Powders within the K-beta "-alumina phase field were prepared. Their chemical composition and lattice constants were characterized by X-ray diffraction (XRD) and chemical analysis. Powders of so-called NH4/H3O-beta "-aluminas and proton-beta "-aluminas were made by ion-exchange and characterized by XRD and X-ray fluorescence analysis. For both sets of powder samples lattice constants were determined. Lattice constants of NH4/H3O-beta "-aluminas still differ too much for direct polycrystal preparation. Proton-beta "-aluminas exhibit two minima. An area is described, where the conditions for a stress free ion-exchange are fulfilled thus allowing the preparation of polycrystals without cracking. The phase field ranges from 80-82 mol% Al2O3, 3-5 mol% MgO, and complementing K2O.