  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.
