A system for growing an ingot from a melt includes a first crucible, a second crucible, and a weir. The first crucible has a first base and a first sidewall that form an outer cavity for containing the melt. The weir is located on top of the first base at a location inward from the first sidewall to inhibit movement of the melt from a location outward of the weir to a location inward of the weir. The second crucible is sized for placement within the outer cavity and has a second base and a second sidewall that form an inner cavity. Related methods are also disclosed.