Segregation in yttrium aluminum garnet: II, theoretical calculations

Calculations based on ionic space-charge models of doped yttrium aluminum garnet (YAG) have been compared to experimental measurements of surface segregation in crystals of various compositions. The comparison allows limits for vacancy-formation energies to be set. The range for anion:cation formation-energy ratios has been established to be 0.20-0.23, based on the reasonable 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. The model explains the experimental observation of calcium at the surface regardless of net acceptor excess or net donor excess. The relationship between vacancy-formation energy and dopant excess has been used to construct segregation maps for YAG, which are useful in materials: design strategies.