Effect of crystallite size and thermodynamic stability on the reversible phase transformation Hausmannite–Mn ₃ O ₄ ⇌ Bixbyite–Mn ₂ O ₃ nanostructures

Abstract We analyze how crystallite size and thermodynamic driving forces govern the reversible phase transformation between tetragonal Hausmannite–Mn 3 O 4 and cubic Bixbyite–Mn 2 O 3 in Mn–O nanoparticles using x-ray diffraction (XRD) and electron microscopy (SEM, HRTEM), complemented by a semi-empirical enthalpy-trend analysis (extended Miedema model). Nanostructured samples were synthesized by combined sonochemical and hydrothermal routes and subsequently annealed in air from 200 ∘ C to 900 ∘ C in 100 ∘ C increments. Crystallographic and morphological analyses show that the forward transformation Mn 3 O 4 → Mn 2 O 3 becomes detectable by XRD near 500 ∘ C, where the phase coherent-domain sizes are 13.86 nm for Mn 3 O 4 and 25.57 nm for Mn 2 O 3 . The reverse transformation Mn 2 O 3 → Mn 3 O 4 is observed at 900 ∘ C (for bulk crystals, the forward oxidation and reverse reduction are typically reported near 900 ∘ C and 1100 ∘ C, respectively, depending on atmosphere). The forward step proceeds via a topotactic, structure-preserving pathway governed by an operational critical crystallite size of the parent Mn 3 O 4 (defined here as the Mn 3 O 4 domain size at the onset of Mn 2 O 3 detectability, ∼13.9 nm in this dataset) and diffusion-controlled oxygen transport. The reverse step is attributed to oxygen loss and lattice reconstruction while retaining partial lattice coherence. The morphological evolution from granular aggregates to octahedral particles is consistent with Ostwald ripening and coalescence-driven growth. The thermodynamic analysis indicates a slight enthalpic preference for Bixbyite–Mn 2 O 3 (Δ H s = −82.39 kJ/(mol atom)) over Hausmannite–Mn 3 O 4 (Δ H s = −80.82 kJ/(mol atom)). In this context, the reversible behavior under annealing in air is interpreted within a Gibbs free-energy framework for an oxygen-open system, Δ G ( T , p O 2 ), where entropy and oxygen chemical potential govern the transformation direction, while Miedema-derived Δ H s values are used only as comparative stability trends.