Enthalpies of a binary alloy during solidification

The purpose of the paper is to present a method of calculating the enthalpy of a dendritic alloy during solidification. The enthalpies of the dendritic solid and interdendritic liquid of alloys of the Pb-Sn system are evaluated, but the method could be applied to other binaries as well. The enthalpies are consistent with a recent evaluation of the thermodynamics of Pb-Sn alloys and with the redistribution of solute during dendritic solidification. Because of the heat of mixing in Pb-Sn alloys, the interdendritic liquid of hypoeutectic alloys (Pb-rich) of less than 50 wt pct Sn has enthalpies that increase as temperature decreases during solidification. For some concentrations of Sn, the enthalpy of the dendritic solid at the solid-liquid interface also increases with decreasing temperature during solidification. Of particular concern in formulating the energy equation is the fact that the heat of fusion during solidification increases as much as 80 pct for hypoeutectic alloys and decreases as much as 325 pct for hypereutectic alloys. Thus the often applied assumptions of a constant specific heat and/or a constant heat of solidification could lead to errors in numerical modeling of temperature fields for dendritic solidification processes.