Segregation in yttrium aluminum garnet: II, theoretical calculations

Calculations based on ionic space-charge models of doped yttrium aluminum g arnet (YAG) have been compared to experimental measurements of surface segr egation in crystals of various compositions. The comparison allows limits f or vacancy-formation energies to be set. The range for anion:cation formati on-energy ratios has been established to be 0.20-0.23, based on the reasona ble assumptions that the formation energy of the yttrium ion is 75% of that of the aluminum ion and the Schottky defect formation energy is 4.2 eV. Th e model explains the experimental observation of calcium at the surface reg ardless of net acceptor excess or net donor excess. The relationship betwee n vacancy-formation energy and dopant excess has been used to construct seg regation maps for YAG, which are useful in materials: design strategies.