The phase transformation of multicomponent aluminosilicates on liquidus curves becomes an important parameter in the prediction of the slag behavior upon cooling. Three major factors are taken into consideration: (1) thermodynamic driving forces for a selection of stable phases on liquidus curves, such as free energies of components at various temperatures, (2) the effect of free energy of mixing on the tendency to phase segregation in liquid solution on cooling, and (3) free energy change at the solid-melt interface and entropy of fusion and their effects on the morphology of the crystalline phase(s). In order to identify the solid phase(s) crystallized from ash slag it is proposed, first, to calculate major binary free energy composition diagrams based on major oxides in ash and, second, to select phase(s) with the free energy and composition constrained by free energy diagrams. It is postulated that the free energy of the solid-melt interface plays a significant role in the selection of crystal size; the small Delta G(int) constrains the formation of fine crystallites, while the large Delta G(int) indicates the formation of large crystals in a slag. It is quite apparent that the low Delta G(int) contributes to lowering the activation energy of nucleation. Both examples, the nucleation of fine crystallites and the grwoth of large crystals, are evident in Beulah and Illinois No. 6 ash slags. In ash slags the phase transformation may occur either by nucleation or by spinodal decomposition, both of which are recorded in Beulah and Gascoyne ash slags. The spinodal decomposition causes a sharp increase of slag's viscosity. The differential thermal analysis (DTA) technique shows endotherms in Pittsburgh No. 8 and Gascoyne White ash slags, on heating, near and above the temperature of critical viscosity that are assigned to the dissolution of solid phases into the melt and anomalies in melt thermal conductivity, respectively.