Solids, binary systems melting

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. 

Figure 4.10 (a)-(i) Phase diagrams of the hypothetical binary system A-B consisting of regular solid and liquid solution phases for selected combinations of Q q and Qs°l. The entropy of fusion of compounds A and B is 10 J K 1 mol-l while the melting temperatures are 800 and 1000 K. 

The first system concerns refractory (high melting) alloys, the second one very low melting (close to room temperature) alloys. However, both diagrams are representative of the melting behaviour of binary systems in which the two components are mutually and completely (in all proportions) soluble with each other in the liquid and in the solid state. 

Figure 2.1. Examples of melting phase diagrams of binary systems showing complete mutual solubility in the solid and in the liquid states (L liquid field, S solid field). The melting behaviour of the Mo-V, Cs-Rb and Ca-Sr alloys is presented. Notice the different ranges of temperature involved. The melting points of the pure metal components are shown on the corresponding vertical axes. The Cs-Rb is an example of a system showing a minimum in the melting temperature. In the Sr-Ca system complete mutual solid solubility is shown in both the allotropic forms a and (3 of the two metals.

Figure 2.9. Examples of melting phase diagrams of binary systems showing complete mutual solubility in the liquid state and, at high temperature only, in the solid state. By lowering the temperature, however, the continuous solid solution decomposes into two phases. In (d) a schematic representation of NiAu or PtAu type diagrams is shown as formed by two generic components A and B.

Temperature, pressure, and concentration can affect phase equilibria in a two-component or binary system, although the effect of pressure is usually negligible and data can be shown on a two-dimensional temperature-concentration plot. Three basic types of binary system — eutectics, solid solutions, and systems with compound formation—are considered and, although the terminology used is specific to melt systems, the types of behaviour described may also be exhibited by aqueous solutions of salts, since, as Mullin 3-1 points out, there is no fundamental difference in behaviour between a melt and a solution. 

A melt is a liquid or a liquid mixture at a temperature near its freezing point and melt crystallisation is the process of separating the components of a liquid mixture by cooling until crystallised solid is deposited from the liquid phase. Where the crystallisation process is used to separate, or partially separate, the components, the composition of the crystallised solid will differ from that of the liquid mixture from which it is deposited. The ease or difficulty of separating one component from a multi-component mixture by crystallisation may be represented by a phase diagram as shown in Figures 15.4 and 15.5, both of which depict binary systems — the former depicts a eutectic, and the latter a continuous series of solid solutions. These two systems behave quite differently on freezing since a eutectic system can deposit a pure component, whereas a solid solution can only deposit a mixture of components. 

Typically, the liquidus lines of a binary system curve down and intersect with the solidus line at the eutectic point, where a liquid coexists with the solid phases of both components. In this sense, the mixture of two solvents should have an expanded liquid range with a lower melting temperature than that of either solvent individually. As Figure 4 shows, the most popular solvent combination used for lithium ion technology, LiPFe/EC/DMC, has liquidus lines below the mp of either EC or DMC, and the eutectic point lies at —7.6 °C with molar fractions of - 0.30 EC and "-"0.70 DMC. This composition corresponds to volume fractions of 0.24 EC and 0.76 DMC or weight fractions of 0.28 EC and 0.71 DMC. Due to the high mp of both EC (36 X) and DMC (4.6 X), this low-temperature limit is rather high and needs improvement if applications in cold environments are to be considered. 

Eutectic diagrams (from Greek svtt]ktoo- easily melted ) represent the T-x melting behavior for binary systems with completely immiscible solid phases a, /3. The solid a, /3 phases often correspond to (virtually) pure components A, B, respectively, so we may treat phase and component labels (rather loosely) as interchangeable in this limit. 

In Figure 14.20c, the pressure is 124 MPa. At this pressure the melting curves for water and for acetonitrile intersect the (liquid + liquid) curve at the same temperature. Thus, both ice and solid acetonitrile are in equilibrium with the two liquid phases. The temperature where this occurs is a quadruple point, with four phases in equilibrium. This quadruple point for a binary system, like the triple point for a pure substance, is invariant with zero degrees of freedom. That is, it occurs only at a specific pressure and temperature, and the compositions of all four phases in equilibrium are fixed. 

The A-B binary system behaves ideally in both its liquid and solid solutions. The element A melts at 1.S00K with the heat of fusion of 14,700 Jmol 1, and the heat... 

Generally, these factors can act either in the same direction, strengthening the effect of each other, or in the opposite direction, thereby weakening this effect. In the former case, the final result is quite obvious, whereas in the latter it is hardly predictable a priori. For example, in the Ni-Bi binary system the melting point of nickel is 1455°C, while that of bismuth is 271°C. Atomic radii are 0.124 nm and 0.182 nm, respectively. From the point of view of melting temperatures, bismuth may be expected to be more mobile in the nickel bismuthides in the solid state, whereas from the point of view of atomic radii smaller nickel atoms must diffuse much faster. In this particular case, the effect of the difference in the melting points is known to prevail over effect of the difference in the atomic radii.149 150... 

Although the assumption of a quasistationary distribution of the concentration of component A within the diffusion boundary layer seems to be very rough, nevertheless under conditions of sufficiently intensive convection the dissolution kinetics of solids in liquids is well described by equations (5.1) and (5.8)-(5.10) (see Refs 301, 303, 304, 306-308). Clearly, these equations are generally applicable at a low solubility of the solid in the liquid phase (about 10-100 kg m or up to 5 mass %). Note that they may also describe fairly well the dissolution process in systems of much higher solubility. An example is the Al-Ni binary system in which the solubility of nickel in aluminium amounts to 10 mass % even at a relatively low temperature of 700°C (in comparison with the melting point of aluminium, 660°C).308... 

The crystallization temperature depends on the composition of the mixture to be treated. The cooling diagram shows that a eutectic exists between p-xylene and each of the other components of the mixture. In the case of the m, p-xyiene binary system, the eutectic contains 13 per cent p-xylene and melts at —52 C (Fig. 4.10). It separates two iiquidus curves ME in equilibrium with solid m-xylene, PE in equilibrium with solid p-xylene. Provided that the initial mixture contains more than 13 per cent p-xyleoe. crystals of pure p-xylene are obtained by cooling to — 52 and a mother liquor, whose composition is that of the eutectic. However, it qan be noticed (bat the existence of the eutectic leads to limited recovery, and that this recovery requires beat exchanges at low temperature. 

The temperature-composition phase diagram constructed from thermal arrests observed in the MoFe-UFa system is characteristic of a binary system forming solid solutions, a minimum-melting mixture (22 mole % UFe at 13.7°C.), and a solid-miscibility gap. The maximum solid solubility of MoFq in the UFe lattice is about 30 mole % MoFe, whereas the maximum solid solubility of UFe in the MoFe lattice is 12 to 18 mole % UFe- The temperature of the solid-state transformation of MoFe increases from ——lO C. in pure MoFe to 5°C. in mixtures with UFe, indicating that the solid solubility of UFe is greater in the low temperature form of MoFe than in the high temperature form of MoFe- This solid-solubility relationship is consistent with the crystal structures of the pure components The low temperature form of MoFe has an orthorhombic structure similar to that of UFe. 

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