Size-Driven Structural and Thermodynamic Complexity in Iron Oxides

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Science  21 Mar 2008:
Vol. 319, Issue 5870, pp. 1635-1638
DOI: 10.1126/science.1148614


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.

It is hard to find a process or environment in which iron oxides do not participate. From the surface of Mars to the depths of Earth, from old rusting factories to high-tech magnetic recording devices, from pigeon brains and magnetotactic bacteria to drug delivery systems, anhydrous and hydrated iron oxides are ubiquitous. They are constituents of rocks and soils, products of corrosion and bacterial processes, and sources of iron as a nutrient. They have many commercial applications: pigments, catalysts, medical devices, sensors, and recording media. Nanotechnology increasingly makes use of iron oxide nanoparticles and thin films.

Iron oxides exist in a bewildering variety of polymorphs (1). Anhydrous ferric oxides include hematite (α-Fe2O3), maghemite (γ-Fe2O3), and the less common ϵ- and β-Fe2O3. Fe3O4 (magnetite) and Fe1–xO (wüstite) contain both ferric and ferrous iron. Maghemite and magnetite, both spinels, can form a continuous solid solution. The oxyhydroxides, nominally FeOOH, include goethite, lepidocrocite, akaganeite, and several other polymorphs. They often contain excess water. More hydrated forms such as ferrihydrite, nominally Fe(OH)3, have even more variable water content. Hydrated phases containing both ferrous and ferric iron include the green rusts, layered hydroxides with different anions in the interlayer. A further complication is that many iron oxides, both in nature and in the laboratory, are exceedingly fine-grained (nanophase) and therefore hard to characterize.

This complexity has meant that until recently, knowledge of the structural details, thermodynamics, and reactivity of iron oxides has been lacking. One could not understand or predict which phases form under what conditions, which polymorphs are stable and which metastable, and when and how they transform. These questions are important because each material has unique physical properties, chemical reactivity, and bioavailability. Furthermore, physical and chemical properties commonly change with particle size and degree of hydration. New structural, spectroscopic, and thermodynamic approaches are now enabling more sophisticated characterization and a more quantitative approach to phase stability. Here, we summarize thermodynamic data and discuss the current understanding of the factors affecting the occurrence and stability of various iron oxides. A key point is the importance of particle size and hydration in determining the energetics and in stabilizing, at the nanoscale, phases metastable in the bulk.

Synthesis, Structure, and Thermodynamic Properties

The synthesis and characterization of iron oxides with well-defined crystal structure, chemical composition, particle size, and hydration state are essential to determining their thermodynamic and kinetic parameters. Oxyhydroxides are normally obtained by precipitation from aqueous solution (1). Particle size is controlled by initial iron concentration, organic additives, pH, and temperature. Wet methods for synthesizing anhydrous iron oxides (Fe2O3 and/or Fe3O4) include those above as well as methods that use surfactants and templates (2, 3) to prevent agglomeration. Dry methods, such as laser-induced pyrolysis of organometallic precursors (4) and ball milling (2), are effective for Fe2O3 and Fe3O4, especially for particle sizes less than 5 nm.

The structures of crystalline bulk iron oxides are well known (1). They are based on hexagonal or cubic packing of oxygen with iron ions occupying octahedral interstices. The exceptions are the structure of akaganeite, based on a body-centered cubic arrangement of oxygen, and those of maghemite and magnetite, containing abundant tetrahedral iron.

The structure of nanoparticles often varies as a function of their size and the surrounding medium. Hematite nanoparticles may vary in structure and may possess maghemite-like structures (i.e., tetrahedral defects near the surface) (5). The surface regions in lepidocrocite nanoparticles are sufficiently different from the bulk that their respective signals can be recognized in Mössbauer spectra (6). Recent studies of nanoakaganeite show that at very high surface areas, where particle size becomes comparable to a few unit cells, akaganeite may contain goethite-like structural features possibly related to the collapse of exposed tunnels (7).

Ferrihydrite is widespread and has the smallest particle size of all iron oxides. There are still debates about its structure: Is it a single phase with iron both octahedrally and tetrahedrally coordinated (8), or a mixture of phases with variable structure and crystallinity (9)? The nature of its extensive disorder is still controversial. Comparison of various results is further complicated because each synthesis potentially yields a slightly different product and the structural properties of the particles appear to be size-dependent. Also, during characterization, the particles may be altered by high vacuum and beam damage in the electron microscope. This complexity emphasizes the need to investigate the surface and bulk structure and energetics of not only perfect single crystals (not always available and, when available, not necessarily relevant to common materials) but also nanoparticles and poorly crystalline materials. Because of chemical and structural variability, it is also critical to determine chemical composition, including water content, surface area, and particle size (and its distribution). Once well-characterized materials are identified, physical, structural, spectroscopic, and thermodynamic studies on them can be compared and interpreted with reference to better-constrained variables. Much recent research is taking this direction and applying a combination of different techniques to the same well-characterized samples.

