Interaction parameter, solid solutions

The nature of the exchange interaction in solid solutions La,Eu,, B6 was investigated by Mercurio et al. (1979). Samples were prepared by borothermal reduction of mixed oxides at 1550°C in high vacuum (X-ray and chemical analysis). No lattice parameter data were given. 

Because the appearance of a superlattice is usually well characterized qualitatively in terms of an interaction parameter w which has nothing to do, in the usual treatments, with the melting of the parent solid solution, one does not expect to find a simple relationship between the critical temperature for disordering of the superlattice, and Ts, the solidus temperature of the corresponding solid... 

Figure 10. Adsorbed cation coverage as a function of electrode potential, assuming a cation interaction parameter / = 6.18 The solid line is the steady-state solution, whereas the broken line is the quasi-steady solution. Open circles indicate the unstable area. (From G. L. Griffin, J. Electrochettu Soc. 131, 18, 1984, Fig. 1. Reproduced by permission of The Electrochemical Society, Inc.)...

Fig. 51 Phase diagram for PS-PI diblock copolymer (Mn = 33 kg/mol, 31vol% PS) as function of temperature, T, and polymer volume fraction, cp, for solutions in dioctyl ph-thalate (DOP), di-n-butyl phthalate (DBP), diethyl phthalate (DEP) and M-tetradecane (C14). ( ) ODT (o) OOT ( ) dilute solution critical micelle temperature, cmt. Subscript 1 identifies phase as normal (PS chains reside in minor domains) subscript 2 indicates inverted phases (PS chains located in major domains). Phase boundaries are drawn as guide to eye, except for DOP in which OOT and ODT phase boundaries (solid lines) show previously determined scaling of PS-PI interaction parameter (xodt

Figure 4. Distribution of the ionic compounds AX and BX over the solid phase and the aqueous phase for different values of the distribution parameter D under the assumption that AX and BX form homogeneous regular solid solutions with a negative value for the interaction parameter W.

In this way and by numerical evaluation, Driessens (2) proved that the experimental activities could be explained on the basis of substitutional disorder, according to Equation (27), within the limits of experimental error. It seems, therefore, that measurements of distribution coefficients and the resulting activities calculated by the method of Kirgintsev and Trushnikova (16) do not distinguish between the regular character of solid solutions and the possibility of substitional disorder. However, the latter can be discerned by X-ray or neutron diffraction or by NMR or magnetic measurements. It can be shown that substitutional disorder always results in negative values of the interaction parameter W due to the fact that... 

If the solid solution is regular, with an interaction parameter W (cf. section 3.8.4), the equilibrium distribution curve is defined by... 

As outlined in section 10.1, the presence of trace elements in crystals is attributable to several processes, the most important one being the formation of substitutional solid solutions. The ease of substitution depends on the magnitude of interactions between trace element and carrier. We have already seen (section 3.8.4) that macroscopic interaction parameter W can be related to microscopic interactions in a regular solution of the zeroth principle ... 

For dilute solid solutions A(+B],B2,...) the interaction parameter formalism as outlined in Section 2.2 is adequate. 

Two models are frequently used to predict the activity coefficient of the solid the regular solution model (93) and the DLP (delta-lattice-parameter) model (94). With both models, the activity coefficient of component i, yf, is calculated in terms of the interaction parameter, ft, by the expression... 

The interaction parameter, ft, is a fitting parameter in the regular solution model that can be found from liquid-solid equilibrium data (93). With the DLP model, the interaction parameter is calculated from the lattice parameters of the binary compounds. For a compound semiconductor AiJB C, ft is computed from the lattice constants aAC and aBC of the binary compounds from the following expression... 

A statistical thermodynamic equation for gas adsorption on synthetic zeolites is derived using solid solution theory. Both adsorbate-adsorbate and adsorbate-adsorbent interactions are calculated and used as parameters in the equation. Adsorption isotherms are calculated for argon, nitrogen, ammonia, and nitrous oxide. The solution equation appears valid for a wide range of gas adsorption on zeolites. 

Amandykov and Gurov [155,184] have extended Kikuchi s approach to the case when the TSM is used (QCA, R — 1). According to these authors, the expression for the correlation cofactor depends on the parameter of the AC interaction with the neighboring species. Therefore, this behavior exerts a significant effect on the concentration dependence of the diffusion coefficients. The potential of atoms interaction at any distances has been applied to the construction of the kinetic equation describing the diffusion decomposition of solid solutions [185]. 

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