The change of the phonon contribution to the free energy, AF, due to the interaction between an adatom and an impurity substrate atom is calculated by expressing AF as a contour integral in the complex-frequency plane and evaluating it directly along a suitably chosen contour numerically. Results are given as a function of the ad atomsurface bond force constant, the mass defect of the impurity atom, and the ad atomimpurity separation for both a one-dimensional and a three-dimensional simple cubic model substrate.