Asymptotic Giant Branch (AGB) stars contribute a major part to the global dust budget in galaxies. Owing to their refractory nature alumina (stoichiometric formula AlO) is a promising candidate to be the first condensate emerging in the atmospheres of oxygen-rich AGB stars. Strong evidence for that is supplied by the presence of alumina in pristine meteorites and a broad spectral feature observed around ∼ 13 μm. The emergence of a specific condensate depends on the thermal stability of the solid, the gas density and its composition. The evaluation of the condensates is based on macroscopic bulk properties. The growth and size distribution of dust grains is commonly described by Classical Nucleation Theory (CNT). We question the applicability of CNT in an expanding circumstellar envelope as CNT presumes thermodynamic equilibrium and requires, in practise, seed nuclei on which material can condense. However, nano-sized molecular clusters differ significantly from bulk analogues. Quantum effects of the clusters lead to non-crystalline structures, whose characteristics (energy, geometry) differ substantially, compared to the bulk material. Hence, a kinetic quantum-chemical treatment involving various transition states describes dust nucleation most accurately. However, such a treatment is prohibitive for systems with more than 10 atoms. We discuss the viability of chemical-kinetic routes towards the formation of the monomer (Al2O3) and the dimer (Al4O6) of alumina.