Isomorphism and polymorphism

Similarities and differences in crystal structure across substances are described by two related terms.

i. Isomorphism : Two or more substances that have the same crystal structure are said to be isomorphous. Such isomorphous substances also share the same atomic ratio in their chemical composition: NaF and MgO form one isomorphous pair, with an atomic ratio of 1:1, and $NaNO_3$ and $CaCO_3$ form another, with a 1:1:3 ratio of their constituent atoms.

ii. Polymorphism : A single substance that exists in two or more crystalline forms is said to be polymorphous, and the individual forms are called polymorphs of that substance. Polymorphs form under different conditions of crystallisation: calcite and aragonite are two polymorphic forms of calcium carbonate, and $\alpha$-quartz, $\beta$-quartz and cristobalite are three of the several polymorphic forms of silica. Polymorphism occurring among elements is given the special name allotropy -- diamond, graphite and fullerene are three allotropic (polymorphic) forms of the element carbon. …