A model of impurity distribution based on tolerance degree of crystals was performed, expressions of cases like one kind of ions on one certain kind of lattice sites, one kind of species on more than one kind of sites and two or more kinds of ions on one kind of sites were delivered in premise of no crystal structural change and keeping high quality of crystal, no matter what growth conditions were. It also provides a method of improving concentrations of needed doping ions in crystals. Accordingly we have calculated maximum concentration of Ti³⁺ in sapphire to be 1.75×10¹⁹/cm³, in right trends of magnitudes with experiment data.

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