Redox-structure dependence of molten iron oxides

The atomic structural arrangements of liquid iron oxides affect the thermophysical and thermodynamic properties associated with the steelmaking process and magma flows. Here, the structures of stable and supercooled iron oxide melts have been investigated as a function of oxygen fugacity and temperature, using x-ray diffraction and aerodynamic levitation with laser heating. Total x-ray structure factors and their corresponding pair distribution functions were measured for temperatures ranging from 1973 K in the stable melt, to 1573 K in the deeply supercooled liquid region, over a wide range of oxygen partial pressures. Empirical potential structure refinement yields average Fe–O coordination numbers ranging from ~4.5 to ~5 over the region FeO to Fe2O3, significantly lower than most existing reports. Ferric iron is dominated by FeO4, FeO5 and FeO6 units in the oxygen rich melt. For ferrous iron under reducing conditions FeO4 and FeO5 units dominate, in stark contrast to crystalline FeO. Knowing the atomic structure of liquid iron oxide is key to understanding steelmaking processes and magma flows. Here, Fe-O atomic coordination numbers are determined during levitation melting at a range of temperatures and oxygen partial pressures, revealing low coordination numbers.

M olten iron oxide plays a crucial role in iron, steel, and copper production 1,2 and has a major role in determining the behavior and properties of magmatic liquids [3][4][5][6] . Iron redox has previously been studied in multicomponent silicate liquids and glasses 3,7,8 , where the oxidation states and coordination numbers have a direct effect on melt viscosity, density, phase stability, and heat capacity 7 . However, the assignment of the local Fe coordination environment and its relationship to the oxidation state is not straightforward. This is because iron redox depends on many factors, including oxygen partial pressure, temperature, and composition. Wilke 7 has pointed out that the Fe coordination by oxygen in widely studied glass analogues is likely to differ from those found in high temperature melts. Consequently, the structural role of Fe is poorly understood due to the difficulty of studying liquids at high temperatures using direct methods 9 . Under oxidizing conditions, no suitable containers exist, and oxygen pressures of several atmospheres or supercooling are essential to stabilize molten Fe 2 O 3 . To our knowledge, the only structural measurements on a pure iron oxide melt are two 40-year-old X-ray diffraction studies by Waseda et al. 10,11 at compositions close to FeO, and two X-ray absorption near edge studies 12,13 .
Structural interpretation of experimental data is complicated by the fact that both ferrous (Fe 2+ ) and ferric (Fe 3+ ) iron co-exist in melts, and both can be in a range of coordination environments. Fe 2+ is the most abundant iron species in magmas and is usually 6-fold in crystalline minerals at ambient pressure. In the liquid state however, it has been debated if Fe 2+ is primarily 5-or 6-fold coordinated by oxygen 14,15 or 4-fold 9,16 . Historically Fe 2+ was considered as being distributed between sites coordinated by either 4 or 6 oxygen atoms based on crystal structures 16,17 . However, it has also been suggested that Fe in the melt, similar to Al, can also be 5-fold coordinated by oxygen 8,18 . This has been supported by the fact that in some minerals Fe-O polyhedra exist with 5-short bonds 5 . A bimodal distribution between 4-and 6fold Fe 2+ in molten FeO would be in contrast to other mixed coordination oxide melts, such as Al 2 O 3 , TiO 2 or MgO, in which liquids and glasses contain a single distribution of metal-oxygen bond distances, representing a mixture of 4, 5, and 6 coordinated units 19,20 . The coordination environment of Fe 3+ is similarly unclear. In crystalline Fe 3 O 4 , ε-Fe 2 O 3 , and γ-Fe 2 O 3 , Fe atoms reside mainly in octahedral coordination with some tetrahedral sites. Contrastingly, in a soda-lime-silica glass Fe 3+ has been considered to be tetrahedrally surrounded by oxygen atoms, along with minority higher coordination environments 21 , while measurements on Fe 3+ in aluminosilicates indicate primarily 5-or 6fold coordination in the liquid state 15,16 , implying considerable compositional dependence.
Here we have determined the structures of liquid FeO x (1.0 ≲ x ≲ 1.5) over a wide range of oxidation states and temperatures, using a combination of aerodynamic levitation with laser heating in various gas mixtures and high-energy X-ray diffraction. Levitation methods enable access to the oxidizing and metastable regions of the Fe-O phase diagram without interference from crucible materials, as well as the ability to supercool the liquid by the elimination of heterogeneous crystal nucleation caused by a container. Atomistic models have been obtained using Empirical Potential Structure Refinement (EPSR) modeling, see Table 1. The local Fe-O coordination number in FeO x melts is found to have majority populations of 4-and 5-fold polyhedra across a wide range of oxidation states, with structures that are very different from the crystalline phases. At the same time, the new data highlights gaps in our understanding of the structural role of iron, even in the pure FeO x system.

