Solubility liquidus

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 electrolysis temperature affects the electrolyte conductivity, the overpotential, and the solubility of the electrodeposit in aqueous as well as in molten salt systems. The effect of temperature is particularly important in the latter case. The lower limit of the temperature of operation is set by the liquidus temperature of the bath and the solubility of the solute. Generally, the temperature chosen is at least 50 °C above the melting temperature of... 

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 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]. 

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). 

In the solubility poly therms in the M(OR)n-ROH (M = Li, Mg, Ca, Sr, Ba R = Me, Et) systems, the shape of the liquidus lines has usually a specific character the solubility of solvates increases with temperature up to their partial or complete desolvation in contact with the solvent. The sign of the AH for dissolution changes at this point, and the solubility of the M(OR) or less solvated forms decreases drastically with temperature (see solubility poly therms for LiOMe, LiOEt in the Fig. 3.1). The polarity of the M-0 bonds in MOR and Ba(OR)2 — the first members of the homologous series — causes their ability to electrolytic dissociation and noticeable conductivity for their solutions in polar solvents (its value in alcohols is only several times lower than that of such strong electrolytes as NaOH and KOH) [112],... 

Consider an aluminum-rich binary aluminum-silicon alloy. The melting temperature of aluminum is 660 °C, and the eutectic is at 577 °C and 12.6 wt% Si. The maximum solubility of silicon in aluminum is 1.65% Si at 577 °C. The liquidus and solidus can be approximated by straight lines. The difflisivity of silicon in liquid aluminum is 8 x 10-8 m2/s. Freezing occurs at a rate of 10 pm/s. 

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. 

The typical features of the phase diagram of Al-rare earth alloys are high liquid solubility, low solid solubility of rare earths and relatively low liquidus temperatures. The low diffusivity of rare earths in these alloys is an attractive feature from the point of view of the thermal stability of the dispersoids. 

In many cases, there is partial solid solubility between the pure components of a binary system, as in the Pb-Sn phase diagram of Figure 11.5, for example. The solubility limits of one component in the other are given by solvus lines. Note that the solid solubility limits are not reciprocal. Lead will dissolve up to 18.3 percent Sn, but Sn will dissolve only up to 2.2 percent Pb. In Figure 11.5, there are two two-phase fields. Each is bounded by a distinct solvus and liquidus line, and the common sofidus line. One two-phase field consists of a mixmre of eutectic crystals and crystals containing Sn solute dissolved in Pb solvent. The other two-phase field consists of a mixture of eutectic crystals and crystals containing Pb solute dissolved in Sn solvent. 

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