Binary solids

A brief discussion of sohd-liquid phase equihbrium is presented prior to discussing specific crystalhzation methods. Figures 20-1 and 20-2 illustrate the phase diagrams for binary sohd-solution and eutectic systems, respectively. In the case of binary solid-solution systems, illustrated in Fig. 20-1, the liquid and solid phases contain equilibrium quantities of both components in a manner similar to vapor-hquid phase behavior. This type of behavior causes separation difficulties since multiple stages are required. In principle, however, high purity... 

The dominant mechanism of purification for column crystallization of solid-solution systems is recrystallization. The rate of mass transfer resulting from recrystallization is related to the concentrations of the solid phase and free liquid which are in intimate contact. A model based on height-of-transfer-unit (HTU) concepts representing the composition profile in the purification section for the high-melting component of a binary solid-solution system has been reported by Powers et al. (in Zief and Wilcox, op. cit., p. 363) for total-reflux operation. Typical data for the purification of a solid-solution system, azobenzene-stilbene, are shown in Fig. 20-10. The column crystallizer was operated at total reflux. The solid line through the data was com-putecfby Powers et al. (op. cit., p. 364) by using an experimental HTU value of 3.3 cm. 

Considering first the case of homogeneous binary solids consisting of a matrix M in which atoms A are embedded ... 

Figure 49 shows a set of bed collapsing curves for a Geldart Group A-A (for Geldart s classification of solid particles, see Geldart, 1972, 1973) binary solids mixture, two closely sized alumina powders, of average particle diameter 104 and 66 microns, respectively. The curve on the extreme left with 0% fines represents the pure coarse component, which is... 

Models can be constructed in this manner (e.g., Bourcier, 1985), but most modelers choose for practical reasons to consider only minerals of fixed composition. The data needed to calculate activities in even binary solid solutions are, for the... 

The distribution of componentsof binary solid solutions over the solid phase and the aqueous phase has been studied for a number of systems. Table I contains a summary of some of these systems with references. This literature review is not complete more data are available especially for rare earth and actinide compounds, which primarily obey type I Equations to a good approximation. In the following sections, the theory above will be applied to some special systems which are relevant to the fields of analytical chemistry, inorganic chemistry, mineralogy, oceanography and biominerals. 

Figure 8. Free enthalpy of mixing G of binary solid solutions (regular) Ca,. (PO ) OH F as a function of x at W/2.303 RT = 1.4.

By examining the compositional dependence of the equilibrium constant, the provisional thermodynamic properties of the solid solutions can be determined. Activity coefficients for solid phase components may be derived from an application of the Gibbs-Duhem equation to the measured compositional dependence of the equilibrium constant in binary solid solutions (10). 

Table 3.1. An example of crystallochemical description of an alloy system. Binary solid phases in the Al-Cu system.

Moritomi, H., Yamagishi, T. and Chiba, T. Chem. Eng. Sci. 41 (1986) 297. Prediction of complete mixing of liquid-fluidized binary solid particles. 

Figure 7J Gibbs free energy curves and T-X phase stability relations between a phase with complete miscibility of components (silicate melt L) and a binary solid mixture with partial miscibility of components (crystals ]8). 

Soluble heptapnicanortricyclane anions [Pny] (Fig. 3a) and trishomocubane-shaped (ufosane-like) anions [Pnn] (Fig. 3d) are very common and known as in the binary solids for Pn = P, As, Sb (Table 2). Oxidative coupling of these monomers leads to the dimers [Pny-Pny]" and [Pnn-Pnn]" for Pn = P and As (Fig. 3b, e), which - as observed for the tetrel element clusters - have an external homoatomic bond, but in this case the structures of the monomeric units are fully retained upon dimerization. A trimeric oxidative coupling product of [Py] is the... 

