A method of hydrothermally synthesizing sapphire single crystals doped with trivalent metal ions in a crystal-growth autoclave including a crystal-growth zone and nutrient-dissolution zone in fluid communication with the crystal-growth zone is provided. Implementations of the method including situating within the crystal-growth zone at least one sapphire-based seed crystal and situating within the nutrient-dissolution zone an aluminum-containing material to serve as nutrient. An acidic, trivalent-metal-ion-containing growth solution is introduced into the cavity in a quantity sufficient, at least when heated to a predetermined average temperature, to immerse the at least one seed crystal and the nutrient in the growth solution. The growth solution is selected such that sapphire exhibits retrograde solubility therein and the growth process is carried out while maintaining an interior-cavity pressure within a range between and including each of 3.5 kilopounds per square inch and 25 kilopounds per square inch and while maintaining a temperature differential between the crystal-growth and nutrient-dissolution zones such that the average temperature within the crystal-growth zone is higher than the average temperature within the nutrient-dissolution zone.