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DOE OSTI2021

A Machine Learning Approach for the Prediction of Formability and Thermodynamic Stability of Single and Double Perovskite Oxides

Perovskite oxides continue to attract huge interest due to their fascinating and wide-ranging properties for diverse applications. The tunability of these properties may be further enhanced by increasing their compositional complexity via double perovskite-ordered configurations containing multiple cations. In this work, we focus on an exhaustive chemical space of single and double oxide perovskites and optimally explore this space to identify novel compositions that are likely to form stable compounds. Critically, we examine the relationship between formability, the practical ability to synthesize a compound, and stability, the thermodynamic preference to form the structure. Our formability and stability training data sets were enumerated from the available experimental literature and in-house density functional theory computations and contained 1505 and 3469 examples, respectively, representing state-of-the-art in the current open literature in perovskite and double perovskite compounds. Subsequently, cross-validated and highly accurate machine learning classification models are built using these training data sets and employed to screen for novel stable oxide perovskites. The study identifies (1) atomic features relevant to prediction of formability and stability in perovskite and double perovskite compounds, (2) the importance of including energy contributions due to local structural relaxations going beyond the high symmetry perovskite phase, and (3) 437,828 double perovskite compounds that are likely to be stable and 891,188 compounds that are likely to be formable. From the intersection of this large chemical space of formable and stable oxide perovskites, 414 compositions are identified as the most promising candidates for future experimental synthesis of novel oxide perovskites. The developed models may be generalized and have implications beyond perovskite discovery if applied to other families of compounds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Kinetic versus Thermodynamic Stability of LLZO in Contact with Lithium Metal

Li 7 La 3 Zr 2 O 12 (LLZO) garnet-based oxides are a promising class of solid electrolytes used as the separator in all-solid-state batteries (ASSBs). While LLZO is considered to have a wide electrochemical stability window, its intrinsic stability in contact with lithium metal is not sufficiently well understood, and there is still a debate on the key question of whether LLZO does or does not form passivation layers before and during cycling. Utilizing both in situ and operando X-ray photoelectron spectroscopy techniques, in this work we reveal the presence of a kinetic barrier to the reduction of LLZO by Li metal, with the extent of oxygen-deficient interphase (ODI) formation depending sensitively on the energetics of Li metal arriving at the Li vertical bar LLZO interface. Despite the clear presence of a kinetic barrier to reduction, the electrochemical response of the Li vertical bar LLZO interface is unchanged by the presence of the ODI, indicating that ODI formation during electrochemical cycling does not hinder charge transfer across the Li vertical bar LLZO interface. Overall, these results reveal that the reactivity of LLZO with Li metal depends not only on the material properties of the adjoining phases (i.e., surface purity and active contact) and their resulting thermodynamic stability but also on the energy input at the interface and the resulting reaction kinetics. Furthermore, the presence of a kinetic barrier to reduction highlights the additional complexities governing the reactivity of solid-state interfaces in ASSBs and underscores the importance of operando characterization of interfacial stability to design more robust, high-performance protection strategies for solid electrolytes in contact with reactive electrodes.

25 ENERGY STORAGE↗

DOE OSTI2022

Shape Control of Colloidal Semiconductor Nanocrystals through Thermodynamically Driven Aggregative Growth

The optoelectronic properties of colloidal semiconductor nanocrystals (NCs) can be manipulated by changing their geometric shapes. The precise synthetic control over particle morphologies, however, has remained elusive. Conventional growth techniques rely on the kinetic assembly of atomic units, where supersaturation and precipitation processes can lead to a broad distribution of particle shapes. In this paper, we demonstrate that replacing atomic precursors with small-size nanocrystals as building blocks for larger colloids offers an easier, more predictive control over nanoparticle shape evolution. The reported growth strategy is illustrated via shape-selective syntheses of CdSe and CdS NC cubes, spheres, rods, as well as unprecedented “donut” and ring-like structures. Growth of desired particle morphologies was achieved by choosing an appropriate reaction solvent that minimizes the surface free energy through a unique shape formation. This so-called "aggregative growth mechanism" is explained using a thermodynamic model for interacting viscous colloids. We expect that this novel growth strategy will offer a viable platform for shape–selective synthesis of many inorganic colloids, providing pathways to optimizable optoelectronic materials.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Fundamental Thermodynamic, Kinetic, and Mechanical Properties of Lithium and Its Alloys

