Solidus and liquidus curves

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. 

For solid-liquid equilibrium also the latent heats are usually positive, and it follows that the slopes at corresponding points on the solidus and liquidus curves at constant pressure also have the same sign. If the latent heats were not positive, then the slopes could be the same or different. 

The solidus and liquidus curves coincide and reduce to a single horizontal line. Two examples of this behaviour may be mentioned first, the c -camphroxime + -camphroxime system studied by Adriani and secondly the di-chloro- + chlorobromo ethyl acetamide system, f... 

Another important projection of the PvT-diagram is the PT-graph (see Figure 2.5). In this projection, the dew-point line coincides with the boiling point in the vapor pressure curve. Similarly, solidus and liquidus curve coincide in the melting curve. The phase transition between the solid state and the gaseous state is described by the sublimation curve. Vapor pressure curve, melting curve, and sublimation curve meet at the triple point, where the three phases vapor, liquid, and solid coexist in equilibrium. The triple point of water is very well known and can be reproduced in a so-called triple point cell. It is used as a fix point of the International Temperature Scale ITS-90 [4] (Tt, = 273.16 K or = 0.01"C, Ptr = 611.657 0.01 Pa). The vapor pressure curve ends at the critical point no liquid exists above the critical temperature T. ... 

Figure 13.15 Representation of the freezing process for the liquid nanoparticle (a) and melting of the solid nanoparticle (b) at fixed size R and initial composition Q. Fragments of solidus and liquidus curves of the same particle (a, b). The melting and freezing loops between solidus and liquidus...

Figure 1.9 is a temperature versus composition diagram for a hypothetical binary system with a minimum in the solidus and liquidus curves and a miscibility gap in the solid state. This is similar to the binary... 

Equation (6.84) may be arranged to give the phase boundaries of the solidus and liquidus curves as... 

In this way, the complete solidus and liquidus curves of the binary phase diagram can be calculated. The only data required are the melting temperatures of the pure substances, and T g, and the corresponding heats of fusion, AHm,A and AHm.B, respectively. 

The other single phase region is the liquid L. In addition to the two phase a+0 region, there are two other two phase regions L + a and L + 0. Just as in the isomorphous diagram the solidus and liquidus lines are connected by tie-lines of constant temperature. In a like manner, the a + 0 region is also considered to possess tie-lines joining the two solid-solution or solvus curves. 

The phase diagram as constructed by Markova et al. showed a minimum in the liquidus and solidus curves at about 1330°C and at a composition of about 45 at% Y. However, comparison with the work of Spedding et al. (1973) on Er-Y and related systems suggests that no minimum exists. Thus their diagram has been modified to the more likely construction shown in fig. 107. In this diagram there is a gradual nonlinear increase in the solidus and liquidus temperatures as the yttrium... 

More advanced techniques are now available and section 4.2.1.2 described differential scanning calorimetry (DSC) and differential thermal analysis (DTA). DTA, in particular, is widely used for determination of liquidus and solidus points and an excellent case of its application is in the In-Pb system studied by Evans and Prince (1978) who used a DTA technique after Smith (1940). In this method the rate of heat transfer between specimen and furnace is maintained at a constant value and cooling curves determined during solidification. During the solidification process itself cooling rates of the order of 1.25°C min" were used. This particular paper is of great interest in that it shows a very precise determination of the liquidus, but clearly demonstrates the problems associated widi determining solidus temperatures. 

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