Equilibrium solidification in a semitransparent planar layer is studied using an isothermal mushy zone model. The layer is made up of a pure material being emitting, absorbing and isotropically scattering and is subject to radiative and convective cooling. The model involves solving simultaneously the transient energy equation and the radiation transport equation. An implicit finite volume scheme is employed to solve the energy equation, with the discrete ordinate method being used to deal with the radiation transport. A systematical parametric study is performed and the effects of various materials optical properties and processing conditions are investigated. It is found that decreasing the optical thickness and increasing the scattering albedo both lead to a wider mushy zone and a slower rate of solidification.