Lithium alloying reactions are beneficial in promoting uniform plating and stripping of lithium metal in all-solid-state batteries. First-principles calculations are performed to predict thermodynamic, kinetic, and mechanical properties of lithium and several important Li–M alloys (M = Mg, Ag, Zn, Al, Ga, In, Sn, Sb, and Bi). While the Li–Mg binary system forms a solid solution, most other lithium–metal alloys prefer stoichiometric intermetallic compounds with common local motifs that enable fast Li diffusion. Lithium and Li-rich alloys exhibit an unusually flat energy landscape along paths that connect BCC to close-packed structures like FCC and HCP, with important implications for mechanical properties. Very low migration barriers for Li diffusion that rival those of superion conductors are predicted, both in pure Li and in Li–M intermetallics. However, vacancy concentration, which is crucial for substitutional diffusion, is predicted to be low in metallic Li and most Li–M intermetallics. Compounds such as B32 LiAl and LiGa as well as D0 3 Li 3 Sb and Li 3 Bi exhibit structural vacancies at higher ends of their voltage windows, which together with low migration barriers leads to exceptionally high Li mobilities. In the Li–Mg solid solution, the addition of Mg is found to decrease the vacancy tracer diffusion coefficient by an order of magnitude.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Acid Gas Stability of Zeolitic Imidazolate Frameworks: Generalized Kinetic and Thermodynamic Characteristics

Here, acid gases such as SO 2 and CO 2 are present in many environments in which the use of nanoporous metal-organic frameworks (MOFs) is envisaged. Among metal-organic frameworks, zeolitic imidazolate frameworks (ZIFs) have been extensively explored as membranes or adsorbents. However, there is little systematic knowledge of the effects of acid gas exposure on the structure of ZIFs, in particular the mechanistic aspects of ZIF degradation by acid gases as well as the effects of ZIF crystal topology and linker composition on their stability. Here we present a generalized and quantitative investigation of the kinetic and thermodynamic acid gas stability of a diverse range of ZIF materials. The stability of 16 ZIFs (of SOD, RHO, ANA, and GME topologies) under different environments – humid air, liquid water, and acid gases CO 2 and SO 2 (dry, humid, and aqueous) – are investigated by a suite of experimental and computational methods. The kinetics of ZIF degradation under exposure to humid SO 2 is studied in detail, and effective rate constants for acid gas degradation of ZIFs are reported for the first time. Remarkably, the kinetics of degradation of the diverse ZIFs correlate strongly with the linker pKa and ZIF water adsorption in a manner contrary to that expected from previous predictions in the literature. Furthermore, we find that the material ZIF-71 (RHO topology) shows much higher stability relative to the other ZIFs in humid SO 2 and CO 2 environments.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Thermodynamic and mass transfer modeling of carbon dioxide absorption into aqueous 2-amino-2-methyl-1-propanol

Explanations for the mass transfer behavior of 2-amino-2-methyl-1-propanol (AMP) are conflicting, despite extensive study of the amine for CO 2 capture. At equilibrium, aqueous AMP reacts with CO 2 to give bicarbonate in a 1:1 ratio. While this is the same stoichiometry as a tertiary amine, the reaction rate of AMP is 100 times faster. This work aims to explain the mass transfer behavior of AMP, specifically the stoichiometry and kinetics. An eNRTL thermodynamic model was used to regress wetted-wall column mass transfer data with two activity-based reactions: formation of carbamate and formation of bicarbonate. Data spanned 40–100 C and 0.15–0.60 mol CO 2 /mol alk). The fitted carbamate rate constant is three orders of magnitude greater than the bicarbonate rate constant. Rapid carbamate formation explains the kinetics, while the stoichiometry is explained by the carbamate reverting in the bulk liquid to allow CO 2 to form bicarbonate. Understanding the role of carbamate formation and diffusion in hindered amines enables optimizing solvent amine concentration by balancing viscosity and free amine concentration. Furthermore, this improves absorber design for CO 2 capture.

