Solubility liquidus curve

At any point along the liquidus curves TA-eAB and Te-eAB, there exist two phases-either solid A -i- melt, or solid B -i- melt Consequently, the degree of freedom F is 1 that is, either the temperature or the composition can be altered without changing the number of phases present (univariant equilibrium). At the eutectic point Oab the two solid phases A and B are in equilibrium with the melt Thus, the number of phases is P = 3, and F = 0, since any variation of the temperature or the composition will invariably displace the system from point Oab at which two solubility (liquidus) curves intersect (invariant equilibrium). 

The immiscibility in the liquid phase was observed for [CjoCilm]Cl with water and for [C8Qlm]Cl wifh water and 1-octanol [51]. For both salts the solubility in 1-octanol was higher than that in water. Only [C8Cilm]Cl was liquid at room temperature (melting point, = 285.4 K) [51]. The binary mixtures of [Ci2Cilm]Cl with n-alkanes and ethers have shown a very flat liquidus curve, but only in [C42Cjlm]Cl + n-dodecane, or methyl 1,1-dimeth-ylether] the immiscibility in the liquid phase was observed for the very low solvent mole fraction [95]. 

The saturation concentration is equal to the solubility of a solid in a liquid at a given temperature. Therefore, its value can in principle be found from the liquidus curve of the equilibrium phase diagram of the A-B binary system (see Fig. 1.1). 

Applying pressurized gases for melt crystallization is advantageous due to their enhanced solubility in liquids. Correspondingly the freezing curve (liquidus curve) depends on pressure, sort of gas and melt. In this the effects of inert gases (i.e. N2) are small and similar to static pressure, but those of more soluble gases (i.e. C02) are much more distinct. 

Fig. 7-29. Phase diagram solvent freezing. LC Liquidus curve SC Solubility curve SOC Solidus curve 1 Temperature...

The liquidus curve was determined by the solubility method. The Cd-clathrate composition at different temperatures was determined by the analysis of the crystals, formed during the isothermal evaporation of the saturated solution after drying them by filter paper (at the same temperature). The most accurate data on the clathrates composition were obtained at room temperature by the saturation of the. initial complexes by 4-methylpyridine through the gas phase. 

Savitskii et al. (1966) reported on the Sc-Re phase diagram. It follows from the figure in their paper that the liquidus curve in the phase diagram and the boundaries of some phase fields need additional refinement. Two binary compounds occur in this system (table 4). pSc dissolves <1 at.% Re, and the solubility of scandium in solid rhenium does not exceed 5-6at.%. Gschneidner (1975) presented the data of Savitskii et al., however he corrected in the figure of the phase diagram the temperatures of some phase transitions with the accepted values. 

In each hatched two-phase region, the lever rule (Section 7.3.2) can be used as usual to determine the relative amounts of the two phases at opposite ends of the tie-line. However, the quantity of precipitated solid a and/or /3 is usually of less interest than the composition of the melt, so the principal focus is on the two liquidus lines that meet at the eutectic point. These liquidus lines are also called solubility curves or freezing-point depression curves, in that they map both the saturation-solubility limits (horizontal variations) as well as the freezing-point depression of the liquid (vertical variations). 

The solubility is defined with respect to a second precipitated phase. The solubility of an impurity is the maximum concentration, which can be incorporated in the liquid or solid phase without precipitating a second phase. For most impurities in solid silicon at high-temperatures, equilibrium is achieved with the liquid phase governed by the liquidus in the phase diagram. Solid solubility is temperature-dependent as represented by the solidus or solvent curves in the phase diagram. At lower temperatures, the reference phase is usually a compound or an impurity-rich alloy. When the impurity is volatile, the saturated crystal is in equilibrium with the vapor, and the impurity solubility also depends on its vapor pressure. 

In general, the various experimental techniques differ in sensitivity, and therefore in usefulness, from one portion of the phase diagram to another. Thus, thermal analysis is the best method for determining the liquidus and solidus, including eutectic and peritectic horizontals, but it may fail to reveal the existence of eutectoid and peritectoid horizontals because of the sluggishness of some solid-state reactions or the small heat effects involved. Such features of the diagram are best determined by microscopic examination or x-ray diffraction, and the same applies to the determination of solvus (solid solubility) curves. 

A typical example of a system in which the components do not combine to form a chemical compound is shown in Figure 4A. Curves AB and BC represent the temperatures at which homogeneous liquid solutions of naphthalene in benzene begin to freeze or to crystallize. The curves also represent, therefore, the temperatures above which mixtures of these two components are completely liquid. The name liquidus is generally given to this type of curve. In aqueous systems of this type one liquidus is the freezing point curve, the other the normal solubility curve. Line DBF represents the temperature at which solid mixtures... 

Figure 3.4 Graphical demonstration ofthe relationship between the liquidus lines of A in the binary phase diagram A - solvent and the solubility curve of A in the solvent.

Figure 13.14 Freezing and meiting as examples of liquid-solid transition in bulk material [R- = oo). Representation of the T-C diagram of a small particle at fixed dimension Ri < Ri (solubility curve is shown for liquidus). Point Pi indicates the initial composition Co before nucleation, point Pi characterizes equilibrium composition Cp...

Liquidus is the solubility curve for liquid particle. So in our Interpretation, the Hquidus curve is in a temperature-concentration diagram, the line connecting the temperatures at which freezing is just started for various compositions of a starting Hquid phase. ... 

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