Terfenol is a rare earth-iron alloy that was first developed at the Naval Ordinance Laboratory because of its rare magnetostrictive properties. Terfenol is composed of terbium and dysprosium combined with iron in a composition Tb{sub x}Dy{sub 1{minus}x}Fe{sub 2}, where x{approximately}0.3. The objective of this work was to determine the growth characteristics of Terfenol and its dependence on solidification rate, temperature gradient, and stoichiometry. Specific goals of this work were to verify the phase equilibria that is currently accepted for the systems DyFe{sub 2} and TbFe{sub 2}, and establish the phase equilibria near the composition Tb{sub 0.3}Dy{sub 0.7}Fe{sub 2}; establish that Terfenol grows directly from the liquid and that the reaction is occurring under metastable conditions; evaluate whether or not Terfenol can be grown under plane front conditions with a new radiofrequency float zone apparatus, and; determine whether or not <111> seeded crystals can be grown and <111> single crystals produced by elimination of dendrites employing growth methods capable of achieving high gradient/solidification rate ratios.