Phase liquidus curve

The binary system lead-thallium shows an unusual type of phase diagram. Fig. 1, taken from Hansen (1936), represents in the main the results obtained by Kumakow Pushin (1907) and by Lewkonja (1907). The liquidus curve in the wide solid-solution region has a maximum at about 63 atomic percent thallium. The nature of this maximum has not previously been made clear. 

For the alloy marked 1 , on cooling, the liquidus curve was intercepted at a relatively high temperature and there was a fair temperature interval during which for the Mg crystals it was possible to grow within the remaining part of liquid. The solidification finally ended at the eutectic temperature. At this temperature the eutectic crystallization occurs (L (Mg) + Cu2Mg) in isothermal conditions, where the simultaneous separation of the two solid phases results in a fine mixture... 

Figure 2.40. Phase diagram of the Mg-Cu alloy system. For the alloys marked (1) (at 5 at.% Cu) and (2) (at 20 at.% Cu), the DTA curves are shown on the right. Notice that, on cooling, a sharp thermal effect due to the invariant eutectic transformation is observed. At higher temperature the crossing of the liquidus curves is detected. (The coordinates of the eutectic point are 485°C and 14.5 at.% Cu.)...

Figure 7.9A shows the NaAlSi04-Si02 (nepheline-silica) system, after Schairer and Bowen (1956). Let us first examine the Si02-rich side of the join. At P = 1 bar, the pure component Si02 crystallizes in the cristobalite form (Cr) at r = 1713 °C (cf figure 2.6). At P = 1470 °C, there is a phase transition to tridymite (Tr), which does not appreciably affect the form of the liquidus curve, which reaches the eutectic point at P = 1062 °C. 

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 interesting influence of the cation on the SLE diagram IL + water can be observed [99,100] from the diagrams of ammonium salts [(Cio)2(Q)2N][N03] and [Be(Ci)2C N][N03]. Simple liquidus curve and no immiscibility in the liquid phase for the didecyldimethylammonium cation with the eutectic point shifted strongly to the solvent-rich side was noted (see Figure 1.11). 

Figure 1.12 Influence of pressure on the liquidus curve of [CjCjIm][CjS04] (1) + 1-hexanol (2) up to 360 MPa (Adapted from Domariska, U. and Morawski, R, Green Chem., 9, 361, 2007.) experimental points (O), solid line, description with the Yang equation. (Adapted from Yang, M. et al.. Fluid Phase Equilib., 204, 55, 2003.)...

The general case of two compounds forming a continuous series of solid solutions may now be considered. The components are completely miscible in the solid state and also in the liquid state. Three different types of curves are known. The most important is that in which the freezing points (or melting points) of all mixtures lie between the freezing points (or melting points) of the pure components. The equilibrium diagram is shown in Fig. 1,16, 1. The liquidus curve portrays the composition of the liquid phase in equilibrium with solid, the composition of... 

The two upper curves, termed the liquidus curve, define the temperatures at which Au-Si alloys begin to solidify. The curves meet at 363°C at an alloy composition containing 18.6 atomic percent Si. At this temperature, all Au-Si alloys, irrespective of composition, complete their solidification by the eutectic separation of a fine mixture of Au and Si from the liquid phase containing 18.5 atomic percent Si. The horizontal line at 363°C is called the solidus because below such a line all of the alloys arc completely solid. 

A major complication in the analysis of convection and segregation in melt crystal growth is the need for simultaneous calculation of the melt-crystal interface shape with the temperature, velocity, and pressure fields. For low growth rates, for which the assumption of local thermal equilibrium is valid, the shape of the solidification interface dDbI is given by the shape of the liquidus curve Tm(c) for the binary phase diagram ... 

The bottom line of the diagram is called the liquidus curve. This line represents a collection of the melting points of all mixtures and of the pure components A and B. The top line is called the solidus curve and is a collection of all the solidification points of all mixtures and the pure substances A and B. In the L field one liquid phase and in the S field one solid phase occur. In the L + S field a solid and a liquid phase are present. How should such a diagram be read First of all it is important to realise that every point in the diagram represents a system which is characterized by a temperature, com-... 

In this manner, the criterion, Pn(p) exp[At / Ate -1] = U represents the liquidus curve in the composition-temperature phase equilibrium diagram. Clearly, the shape of the L "( p, T ) = 1 curve must be parallel with the configuration probability, P"(p). The correspondence between these physical arguments and an actual phase equilibrium diagram (the Li-Hg system) for Ti.Tm, and T2 is illustrated in Fig. 12. 

Correlation b) there are a number of systems in which an AB2 compound exists with Ra + Rb. The fact that the liquidus curves associated with these compounds indeed follow the correlation is demonstrated in Fig. 15. The sole exception, CaAl2, is.probably due to experimental error. The Au-Na system, in which the originally reported phase diagram [18] shows a contradiction to the correlation whereas the revised phase diagram [19] conforms to the correlation, is an example of such an error (Fig. 16). 

Fig. 14. Phase diagrams containing II-VF or III-V compounds which assume the B-3 type structure. Consistently gentle liquidus curves associated with these compounds are observed.

Fig. 15. Phase diagrams containing AB2 compounds (where RA Rb). Liquidus curves leaning toward the element with the larger atomic radius is observed.

On the Eutectic Composition A eutectic system is best represented by the Ag-Cu phase diagram as shown in Fig 16. As explained earlier, the eutectic point is the point at which two liquidus curves meet. And the horizontal line intersecting the eutectic point is known as eutectic line. Normally, the eutectic composition of 28.1 at. % Cu below eutectic line is left open [29] as shown in Fig. 16-(a). However in a strict sense this is not correct and in my view as well as in the view of a few other scientists [30], the eutectic composition should be indicated with a straight vertical solid or dotted line as shown in Fig.l6-(b). We shall now examine in detail the reason for the correctness of such view i.e., indicating the eutectic composition by a solid or dotted vertical line as shown in Fig. 16-(b). 

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). 

In the preceding cases the solidus and liquidus curves meet tangentially to an isothermal line at a congruent point the solution freezes at this temperature without any change in composition. Au—Ni alloys exhibit the behavior depicted in Fig. 3.15.2. Inasmuch as AHC > 0 for this case, the solid solution for T < Tc is less stable than a mixture of phases this is indicated by the dotted curve at the bottom of the diagram. 

A general feature of the phase diagrams explored in Figs. 3.15.7 and 3.15.8 is the existence of a maximum in the solidus and liquidus curves, corresponding to the composition of the intermediate f) phase. This reflects the composition at which G, and Gs first become tangent to each other. However, this point generally does not coincide exactly with the minimum in G the composition of the intermediate phase then does not agree precisely with the ideal stoichiometric formula for the phase. 

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