Yes Crystal lattice constants change with the size of ions. Ionic sizes in different coordination polyhedra are tabulated in: @article{Shannon1969a,
author = {Shannon, R. D. and Prewitt, C. T. },
title = {"{Effective Ionic Radii in Oxides and Fluorides.}"},
journal = {Acta. Cryst.},
year = {1969},
volume = {B25},
pages = {925-946},
d- spacing shifting can tell you if the substitution has happened by bigger or smaller ions than the host ions. By mapping different ions substitutions effect on the lattice parameter, you may get an idea of the type of ions that has gone into the lattice. then by process history and using rietveld refinement, you can zero in to the nearly exact ions that has been doped.
Note: sometimes, lattice parameter can go down even with substitution with bigger ions, may be due to oxygen vacancy creation.
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