The effect of the formation of a random distribution of elements and of lattice defects in a solid during solidification processes on the thermodynamics is discussed. The relationships describing the change in melting point and the composition of the solid phase from those in the equilibrium state are derived. The effect between different species and vacancies on the interaction is discussed. The derived models are used to illustrate the effect in some aluminium and copper based alloys. The models are also used to describe the formation of divacancies and a short range ordered structure in the equilibrium state. The formation of a compounds between vacancies and alloying elements are described by the models.