A melt encasement (fluxing) technique has been used to systematically study the velocity-undercooling relationship in samples of pure Ge and Ge doped with 0.01 at % Fe at undercoolings up to 300 K. The apparatus was designed such that it was possible to view the sample throughout the experiment, allowing solidification velocity measurements to be made. These velocity measurements were subsequently correlated with the as-solidified microstructure. From a combination of growth velocity measurements and microstructural characterisation it was possible to identify a change in growth morphology from faceted to non-faceted growth in both the pure metal and the dilute alloy. This transition occurred at a lower undercooling in the dilute alloy (Delta T>150 K) than in the pure metal (Delta T>170 K). Spontaneous grain refinement was also observed at Delta T > 210 K in Ge-Fe and at Delta T > 270 K in pure Ge. These transitions are discussed and a mechanisms for the change in growth morphology with small amounts of impurity is suggested.