Crystals of non-stoichiometric K-Na-Ba ferrite, with beta " -alumina structure type and chemical formula K0.30Na0.62Ba0.62Fe10.44Mg0.29O17, were prepared by a partial ionic exchange from a K-Na-beta " -ferrite. The ion exchange was performed in a Ba(NO3)(2)-KNO3 eutectic melt at 650 degreesC for 15 min. The study of a single crystal with X-ray diffraction (MoK alpha radiation), resulted in the R (3) over barm space group, with a = b = 5.9436(7) Angstrom, c=35.743(7) Angstrom and Z = 3 The structure determination was based on the beta " -alumina structure model(Na1+xAl11-xMgxO17), where the Na atom sites are occupied by (Ba, K, Na) and the Al ones by Fe. The investigation on the electron density of the conduction plane (z=1/6) gave trigonal distribution around the middle position (0,0,1/6) for (K-Na-Ba) atoms. This distribution can be described by a partial occupation of two sites (18 h) with coordinates 0.056, 0.028, 1/6 and 0.26, 0.13, 1/6, by (K, Na, Ba) atoms with a consequent decrement of the site occupation factors. Refinement of the cation population parameters, and positional and anisotropic thermal parameters for all atoms, resulted in the final residual factor R-1 = 0.057.