Isomorphous replacement (IR) is historically the most common approach to solving the phase problem in X-ray crystallography studies of proteins.
The addition of the heavy atom (or ion) to the structure should not affect the crystal formation or unit cell dimensions in comparison to its native form, hence, they should be isomorphic.
Single isomorphous replacement is possible, but gives an ambiguious result with two possible phases; density modification is required to resolve the ambiguity.
An early demonstration of isomorphous replacement in crystallography came in 1927 with a paper reporting the x-ray crystal structures of a series of alum compounds from Cork.
The first demonstration of isomorphous replacement in protein crystallography was in 1954 with a paper from David W. Green, Vernon Ingram, and Max Perutz.