Thermodynamics of Fe₃O₄–Co₃O₄and Fe₃O₄–Mn₃O₄spinel solid solutions at the bulk and nanoscale

Abstract

High temperature oxide melt solution calorimetry has been performed to investigate the enthalpies of mixing (ΔmixH) of bulk and nanophase (1 -x)Fe3O4-xM3O4 (M = Co, Mn) spinel solid solutions. The entropies of mixing (ΔmixS) were calculated from the configurational entropies based on cation distributions, and the Gibbs free energies of mixing (ΔmixG) were obtained. The ΔmixH and ΔmixG for the (1 -x)Fe3O4-xCo3O4 system are negative over the complete solid solution range, for both macroscopic and nanoparticulate materials. In (1 -x)Fe3O4-xMn3O4, the formation enthalpies of cubic Fe3O4 (magnetite) and tetragonal Mn3O4 (hausmannite) are negative for Mn3O4 mole fractions less than 0.67 and slightly positive for higher manganese content. Relative to cubic Fe3O4 and cubic Mn3O4 (stable at high temperature), the enthalpies and Gibbs energies of mixing are negative over the entire composition range. A combination of measured mixing enthalpies and reported Gibbs energies in the literature provides experimental entropies of mixing. The experimental entropies of mixing are consistent with those calculated from cation distributions for x > 0.3 but are smaller than those predicted for x < 0.3. This discrepancy may be related to the calculations, having treated Fe(2+) and Fe(3+) as distinguishable species. The measured surface energies of the (1 -x)Fe3O4-xM3O4 solid solutions are in the range of 0.6-0.9 J m(-2), similar to those of many other spinels. Because the surface energies are relatively constant, the thermodynamics of mixing at a given particle size throughout the solid solution can be considered independent of the particular particle size, thus confirming and extending the conclusions of a recent study on iron spinels.

High-Temperature Oxidation in Dry and Humid Atmospheres of the Equiatomic CrMnFeCoNi and CrCoNi High- and Medium-Entropy Alloys

“…Fe 2+/3+ has a similar ionic radius as Mn 2+/3+ and can therefore easily occupy these free sites in the hausmannite type crystal structure, and the structure stays stable until 30% (atomic percent) of Fe. With higher Fe content, the tetragonal hausmannite becomes structurally unstable and transforms into a cubic spineltype crystal structure [43]. In the present study, small amounts of Fe are likely present in Mn 3 O 4 .…”

Thermodynamics of copper‐manganese and copper‐iron spinel solid solutions

“…The drop solution enthalpies were measured in a custom‐made isoperibol Tian‐Calvet twin microcalorimeter described previously . Pellets of approximately 5 mg were loosely pressed, weighed on a microbalance, and dropped from room temperature into molten 3Na 2 O·4MoO 3 solvent at 702°C.…”

“…Miyahara attributed this anomalous behavior as arising from two opposing effects, namely a distortion with c / a >1 caused by the Mn 3+ ions at octahedral sites compensated by an opposing distortion with c/a <1 due to Cu 2+ ions at the tetrahedral sites . Investigations on Cu x Mn 3− x O 4 spinels revealed that Cu 2+ has a lower octahedral site preference than Mn 3+ and thus manganese has a greater tendency to occupy octahedral sites . Spinel ferrites, Cu x Fe 3− x O 4 , normally have a cubic structure, however it has been suggested that copper ferrite can exist in tetragonal form when annealed below 950°C .…”

Structural and magnetic properties of frustrated GaxMn(3-x)O4(1.2 ≤ x ≤ 1.6) spinels

“…It is known that the cation distribution in spinels is explained by the cation site preference. Based on literature data 31 , the Mn 3+ cations strongly prefer the octahedral sites, whereas Mn 2+ et Ga 3+ are randomly distributed over both tetrahedral and octahedral sites. The cation distribution in that case is given by (Mn 2+ 1…”