The cross sections for the elastic scattering reactions 112,124 Sn(α,α) 112,124 Sn at energies above and below the Coulomb barrier are presented and compared to predictions for global α-nucleus potentials. The high precision of the new data allows a study of the global α-nucleus potentials at both the proton and neutron-rich sides of an isotopic chain. In addition, local α-nucleus potentials have been extracted for both nuclei, and used to reproduce elastic scattering data at higher energies. Predictions from the capture cross section of the reaction 112 Sn(α,γ) 116 Te at astrophysically relevant energies are presented and compared to experimental data.