We ensured a thorough sampling by starting with 200 structures, for each cluster size and optimizing more if there was fewer than 20% duplicates in the computed ensemble. The potential energy surface (PES) for Pt 1 on alumina was obtained by calculating the energy of a single Pt atom at each point on a fine 11×11 grid partitioning the unit cell. Since the latice is hexagonal, the shape of the unit cell is rhombic, with side of 4.840 Åand an angle of 120 degree. Hence, the shape of the mesh was also rhombic. The calculations were performed with projected augmented wave density functional theory (PAW-DFT) with the Vienna Ab-initio Simulation Package (VASP) version 5.4.4. A plane-wave KE cutoff of 400 eV, a convergence parameter of 10 -6 eV, and Gaussian smearing with a sigma value of 0.1 eV were used for the relaxation. The geometry relaxation would proceed until the forces on all atoms are below 0.01 eVÅ -1 . The α-Al 2 O 3 (0001) surface was modeled as previously, as a (3×3) unit cell with four trilayers in the z-direction, and a 15 Åvacuum gap. The lower half of the slab was fixed to the bulk positions. Due to the large size of the supercell, only Γ k-point sampling was used. Once each cluster size was considered suitably sampled, the isomers within a 0.4 eV cutoff from the global minimum (GM) were selected as the thermodynamically-accessible ensemble. The energies of these isomers were used in the metropolis Monte Carlo simulations of sintering. See the Figure for the ensembles of Pt 2-8 isomers and their Boltzmann populations at 750K. Bonding analysis was performed using LOBSTER, using the PBEVaspFit basis set, with a projection basis of 5p5d6s for Pt, 3s3p for Al, and 2s2p for O. Absolute charge spilling was under 1.1% for all calculations.