Example 4.1. Suppose olivine and garnet are in contact and olivine is on the left-hand side (x<0). Ignore the anisotropic diffusion effect in olivine. Suppose Fe-Mg interdiffusion between the two minerals may be treated as one dimensional. Assume olivine is a binary solid solution between fayalite and forsterite, and garnet is a binary solid solution between almandine and pyrope. Hence, Cpe + CMg= 1 for both phases, where C is mole fraction. Let initial Fe/(Fe- -Mg) = 0.12 in olivine and 0.2 in garnet. Let Xq = (Fe/Mg)gt/ (Fe/Mg)oi = 3, >Fe-Mg,oi = 10 ° mm+s, and Dpe-Mg,gt =... 

Spinodal decompositions, often observed in binary solid solutions of metals and in glasses, on the other hand, arise from thermodynamic instabilities caused by composition (Cahn, 1968). A special feature of this type of solid state transformation is the absence of any nucleation barrier. There is a class of transformation called eutectoid decomposition in which a single phase decomposes into two coupled phases of different compositions, the morphology generally consisting of parallel lamellae or of rods of one phase in the matrix of the other. 

When = 0, then = 1 and the chemical potential Ac is that of the binary solid AC(s), Ac- This, of course, is also the Gibbs energy of AC(s). Since the restriction that be confined to values near unity is intended to apply to the end members of the solid solution, Ac as well as Ac are independent of also. Similarly, when = 1, then = 1 and Ac equals the Gibbs energy of BC(s), Ac-... 

A hydride formed in the reaction of a binary solid-solution alloy with hydrogen can be considered as a solid solution of two binary hydrides and will have properties related to the properties of the constituent binary hydrides. An intermetallic-compound hydride, however, formed in accordance with Reaction... 

The T-x diagrams for binary solid-liquid systems can be categorized into four primary types ... 

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. 

In many cases, p is rather insensitive to the composition (NAO) because both A21 and B2+ are rendered mobile by the same vacancies in the same sublattice. In deriving Eqn. (8.11), we have assumed that (A, B)0 is an ideal quasi-binary solid solution. Analogous to Eqn. (8.6), Eqn. (8.11) has to be integrated under the restricting condition of the conservation of cation species A and B. There is no analytical solution to this problem, but a numerical solution has been presented in [H. Schmalzried, et al. (1979)]. 

Spherical Particle during Diffusion-Limited Growth in an Isothermal Binary Solid. This problem was analyzed by Mullins and Sekerka who found expressions for the rate of growth or decay of shape perturbations to a spherical H-rich /3-phase particle of fixed composition growing in an a matrix as in Section 20.2.1 [9]. Perturbations are written in the form of spherical harmonics. Steps to solve this problem are ... 

CARBIDES. A binary solid compound of carbon and another element. The most familiar carbides are those of calcium, tungsten, silicon, boron, and iron (cemcntitc) Two factors have an important bearing on the properties of carbides (1) the difference in electronegativity between carbon and the second elemenl. and (2) whether the second element is a transition metal. Saltlike carbides of alkali metals are obtained by reaction with acetylene. Those ohlained from silver, copper, and mercury sails are explosive. See also Carbon and Iron Metals, Alloys, and Steels. 

The case of binary solid-liquid equilibrium permits one to focus on liquid-phase nonidealities because the activity coefficient of solid component ij, Yjj, equals unity. Aselage et al. (148) investigated the liquid-solution behavior in the well-characterized Ga-Sb and In-Sb systems. The availability of a thermodynamically consistent data base (measurements of liquidus, component activity, and enthalpy of mixing) provided the opportunity to examine a variety of solution models. Little difference was found among seven models in their ability to fit the combined data base, although asymmetric models are expected to perform better in some systems. 

The successful conversion of graphite to diamond involves crystallizing the diamond from a liquid melt. The solvent most often used is nickel metal, or alloys of nickel with other ferrous metals. The reason for this success can be seen by referring to Figure 15.7, the binary (solid + liquid) phase diagram for (nickel + carbon).u8 We note from the figure that (Ni + C) forms a simple... 

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