That happens because the U shape of the Gibbs free energy curves regarding the chemical composition of both phases, liquid and solid. Notice that the minimum of both curves don't change much with temperature. There is a temperature, however, that gives a comon tanget with a maximimum difference in chemical composition. Notice that there is a maximum length of the tie line in this case. As the temperature increases or decreases the Gibbs free energy curves go up and down and since the mininum don't change much, the comon tangent get's more and more inclinated producing shorter tie lines until solidus and liquidus meet at the melting point of the pure compounds. Therefore the resulting curvature upwards and downwards are actualy caused by a horizotal (chemical) separation (or segregation) of both phases for each temperature. Take a look at these slides: https://www.slideserve.com/tamika/binary-phase-diagrams

Actually this is not the case. For example, in the Au-Pd binary both liquidus and solidus are above the line, connecting m.p. of the components, and both liquidus and solidus are convex upwards. There seems to be many analogous cases.

Moreover, your statement definitely contradicts to existence of the extrema (minima and/or maxima) of the melting curves, which are not unusual in phase diagrams.

In principle, the line connecting the m.p. falls to two-phase region, only when the so-called T_0 line (line of equal Gibbs energies of both phases) is close to the line connecting m.p. of components. The condition of realization of this case can be found by writing down of some appropriate models of liquid and solid with further equating of both.

Hi

Isomorphous System is a System which satisfies all Hume-Rothery Rules of Solid Solubility,a typical loop type of phase diagram with single phase( liquid) above and two phases (liquid and solid) in between followed by single solid phase at bottom with end points tagged onto the melting points of two elements. liquidus(line joining points with begining of solidification) and solidus (line connecting points with end of solidification),ideally these line should be above and below the line connecting melting points of both elements but sporadic instances might occur with both liquidus and solidus both being occurring upwards above(few cases) the line joining the melting points,below(rare or null). i visualize the chemical potential,fugacity and Free energy of Mixing of these peculiar elements together may be playing vital significant role either in bringing out convexity upwards or concave.

thanks & regards,

g.sudhakar

phd(materials engineering)

hcu.