Does cluster encapsulation inhibit sintering? Stabilization of size-selected Pt clusters on Fe$_3$O$_4$(001) by SMSI

The metastability of supported metal nanoparticles limits their application in heterogeneous catalysis at elevated temperatures due to their tendency to sinter. One strategy to overcome these thermodynamic limits on reducible oxide supports is encapsulation via strong metal-support interaction (SMSI). While annealing-induced encapsulation is a well-explored phenomenon for extended nanoparticles, it is as yet unknown whether the same mechanisms hold for sub-nanometer clusters, where concomitant sintering and alloying might play a significant role. In this article, we explore the encapsulation and stability of size-selected Pt$_5$, Pt$_{10}$ and Pt$_{19}$ clusters deposited on Fe$_3$O$_4$(001). In a multimodal approach using temperature-programmed desorption (TPD), x-ray photoelectron spectroscopy (XPS) and scanning tunneling microscopy (STM), we demonstrate that SMSI indeed leads to the formation of a defective, FeO-like conglomerate encapsulating the clusters. By stepwise annealing up to 1023 K, we observe the succession of encapsulation, cluster coalescence and Ostwald ripening, resulting in square-shaped crystalline Pt particles, independent of the initial cluster sizes. The respective sintering onset temperatures scale with the cluster footprint and thus size. Remarkably, while small encapsulated clusters can still diffuse as a whole, atom detachment and thus Ostwald ripening are successfully suppressed up to 823 K, i.e. 200 K above the H\"uttig temperature that indicates the thermodynamic stability limit.