Site occupancy, solids

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.

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... 

The earliest theoretical predictions on the state of interfaces were made by Burton, Cabrera, and Frank [11[, who demonstrated that the interface would, in most cases, be rough at the growth temperature for metal crystals. Jackson [13[ suggested a system in which the solid and liquid phases are separated by an interface with one-layer thickness, and he calculated the energy changes as a function of the ratio of site occupancy of the constituent unit on the interface. When the site occupancy ratio was 50%, the interface was rough, whereas 0 or 100% site occupancy... 

A consequence of the occupation of more than one site in solid inclusion complexes is illustrated with a single example, although many more are available in the literature. Detailed study of arylalkyl ketones included in deoxycolic acid (DCA) channels have been carried out by Lahav, Leiserowitz,... 

The alnicos are polycrystalline solids, in which very complex structural disorder generally occurs, due to the wide variety of deviations from periodicity that may be present. Physical disorder corresponds to the displacement of atoms, and/or the presence of amorphous regions and non-uniform crystallite sizes, while chemical disorder corresponds to site occupation by impurity atoms, and/or the presence of vacancies accompanied by variable valence states of... 

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. 

Fig. 5.10. Calculations of the properties of olivine solid solutions (see Ottonello, 1987, for full details and data sources) (a) Calculated phase field boundaries in the system (Mn,Mg),Si04 full circles are calculated boundaries, dashed curves are extrapolated, dotted lines are experimental solubility gap. (b) Plot of site occupancy versus molar composition along the binary join (Ni,Mg)2Si04-...

Recently the new SRT approach has been generalized further to take into account the energetic heterogeneity of the actual adsorption systems and the possible role of the interactions between the adsorbed molecules. [10-20] Most recently, the authors have shown, that the SRT approach can be successfully applied to describe the multi-site-occupancy adsorption of molecules which do not dissociate after being adsorbed. [14] Compact simple analytical expressions were developed, and next used successfully to correlate experimental data for adsorption/desorption kinetics in various gas/solid systems. The purpose of this presentation is to show, that the new SRT approach can be also applied to represent the kinetics of dissociative gas adsorption on solids. That kinetics is of a crucial importance in a variety of catalytic reactions occurring on solid surfaces. 

Panczyk T. and Rudzinsld W., Kinetics of Multi-Site-Occupancy Adsorption on Heterogeneous Solid Sur ces A Statistical Rate Theory Approach, J. Phys. Chem., 106(2002) pp.7846-7851. 

In natural waters, other surface reactions will be occurring simultaneously. These include protonation and deprotonation of the >FeOH site at the inner o-plane and complexation of other cations and anions to either the inner (o) or outer (IS) surface planes. Expressions similar to Equation (5) above can be written for each of these reactions. In most studies, the activity coefficients of surface species are assumed to be equal to unity thus, the activities of the surface sites and surface species are equal to their concentrations. Different standard states for the activities of surface sites and species have been defined either explicitly or implicitly in different studies (Sverjensky, 2003). Sveijensky (2003) notes that the use of a hypothetical 1.0 M standard state or similar convention for the activities of surface sites and surface species leads to surface-complexation constants that are directly dependent on the site density and surface area of the sorbent. He defines a standard state for surfaces sites and species that is based on site occupancy and produces equilibrium constants independent of these properties of the solids. For more details about the properties of the electrical double layer, methods to calculate surface specia-tion and alternative models for activity coefficients for surface sites, the reader should refer to the reference cited above and other works cited therein. 

Because the length difference of the two miscible components is small, the disorder is considered mainly in terms of site occupancies close to the lamellar surface.159 163 Thus, alkane solid solutions provide good models of surface disorder, which has been studied by infrared and Raman spectros-... 

Sverjensky (2003) proposed new standard states, leading to equilibrium constants independent of the surface area, site density, and the amount of the solid sorbent. These new standard states are dependent only on surface site occupancy and can be used with any surface complexation model. Different standard states are defined for the activities of the sorbent sites and the sorbate species. The theoretical relationships that apply for all adsorption reactions are developed below using Eq. (6.6) as an example reaction. 

Fig. 3-21. Percolation into random uncorrelated media with varying site occupation probabilities (areal porosities). Solids are black. Continuity of major percolation paths from upper boundary indicated by shading.

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

Subsequent to an extensive review of brittle micas (Guggenheim 1984), additional crystal-chemical details of clintonite-IM (space group C2/m) were reported by MacKinney et al. (1988) and Alietti et al. (1997). These studies confirmed that natural clintonite crystals do not vary extensively in composition (i) the octahedral sites contain predominant Mg and Al with Fe to <7% of the octahedral-site occupancy (ii) the extent of the substitution Mg.2 " Si (A1,D), which involves the solid solution of... 

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