The thermodynamics of formation of iron oxides, as of any materials, is governed by enthalpy (ΔH) and entropy (ΔS) terms, such that the Gibbs free energy (ΔG) is given by ΔG = ΔHTΔS, where T is absolute temperature. Enthalpies of formation are determined by solution calorimetric techniques, with a molten oxide solvent used for anhydrous and moderately hydrated iron oxides, and aqueous acid for some heavily hydrated materials (4, 7, 1015). New developments and significant improvements of sensitivity of older calorimetric techniques (7, 1016) enabled measurements of enthalpy differences between coarse- and fine-grained samples and studying the effects of hydration. Standard entropies (S°298) are obtained from heat capacity measurements from cryogenic to room temperatures (17). Free energies can be obtained from aqueous solubility, but the sample variability discussed above and the difficulty of obtaining reversed equilibrium often make such measurements problematic. Thus, combining measured enthalpy and entropy to obtain free energy is generally a more reliable method (Table 1).

Table 1.

Thermodynamic data for iron oxides. Enthalpies of formation (Embedded Image) and Gibbs free energies of formation (Embedded Image) are for conditions of 298 K and 1 bar. Surface enthalpies are given for anhydrous (ΔHs) and hydrated (Embedded Image) surfaces. Most of the data are taken from the references cited. Values of Gibbs free energy without citations were calculated from corresponding values of standard enthalpies and entropies.

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For coarse particles at ambient conditions, hematite is the most stable Fe2O3 polymorph, lower in Gibbs free energy than γ-or ϵ-Fe2O3, and goethite is the most stable FeOOH phase, lower in Gibbs free energy than a host of other oxyhydroxides (Table 1). However, the other polymorphs are not much higher in enthalpy and are similar in entropy. Thus, ΔG generally follows similar trends to ΔH and the other polymorphs are only slightly higher in Gibbs free energy. Therefore, being only slightly metastable, they are kinetically accessible when precipitated from aqueous solution. Moreover, they are often thermodynamically stabilized as small particles (see below).

Stability at the Nanoscale

Small particles are expected to have higher enthalpies and free energies than large crystals because of a positive surface energy. In contact with water and in most terrestrial environments, the particle surfaces are hydrated. Indeed, nanoparticles hold on to their water tenaciously. Thus, the thermodynamics of different polymorphs at the nanoscale will depend on the energetics of the bulk polymorphs, the particle size (or surface area), and the extent of hydration. To separate these factors, much recent effort has gone into combining solution calorimetry of well-characterized samples of different polymorphs (with known surface area and water content) with measurements of the heat of adsorption of water vapor (1013, 15, 18). A new approach to measuring enthalpies of water adsorption combines a microcalorimeter coupled to a gas-adsorption analytical system (19). This combined system enables precise gas dosing, volumetric detection of amount of adsorbed water, and simultaneous measurement of heat effect and adsorption isotherm (amount of adsorbed water versus pressure). This method provides relatively rapid, automated, and high-resolution measurement of heat of adsorption as a function of surface coverage.

Figure 1 shows the differential heats of adsorption of water versus coverage for a number of iron oxides and oxyhydroxides, together with corresponding values of integral heats of adsorption. The integral adds all the differential heats up to a coverage where the heat of adsorption is simply the heat of condensation (–44 kJ per mole of H2O) and further water is merely physisorbed. The water adsorption enthalpies for different FeOOH polymorphs show similar behavior. The values for maghemite and nano-hematite are also similar to those for oxyhydroxides. These similarities imply that surface bonding for water on all these phases is similar, and they suggest the possibility that all nanoparticle surfaces can be reconstructed to a relatively common structure. The most tightly held water at initial low coverage is bound more strongly than in the liquid by about 60 kJ mol–1. Recent data suggest that coarse hematite behaves differently from hematite nanoparticles (see Fig. 1) and holds water more tightly than do nanoparticles by a factor of 2. Because the distribution of orientations of surface planes exposed and possible surface reconstruction in each sample cannot be quantified, comparisons of different samples are difficult. However, the strongly exothermic enthalpies suggest that H2O on the larger particles may dissociate into tightly bound OH groups to satisfy incomplete bonding geometries on the initial surface. Such high-energy surface sites may never be made available on the nanoparticles because they cannot be fully dehydrated without coarsening, whereas coarse hematite can be outgassed at higher temperatures.

Fig. 1.

