Complex ideal solid solutions

Distribution Laws for Complex Ideal Solid Solutions. Let AnX and BnX be two ionic compounds which form a series of solid solutions of the Formula ... 

The phenomena of surface precipitation and isomorphic substitutions described above and in Chapters 3.5, 6.5 and 6.6 are hampered because equilibrium is seldom established. The initial surface reaction, e.g., the surface complex formation on the surface of an oxide or carbonate fulfills many criteria of a reversible equilibrium. If we form on the outer layer of the solid phase a coprecipitate (isomorphic substitutions) we may still ideally have a metastable equilibrium. The extent of incipient adsorption, e.g., of HPOjj on FeOOH(s) or of Cd2+ on caicite is certainly dependent on the surface charge of the sorbing solid, and thus on pH of the solution etc. even the kinetics of the reaction will be influenced by the surface charge but the final solid solution, if it were in equilibrium, would not depend on the surface charge and the solution variables which influence the adsorption process i.e., the extent of isomorphic substitution for the ideal solid solution is given by the equilibrium that describes the formation of the solid solution (and not by the rates by which these compositions are formed). Many surface phenomena that are encountered in laboratory studies and in field observations are characterized by partial, or metastable equilibrium or by non-equilibrium relations. Reversibility of the apparent equilibrium or congruence in dissolution or precipitation can often not be assumed. 

Substitutional Disorder In Regular Solid Solutions. Most simple ionic solutions in which substitution occurs in one sublattice only are not ideal, but regular 2, J3) Most complex ionic solid solutions in which substitution occurs in more than one sublattice are not only regular in the sense of Hildebrand s definition (15) but also exhibit substitutional disorder. The Equations describing the activities of the components as a function of the composition of their solid solutions are rather complex ( 7, V7, 1 ), and these can be evaluated best for each individual case. Both type II and type III distributions can result from these conditions. 

Figure 13.29. Schematic sorption isotherms of a metal ion (Me) on an oxide (XO ) at constant pH (a) adsorption only (H) adsorption and surface precipitation via ideal solid solution (c) adsorption and heterogeneous nucleation in the absence of a free energy nucleation barrier (AG 0) adsorption and heterogeneous nucleation of a metastable precursor (e) same as in (3) but with transformation of the precursor into the stable phase. The arrows show the isotherm evolution for continual addition of dissolved Me. The initial isotherm with the slope of 1 (in the double logarithmic plot) corresponds to a Langmuir isotherm (surface complex formation equilibrium). [Me]s , = solubility concentration of Me for the stable metal oxide [Me]p = solubility concentration of Me for a metastable precursor (e.g., a hydrated Me oxide phase). (From Van Cappellen, 1991.)...

The solid solution model implemented by Farley et al. (1985) allows for surface complexation at low surface coverages and co-precipitation of the metal hydroxide phase as a solid solution containing sorbing and sorbent ions. In an ideal solid solution, the solid phase activities are given by ... 

The situation is more complex for non-ideal solid solutions because the partial molar volume of each constituent varies as a function of composition. Selective oxidation of one constituent of a solid solution results in concentration gradients for all constituents in the alloy underlying the oxide scale. Therefore, local variations of partial molar volumes result in local volume changes that must be accommodated by an additional displacement field parallel to the growth and diffusion direction to maintain the system in a stress-free state. An accurate evaluation of such a volume change and the related displacement field requires many data, often not available, to determine or calculate concentration profiles and partial molar volumes. However, the assumption of ideal solution behaviour would often provide estimated values of a sufficient accuracy. 

Mossbauer spectroscopy involves the measurement of minute frequency shifts in the resonant gamma-ray absorption cross-section of a target nucleus (most commonly Fe occasionally Sn, Au, and a few others) embedded in a solid material. Because Mossbauer spectroscopy directly probes the chemical properties of the target nucleus, it is ideally suited to studies of complex materials and Fe-poor solid solutions. Mossbauer studies are commonly used to infer properties like oxidation states and coordination number at the site occupied by the target atom (Flawthome 1988). Mossbauer-based fractionation models are based on an extension of Equations (4) and (5) (Bigeleisen and Mayer 1947), which relate a to either sums of squares of vibrational frequencies or a sum of force constants. In the Polyakov (1997)... 

An a priori analysis on the reactivity and peculiarities of chemical behavior of molecules is a rather difficult but quite solvable task of theoretical chemistry. If molecules interact with a sohd surface, the complexity of its solution increases repeatedly. This is cause by the circumstances as follows firstly, an interaction occurs between two systems of different nature — molecule and surface that can be considered to be endless at the scale of partner secondly, it is difficult to simulate a surface adequately that is a macrodefect of the crystal periodic structure. Moreover, a definite grade of amorphization of surface layer is a characteristic of even typical crystal [125]. Taking into account probable relaxation and reconstruction of real surface as compared with ideal one, obtaining valid structural information on surface and subsurface layer of solids seems to be rather problematic. A cluster model of solid and its surface that is natural for chemists operating terms of local chemical bonds (despite that it is not quite suitable for the systems with covalent bond) may be considered to be fit for the objects with ionic bonds that are objects of our investigation. 

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