Ideal Solid Solutions

The combination of properties discussed above makes the transition metal carbides, nitrides, and their solid solutions ideal materials for applications requiring rigidity and resistance to deformation, abrasive wear, and corrosion. 

Chemical reaction - formation of intermetollic compounds Diffusion in solid solutions (dilute ideal solutions between solute 300 to 5 X 1 O ... 

When a pure metal A is alloyed with a small amount of element B, the result is ideally a homogeneous random mixture of the two atomic species A and B, which is known as a solid solution of in 4. The solute B atoms may take up either interstitial or substitutional positions with respect to the solvent atoms A, as illustrated in Figs. 20.37a and b, respectively. Interstitial solid solutions are only formed with solute atoms that are much smaller than the solvent atoms, as is obvious from Fig. 20.37a for the purpose of this section only three interstitial solid solutions are of importance, i.e. Fc-C, Fe-N and Fe-H. On the other hand, the solid solutions formed between two metals, as for example in Cu-Ag and Cu-Ni alloys, are always substitutional (Fig. 20.376). Occasionally, substitutional solid solutions are formed in which the... 

At the same time it is recognized that the pairs of substances which, on mixing, are most likely to obey Raoult s law are those whose particles are most nearly alike and therefore interchangeable. Obviously no species of particles is likely to fulfill this condition better than the isotopes of an element. Among the isotopes of any element the only difference between the various particles is, of course, a nuclear difference among the isotopes of a heavy element the mass difference is trivial and the various species of particles are interchangeable. Whether the element is in its liquid or solid form, the isotopes of a heavy element form an ideal solution. Before discussing this problem we shall first consider the solution of a solid solute in a liquid solvent. 

A dependence of w upon composition must also be adduced in the case of the Fe-Ni solid solutions. Over the range from 0 to 56 at. per cent Ni, these solid solutions exhibit essentially ideal behavior,39 so that w 0. Since the FeNi3 superlattice appears at lower temperatures, either w is markedly different at compositions about 75 at. per cent Ni than at lower Ni contents, or w 0 for the solid solutions about the superlattice. Either possibility represents a deviation from the requirements of the quasi-chemical theories. 

Table II also demonstrates the discrepancy existing between E0/RTe calculated by the Yang-Li quasi-chemical theory and the experimental ratio. E0 is the energy difference between a fully ordered superlattice and the corresponding solid solution with an ideally random atom species distribution. It is a quantity that can only be estimated from existing experimental information, but the disparity between theory and experiment is beyond question.

Figure 1. Ideal pressure-composition isotherms showing the hydrogen solid-solution phase, a, and the hydride phase, j3. The plateau marks the region of coexistence of the a and fl phases. As the temperature is increased the plateau narrows and eventually disappears at some consolule temperature...

It is essentially a phase diagram which consists of a family of isotherms that relate the equilibrium pressure of hydrogen to the H content of the metal. Initially the isotherm ascends steeply as hydrogen dissolves in the metal to form a solid solution, which by convention is designated as the a phase. At low concentrations the behaviour is ideal and the isotherm obeys Sievert s Law, i.e.,... 

We will see later that this same equation applies to the mixing of liquids or solids when ideal solutions form. 

Assume ideal solution behavior with no solid solutions and constant Afus m and... 

Essentially this formula has been suggested before. Tschermak in 1894 wrote 6 m10Zm.2iS 64/513, and Kretschmer adopted the more general expression (CuJZnv), SbS3+v/2, with x + y = 3. Machatschki pointed out the existence of excess sulfur over that required by the formula Cu3SbS3, but preferred to retain this expression as the ideal formula, and to consider the excess sulfur as due to solid solutions of a type discussed later. 

The possibility of the expression of the entropy of hydrogen as the sum of these terms was first noted by Giauque, who observed that it indicated the formation of nearly ideal solid solutions between symmetrical and antisymmetrical hydrogen and the retention of the quantum weight 9 for the latter. 

Solubility equilibria are described quantitatively by the equilibrium constant for solid dissolution, Ksp (the solubility product). Formally, this equilibrium constant should be written as the activity of the products divided by that of the reactants, including the solid. However, since the activity of any pure solid is defined as 1.0, the solid is commonly left out of the equilibrium constant expression. The activity of the solid is important in natural systems where the solids are frequently not pure, but are mixtures. In such a case, the activity of a solid component that forms part of an "ideal" solid solution is defined as its mole fraction in the solid phase. Empirically, it appears that most solid solutions are far from ideal, with the dilute component having an activity considerably greater than its mole fraction. Nevertheless, the point remains that not all solid components found in an aquatic system have unit activity, and thus their solubility will be less than that defined by the solubility constant in its conventional form. 

In this case, the melting point of the ideal solid solution should increase linearly as the ration of B/A increases. However, it usually does not. 

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... 

Some of the major questions that semiconductor characterization techniques aim to address are the concentration and mobility of carriers and their level of compensation, the chemical nature and local structure of electrically-active dopants and their energy separations from the VB or CB, the existence of polytypes, the overall crystalline quality or perfection, the existence of stacking faults or dislocations, and the effects of annealing upon activation of electrically-active dopants. For semiconductor alloys, that are extensively used to tailor optoelectronic properties such as the wavelength of light emission, the question of whether the solid-solutions are ideal or exhibit preferential clustering of component atoms is important. The next... 

Figure 1.9 Vegard s law relating unit cell parameters to composition for solid solutions and alloys (a) ideal Vegard s law behavior (b) negative deviation from Vegard s law and (c) positive deviation from Vegard s law.

Let us consider a binary system for which both the liquid and solid solutions are assumed to be ideal or near ideal in a more formal way. It follows from their near-... 

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). 

Negative deviation from ideal behaviour in the solid state stabilizes the solid solution. 2so1 = -10 kJ mol-1, combined with an ideal liquid or a liquid which shows positive deviation from ideality, gives rise to a maximum in the liquidus temperature for intermediate compositions see Figures 4.10(h) and (i). Finally, negative and close to equal deviations from ideality in the liquid and solid states produces a phase diagram with a shallow minimum or maximum for the liquidus temperature, as shown in Figure 4.10(g). 

In the ideal solid solution model used, the enthalpy and entropy of oxidation are independent of composition. 

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 ... 

---