Results
The FeOx phase diagram. The locations of our liquid FeO x X-ray measurements within the FeO-Fe 2 O 3 region of the phase diagram 22 are shown in Fig. 1. At temperatures of ∼1673 K and below, the more oxidized liquids are deeply supercooled into the Wustite-Magnetite-Hematite phase fields. The x-ray data at ∼1973 K traverse the entire stable single-phase oxide liquid region. Our most reducing gas atmosphere (99CO:1CO 2 ) is expected to bring the sample within the large miscibility gap between the liquid oxide and metal, however, buoyancy effects lead to measurement of the oxide melt portion only, see Supplementary Figs. S1 and S2 in the high energy X-ray experiments section for a detailed discussion.  We note that X-ray diffraction cannot readily distinguish between Fe 2+ and Fe 3+ and the Fe 2+ parameters have not been widely tested in the literature. decreases from the most oxidizing to the most reducing atmosphere, and the peak position increases from 1.92(1) Å to 1.95(1) Å (Fig. 2). This indicates that on average the Fe 2+ -O bond lengths are longer (and weaker) than Fe 3+ -O. Concomitantly, the second peak in D(r) shifts from 3.34(3) Å to 3.15(2) Å with a decrease of intensity, which is attributed to changes in the relative amounts of Fe 2+ -Fe 2+ , Fe 2+ -Fe 3+ and Fe 3+ -Fe 3+ neighbors which each have different pair distances. In evaluating the local Fe-O coordination numbers, the method of choice of cut-off distance was typically found to shift the absolute values of n FeO by ±0.5, but did not affect the trend observed and plotted in Fig. 3. Here we define three criteria for the cut-off distance (i) the first minimum in g ij (r) (ii) first minimum in r 2 g ij (r) and (iii) a fixed value, where the Fe 2+ -O and Fe 3+ -O radial cut-off distances were chosen separately, see Supplementary Figs. S3-S5 in the extraction of coordination numbers section. The Fe-O coordination number was obtained using all three methods, and the average n FeO, was determined as a function of Fe 3+ /ΣFe, and is shown in Fig. 3a.
EPSR modeling. In our EPSR models, which represent best fits of 3-dimensional atomic arrangements at the expected densities that reproduce our experimental data, n FeO is typically found to increase from ∼4.  10 have reported an Fe-O peak position of 2.06 Å and n FeO = 5.5 at 1673 K using X-ray diffraction in a dry Argon atmosphere, and r FeO = 2.16 Å and n FeO = 5.7 at 1693 K using anomalous x-ray scattering 11 . A re-analysis of the Waseda et al. 10 diffraction data through direct Fourier transformation of the digitized S(Q) and EPSR modeling reveals n FeO = 4.6(4), in line with our findings. In addition, we note that n FeO ≈ 5 for our most oxidized melt (92% Fe 3+ ) approaches that found in the crystalline form of γ-Fe 2 O 3 , despite substantial differences in populations of 4-, 5-and 6-fold Fe-O polyhedra.

