Consider a eutectic binary system A-B. Discuss the three idealized cases of solidification of a one-dimensional bar for an A-rich alloy where the concentration of B is below its solubility limit at the eutectic temperature. List the assumptions made for each case; draw and briefly explain the concentration profiles of B in the fully solidified bar. Which of the three cases is used to describe the dopant/impurity distribution in single crystals grown by the Bridgman technique?