Solid solutions complications

Questions of the analytic control of maintenance of the bivalent metals cations to their joint presence in materials of diverse fixing always were actual. A simultaneous presence in their composition of two cations with like descriptions makes analysis by sufficiently complicated process. Determination of composition still more complicates, if analyzed object is a solid solution, in which side by side with pair of cations (for example, Mg " -Co ", Mn -Co, Zn -Co ) attends diphosphate anion. Their analysis demands for individual approach to working of methods using to each concrete cations pair. 

No one tries to remember exact details of this or similar alloys. But the point of all these complicated additions of foreign atoms to the nickel is straightforward. It is (a) to have as many atoms in solid solution as possible (the cobalt the tungsten and the chromium) (b) to form stable, hard precipitates of compounds like Ni3Al, Ni3 Ii, MoC,... 

When other elements dissolve in a metal to form a solid solution they make the metal harder. The solute atoms differ in size, stiffness and charge from the solvent atoms. Because of this the randomly distributed solute atoms interact with dislocations and make it harder for them to move. The theory of solution hardening is rather complicated, but it predicts the following result for the yield strength... 

Eqn(3) allows a direct determination of LRO-parameter from resistivity measurement by using the constant A as a fit parameter. Eqn(l) is of more complicated character, where besides the SRO-parameters in the different coordination spheres there enter details of the band structure (Y,) which influence sign and magnitude of resistivity variation with degree of SRO. However, restricting to nearest neighbours and using an adequate model for the dependence of a on temperature and concentration, reliable SRO-parameters have been deduced from resistivity measurement for several solid solutions. ... 

The crystallization of glassy Pd-Ni-P and Pd-Cu-P alloys is complicated by the formation of metastable crystalline phaf s [26]. The final (stable) crystallization product consists of a mixture of a (Pd,Ni) or (Pd,Cu) fee solid solution and more than one kind of metal phosphide of low crystallographic symmetry. Donovan et al. [27] used transmission electron microscopy (TEM) and X-ray microanalysis to study the microstructure of slowly cooled crystalline Pd4oNi4oP2o- They identified the compositions of the metal phosphides to be Pd34Ni45P2j and Pdg8Ni[4Pjg. 

Two product barrier layers are formed and the continuation of reaction requires that A is transported across CB and C across AD, assuming that the (usually smaller) cations are the mobile species. The interface reactions involved and the mechanisms of ion migration are similar to those already described for other systems. (It is also possible that solid solutions will be formed.) As Welch [111] has pointed out, reaction between solids, however complex they may be, can (usually) be resolved into a series of interactions between two phases. In complicated processes an increased number of phases, interfaces, and migrant entities must be characterized and this requires an appropriate increase in the number of variables measured, with all the attendant difficulties and limitations. However, the careful selection of components of the reactant mixture (e.g. the use of a common ion) or the imaginative design of reactant disposition can sometimes result in a significant simplification of the problems of interpretation, as is seen in some of the examples cited below. 

As was discussed earlier in Section 1.2.8 a complication arises in that two of these properties (solubility and vapor pressure) are dependent on whether the solute is in the liquid or solid state. Solid solutes have lower solubilities and vapor pressures than they would have if they had been liquids. The ratio of the (actual) solid to the (hypothetical supercooled) liquid solubility or vapor pressure is termed the fugacity ratio F and can be estimated from the melting point and the entropy of fusion. This correction eliminates the effect of melting point, which depends on the stability of the solid crystalline phase, which in turn is a function of molecular symmetry and other factors. For solid solutes, the correct property to plot is the calculated or extrapolated supercooled liquid solubility. This is calculated in this handbook using where possible a measured entropy of fusion, or in the absence of such data the Walden s Rule relationship suggested by Yalkowsky (1979) which implies an entropy of fusion of 56 J/mol-K or 13.5 cal/mol-K (e.u.)... 

Figure 6 illustrates a more complicated situation. The sample was a plain iron-carbon steel—an iron foil carburized to about 5 atomic % carbon and then quenched. One sees a rather complex pattern. There is a large central peak from some untransformed high temperature face-centered phase of iron containing carbon in solid solution, retained austenite. There is a strong six-line pattern coming from martensite, a distorted body-centered solid solution of carbon in iron. We also see a... 

The basic question is how to perform extrapolations so as to obtain a consistent set of values, taking into account various complications such as the potential presence of mechanical instability. Additional complications arise for elements which have a magnetic component in their Gibbs energy, as this gives rise to a markedly non-linear contribution with temperature. This chapter will concern itself with various aspects of these problems and also how to estimate the thermodynamic properties of metastable solid solutions and compound phases, where similar problems arise when it is impossible to obtain data by experimental methods. 

Whilst charcoal possesses this property to a marked extent similar phenomena are to be noted at all solid surfaces. A gas brought into contact with a solid surface will be adsorbed into the surface to- an extent which is dependent on several factors, the nature of the gas and solid, the partial pressure of the gas and the characteristic structure of the exposed surface. This phenomenon of adsorption is, however, frequently complicated by solution of the gas in the solid to form solid solutions or compounds with the solid. The term sorption has been proposed by McBain to include the two phenomena of absorption and adsorption. Our attention will be limited to the characteristics of adsorption. 

In fact, the presence of solid solutions considerably effects the homogeneity of the mixture, preventing the formation of inner cracks and fissures. If the solidifying point of the eutectic is too low (i.e. below 60°C) the explosive may exude from the shell, whereas too high a solidifying point hinders melting, and in turn complicates the process of filling the shell. 

Defect thermodynamics is more complicated when applied to binary (or multi-component) compound crystals. For binary systems, there is one more independent thermodynamic variable to control. In the case of extended binary solid solutions, one would normally choose a composition variable for this purpose. For compounds with very narrow ranges of homogeneity (i.e., point defect concentrations), however, the composition is obviously not a convenient variable. The more natural choice is the chemical potential of one of the two components of the compound crystal. In practice one will often use the vapor pressure ( activity) of this component. 

Molecular Weight. Measurement of intrinsic viscosity in water is the most commonly used method to determine the molecular weight of poly(ethylene oxide) resins. However, there are several problems associated with these measurements (86,87). The dissolved polymer is susceptible to oxidative and shear degradation, which is accelerated by filtration or dialysis. If the solution is purified by centrifugation, precipitation of the highest molecular weight polymers can occur and the presence of residual catalyst by-products, which remain as dispersed, insoluble solids, further complicates purification. 

Therefore, we must compare data for different ionic strengths as well as for different temperatures and pressures, Moreover, the calculated data refer to pure solids whereas the floor of the sea consists of only a few comparatively pure solids and an overwhelming mass of complicated solid solutions. 

It is unusual to find systems that follow the ideal solution prediction as well as does (benzene+ 1,4-dimethylbenzene). Significant deviations from ideal solution behavior are common. Solid-phase transitions, solid compound formation, and (liquid 4- liquid) equilibria often complicate the phase diagram. Solid solutions are also present in some systems, although limited solid phase solubility is not uncommon. Our intent is to look at more complicated examples. As we do so, we will see, once again, how useful the phase diagram is in summarizing a large amount of information. 

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