What is the idealized case of unidirectional solidification that is being used to describe the solute profile in single crystals grown by the Czochralski technique? Give the assumptions made for this case and plot the solute profile as a function of distance in the fully solidified bar. Determine the portion of the bar that can be used for wafer production from a Si single crystal for a Cu purity level requirement of 1 ppb when the Cu concentration in the melt is 1ppm. The partition coefficient is 0.0005?