Interpretation and calculation of first-melting projections of phase diagrams

• First-melting projections of phase diagrams are defined.
• In most systems they are identical to solidus projections.
• They obey the same topological rules as isothermal sections.
• Exceptions occur only in systems with catatectics or retrograde solid solubility.
• An algorithm to calculate first-melting projections thermodynamically is outlined.

The first-melting projection of the phase diagram of a ternary or higher-order system shows the temperature at which a liquid phase first appears upon heating at any given composition in a system at thermodynamic equilibrium. In most systems, first-melting projections are identical to solidus projections. It is shown that they obey the same well-known topological rules as isothermal sections of phase diagrams. Hence, their interpretation is straightforward. Only in systems with catatectic invariants or retrograde solid solubility do exceptions to these rules occur, and then only over limited composition regions. In these regions the first-melting and solidus projections are not identical. In such cases it is preferable to plot the first-melting projection which is always single-valued at all compositions. A general algorithm for calculating first-melting projections thermodynamically is outlined.