Solid solution composition

Fig. 22 Dissolution fates of various griseofulvin and gri-seofulvin-succinic acid samples as determined by the oscillating bottle method. , griseofulvin, crystalline A, griseofulvin, micronized , eutectic mixture 0> physical mixture at eutectic composition , solid solution A, physical mixture at solid solution composition. The dashed line indicates the equilibrium solubility of griseofulvin in water. (From Ref. 41.).

Fig. 5.6 (A) TEM micrograph of alginate-Ni50Co5o nanocomposites (B) correlation between alginate-NiCo solid solution composition and face-centered cubic crystal parameters. (Adapted from [50]).

Finally, it is not appropriate to derive thermodynamic properties of solid solutions from experimental distribution coefficients unless it can be shown independently that equilibrium has been established. One possible exception applies to trace substitution where the assumptions of stoichiometric saturation and unit activity for the predominant component allow close approximation of equilibrium behavior for the trace components (9). The method of Thorstenson and Plummer (10) based on the compositional dependence of the equilibrium constant, as used in this study, is well suited to testing equilibrium for all solid solution compositions. However, because equilibrium has not been found, the thermodynamic properties of the KCl-KBr solid solutions remain provisional until the observed compositional dependence of the equilibrium constant can be verified. One means of verification is the demonstration that recrystallization in the KCl-KBr-H20 system occurs at stoichiometric saturation. 

We wish to determine under isothermal and isobaric conditions the concentration of defects as a function of the solid solution composition (e.g NB in alloy (A, B)). Consider a vacancy, the formation Gibbs energy of which is now a function of NB. In ideal (A, B) solutions, we may safely assume that the local composition in the vicinity of the vacancy does not differ much from Ns and /VA in the undisturbed bulk. Therefore, we may write the vacancy formation Gibbs energy Gy(NE) (see Eqn. (2.50)) as a series expansion G%(NE) = Gv(0) + A Gv Ab+ higher order terms, so that AGv = Gv(Nb = l)-Gv(AfB = 0). It is still true (as was shown in Section 2.3) that the vacancy chemical potential /Uy in the homogeneous equilibrium alloy is zero. Thus, we have (see Eqn. (2.57))... 

To demonstrate the viability of the synthesis and characterization approach in the present workflow, two binary Pt-Fe alloy libraries were designed, synthesized and characterized by XRD (Figs. 11.4 to 11.6) [19]. One library (Fig. 11.5) was characterized as synthesized, while the other (Fig. 11.6) was annealed at 400 °C for 12 h in a hydrogen/argon atmosphere. Pt-Fe is a well-known binary alloy system, exhibiting both substitutional solid solution compositional ranges and intermetal-lic compounds. 

The reactions in Eqs. 5.1 and 5.2, taken in the broadest geochemical sense, refer only to the replacement of one ion by another existing in a solid structure. Thus, for example, Eq. 5.1 could be applied to provide a description of solid solution composition alternate to that in Section 3.3. Instead of basing the composition of Al-goethiteon the solid components diaspore and goethite, as in Eq. 3.41, one could describe a continuum of possible compositions by combining Eqs. 3.39a and 3.39b into the cation exchange reaction... 

Solid solutions of two or more semiconductors are formed where the lattice sites are interdispersed with the solid solution components. In these systems, the band gap can be customized by means of changes in the solid solution composition. Examples of semiconductor alloys include GaN—ZnO (Maeda et al., 2005) ZnO-GeO (Domen and Yashima, 2007), ZnS—CdS (Kakuta et al., 1985), ZnS— AgInS2 (Tsuji et al., 2004), and CdS—CdSe (Kambe et al., 1984). 

The inverse or mass-balance modeling approach provides additional constraints on reactant and product mineral phases when the mineral mass transfers are plotted as a function of the range of solid solution compositions. Bowser and... 

Figure 7 Mineral mass transfer coefficients versus smectite solid solution composition for Wyman Creek mass balances, Inyo Mountains (Bowser and Jones, 2002). Upper and lower bounds on possible smectite compositions are where goethite and K-feldspar mass transfers are equal to zero.

The first two terms describe mechanical mixing of endmembers A and B, the third is the ideal solution mixing term, and the last term is the regular solution contribution, in which is not so independent, the solution is not regular). The term (oNJ n in Eq. (1.39) is also sometimes called the excess Gibbs free energy of mixing, or AG (excess). 

Stoichiometric saturation was formally defined by Thorstenson and Plummer (1). These authors argued that solid-solution compositions typically remain invariant during solid aqueous-phase reactions in low-temperature geological environments, thereby preventing attainment of thermodynamic equilibrium. Thorstenson and Plummer defined stoichiometric saturation as the pseudoequilibrium state which may occur between an aqueous-phase and a multi-component solid-solution, "in situations where the composition of the solid phase remains invariant, owing to kinetic restrictions, even though the solid phase may be a part of a continuous compositional scries". 

Despite the above problems, mixing parameters estimated from miscibility gap information will still be an improvement over the assumption of an ideal solid-solution model, ao parameters estimated from data in Palache et al. (20) and Busenberg and Plummer (21) are presented in table I for a few low-temperature mineral groups. Because of the large uncertainties in the data and in the estimation procedure, a sub-regular model is usually unwarranted. As a result, these estimated ao values presented should be used only for solid-solution compositions on a single side of the miscibility gap, i.e. only up to the given miscibility fraction. 

We have now said everything necessary about activities and standard states, but the overall effect for the newcomer is often one of confusion at this stage. To try to draw the various threads together we consider in Figure 12.5a a hypothetical three-phase equilibrium at temperature T and pressure P. A solid crystalline solution of B in A is in contact with an aqueous solution of A(aq) and B(a<7), which is in turn in contact with a vapor phase containing A(v) and B(v) in addition to water vapor. We can suppose the dissolution of (A,B)(5) to be stoichiometric so that the ratio of A to B is the same in all three phases, but this is irrelevant to our development as we consider only component A. Let s say that for a solid solution composition of A"a = 0.5, Vr = 0.5, the concentration of A aq) at equilibrium rri/ ) is 10 molal, and the fugacity of A in the vapor (/a) is 10 bars. Assuming activity coefficients in the solid and liquid... 

C, 1 bar is 10 bar. The pyrrhotite in this equilibrium is Feo.gaS, which may be considered as a solid solution composition in the system FeS — Sa. The activity of FeS in this pyrrhotite is 0.46 based on a standard state of pure stoichiometric FeS at the same P and T. The pyrite is pure stoichiometric FeSa. Calculate ArG° for the reaction forming pyrite from pyrrhotite and Sa gas at this P, T. 

Solid solution composition and grain boundary segregation... 

Solid solution composition plays an important role in SeC propagation. In many cases, the composition determines the nature of See in austenitic stainless steels [67]. In the case of brasses, dealloying controls the See mechanism [68]. 

TABLE 2. Values of the emf of Cell (2) Activily of AlSb and GaSb Excess hitegral Gibbs Free Energy of Formation of the AlSb and GaSb Solid Solution at 855°K for Different Solid Solution Compositions... 

Fig. lb. Cr-Fe-V. The composition dependencies of lattice parameters of the a8 V jCri Jc2 solid solution Composition... 

Figure 1.1 Combustion temperature versus solid solution composition. m-Nj content (relative units).

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