Bottom-up dust nucleation theory in oxygen-rich evolved stars II. Magnesium and calcium aluminate clusters

Context. Spinel (MgAl2O4) and krotite (CaAl2O4) are alternative candidates to alumina (Al2O3) as primary dust condensates in the atmospheres of oxygen-rich evolved stars. Moreover, spinel was proposed as a potential carrier of the circumstellar 13 μm feature. However, the formation of nucleating spinel clusters is challenging; in particular, the inclusion of Mg constitutes a kinetic bottleneck. Aims. We aim to understand the initial steps of cosmic dust formation (i.e. nucleation) in oxygen-rich environments using a quantum-chemical bottom-up approach. Methods. Starting with an elemental gas-phase composition, we constructed a detailed chemical-kinetic network that describes the formation and destruction of magnesium-, calcium-, and aluminium-bearing molecules as well as the smallest dust-forming (MgAl2O4)1 and (CaAl2O4)1 monomer clusters. Different formation scenarios with exothermic pathways were explored, including the alumina (Al2O3) cluster chemistry studied in Paper I of this series. The resulting extensive network was applied to two model stars, a semi-regular variable and a Mira-type star, and to different circumstellar gas trajectories, including a non-pulsating outflow and a pulsating model. We employed global optimisation techniques to find the most favourable (MgAl2O4)n, (CaAl2O4)n, and mixed (MgxCa(1−x)Al2O4)n isomers, with n = 1–7 and x∈[0..1], and we used high level quantum-chemical methods to determine their potential energies. The growth of larger clusters with n = 2–7 is described by the temperature-dependent Gibbs free energies. Results. In the considered stellar outflow models, spinel clusters do not form in significant amounts. However, we find that in the Mira-type non-pulsating model CaAl2O3(OH)2, a hydroxylated form of the calcium aluminate krotite monomer forms at abundances as large as 2 × 10−8 at 3 stellar radii, corresponding to a dust-to-gas mass ratio of 1.5 × 10−6. Moreover, we present global minimum (GM) candidates for (MgAl2O4)n and (CaAl2O4)n, where n = 1–7. For cluster sizes n = 3–7, we find new, hitherto unreported GM candidates. All spinel GM candidates found are energetically more favourable than their corresponding magnesium-rich silicate clusters with an olivine stoichiometry, namely (Mg2SiO4)n. Moreover, calcium aluminate clusters, (CaAl2O4)n, are more favourable than their Mg-rich counterparts; the latter show a gradual enhancement in stability when Mg atoms are substituted step by step with Ca. Conclusions. Alumin