Discussion
Although we obtain Fe-O coordination numbers in reducing atmospheres that are substantially lower than the octahedral coordination found in Wustite, our measurements are in good agreement with first principles molecular dynamics (MD) calculations in related liquid systems (but none have yet been performed on FeO x ). For example, it is found that n Fe2+-O = 4.5 in  where Mg 2+ has only a slightly smaller ionic radius than Fe 2+ . In the fayalite system, Alderman et al. 25 found n FeO = 4.4 by x-ray diffraction, in reasonable agreement with Ramo and Stixrude 23 . Also values of 4.5 (Sun et al. 26 ) and 4.7 (Guillot et al. 27 ) have been predicted using classical MD simulations. Classical MD calculations of molten FeO by Seo et al. 28 predict n FeO = 4.2, and are able to reproduce transport properties of the FeO-SiO 2 system, although the model density is significantly lower than experiments would suggest 29 . To explore this further, we have carried out a series of classical MD simulations of molten FeO using seven published inter-atomic pair potential sets (see Table 2 and Supplementary Table S1 and Figs. S6-S8) and found the Guillot and Sator fayalite potential 27 to be in the best (but not complete) agreement with the expected density and our experimental diffraction data, with n Fe2+-O = 4.8, and four-and five-fold Fe-O polyhedral units dominating. However, no classical interatomic potential available for mixed valence iron oxides in the literature was found to reproduce the trend observed in Fig. 3. A deeper understanding of the relative changes in n FeO can be obtained from an interrogation of the average coordination numbers of n Fe2+O and n Fe3+O. The coordination numbers of Fe 2+ -O and Fe 3+ -O in our EPSR models are similar to one another (and mostly invariant with temperature), similar to XANES findings in iron silicate glasses 18 , as both are found to increase with Fe 3+ /ΣFe, see Fig. 3b. Moreover, our EPSR models show that liquid FeO x primarily consists of 4-, 5-and 6-fold coordinated Fe 2+ and Fe 3+ atoms, and their relative populations vary with Fe 3+ /ΣFe (Fig. 4). No evidence was found for a bimodal FeO 4 and FeO 6 distribution in the liquid. Instead, a substantial amount of Fe 3+ (38-49%) and Fe 2+ (26-41%) are found in 5-fold coordination indicating that this is a dominant species in all FeO x melts. For ferrous iron, our EPSR models show Fe 2+ predominantly occupies 4-and 5-coordinated sites, which is consistent with other divalent cations e.g. Ni 2+ , Fe 2+ , and Mg 2+ in molten silicates 30 . For ferric iron, Fe 3+ , 4-fold and 5-fold polyhedra also dominate at low Fe 3+ /ΣFe, but for Fe 3+ /ΣFe >40% the number of 6-fold Fe 3+ increases and the number of 4-fold Fe 3+ decreases. This is opposite to the trend reported for binary silicate melts by Mysen 15 , which indicated n Fe3+-O decreases from 6 to 4 with increasing Fe 3+ /ΣFe. In addition, it is a more complex scenario than that proposed by Hayashi et al. 17 who only considered the existence of tetrahedral and octahedral Fe-O units in sodium-iron-silicate melts.
An alternative view of the change in liquid structure with redox can be obtained through the extraction of the oxygen-iron coordination number n OFe . In Fig. 3c, n OFe tends toward~3.5 in pure O 2 gas close to that found in γ-Fe 2 O 3 , but this increases only slightly to~4.5 around FeO (compared to 6 in the crystalline phase). An analysis of the fraction of OFe coordination species with Fe 3+ /ΣFe in Fig. 4c in our EPSR models shows a dramatic effect. We find that the dominant OFe 4 units account for approximately half the species in the melt and this remains relatively constant with Fe 3+ /ΣFe. For Fe 3+ rich melts OFe 3 units account for almost all of the remaining oxygen connectivity. As the availability of oxygen decreases and the percentage of Fe 2+ increases, the OFe 3 units are partially replaced by FeO 5 units.
Finally, we consider the relationship between the presence of various local atomic structural units and the physical properties of liquid iron oxide slags. In binary ferrite melts it has been suggested that the atomic fraction of Fe 3+ O 4 is the main factor in controlling the viscosity and the abundance of Fe 2+ and Fe 3+ O 6 units are main contributors to the electrical conductivity 31 . In addition, chemical reaction rates in the iron and steel making process are determined by concentrations and activities, where the activity is dependent upon bond strengths in different coordination environments 17 . However, a comparison of our diffraction data with a survey of classical MD simulations performed using various potentials in the literature has revealed the shortcomings of many interatomic potentials across the compositional range of FeO x melts, see Supplementary Fig. S7. Hence more sophisticated theoretical work and/or ab initio simulations are necessary to elucidate the precise ratios of 4-, 5-and 6-fold coordinated Fe 2+ -O and Fe 3+ -O in liquid FeO x , particularly in order to understand transport properties, and to address chargetransfer and small-polaron conductance phenomena. In fact, during the writing of this article we note that two ab initio molecular dynamics simulations on FeO x -bearing silicate melts have been published 32,33 . It is anticipated that our experimental pair distribution functions for molten iron oxides presented herein will provide ambient-pressure benchmarks to test models relevant to a wide range of industrial and natural processes.

