The Gibbs free energy of mixing can be used to calculate the phase diagram of any system. One of the simplest systems is spinodal decomposition where one phase separates into two distinct phases upon cooling. A separate energy diagram must be calculated for each temperature. The free energy curve for 500C is shown in Figure 1(a), and the position of the common tangent line determines the compositions of the phase boundaries on the phase diagram in Figure 1(b).
Figure 1 (a): Gibbs Free Energy for 500C.
Figure 1 (b): Spinodal Decomposition Phase Diagram.
An important type of steel in stainless steel. In stainless steel, chrome is added in small amounts to prevent corrosion. The phase diagrams for 4 different carbon concentrations of stainless steel are shown in figure 2.
Figure 2: Fe-Cr-C Phase Diagram of 4 Carbon Concentrations.
A very good model on an ideal solution is the gold-silver system shown in Figure 3. These two elements have a complete range of solid solution for all concentrations.
Figure 3: Au-Ag Phase diagram
Steel generally consists of three main phases; austenite, ferrite, and pearlite. Austenite has the FCC structure and is present when steel is quenched from high temperatures. Ferrite is the lower equilibrium phase of iron, and it has a BCC crystal structure. Pearlite is at the eutectoid composition (0.77wt%C) of iron-carbon system and contains alternating layers of ferrite and cementite (Fe3C). Real steels will often contain some amount of all three of these phases which are shown in Figure 4.
(a)
(b)
(c)
Figure 4: Optical Microscopy Images of (a) Austenite, (b) Ferrite, and (c) Pearlite.
The lead-tin system is a simple eutectic system of alpha (Pb rich) and beta (Sn rich) phases. Images of this system for two compositions are shown in Figure 5where the dark regions are the alpha phase and the light regions are the beta phase. The lamellar (layered) structure is a eutectic composition.
(a)
(b)
Figure 5: Optical Microscopy Images of (a) 40wt% Sn and (b) 61.9wt% Sn (eutectic).