Gallium is zone refined in a stationary, vertical, double annulus refiner. Impure gallium is contained between walls of a first annulus that are made of a material that does not impart impurities to the gallium. At least one of the walls is made of a flexible material. A cooling fluid is circulated through a second annulus enveloping the first annulus. The gallium is zone refined by moving through the gallium ingot one or more molten zones formed by radio frequency waves from at least one reciprocating radio frequency heating induction coil. After the necessary number of passes, the ingot is cropped without introducing contaminants and refined gallium with purities between 79 and 89 is recovered. LEC single crystal GaAs made with the so refined gallium has very uniform electrical characteristics.