critical role of a site with restricted geometry, the last replaced in the Na-containing phase (Lee et al. 1998, 1999).

Figure 3.9.2 Supramolecular chain-like arrays with a flattened step-ladder topology in 2. CjHj mediated by Sn.., 7t interactions. Note that the toluene molecule Is disordered about a center of inversion so that the methyl groups have 50% site occupancy factors only...

Figure 24.10 ORTEP drawing of the (E,E)-4MeO crystal as the intermediate structure during the polymerization with a site occupancy factor of 53% for poly[(E,E)-4MeO],...

Not all materials are so well behaved. For example, many metal alloys have considerable composition ranges and a correct calculation of the intensities of diffracted beams needs inclusion of a site occupancy factor. For example, the disordered gold-copper alloy Au Cu, is able to take compositions with x varying from 1, pure gold, to 0, pure copper. The structure of the alloy is the copper (Al) structure, (see Chapter 1), but in the alloy the sites occupied by the metal atoms contain a mixture of Cu and Au, (Figure 8.1). This situation can be described by giving a site occupancy factor to each type of atom. For example,... 

Many other examples of the use of site occupancy factors could be cited, especially in mineralogy, where most natural crystals have a mixed population of atoms occupying the various crystallographic cites. 

The oxides A1203 and Cr203 form a complete solid solution AIvCr2 03. The site occupancy factor for the cations in the crystal AlCr03 is ... 

The fluorite structure non-stoichiometric oxide Ca20+i Zr40+9Oi.9 has a site occupancy factor for O equal to ... 

For every atom in the model that is located on a general position in the unit cell, there are three atomic coordinates and one or six atomic displacement parameters (one for isotropic, six for anisotropic models) to be refined. In addition there is one overall scale factor per structure (osf, or the first free variable in SHELXL see Section 2.7) and possibly several additional scale factors, like tbe batch scale factors in the refinement of twirmed structures, the Flack-x parameter for non-centrosymmetric structures, one parameter for extinction, etc. In addition to the overall scale factor, SHELXL allows for up to 98 additional free variables to be refined independently. These variables can be tied to site occupancy factors (see Chapter 5) and a variety of other parameters such as interatomic distances. 

One constraint foimd in practically every refinement is toe site occupancy factor. In toe absence of disorder it is fixed to unity, which means that the atom site is fuUy occupied (in other words toe atom is present at that site in every unit cell). For atoms disordered over two sites in toe unit cell, toe ratio of toe two site occupancy factors can be refined, but generally their sum is still constrained to unity. 

Table 2.1 Examples of special position constraints on coordinates, anisotropic displacement parameters and site occupancy factors...

As their name suggests, free variables can be used to refine a multitude of different parameters and facilitate the formulation of constraints and restraints. The first free variable is always the overall scale factor (osf), which is used to bring the reflections in the dataset to an absolute scale. The example in Section 4.4.3 shows the effects of incorrect scaling on the refinement. Additional free variables can be linked to the site occupancy factors (sof) of groups of disordered atoms (for details see Chapter 5), but can also be related to other atomic parameters (x, y, z, sof, U, etc.) and even interatomic distances, chiral volumes, and other parameters. 

In the next step, the ratio of the two components has to be taken into account. If the disorder does not involve any special positions, the occupancies of both components are allowed to possess any ratio. It is important, however, that the site occupancy factors (sof) sum up to exactly one. 

The site occupancy factors must take into account the multiplicity of the special position. For example, in the case of a mirror plane, a twofold axis and an inversion centre, the so/instmction has to possess the value 10.5 0 0 0. A threefold axis causes a 0/instruction of 10.3333 and a fourfold axis one of 10.2500, and so forth. SHELXL generates these site occupancy factors automatically only for atoms on or very close to special positions, but not necessarily for all atoms involved in a disorder about a special position. 

Note that the correct site occupancy factor instructions of Al(l) and Al(2) (both in PART 1) are 20.5000 and not 21.0000,as they lie on the crystallographic twofold axis. 

Do not forget to change the site occupancy factors and to set the second free variable, as well as to give the similarity restraints (SAME) and SIMU, delu and FLAT for the disordered atoms as it has been done in the file tol-02.ins. Take also into account the symmetry equivalents (use EQIV). 

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