Binary systems crystallization

Metivaud V, Lefevre A, Ventola L, Negrier P, Moreno E, Calvet T, Mondieig D, Cuevas-Diarte MA (2005) Hexadecane (C16H34) - - 1-hexadecanol (C16H33OH) binary system crystal structures of the components and experimental phase diagram. Application to thermal protection of liquids. Chem Mater 17 3302-3310... 

An alloy is said to be of Type II if neither the AC nor the BC component has the structure a as its stable crystal form at the temperature range T]. Instead, another phase (P) is stable at T, whereas the a-phase does exist in the phase diagram of the constituents at some different temperature range. It then appears that the alloy environment stabilizes the high-temperature phase of the constituent binary systems. Type II alloys exhibit a a P phase transition at some critical composition Xc, which generally depends on the preparation conditions and temperature. Correspondingly, the alloy properties (e.g., lattice constant, band gaps) often show a derivative discontinuity at Xc. 

The relative amount of the different phases present at a given equilibrium is given by the lever rule. When the equilibrium involves only two phases, the calculation is the same as for a binary system, as considered earlier. Let us apply the lever rule to a situation where we have started out with a liquid with composition P and the crystallization has taken place until the liquid has reached the composition 2 in Figure 4.17(a). The liquid with composition 2 is here in equilibrium with a with composition 2. The relative amount of liquid is then given by... 

Figure 7.13 Compositional trends in plagioclase binary system during crystallization in open or closed systems.

Binary Systems and Related Compounds.—Halides. The thermodynamics of gas-phase equilibria in the W-F2 and W-F2-H2 systems at high temperatures have been described.The Raman spectrum of solid MoF exhibits Mo—F stretching bands at 746, 722, and 690 cm These results suggest that the compound has a similar structure to NbF4, with each molybdenum co-ordinated to six fluorine atoms.The Raman spectrum of crystalline M0F5 has also been reported and interpreted in terms of the crystal structure.The electronic spectrum of liquid M0F5 has been determined and shown to be consistent with a trigonal-bipyramidal molecular unit. ... 

Transition Region Considerations. The conductance of a binary system can be approached from the values of conductivity of the pure electrolyte one follows the variation of conductance as one adds water or other second component to the pure electrolyte. The same approach is useful for other electrochemical properties as well the e.m. f. and the anodic behaviour of light, active metals, for instance. The structure of water in this "transition region" (TR), and therefore its reactions, can be expected to be quite different from its structure and reactions, in dilute aqueous solutions. (The same is true in relation to other non-conducting solvents.) The molecular structure of any liquid can be assumed to be close to that of the crystals from which it is derived. The narrower is the temperature gap between the liquid and the solidus curve, the closer are the structures of liquid and solid. In the composition regions between the pure water and a eutectic point the structure of the liquid is basically like that of water between eutectic and the pure salt or its hydrates the structure is basically that of these compounds. At the eutectic point, the conductance-isotherm runs through a maximum and the viscosity-isotherm breaks. Examples are shown in (125). 

Other general cases in binary systems are referred to as interdiffusion or binary diffusion. For example, Fe-Mg diffusion between two olivine crystals of different Xpo (mole fraction of forsterite Mg2Si04) is called Fe-Mg interdiffusion. Inter-diffusivity often varies across the profile because there are major concentration changes, and diffusivity usually depends on composition. 

Three-Phase Transformations in Binary Systems. Although this chapter focuses on the equilibrium between phases in binary component systems, we have already seen that in the case of a entectic point, phase transformations that occur over minute temperature fluctuations can be represented on phase diagrams as well. These transformations are known as three-phase transformations, becanse they involve three distinct phases that coexist at the transformation temperature. Then-characteristic shapes as they occnr in binary component phase diagrams are summarized in Table 2.3. Here, the Greek letters a, f), y, and so on, designate solid phases, and L designates the liquid phase. Subscripts differentiate between immiscible phases of different compositions. For example, Lj and Ljj are immiscible liquids, and a and a are allotropic solid phases (different crystal structures). 

The temperature of initial crystallization of one of the components of a binary system on cooling is not a CST or cloud point. Some confusion exists in the literature from reporting crystallization points as CST. Many such observations have been corrected for use in these tables by placing the prefix < before the temperature. 

In a binary system more than two fluid phases are possible. For instance a mixture of pentanol and water can split into two liquid phases with a different composition a water-rich liquid phase and a pentanol-rich liquid-phase. If these two liquid phases are in equilibrium with a vapour phase we have a three-phase equilibrium. The existence of two pure solid phases is an often occuring case, but it is also possible that solid solutions or mixed crystals are formed and that solids exists in more than one crystal structure. 

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 a single sublattice crystal (A, B) with a fixed number of lattice sites and a negligible fraction of vacancies, the sum of the fluxes of A and B has to vanish if the number of sites is to be conserved. We just noted that if we formulate the A and B fluxes in the binary system as usual, they will not be equal in opposite directions because of the differing mobilities (bA 4= bB). However, if we have a local production (annihilation) of lattice sites which operates in such a way as to compensate for any differences in the two fluxes by the local lattice shift velocity, vL, we then obtain... 

The vacancy flux and the corresponding lattice shift vanish if bA = bB. In agreement with the irreversible thermodynamics of binary systems i.e., if local equilibrium prevails), there is only one single independent kinetic coefficient, D, necessary for a unique description of the chemical interdiffusion process. Information about individual mobilities and diffusivities can be obtained only from additional knowledge about vL, which must include concepts of the crystal lattice and point defects. 

Eqn. (8.71) constitutes (n-1) differential equations for the spatial distribution of n components in the crystal. The set of equations is complete if the conservation of matter is taken into account. For a binary system (1—2), Eqn. (8.71) is particularly simple to handle since it reduces to... 

Chapters 6 and 7 dealt with solid state reactions in which the product separates the reactants spatially. For binary (or quasi-binary) systems, reactive growth is the only mode possible for an isothermal heterogeneous solid state reaction if local equilibrium prevails and phase transitions are disregarded. In ternary (and higher) systems, another reactive growth mode can occur. This is the internal reaction mode. The reaction product does not form at the contacting surfaces of the two reactants as discussed in Chapters 6 and 7, but instead forms within the interior of one of the reactants or within a solvent crystal. 

The equilibrium interfaces of fluid systems possess one variant chemical potential less than isolated bulk phases with the same number of components. This is due to the additional condition of heterogeneous equilibrium and follows from Gibbs phase rule. As a result, the equilibrium interface of a binary system is invariant at any given P and T, whereas the interface between the phases a and /3 of a ternary system is (mono-) variant. However, we will see later that for multiphase crystals with coherent boundaries, the situation is more complicated. 

In practice, it is often feasible to reduce the multicomponent crystal in respect of its transport behavior to a quasi-binary system. Let us assume that the diffusion coefficients are DA>DB>DC, Dd, etc. The quasi-binary approach considers C, D, etc. as practically immobile, which means that A and B are interdiffusing in the im-... 

Let us inspect more closely the inhomogeneous binary system in Figure 11-3 without external forces. At t = 0, the two crystals A and B (AX and BX) are brought in contact. As t oo, the crystals a and fi have equilibrated. This means that either the a/ft boundary has been shifted to its final position or one of the reactant crystals has been consumed (which only depends on the initial volume ratio VA(t = 0)/VB(t = 0)). 

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