Differential enthalpies of water vapor adsorption for different iron oxides, together with values of integral enthalpies of adsorption relative to liquid water. [Data from (4, 1013, 18)]

To derive surface enthalpy, one must separate the effect on measured enthalpy of surface area from that of water adsorption. This can be done in two ways. If one considers the water to be adsorbed with an enthalpy equal to its heat of condensation, then the resulting corrected solution calorimetric data (14), plotted versus the surface area (Table 1 and Fig. 2), produce the surface enthalpy of the hydrated surface as the slope of the linear fit (1012). This is because any effects associated with differences in enthalpy of water adsorption, resulting from interaction of water with the surface and surface relaxation, are still included in the corrected enthalpy, because the reference state is taken as bulk liquid water. On the other hand, if one uses the measured integral heat of water adsorption to correct for the water adsorption enthalpy, one obtains the surface enthalpy of the anhydrous surface (Table 1 and Fig. 2). Surface energy, enthalpy, and free energy are expected to be very similar, especially at room temperature, and we make no serious distinction among these three terms. We also note that Fig. 2 has surface areas plotted in m2 mol–1, rather than showing particle size or area in m2 g–1. The former is necessary for the slope to represent a surface enthalpy and for the points of crossover to be meaningful.

Fig. 2.

Enthalpy, relative to coarse Fe2O3 (hematite) plus liquid water at 298 K, of various iron oxide and oxyhydroxide polymorphs as a formation of surface area per mole of FeO1.5, FeOOH, or Fe(OH)3. Lines are calculated from data in Table 1. Values for ferrihydrite are approximate because of sample variability and are represented as an elliptical area. Values of surface areas are plotted for formula units FeOOH (oxyhydroxides), Fe(OH)3 (ferrihydrite), and FeO1.5 (hematite and maghemite) for thermodynamic consistency when comparing different compositions. Corresponding values of surface areas (m2 g–1) and average particle size at the crossovers are discussed in the text.

One needs to know surface enthalpies for both hydrated (wet) and anhydrous (dry) surfaces because each is involved in different processes. Wet surfaces are appropriate for phase transformations and reactions in the ambient terrestrial environment (humid air, water, soil). In processes at higher temperatures (metamorphic, igneous, and technological reactions) or near-vacuum conditions (the surface of the Moon and Mars, various deposition chambers and electron microscopes), the enthalpy of the dry surface may be relevant.

Surface enthalpy (whether comparing wet or dry surfaces) is much higher for the anhydrous phases (oxides) than for any of the hydrous phases (oxyhydroxides). This is a general trend also seen in the alumina system (Al2O3 versus AlOOH) (20). A lower surface enthalpy allows oxyhydroxides to exist with larger surface areas and to be thermodynamically more competitive at smaller particle sizes. Figure 3 shows calculated dehydration curves for goethite to hematite (2FeOOH = Fe2O3 +H2O) as a function of temperature and water pressure, for bulk and for 10-nm particles. If coarsening is slower than decomposition, the stability field of the hydrous phase (goethite) expands to significantly higher temperatures, allowing goethite to persist—as an equilibrium phase under the constraint of nearly constant particle size—to temperatures more than 100 K higher than those calculated by straightforward bulk thermodynamics. Once more, this difference emphasizes the need to take nanoscale phenomena into account when considering phase stability and reactivity.

Fig. 3.

Pressure-temperature diagram for the reaction α-FeOOH (goethite) = α-Fe2O3 (hematite) + H2O (fluid). The curve at lower temperature shows the equilibrium among bulk solid phases and water (fluid implies liquid, vapor, or fluid above the critical point), whereas that at higher temperature shows equilibrium for 10-nm particles of hematite and goethite plus water.

Another trend is observed: As metastability of the coarse phase increases, its surface enthalpy decreases. This is a general, perhaps close to universal, trend seen not just in the iron oxides but also in alumina, titania, zirconia, and several other systems (21). Values of surface enthalpies also correlate with the heat of surface hydration and the fraction of strongly bound water. The most stable iron oxide polymorph, hematite, adsorbs water the strongest. The fraction of water that is strongly bound on goethite is 60%, versus 40% for akaganeite and lepidocrocite. Thus, materials with the highest surface enthalpy relax their high-energy surface sites most strongly by the adsorption of water.

The decrease of surface enthalpy with increasing metastability of the bulk polymorph leads to crossovers in enthalpy (and also free energy) of polymorphs at the nanoscale. Thus, γ-Al2O3 becomes stable with respect to α-Al2O3 (corundum) (21), γ-Fe2O3 (maghemite) becomes stable with respect to α-Fe2O3 (hematite), and there are complex crossovers for the FeOOH polymorphs (Fig. 2). The stability field for ferrihydrite is shown only approximately by the ellipse in Fig. 2 because of the variability of samples, the nonexistence of coarse-grained ferrihydrite, and the inability to dehydrate the material significantly.

Thermodynamic Control of Occurrences of Iron Oxides

Knowing the free energy of formation and the surface enthalpy (or free energy) of various iron oxides, one can predict their stability for a given surface area. Thermodynamic crossovers of the stability of iron oxides as a function of their particle size or surface area (Fig. 2) dominate these relations.