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2017

Thermodynamic, Spectroscopic, and Computational Studies of f -Element Complexation by N -Hydroxyethyl-diethylenetriamine- N,N ', N ", N "-tetraacetic Acid

Potentiometric and spectroscopic techniques were combined with DFT calculations to probe the coordination environment and determine thermodynamic features of trivalent f-element complexation by N-hydroxyethyl-diethylenetriamine-N,N',N",N"-tetraacetic acid, HEDTTA. Ligand protonation constants and lanthanide stability constants were determined using potentiometry. Five protonation constants were accessible in I = 2.0 M (H + /Na + )ClO 4 . UV–vis spectroscopy was used to determine stability constants for Nd 3+ and Am 3+ complexation with HEDTTA. Luminescence spectroscopy indicates two water molecules in the inner coordination sphere of the Eu/HEDTTA complex, suggesting HEDTTA is heptadentate. Luminescence data was supported by DFT calculations, which demonstrate that substitution of the acetate pendant arm by a N-hydroxyethyl group weakens the metal–nitrogen bond. This bond elongation is reflected in HEDTTA’s ability to differentiate trivalent actinides from trivalent lanthanides. The trans-lanthanide Ln/HEDTTA complex stability trend is analogous to Ln/DTPA complexation; however, the loss of one chelate ring resulting from structural substitution weakens the complexation by ~3 orders of magnitude. Successful separation of trivalent americium from trivalent lanthanides was demonstrated when HEDTTA was utilized as aqueous holdback complexant in a liquid–liquid system. Time-dependent extraction studies for HEDTTA were compared to diethylenetriamine-N,N,N',N",N"-pentaacetic acid (DTPA) and N-hydroxyethyl-ethylenediamine-N,N',N'-triacetic acid (HEDTA). The results presented here indicate substantially enhanced phase-transfer kinetic rates for mixtures containing HEDTTA.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

DOE OSTI2018

Solution Thermodynamics and Kinetics of Metal Complexation with a Hydroxypyridinone Chelator Designed for Thorium-227 Targeted Alpha Therapy

In this study, the solution chemistry of a chelator developed for 227 Th targeted alpha therapy was probed. The compound of interest is an octadentate ligand comprising four N-methyl-3-hydroxy-pyridine-2-one metal-binding units, two tertiary amine groups, and one carboxylate arm appended for bioconjugation. The seven pK a values of the ligand and the stability constants of complexes formed with Th(IV), Hf(IV), Zr(IV), Gd(III), Eu(III), Al(III), and Fe(III) were determined. The ligand exhibits extreme thermodynamic selectivity toward tetravalent metal ions with a ca. 20 orders of magnitude difference between the formation constant of the Th(IV) species formed at physiological pH, namely [ThL] - , and that of its Eu(III) analogue. Likewise, log β 110 values of 41.7 ± 0.3 and 26.9 ± 0.3 (T = 25 °C) were measured for [ThL] - and [Fe III L] 2- , respectively, highlighting the high affinity and selectivity of the ligand for Th ions over potentially competing endogenous metals. Single crystal X-ray analysis of the Fe(III) complex revealed a dinuclear 2:2 metal:chelator complex crystallizing in the space group P1 - . The formation of this dimeric species is likely favored by several intramolecular hydrogen bonds and the protonation state of the chelator in acidic media. L III edge EXAFS data on the Th(IV) complexes of both the ligand and a monoclonal antibody conjugate revealed the expected mononuclear 1:1 metal:chelator coordination environment. This was also confirmed by high resolution mass spectrometry. Lastly, kinetic experiments demonstrated that labeling the bioconjugated ligand with Th(IV) could be achieved and completed after 1 h at room temperature, reinforcing the high suitability of this chelator for 227 Th targeted alpha therapy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Complexation of Light Trivalent Lanthanides with N-(2-Hydroxyethyl)ethylenediamine-N,N',N'-triacetic Acid in Aqueous Solutions: Thermodynamic Analysis and Coordination Modes

