According to characteristic crystal theory of alloy phases, atomic state of acomponent is split into some characteristic atomic states in the solid solution. Lattice constantsof alloys may be obtained by characteristic lattice constaat additive law, characteristic atomicvolume additive law and characteristic atomic state additive law, but they are not equal in value.Nine lattice constant functions of disordered binary solid solutions are introduced. The functionssuitable for disordered An-Cu alloys and their components have been determined. Lattice constats of Au3Cu, AuCu, AuCu3 and relevant ordered alloys as a function of composition havebeen pradicated. Theoretical values are in good agreement with eXperimental values.