Solution-liquid-solid phase

The Pd-Rh alloy system provides a convenient test case for application of the methodology because of its particularly simple phase diagram, which consists of only the liquid and a fee solid solution phases. 

The mathematical treatment can be further simplified in one particular case, that corresponding to Figure 4.10(a). As we saw in the previous section, in some binary systems the two terminal solid solution phases have very different physical properties and the solid solubility may be neglected for simplicity. If we assume no solid solubility (i.e. as =a =1) and in addition neglect the effect of the heat capacity difference between the solid and liquid components, eqs. (4.29) and (4.30) can be transformed to two equations describing the two liquidus branches ... 

The composition of the equilibrium mixture shows that Br has been enriched significantly in the solid phase in comparison to the liquid phase (D > 1). If one considered the concentrations of aqueous [Br"] and [Ag+], one would infer, by neglecting to consider the presence of a solid solution phase, that the solution is undersaturated with respect to AgBr ([Ag+] [Br ]/KsoA Br = 0.1). Because the aqueous solution is in equilibrium with a solid solution, however, the aqueous solution is saturated with Br. Although the solubility of the salt that represents the major component of the solid phase is only slightly affected by the formation of solid solutions, the solubility of the minor component is appreciably reduced. The observed occurrence of certain metal ions in sediments formed from solutions that appear to be formally (in the absence of any consideration of solid solution formation) unsaturated with respect to the impurity can, in many cases, be explained by solid solution formation. 

Other two-component systems may exhibit either limited solubility or complete insolubility in the solid state. An example with limited solubUity is the silver-copper system, of which the reduced-phase diagram is shown in Figure 13.5. Region L represents a liquid phase, with F = 2, and S and 5s represent solid-solution phases rich in Ag and Cu, respectively, so they are properly called one-phase areas. S2 is a two-phase region, with F= 1, and the curves AB and DF represent the compositions of the two solid-solution phases that are in equilibrium at any... 

A major subdivision of processes is possible on the basis of the principal phase in which the reactions take place. This clearly cannot be a clear-cut division since many processes have a number of steps which involve, in turn, the gas phase, the liquid or solution phase, and the solid phase. By and large, however, the principal characteristic step of each process is associated with either the gas phase or solution, and on this basis a significant subdivision can be made. 

The thermodynamics experiments are subdivided into experiments on calorimetry and heat capacity, Table XVI phase transitions, Table XVII properties of gases, liquids, solids, solutions and mixtures, Table XVIII and finally equilibrium and miscellaneous thermodynamic topics , Table XIX. 

When the liquid and solid-solution phases coexist in equilibrium, the chemical potential of component A must be the same in the liquid and solid phases and similarly for and C. Therefore the sum of the chemical potentials of A and C as well as that for and C is the same in both phases, i.e.,... 

Application of Eqs. (12) and (13) requires in part the specification of the relative chemical potentials in the liquid. The forms adopted are discussed in the following sections. The solid-solution phase is characterized by assuming that its components mix like a quasiregular solution, i.e.,... 

Consider the A-B binary system consisting of liquid solution and a solid solution phases. 

Before presenting some case examples, we note that ab initio calculations are usually carried out for individual molecules (or ions or radicals). Hence, strictly speaking, theoretical results should only be compared with gas-phase experimental data. Cautions should be taken when computational results are compared with data obtained from experiments in the solid state, liquid or solution phase. 

What we mean in this report by equilibrium and disequilibrium requires a brief discussion of definitions. Natural physicochemical systems contain gases, liquids and solids with interfaces forming the boundary between phases and with some solubility of the components from one phase in another depending on the chemical potential of each component. When equilibrium is reached by a heterogeneous system, the rate of transfer of any component between phases is equal in both directions across every interface. This definition demands that all solution reactions in the liquid phase be simultaneously in equilibrium with both gas and solid phases which make contact with that liquid. Homogeneous solution phase reactions, however, are commonly much faster than gas phase or solid phase reactions and faster than gas-liquid, gas-solid and... 

Absolute reaction rates can be affected by molecular diffusion processes that dictate the rates at which collisional encounter complexes occur before reaction. This affect usually shows up in the way reaction rates depend on the physical form of the reactants (gas, liquid, solid, solution, etc.), particularly on concentrations for reactants in gas or hquid phases. Adsorption of reactants onto surfaces can enhance the effective concentrations of reactive species and/or reduce the dimensionahty of the diffusion process. Classic work by Eigen and Richter (14) showed how restricting diffusion to one or two dimensions can dramatically increase potential reaction rates, and this principle has been applied to the kinetics of protein translocation along DNA chains, for example. See References 15 and 16 for more information. 

The equilibrium = f(c ) or the partition between an ionic component in the solid or resin phase and in the fluid phase of multicomponent systems depends on many material properties and the temperature and has to be measured. Things are easier for binary systems in which the ionic species a is exchanged. With the concentration q and the mass fraction in the solid or resin phase and the concentration C3 and the mass fraction in the liquid or solution phase the equilibrium =/(Ca) or a = f (y ) cau be described by the mass actiou equilibriiun Constant or selectivity coefficient (see (9.3-3)) ... 

Plasticizers are frequently incorporated to improve the workability of polymers, but often transform a rigid plastomer into a soft and ductile material. From early times, camphor was used to plasticize nitrocellulose and yield celluloid. Today plasticizers are most common in soft PVC, while unplasticized rigid PVC is also extensively used. Plasticizers may consist of liquids or solids (oils, esters or prepolymers). They are characterized by an extremely low glass-transition temperature, weakening the secondary bond strength in low-crystalline polymers with which they form a solid solution phase. 

Figure 1.9 (a) Phase separation of diblock copolymer (polystyrene-p-polyferrocenyldimethylsilane) guided by substrate strips (adapted from [39] with permission) (b) scheme of liquid-solid-solution (LSS) phase separation and transfer synthetic strategy (reproduced from [41] with permission). 

Amorphous and polycrystalline fibers and near-single crystal whiskers were obtained having diameters of 10-150 nanometers and lengths of several micrometers. Growth of whiskers and short fibers by this method is believed to proceed by a solution-liquid-solid (SLS) phase transformation, suggesting that similar synthesis routes may now also become available for other covalent short fibers and perhaps whiskers. 

In 2005, Li et al developed a general liquid-solid-solution (LSS) strategy for the controlled synthesis of various nanocrystals, including lanthanide-doped UCNPs. In the LSS strategy, oleic acid also acts as a stabihzing agent. Reactants exist in different phases, and reactions occur oifly at the interfaces. This phase separation and transfer mechanism enables a controllable synthesis of monodisperse nanocrystals. Li et further extended this LSS strategy to produce... 

The expression for t in equation (16) is derived assuming that the kinetics of the liquid to crystal transformation are limited by the bulk diffusivity, which is appropriate when the crystal composition differs from that of the liquid, or at compound compositions where substantial diffusion is necessary before the correct spatial relationships that define the ordered structure of the compound are achieved. However, at the temperatures below the To temperature of a disordered solid solution phase, the liquid becomes unstable with respect to a molecularly simple phase of the same composition. Consequently, no long range diffusion is necessary for the liquid to crystal and the kinetics are governed by atom motions of less than one atom in diameter. Then, the transformation is considered to be extremely difficult to suppress and this forms the To criteria for GFA In such cases, it has been suggested that the rate limiting step for aystal growth is proportional to the rate at which... 

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