N-(2-hydroxyethyl)ethylenediamine-N,N',N'-triacetic acid (HEDTA, denoted as H 3 L) is a strong chelating ligand that is widely used in separation of f-elements as relevant to the nuclear fuel cycle. There is much to be known about the structure and composition of the coordination sphere of the complexes of HEDTA with lanthanides. The complexation of HEDTA with light lanthanides (La 3+ , Nd 3+ and Eu 3+ ) was investigated thermodynamically and structurally in aqueous solutions. Potentiometry and microcalorimetry were performed to acquire the complexation constants (25-70°C) and enthalpies (25°C), respectively, at I = 1.0mol·L -1 NaClO 4 . Coordination modes of the complexes were analyzed by luminescence spectroscopy and nuclear magnetic resonance spectroscopy. The results indicate that there are two successive Ln 3+ /HEDTA complexes, LnL(aq) and Ln 2 (H -1 L) 2 2- (Ln 3+ referred to La 3+ , Nd 3+ and Eu 3+ ; H -1 L 4- referred to the deprotonation of the hydroxyl group) during the titration. The hydroxyl group of HEDTA is coordinated in Ln 3+ /HEDTA complex. The dinuclear Ln 2 (H -1 L) 2 2- complex is present as a carboxyl-bridged centrosymmetric dimer, and two carboxyl groups in bridging positions are coordinated to two adjacent Ln 3+ cations. Complexation of the NdL(aq) is exothermic, while formation of the hydrolytic complex Nd 2 (H -1 L) 2 2- is endothermic. Both NdL aq and Nd 2 (H -1 L) 2 2- complexes are driven by entropic force. These data will help to predict the behavior of lanthanides in the separation process where HEDTA is used as the aqueous complexant.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Comment on “Thermodynamic Models for the (HClO 4 + NaClO 4 ){aq} and (HBr + NaBr){aq} Systems at 298.15 K and 0.1 MPa” Authored by Oakes, C. S., Ward, A. L., Chugunov, N. Journal of Chemical & Engineering Data , 68 , 2554–2562

Oakes et al. (2023) published a review article in this journal. In that paper, Oakes et al. (2023) developed thermodynamic models to describe electrolyte solutions for HClO 4 –NaClO 4 –H 2 O and HBr–NaBr–H 2 O systems, based on literature data. In their paper, previously published work from researchers in the field was criticized; some of it is ours. Here, in this brief Comment, we first comment on their models, and then we briefly provide a technical response to that criticism.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2016

Blending Education and Polymer Science: Semiautomated Creation of a Thermodynamic Property Database

Structured databases of chemical and physical properties play a central role in the everyday research activities of scientists and engineers. In materials science, researchers and engineers turn to these databases to quickly query, compare, and aggregate various properties, thereby allowing for the development or application of new materials. The vast majority of these databases have been generated manually, through decades of labor-intensive harvesting of information from the literature, yet while there are many examples of commonly used databases, a significant number of important properties remain locked within the tables, figures, and text of publications. The question addressed in our work is whether and to what extent the process of data collection can be automated. Students of the physical sciences and engineering are often confronted with the challenge of finding and applying property data from the literature, and a central aspect of their education is to develop the critical skills needed to identify such data and discern their meaning or validity. To address shortcomings associated with automated information extraction while simultaneously preparing the next generation of scientists for their future endeavors, we developed a novel course-based approach in which students develop skills in polymer chemistry and physics and apply their knowledge by assisting with the semiautomated creation of a thermodynamic property database.

