Polycrystalline semiconductor rods are converted to dislocation-free monocrystal rods by positioning a polycrystalline rod within a crucible-free zone melt environment with a seed crystal attached to one end thereof, generating a melt zone at the juncture of the seed crystal and the polycrystalline rod, controllably moving the melt zone away from the juncture and through the polycrystalline rod to a select point thereon, uniformly supporting the cone-shaped lower portion of the rod being processed so as to prevent oscillations and the like at the juncture of the rod in the seed crystal and controllably moving the melt zone from the select point to the remainder of the rod. A uniform support is preferably provided by an axially movable funnel-shaped casing which is attached to the seed crystal holding member and which, when moved into its operating position, is filled with a self-adjusting oscillation or vibration dampening means, such as molten metal, metal spheroids, quartz particles, sand, etc.