An apparatus for controlling heat flow within a melt. The apparatus may include a crucible configured to contain the melt where the melt has an exposed surface. The apparatus may also include a heater disposed below a first side of the crucible and configured to supply heat through the melt to the exposed surface, and a heat diffusion barrier assembly comprising at least one heat diffusion barrier disposed within the crucible and defining an isolation region in the melt and an outer region in the melt.