Collaborative/Cooperative Learning↗

DOE OSTI2025

How Thermodynamic, Electronic, and Steric Factors Influence Mesitylcopper Oligomers

Mesitylcopper (CuMes) is a highly versatile organocopper reagent used in both organic and inorganic syntheses. It has previously been shown that CuMes exists as a tetrameric or pentameric cyclic oligomer [CuMes] n (n = 4, 5), both in solution and in the solid state. The bonding arrangement between the [CuMes] units has qualitatively been described as localized three-center twoelectron (3c-2e) bonds. However, the electronic, structural, and thermodynamic forces driving this aggregation are still not well understood. For this reason, we employed density functional theory (DFT) calculations to study mesitylcopper as a monomeric [CuMes] unit and [CuMes]n oligomers with n = 2 to n = 7. We found that there is a strong electronic driving force for aggregation caused by strong mixing between the Cu’s d orbitals and Mes’s π orbitals in oligomers larger than the dimer. This mixing is only optimized in oligomers with n ≥ 3, where the mesityl group is no longer bonded to a single copper center but instead becomes a bridging ligand. Beyond the trimer, steric and entropic factors become relevant for determining the relative stabilities of the different aggregates, with midsized oligomers (n = 4−5) having the optimal balance between the electronic Cu−C bonding character, Cu···Cu attractive forces, entropy, reduced internal ring strain, and reduced steric interactions between the mesityl groups.

Copper↗

DOE OSTI2023

Permittivity Threshold and Thermodynamics of Integer Charge-Transfer Complexation for an Organic Donor–Acceptor Pair

Molecular or chemical-based charge doping provides a means to change the properties (e.g. conductivity) of a material through a complete or partial transfer of charge between its constituents. Understanding how local material environment impacts this process is thus important for controlling the properties of organic materials. This paper presents spectroscopic investigations of molecular charge transfer interactions between a pair of common charge-doping and -transporting materials (2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane, F4TCNQ, and N,N’-Diphenyl-N-N’-di-p-tolylbenzene-1,4-diamine, MPDA). Equilibrium constants associated with charge transfer were determined for donor-acceptor pairs dissolved in a series of solvents covering a range of values of permittivity. A threshold for highly favorable charge separation was observed to occur at a permittivity of ~8-9, with more and less favorable charge separation observed in solvents of higher and lower permittivity, respectively, but with chloroform (permittivity=4.81) exhibiting an anomalously favorable charge separation. Temperature-dependent studies were undertaken to assess the thermodynamics of charge separation. In 1,2- dichloroethane (permittivity=10.36) and chlorobenzene (permittivity=5.62), charge transfer was observed to be both enthalpically and entropically favorable. Charge separation in chloroform is exothermic and entropically disfavored, indicating that specific, inner-shell solvent-solute interactions stabilize the charge-separated complex and result in a net increase in local solution structure. Furthermore, our results provide insight on how modification to the chemical environment may be utilized to support stable charge transfer for molecular doping applications and requiring only modest changes in local permittivity.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Hexagonal Lattices of HIV Capsid Proteins Explored by Simulations Based on a Thermodynamically Consistent Model

HIV capsid proteins (CAs) may self-assemble into a variety of shapes under in vivo and in vitro conditions. Here, we employed simulations based on a residue-level coarse-grained (CG) model with full conformational flexibility to investigate hexagonal lattices, which are the underlying structural pattern for CA aggregations. Facilitated by enhanced sampling simulations to rigorously calculate CA dimerization and polymerization affinities, we calibrated our model to reproduce the experimentally measured affinities. Here using the calibrated model, we performed unbiased simulations on several large systems consisting of 1512 CA subunits, allowing reversible binding and unbinding of the CAs in a thermodynamically consistent manner. In one simulation, a preassembled hexagonal CA sheet developed spontaneous curvatures reminiscent of those observed in experiments, and the edges of the sheet exhibited local curvatures larger than those of the interior. In other simulations starting with randomly distributed CAs at different concentrations, existing CA assemblies grew by binding free capsomeres to the edges and by merging with other assemblies. At high CA concentrations, rapid establishment of predominant aggregates was followed by much slower adjustments toward more regular hexagonal lattices, with increasing numbers of intact CA hexamers and pentamers being formed. Our approach of adapting a general CG model to specific systems by using experimental binding data represents a practical and effective strategy for simulating and elucidating intricate protein aggregations.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2016

