Partial solid solution

There is a number of very pleasing and instructive relationships between adsorption from a binary solution at the solid-solution interface and that at the solution-vapor and the solid-vapor interfaces. The subject is sufficiently specialized, however, that the reader is referred to the general references and, in particular, to Ref. 153. Finally, some studies on the effect of high pressure (up to several thousand atmospheres) on binary adsorption isotherms have been reported [154]. Quite appreciable effects were found, indicating that significant partial molal volume changes may occur on adsorption. 

The partial molar entropy of a component may be measured from the temperature dependence of the activity at constant composition the partial molar enthalpy is then determined as a difference between the partial molar Gibbs free energy and the product of temperature and partial molar entropy. As a consequence, entropy and enthalpy data derived from equilibrium measurements generally have much larger errors than do the data for the free energy. Calorimetric techniques should be used whenever possible to measure the enthalpy of solution. Such techniques are relatively easy for liquid metallic solutions, but decidedly difficult for solid solutions. The most accurate data on solid metallic solutions have been obtained by the indirect method of measuring the heats of dissolution of both the alloy and the mechanical mixture of the components into a liquid metal solvent.05... 

Other ordering systems show striking discrepancies with the predictions of the quasi-chemical theories. Cu-Pt,67 Co-Pt,38 and Pb-Tl36 are binaries the solid solutions of which exhibit a positive partial excess free energy for one of their components, as well as positive excess entropies of solution. Co-Pt goes even further in deviating from theory in that it has a positive enthalpy of solution,... 

Semi-conductor solid solutions, 133 Silver, partial molar heat of solutions in tin, 133... 

The contact angle between electrode and electrolyte solution can be determined using a solid and partially emersed electrode and observing the meniscus rise [68Mor, 69Mor, 71Mor]. (Data obtained with these methods are labelled CA). 

Several experimental parameters have been used to describe the conformation of a polymer adsorbed at the solid-solution interface these include the thickness of the adsorbed layer (photon correlation spectroscopy(J ) (p.c.s.), small angle neutron scattering (2) (s.a.n.s.), ellipsometry (3) and force-distance measurements between adsorbed layers (A), and the surface bound fraction (e.s.r. (5), n.m.r. ( 6), calorimetry (7) and i.r. (8)). However, it is very difficult to describe the adsorbed layer with a single parameter and ideally the segment density profile of the adsorbed chain is required. Recently s.a.n.s. (9) has been used to obtain segment density profiles for polyethylene oxide (PEO) and partially hydrolysed polyvinyl alcohol adsorbed on polystyrene latex. For PEO, two types of system were examined one where the chains were terminally-anchored and the other where the polymer was physically adsorbed from solution. The profiles for these two... 

A solid solution is a crystal structure in which two (or more) atom types are arranged at random over the sites normally occupied by one atom type alone. For example, in the comndum structure solid solution formed by Cr2C>3 and AI2O3, a random mixture of Cr3+ and Al3+ ions occupy the cation sites that are only occupied by one of these in the parent phases. The formula of the solid solution materials is written (Al i JCCrJC)203. In this example, x can vary continuously between 0 and 1.0. In some cases, especially when the atoms involved have different sizes, only partial solid solutions are found, characterized by a composition range in which the span of x is smaller than 1.0. Solid solutions are widely exploited as both the chemical and physical properties of the solid can be varied sensitively by changing the relative amounts of the components of the solid solution. 

This type of defect equilibrium treatment has been used extensively to model the defect chemistry and non-stoichiometry of inorganic substances and has the great advantage that it easily takes several simultaneous defect equilibria into account [22], On the other hand, the way the mass action laws are normally used they are focused on partial thermodynamic properties and not on the integral Gibbs energy. The latter is often preferred in other types of thermodynamic analyses. In such cases the following solid solution approach is an alternative. 

Integral and partial molar enthalpies of mixing in solid solutions may be derived by similar investigations of a series of solid solutions with systematic variation in composition. 

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. 

In most experiments to calculate solubilities the magnesian calcites have been treated as solids of fixed compositions of one component, whereas they are actually a series of at least two-component compounds forming a partial solid solution series. 

Figure 2.33. Ni-Co-O phase diagram (isothermal section at 1600 K). log p02 (oxygen partial pressure) is plotted against the molar fraction in the metallic alloy. The metallic alloy, (Ni, Co) solid solution is stable in (1) and the mixed oxide (Ni, Co)0 solid solution in (3). In the intermediate region (2) we have coexistence of alloy and oxide. For the value of the partial oxygen pressure corresponding to y, within the two-phase field, we will have the alloy of composition xt in equilibrium with an oxide containing the two metals in the ratio x2-...

For these phases the reported formulae generally correspond to an average composition within a solid solution field. This also in relation to a (partially) disordered occupation of the different sites. 

As an example for the specific case of vanadium alloys with palladium, the trend of the average atomic volume of the alloys is shown in Fig. 4.20 and compared with the phase diagram. These data were obtained by Ellner (2004) who studied the solid solutions of several metals (Ti, V, Cr, Mn, Fe, Co and Ni) in palladium. The alloys were heat treated at 800°C and water-quenched. From the unit cell parameters measured by X-ray diffraction methods, the average atomic volume was obtained Vat = c 14 (see Table 4.3). These data together with those of the literature were reported in a graph, and the partial molar (atomic) value of the vanadium volume in Pd solid solution (Fv)... 

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