Site occupancy, fractional

Figure 3. The effect of degree of polymerization on surface coverage (fractional site occupancy) at various polymer concentrations. The solid lines represent the present model and the symbols correspond to the theory of Scheutjens and Fleer. The parameter values are the same as in Figure 2.

Differences in Afor different AB5Hn compounds compared with A for CeCosHs are listed in Table III. The values of these numbers (see Table III), calculated using the fractional site occupations for the 0 phase, can be compared with the experimentally determined entropy differences listed in Table I. The calculated configurational entropy differences (see Table III) agree satisfactorily with the experimental data (see Table I) currently available for seven ABsHn compounds. Structures of some ABsHn compounds deduced from neutron diffraction data (4) are listed in Table I. For compounds whose structures have not been determined, the occupation numbers listed in Table III are in best agreement with the thermodynamic data. 

Crystal structure of (a) ReC>3, and (b) Na W03 (central large circle, Na+ of fractional site occupancy). 

In this expression, y is the fractional site occupation for component i (the number of atoms of component i on the sublattice divided by the total number of sites on that sublattice), Lvtj is an interaction energy parameter for mixing between components i and j on the sublattice, and °G,- z is the Gibbs energy of the compound when the sublattice u is completely occupied by i. 

In this expression, y,- is the fractional site occupation for component i (the number of atoms of component i on the sublattice, divided by the total number of sites on that... 

Sulphide S Layer sequence Fractional site occupancy between successive S layers Reference... 

Grau-Crespo, R., et al. 2007. Symmetry-adapted configurational modelling of fractional site occupancy in sohds. J. Phys. Condens. Matter 19 256201. 

Displacement disorder and fractional site occupation arise from steric constraints. High amounts of these types of disorder occur for example in ff-Al Mgz from incompatibilities in the packing of Friauf polyhedra. Split occupation is also caused by geometrical hindrances. In this case, two lattice sites are too close to be occupied simultaneously. Locally, only one site can be occupied, while the other remains empty, which in the average structure corresponds to an occupation factor of 0.5 for both sites. 

The logic that leads us to this last result also limits the applicability of the ensuing derivation. Applying the fraction of total lattice sites vacant to the immediate vicinity of the first segment makes the model descriptive of a relatively concentrated solution. This is somewhat novel in itself, since theories of solutions more commonly assume dilute conditions. More to the point, the model is unrealistic for dilute solutions where the site occupancy within the domain of a dissolved polymer coil is greater than that for the solution as a whole. We shall return to a model more appropriate for dilute solutions below. For now we continue with the case of the more concentrated solution, realizing... 

Definition of site fractions. The multiple sublattice model is an extension of earlier treatments of the two-sublattice models of Hillert and Steffansson (1970), Harvig (1971) and Hillert and Waldenstrom (1977). It allows for the use of many sublattices and concentration dependent interaction terms on these sublattices. To woiic with sublattice models it is first necessary to define what are known as site fractions, y. These are basically the fiactional site occupation of each of the components on the various sublattices where... 

Essentially, sublattice models originate from the concepts of Temkin (1945) who proposed that two separate sublattices exist in a solid-state crystal for cations and anions. The configurational entropy is then governed by the site occupation of the various cations and anions on their respective sublattices. When the valence of the cations and anions on the sublattices are equal, and electroneutrality is maintained, the model parameters can be represented as described in Section 5.4.2. However, when the valence of the cations and anions varies, the situation becomes more complex and some additional restrictions need to be made. These can be expressed by considering equivalent fractions (/) which, for a sublattice phase with the formula (/, . .. )(M"", . ..), are given by... 

In some thermodynamic models there are also potential minima associated with different site occupations, even though the composition may not vary, e.g., a phase with an order/disorder transformation. This must be handled in a somewhat different fashion and the variation in Gibbs energy as a function of site fraction occupation must be examined. Although this is not, perhaps, traditionally recognised as a miscibility gap, there are a number of similarities in dealing with the problem. In this case, however, it is the occupation of sites which govern the local minima and not the overall composition, per se. 

Unisite catalysis is a non-physiological mode of catalysis in which a very small fraction of the enzyme population contains bound nucleotide in all three catalytic sites. According to the torsional mechanism, only this fraction will contribute to the measured ATPase activity. Based on the site occupancies predicted by the torsional mechanism during ATP hydrolysis (two catalytic sites contain bound MgATP, while one contains bound MgADP -i- PJ, the fraction f in Eq. (9) is predicted to be 0.33, which is in perfect agreement with experiment [48]. 

If mixing in each site is not ideal, would differ from the real equilibrium constant by the quotient of activity coefficients and hence may depend on composition. The measurement of the site occupancy (the fraction of Fe and Mg in each of Ml and M2 sites) is not trivial. There are two methods to determine the intracrystalline site distribution. One is by Mossbauer spectroscopy (MS), in which there are a pair of outer and smaller peaks, which are due to Fe in Ml site, and a pair of inner and larger peaks, which are due to Fe in M2 site (Figure 2-3). The ratio of Fe in Ml site to Fe in M2 site is assumed to be the area ratio of the pair of Ml peaks to the pair of M2 peaks. Using total Fe content from electron microprobe analysis, and the ratio from Mossbauer spectroscopy, Fe(Ml) and Fe(M2) concentrations can be obtained. 

The site fractions of the Si-containing species are one site occupied by SiH4 out of a total of 32 sites, and two sites out of 32 occupied by Si2H4. The site fraction of open sites is 29/32 = 0.906. As is seen in Eq. 11.8, it is necessary to divide the site fraction of each species by the site occupancy number ok to convert to a molar concentration. The concentration of SiH4 (number per unit area) is equal to that of Si2H4. 

The pulmonary system and skin constitute the major routes of entry for xenobiotic materials into the body. The skin has a large surface area of up to two m2 for adults. This large area, along with skin s external exposure, means that it is a common site of contact with toxic substances, especially in the workplace. It has been estimated that about one third of all reported occupational exposures to toxic substances is through skin, and much larger numbers that produce relatively minor symptoms remain unreported.5 Skin maladies constitute a large fraction of occupational and consumer problems with industrial chemicals and consumer products. 

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] ... 

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. 

The quantitative measure of the degree of surface heterogeneity in the model of the one-site-occupancy adsorption is the differential distribution of the fraction of surface sites among corresponding values of adsorption energy e, x(e), such that... 

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