Iron oxides occur ubiquitously in environmental, geological, planetary, and technological settings. They exist in a rich variety of structures and hydration states. They are commonly fine-grained (nanophase) and poorly crystalline. This review summarizes recently measured thermodynamic data on their formation and surface energies. These data are essential for calculating the thermodynamic stability fields of the various iron oxide and oxyhydroxide phases and understanding their occurrence in natural and anthropogenic environments. The competition between surface enthalpy and the energetics of phase transformation leads to the general conclusion that polymorphs metastable as micrometer-sized or larger crystals can often be thermodynamically stabilized at the nanoscale. Such size-driven crossovers in stability help to explain patterns of occurrence of different iron oxides in nature.

Nanoparticle and nanocluster precursors may play a major role in biomineralization. The small differences in enthalpy and free energy among metastable nanoscale phases offer controlled thermodynamic and mechanistic pathways. Clusters and nanoparticles offer concentration and controlled transport of reactants. Control of polymorphism, surface energy, and surface charge on nanoparticles can lead to morphological control and appropriate growth rates of biominerals. Rather than conventional nucleation and growth, assembly of nanoparticles may provide alternative mechanisms for crystal growth. The Ostwald step rule, based on a thermodynamic view of nucleation and growth, is supported by the observation that more metastable phases tend to have lower surface energies. Examples from nonbiological systems, stressing the interplay of thermodynamic and kinetic factors, illustrate features potentially important to biomineralization.

The energetics of the TiO ₂ polymorphs (rutile, anatase, and brookite) were studied by high temperature oxide melt drop solution calorimetry. Relative to bulk rutile, bulk brookite is 0.71 ± 0.38 kJ/mol (6) and bulk anatase is 2.61 ± 0.41 kJ/mol higher in enthalpy. The surface enthalpies of rutile, brookite, and anatase are 2.2 ± 0.2 J/m ² , 1.0 ± 0.2 J/m ² , and 0.4 ± 0.1 J/m ² , respectively. The closely balanced energetics directly confirm the crossover in stability of nanophase polymorphs inferred by Zhang and Banfield (7). An amorphous sample with surface area of 34,600 m ² /mol is 24.25 ± 0.88 kJ/mol higher in enthalpy than bulk rutile.

Amorphous calcium carbonate (ACC) is a metastable phase often observed during low temperature inorganic synthesis and biomineralization. ACC transforms with aging or heating into a less hydrated form, and with time crystallizes to calcite or aragonite. The energetics of transformation and crystallization of synthetic and biogenic (extracted from California purple sea urchin larval spicules, Strongylocentrotus purpuratus ) ACC were studied using isothermal acid solution calorimetry and differential scanning calorimetry. Transformation and crystallization of ACC can follow an energetically downhill sequence: more metastable hydrated ACC → less metastable hydrated ACC⇒anhydrous ACC ∼ biogenic anhydrous ACC⇒vaterite → aragonite → calcite. In a given reaction sequence, not all these phases need to occur. The transformations involve a series of ordering, dehydration, and crystallization processes, each lowering the enthalpy (and free energy) of the system, with crystallization of the dehydrated amorphous material lowering the enthalpy the most. ACC is much more metastable with respect to calcite than the crystalline polymorphs vaterite or aragonite. The anhydrous ACC is less metastable than the hydrated, implying that the structural reorganization during dehydration is exothermic and irreversible. Dehydrated synthetic and anhydrous biogenic ACC are similar in enthalpy. The transformation sequence observed in biomineralization could be mainly energetically driven; the first phase deposited is hydrated ACC, which then converts to anhydrous ACC, and finally crystallizes to calcite. The initial formation of ACC may be a first step in the precipitation of calcite under a wide variety of conditions, including geological CO ₂ sequestration.

Significance: Organic metal halide perovskites are a promising class of materials for next-generation solar cells. However, they are chemically labile, raising questions of thermodynamic stability and posing a significant challenge for their use. This paper provides direct calorimetric measurements of their heats of formation from binary halide constituents. The positive formation enthalpy of methylammonium lead iodide from MAI and PbI ₂ (MA = methylammonium) confirms thermodynamic instability, thus limiting long-term persistence even in the absence of air, moisture, heat, or light. The enthalpy of formation of the iodide, bromide, and chloride perovskite becomes less positive with increasing Goldschmidt tolerance factor, suggesting a criterion in the search for more stable hybrid perovskites.

In the fast-evolving field of halide perovskite semiconductors, the 2D perovskites (A′)₂(A)_n−1M_nX_3n+1 [where A = Cs⁺, CH₃NH₃⁺, HC(NH₂)₂⁺; A′ = ammonium cation acting as spacer; M = Ge²⁺, Sn²⁺, Pb²⁺; and X = Cl⁻, Br⁻, I⁻] have recently made a critical entry. The n value defines the thickness of the 2D layers, which controls the optical and electronic properties. The 2D perovskites have demonstrated preliminary optoelectronic device lifetime superior to their 3D counterparts. They have also attracted fundamental interest as solution-processed quantum wells with structural and physical properties tunable via chemical composition, notably by the n value defining the perovskite layer thickness. The higher members (n > 5) have not been documented, and there are important scientific questions underlying fundamental limits for n. To develop and utilize these materials in technology, it is imperative to understand their thermodynamic stability, fundamental synthetic limitations, and the derived structure–function relationships. We report the effective synthesis of the highest iodide n-members yet, namely (CH₃(CH₂)₂NH₃)₂(CH₃NH₃)₅Pb₆I₁₉ (n = 6) and (CH₃(CH₂)₂NH₃)₂(CH₃NH₃)₆Pb₇I₂₂ (n = 7), and confirm the crystal structure with single-crystal X-ray diffraction, and provide indirect evidence for “(CH₃(CH₂)₂NH₃)₂(CH₃NH₃)₈Pb₉I₂₈” (“n = 9”). Direct HCl solution calorimetric measurements show the compounds with n > 7 have unfavorable enthalpies of formation (ΔH_f), suggesting the formation of higher homologs to be challenging. Finally, we report preliminary n-dependent solar cell efficiency in the range of 9–12.6% in these higher n-members, highlighting the strong promise of these materials for high-performance devices. Significance Organic–inorganic hybrid perovskites are exciting new solar cell materials. In 2D perovskites, the 3D structure is spatially interrupted by a layer of intercalated ions, which may alter both stability and functionality. A major question concerns the limit to which the 2D architecture can be maintained as the thickness of the layers increases. A combination of synthetic chemistry, crystallography, and spectroscopy was used to obtain and identify the thickest 2D halide perovskite characterized to date, having seven layers. Experimentally measured enthalpies of formation as a function of layer thickness show systematic behavior and that higher homologues are energetically unstable, placing a limit on the number of layers possible in a single-phase 2D perovskite. Their application in photovoltaics is discussed.