Solid-liquid interface shape control during crystal growth

This paper deals with the problem of controlling the solid-liquid interface shape during solidification of molten material inside a Bridgman-Stockbarger furnace. The boundary conditions that would achieve the desired interface shape are found using feedback controls. A state-space model of the solidification process is determined by employing the finite element method on the governing conduction equation obtained through the apparent heat capacity formulation. This model is used to design a dynamic controller that would set up a desired interface shape by making use of all available temperature measurements