Let B be an impurity in A, with X << 1. In this limit the non-mixing parts of the free energy can be expressed as linear functions of x, as f0(x) = f0(0) + xf0(0), for both liquid and solid phase. Assume that the liquid mixture is in equilibrium with the solid mixture. Calculate the equilibrium concentration ratio k = xS/xL, called the segregation coefficient. For many systems k << 1, and then a substance may be purified by melting and partial re-solidification, discarding a small fraction of the melt. This principle is widely used in the purification of materials, as in the zone refining of semiconductors. Give a numerical value for k for fos’ – foL’ 1eV and T = 1000 K.