Simulations of thin film growth in the Ag-Ti system are presented using molecular dynamics combined with an adaptive kinetic Monte Carlo method (AKMC) with a modified embedded atom potential fit to ab initio data for the surface energies. For the model, atoms are assumed to deposit normally with a kinetic energy of 1-3 eV, with a typical deposition rate of around 10 monolayers per second, similar to what might be expected in a sputter deposition process. For the growth of Ti on the Ag (100) and Ag (111) surfaces, the Ti adatoms prefer to exchange with the original surface layer atoms creating a mixed Ag/Ti surface. On a silver substrate, up to four mixed layers need to be formed before a pure Ti layer is obtained. Conversely, simulations of Ag depositing onto Ti (0001) showed that in the initial phase of growth, the Ag adatoms prefer to be separated before a complete first layer of Ag was obtained in a close-packed structure. The implementation of a super-basin method within AKMC allowed the simulation of 0.4s of Ti growth on the Ag substrates, with up to 3 new layers added.