The present application discloses a method for preparing a homogeneous ternary or quaternary alloy from a quaternary melt. The method includes providing a family of phase diagrams for the quaternary melt which shows (i) composition/temperature data, (ii) tie lines connecting equilibrium liquid and solid compositions, and (iii) isotherms representing boundaries of a miscibility gap. Based on the family of phase diagrams, a quaternary melt composition and an alloy growth temperature is selected. A quaternary melt having the selected quaternary melt composition is provided and a ternary or quaternary alloy is grown from the quaternary melt at the selected alloy growth temperature. A method for making homogeneous ternary or quaternary alloy from a ternary or quaternary melt is also disclosed, as are homogeneous quaternary single-crystal alloys which are substantially free from crystal defects and which have the formula A.sub.x B.sub.1-x C.sub.y D.sub.1-y, x and y being the same or different and in the range of 0.001 to 0.999.