Liquidus line, slope

The shape, the slope, of the liquidus line (or liquidus surface) is obviously an important point which has to be considered. 

Implied in this discussion is that the exothermic deviation of the trace (in the temperature region where liquid and solid are in equilibrium) should follow the slope of the liquidus line Thus, it is conceivable that the shape of the liquidus line can be predicted from the shape of a single DTA cooling trace of a strategic (e.g. 59 mol% AI2O3) composition. 

Figure 4.17 Graphical determina-tion of the volume-based fictive tem-perature for a glass cooled to temperature T with specific volume ui and then aged so that its specific volume drops to V2, V3, and finally V4. The fictive temperature for the glass at any point in its history is obtained by ex-tending a line with slope ag through the specific volume of the glass until it intersects the extrapolated liquidus line with slope Off. If aging continues until the specific volume lies on the liquidus line, then Tf — T, and aging stops.

The negative sloping liquidus line at low pressures, unique among the rare earth metals, is also an obvious anomaly. Not obvious from a P—T diagram is the fact that in cerium, one has an element which is both an antiferromagnet (/ -Ce) and a superconductor at high pressures, see fig. 12b (a-, a - and a"-Ce). Cerium is indeed a fascinating element. 

The difficulty that arises from partial solubility in the solid phase is considered next. This situation is illustrated by curve A in Fig. 4JZ3. Calorimetry can be used to evaluate the slope of the liquidus line, d7jj /dr2, as is demonstrated by Eq. (3), listed in Fig. 5.29. The slope of the melting temperature with changing concentration is equal to / 7jj, /A//f multipUed by K - 1). In this case, AFTf is the integrated heat of fusion up to Tm and K is the distribution coefficient, the ratio of the solubility in the solid phase to the solubility in the liquid phase. If K is equal to zero, Eq. (3) reverts back into the differential of Eq. (1). The distribution coefficient is concentration-dependent and must be known separately. 

In liquid phase epitaxial growth of compound semiconductor layers, the growth rate depends on the slope of the liquidus line and on the supercooling AT at the time of the initial contact between substrate and growth solution. This is another example that illustrates that the growth kinetics is determined by thermodynamic phase relations. 

Since the thermal arrests were within 1.5°C on both the heating and cooling curves, as is the case for pure metals, the liquidus-solidus line and the solvus line for the bcc hep transformation were drawn as single lines. The transformation temperature of terbium was found to be raised linearly by the addition of holmium but at a greater slope than the melting temperature. Extrapolation of the transformation temperature curve to the solidus showed that the two curves intersect at 90 at% Ho. This confirms the absence of the bcc form at high temperatures in holmium. 

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