Berlinite crystalline powder of uniform particle size and high purity is prepared by repeated thermal cycling to react a mixture of aluminum hydroxide or aluminum oxide and an excess of concentrated phosphoric acid in a sealed pressure vessel. The vessel is preferably held in a horizontal orientation and rotated about a longitudinal axis during the reaction. The product powder is useful in growing large single crystals that have surface acoustic wave applications. Crystalline powder of alpha-gallium orthophosphate may be prepared using the same apparatus and a similar procedure.