Methods
Levitation and high-energy X-ray diffraction experiments. We formed powdered Fe 2 O 3 (purity 99.995%) into roughly 3 mm diameter spheres using a laser hearth melter in the air. Weighed samples were floated in a 200-500 mL/min stream of gas, using a conical nozzle aerodynamic levitator in an enclosure 25 , and heated from above using a 400 W CO 2 laser (Synrad Firestar i401). The droplet surface temperature was measured using 0.9 μm wavelength optical pyrometry (Chino IR-CAS) sighted onto the region of the sample where the X-ray measurements were made. A constant spectral emissivity of ε λ = 0.92 was assumed for The cut-off distances were determined as the average of three criteria, i.e. the first minimum in g ij (r), the first minimum in r 2 g ij (r) and a fixed cut-off value. The fixed cut-off distances were determined by the mean values of several MD simulations performed using various potentials. MD simulation temperatures are either 2000 K (closest T step to the highest experimentally measured T), or else are the lowest liquid temperature simulated prior to the onset of crystallization.
correcting the apparent temperatures and the accuracy of the pyrometer was ∼1% for temperatures in the range 1773-1973 K. The oxygen partial pressure, p(O 2 ), experienced by the sample was controlled using different levitation gas mixtures, either 99CO:1CO 2 , 50CO:50CO 2 , CO 2 (all CO:CO 2 mixtures were 5% with a balance of 95%Ar), 99.9%Ar:0.1%O 2 or pure O 2 , leading to a range of Fe 3+ /ΣFe at equilibrium. The p(O 2 ) were calculated by standard methods 34 , based on the measured droplet surface temperatures and the Fe 3+ /ΣFe ratio was estimated using equation 12 from Jayasuriya et al. 35 , which has previously been found 13 to be in accord with the molten iron oxide data of Darken and Gurry 36 . A detailed evaluation of the effect of errors in the calculated values of Fe 3+ /ΣFe is described in the uncertainty section and Supplementary Fig. S5.
High energy X-ray diffraction was performed at the Advanced Photon Source beamline 6-ID-D, (Argonne, IL, USA) using an incident X-ray beam of wavelength 0.123538 Å (100.36 keV). A Perkin Elmer XRD1621 area detector was placed ∼338 mm downstream of the sample and calibrated using a CeO 2 powder standard (NIST) to provide a wide Q range of 0.5-25.0 Å −1 . The x-ray beam was centered on the top 200 μm of the sample sphere to align with the laser beam and pyrometry measurement and avoid scattering from the levitator components. Before heating a sample, the chamber was purged with the selected process gas for 20 min. The levitated sample was then heated to a temperature just above its melting point, and held for 10-20 s to ensure complete melting. Diffraction patterns were collected for 40 s each in ∼100 K steps in a sequence of decreasing temperatures from 1973 K to at least 1673 K. Only scattered X-ray data from the top half of the Debye-Scherrer cone were used in the analysis to avoid significant attenuation corrections. The x-ray total structure factor S(Q) and the corresponding differential pair-distribution function D (r) = 4πρr[G(r) -1] as a function of temperature and p(O 2 ) were extracted. Details of the high-energy X-ray analysis used have previously been described by Shi et al. 37 from samples prepared in a laser hearth melter 38 . Three-dimensional models describing the atomic structure were obtained using EPSR 39 . The Fe 3+ /ΣFe ratio was estimated using equation 12 from Jayasuriya et al. 35 , which was found to be in accord with the molten iron oxide data of Darken and Gurry 36 .

Atomistic modeling
Empirical potential structure refinement modeling. EPSR 39 were used to obtain atomistic models of liquid FeO x based on the high-energy x-ray diffraction data. The EPSR simulations were performed on ∼6000 ions within a cubic box under periodic boundary conditions, and the temperature dependent densities fixed using the equations of Hara et al. 29 . A Lennard-Jones reference potential with Fe 3+ and O 2− parameters from Weigel et al. 40 was used. For Fe 2+ , the reference potential parameters are given in Table 1, and were modified only slightly from those of Fe 3+ by comparing initial Monte Carlo simulation predictions of the Fe-O bond length distributions to the diffraction data. The starting configuration was built according to the calculated Fe 3+ /ΣFe ratio 35 and, following initial Monte Carlo equilibration, the empirical potential term was refined to improve agreement with scattering data, with the maximum allowed energy amplitude set to ∼30% of initial model energy. Once the goodness-of-fit parameter was minimized, structural data were collected over ensembles of at least 2000 configurations. The resulting EPSR fits were in excellent agreement with the high energy X-ray diffraction data shown in Fig. 2, see Fig. S1.
Classical molecular dynamics simulations. Classical molecular dynamics (MD) simulations with 0% Fe 3+ were performed using the DL_POLY package 41 on a system containing ∼6000 atoms. Several published potentials 27,28,[42][43][44][45] were tested. The results of Monte Carlo simulations under the EPSR reference potentials were used as starting configurations for the MD simulations, which were conducted either in the canonical (NVT) or the isothermal-isobaric (NPT) ensemble, using a Hoover-Nose thermostat or thermostat-barostat, at P = 1 atm and various temperatures. A time step of 1.0 fs was selected, with the first 25000 steps used for equilibration, and particle trajectories typically integrated over a further 50,000 steps (production runs) at each temperature point. The starting temperature was 2700 K and the systems were cooled stepwise in 100 K steps down to 300 K. In some cases (Fe 2+ -rich) crystallization was observed, and in all other cases glass formation occurred. The effect of Fe 3+ /ΣFe on the liquid structure was also investigated using the Teter and Guillot pair potentials 27,42 .

Data availability
The total X-ray structure factors and their corresponding pair distribution functions are provided in the supplementary information.
Received: 21 May 2020; Accepted: 6 September 2020;  35 ). n FeO and n OFe were determined by the average of the three cut-off criteria. The clusters on the right correspond to representative OFe 4 , OFe 3 , and OFe 5 units taken from the EPSR models.