Goethite becomes thermodynamically stable relative to hematite and water at surface areas greater than about 15 m2 g–1 (particle size 60 nm, assuming spherical particles). Lepidocrocite becomes more energetically stable than maghemite and hematite at surface areas greater than 70 m2 g–1 (particle size 12 nm). Akaganeite becomes stable relative to goethite at surface areas greater than 200 m2 g–1 (particle size 5 nm).

The stability field of ferrihydrite overlaps those of many other iron oxides (hematite, maghemite, goethite, akaganeite, and lepidocrocite) (Fig. 2). At these high surface areas, ferrihydrite is thermodynamically very competitive with other iron oxides. This fact alone explains the ease with which ferrihydrite forms in a large variety of environments and persists if no coarsening occurs. Furthermore, variations in the structure of ferrihydrite, and much of the controversy about its structure, may arise because it can form from different oxyhydroxide precursors, over a range of particle sizes, and in a wide range of conditions.

The complex energetic crossovers shown in Fig. 2 are directly applicable to the occurrence of iron oxide minerals in soils. The most striking example is the hematite-goethite pair. Although the stable bulk assemblage at ambient conditions is hematite plus liquid water, Fig. 2 shows that almost any decrease in size leads to stabilization of goethite (22). Hence, particle size exerts major control over the relative stability and formation of hematite and goethite, even though soils represent a system that is too complex to be controlled just by a single variable.

The hematite-goethite equilibrium may be also shifted by variations in temperature, water activity, and the thermodynamics of Fe-Al substitution (23). The direct transformation of hematite to goethite or goethite to hematite has not been observed under ambient conditions, and long-term experiments documenting this transformation are lacking (1). However, water adsorption experiments have shown that hydrated hematite surfaces behave thermodynamically like the surfaces of goethite (18). Thus, perhaps the transformations may begin at the surfaces of nanoparticles, especially at temperatures somewhat above ambient. Transformation in either direction would then happen easily on the exposed goethite-like hydrated surfaces of either phase at the nanoscale. If the transformation occurs by a dissolution-reprecipitation process, those surfaces offer ample nucleation sites. The kinetic hindrance to coarsening below about 400°C ensures that the dehydration curve is that for small particles, with goethite stabilized to higher temperatures than in the bulk (Fig. 3).

Another natural laboratory with abundant iron oxides is the surface of Mars. The suspected presence of hematite was recently confirmed by in situ Mössbauer measurements (24). Earlier experiments performed on both Viking probes and Mars Pathfinder indicate that martian dust contains abundant maghemite (25). This maghemite is probably nanophase, with particle size of about 10 nm. The abundance of maghemite at the surface of Mars is readily explained by Fig. 2. Under dry conditions, as on Mars, maghemite particles become thermodynamically stable with respect to hematite particles at sizes of about 16 nm. Thus, maghemite nanoparticles are stable at the martian surface. Under wet conditions prevalent on Earth, the stabilization of maghemite is less pronounced, and goethite and other oxyhydroxides are competitive at the nanoscale. Although maghemite occurs in terrestrial soils (26), it is generally absent in older terrestrial sediments and rocks, both because of its limited stability in a hydrous environment and because of coarsening and transformation during burial and diagenesis.

During a possible solid-state akaganeite-goethite transformation involving biomineralization, the particle size of goethite is found to be bigger than that of akaganeite (3), supporting the stability crossovers presented here. According to recent structural observations (7), this transformation need not involve severe reconstruction, because fragments of the collapsed tunnels of akaganeite resemble structural blocks of goethite.

Transformation of lepidocrocite to goethite is not structurally straightforward, and only dissolution-reprecipitation mechanisms have been described in laboratory studies. The goethite is reported to have bigger particle size than the initial dissolving lepidocrocite (27). However, in natural systems, lepidocrocite crystals both larger and smaller than coexisting goethite have been reported (28, 29). Goethite and lepidocrocite may often crystallize simultaneously from a ferrous iron source (29). Their further coarsening and/or transformation depends on iron oxide thermodynamics but may also be influenced by temperature and the presence of silicates and carbonates (1).

Figure 2 also supports observations that lepidocrocite, especially when fine-grained, first transforms to maghemite (upon heating and/or in vacuum) and only then to hematite. This is consistent with the thermodynamic stability of maghemite relative to hematite at particle sizes less than about 16 nm. A direct size-driven phase transition between hematite and maghemite was observed with ball milling (30). It also supports the calculated size-related stability.

We conclude that the size-driven thermodynamic differences among iron oxide phases that are closely balanced in overall thermodynamic properties must be taken into account if we are to understand and predict the formation, stability, and transformation of these complex materials in geologic, environmental, and industrial settings.

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