Simple ideal solid solutions

Distribution Laws For Simple Ideal solid solutions. If a solid solution of Formula (2) is in eguilibrium with an agueous phase (ag), the distribution of A and B ions between the agueous phase and the solid phase (s) can be represented by ... 

To meet the difficulties presented by metal systems, various wider definitions of chemical combination in terms of crystal structure have been proposed. For example, it has been suggested that we should regard an ideal chemical compound as one in which structurally equivalent positions are occupied by chemically identical atoms, and an ideal solid solution as a structure in which all atoms are structurally equivalent. It is clear that such a definition of chemical combination embraces all the generally accepted compounds, but it is not without objection when applied to metal systems. Thus, to take only one example, the ft phase in the silver-cadmium system already discussed has, in its ordered state, the simple caesium chloride structure and must therefore... 

Positive deviations from ideal behaviour for the solid solution give rise to a miscibility gap in the solid state at low temperatures, as evident in Figures 4.10(a)-(c). Combined with an ideal liquid or negative deviation from ideal behaviour in the liquid state, simple eutectic systems result, as exemplified in Figures 4.10(a) and (b). Positive deviation from ideal behaviour in both solutions may result in a phase diagram like that shown in Figure 4.10(c). 

Solid electrolytes are frequently used in studies of solid compounds and solid solutions. The establishment of cell equilibrium ideally requires that the electrolyte is a pure ionic conductor of only one particular type of cation or anion. If such an ideal electrolyte is available, the activity of that species can be determined and the Gibbs energy of formation of a compound may, if an appropriate cell is constructed, be derived. A simple example is a cell for the determination of the Gibbs energy of formation of NiO ... 

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. 

The fugacity coefficient of the solid solute dissolved in the fluid phase (0 ) has been obtained using cubic equations of state (52) and statistical mechanical perturbation theory (53). The enhancement factor, E, shown as the quantity in brackets in equation 2, is defined as the real solubility divided by the solubility in an ideal gas. The solubility in an ideal gas is simply the vapor pressure of the solid over the pressure. Enhancement factors of 104 are common for supercritical systems. Notable exceptions such as the squalane—carbon dioxide system may have enhancement factors greater than 1010. Solubility data can be reduced to a simple form by plotting the logarithm of the enhancement factor vs density, resulting in a fairly linear relationship (52). 

Dyeing is normally readily accomplished in aqueous solution, often in the presence of a fixing agent, or mordant. This is ideal for cotton, silk and wool, but not for certain synthetic fibers, such as nylon and polyester. The latter are plastic in nature, and require disperse dyes. Here the dyeing process involves heating the fiber in an aqueous dispersion of a water-insoluble dye. A solid solution is formed in the fiber. In order to penetrate synthetic fibers, a small dye molecule is required, for which simple water-insoluble mono-azo dyes are ideal. Apart from yellow dyes (where phenolic components are common), these are usually based on /V,/V-dialkylated aniline coupling components that permit a wide range of shades to be obtained. 

The structural properties of the metal systems described above naturally challenge consideration from a purely chemical point of view, for occasionally the results of structure analysis cannot readily be reconciled with accepted chemical principles and demand a re-orientation of the chemical picture of the metallic state. It has often been the practice of the metallurgist to seek to represent the several phases in an alloy system by simple chemical formulae corresponding to idealized stoichiometric compositions, departures from which were interpreted as solid solution in the ideal phase of excess of one or other of the components. Such formulae inevitably tend to convey the impression, implicitly if not explicitly, that these phases are to be regarded as definite chemical compounds, and it is necessary to consider carefully to what extent such a viewpoint is justifiable, and even whether there are valid grounds for attributing to the phases any formulae at all. 

All the DSC methods of purity determination depend on the applicability of the van t Hoff equation. This restricts the method to systems where the impurity forms a simple eutectic phase diagram with the major component that is, the impurity or impurities are soluble in the melt and the components do not form solid solutions (53). Use of the van t Hoff equation assumes that the solution of impurity in major components above the melting point is an ideal solution in the thermodynamics sense. Also, the method assumes that the solid-liquid system is essentially in true thermodynamic equilibrium during the measurements. Failure to meet any of these conditions will lead to erroneous results. Other possible errors are associated with the instrumentation employed. This involves the use of the smallest possible sample size consistent with homogeneity (50), proper encapsulation to minimize temperature gradients within the sample, and the slowest possible heating rate lo approach equilibrium conditions. It is recommended that the melting... 

For a simple system in which a solid solution is not formed and an ideal solution in the melt is formed, the mole fraction of solute impurity, component 2) in the solvent [component 1K is given by... 

Most modem quantitative trace element geochemistry assumes that trace elements are present in a mineral in solid solution through substitution and that their concentrations can be described in terms of equilibrium thermodynamics. Trace elements may mix in either an ideal or a non-ideal way in their host mineral. Their very low concentrations, however, lead to relatively simple relationships between composition and activity. When mixing is ideal the relationship between activity and composition is given by RaoulFs Law, i.e. 

Equation (7.17) can also be derived from reasonably simple statistical considerations which have nothing to do with the physical state of the particles. In other words it applies equally to ideal gas, liquid, and solid solutions. 

The elementary cell or lattice is the lowest structural level of a crystal. The lattice is characterized by a space symmetry group, atom positions and thermal displacement parameters of the atoms as well as by the position occupancies. In principle, the lattice is the smallest building block for creating an ideal crystal of any size by simple translations, and it is the lattice that is responsible for the fundamental parameter. Therefore, it is extremely important to perform the structure refinement of a crystal obtained, especially if the crystal represents a solid solution compound or demonstrates unusual properties or has unknown oxygen content or is assumed to form a new structure modification. 

Wood s data give the very simple relationship that activity of CaTs is nearly equal to its mole fraction in diopside-CaTs solid solutions. This would be true of an ideal solution of completely ordered CaTs and diopside end members. However, as Wood pointed out, the recent X-ray crystallographic study of... 

However, although simple binary or tertiary systems can be used to demonstrate the basic principles, they are of little use in understanding more complex real systems such as palm oil or AMF. In a real fat there are always solid solutions, and these affect the ideal solubility curve, causing it to deviate from the straight line as shown in Figure 2, which demonstrates this in terms of the phase behavior of PPP and 2-oleodipalmitate (POP). At all temperatures, the actual solubility is higher than the ideal solubility. 

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