Thermodynamics and kinetics of gas storage in porous liquids

The recent synthesis of organic molecular liquids with permanent porosity (Giri et al., Nature, 2015, 527, 216) opens up exciting new avenues for gas capture, storage, and separation. Using molecular dynamics simulations, we study the thermodynamics and kinetics for the storage of CH 4 , CO 2 , and N 2 molecules in porous liquids consisting of crown-ether substituted cage molecules in a 15-crown-5 solvent. It is found that the gas storage capacity per cage molecule follows the order of CH 4 > CO 2 > N 2 , which does not correlate simply with the size of gas molecules. Different gas molecules are stored inside the cage differently, e.g., CO 2 molecules prefer the cage s core while CH 4 molecules favor both the core and the branch regions. All gas molecules considered can enter the cage essentially without energy barriers, and their dynamics inside the cage are only slightly hindered by the nanoscale confinement. In addition, all gas molecules can leave the cage on nanosecond time scale by overcoming a modest energy penalty. The molecular mechanisms of these observations are clarified.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

Thermodynamics of Reactions Affected by Medium Reorganization

We present a thermodynamic analysis of the activation barrier for reactions which can be monitored through the difference in the energies of reactants and products defined as the reaction coordinate (electron and atom transfer, enzyme catalysis, etc). The free-energy surfaces along the reaction coordinate are separated into the enthalpy and entropy surfaces. For the Gaussian statistics of the reaction coordinate, the free-energy surfaces are parabolas, and the entropy surface is an inverted parabola. Its maximum coincides with the transition state for reactions with zero value of the reaction free energy. Maximum entropic depression of the activation barrier, anticipated by the concept of transition-state ensembles, can be achieved for such reactions. From Onsager’s reversibility, the entropy of equilibrium fluctuations encodes the entropic component of the activation barrier. The reorganization entropy thus becomes the critical parameter of the theory reducing the problem of activation entropy to the problem of reorganization entropy. Standard solvation theories do not provide reorganization entropy sufficient for the barrier depression. Complex media, characterized by many relaxation processes, need to be involved and proteins provide several routes for achieving large entropic effects related to incomplete (nonergodic) sampling of the complex energy landscape and active role of water in the reaction mechanism.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Measurement of Three Transport Coefficients and the Thermodynamic Factor in Block Copolymer Electrolytes with Different Morphologies

The design and engineering of composite materials is one strategy to satisfy the materials needs of systems with multiple orthogonal property requirements. In the case of rechargeable batteries with lithium metal anodes, the system requires a separator with fast lithium ion transport and good mechanical strength. In this work, we focus on the system polystyrene-block-poly(ethylene oxide) (SEO) with bis(trifluoromethane)sulfonimide lithium salt (LiTFSI). Ion transport occurs in the salt-containing poly(ethylene oxide)-rich domains. Mechanical rigidity arises due to the glassy nature of polystyrene (PS). If we assume that the salt does not interact with the PS-rich domains, we can describe ion transport in the electrolyte by three transport parameters (ionic conductivity, κ, salt diffusion coefficient, D, and cation transference number, t + 0 ) and a thermodynamic factor, T f . By systematically varying the volume fraction of the conducting phase, Φ c between 0.29 and 1.0, and chain length, N between 80 and 8000, we elucidate the role of morphology on ion transport. We find that κ is the strongest function of morphology, varying by three full orders of magnitude, while D is a weaker function of morphology. To calculate t + 0 and T f , we measure the current fraction, ρ + , and the open circuit potential, U, of concentration cells. We find that ρ + and U follow universal trends as a function of salt concentration, regardless of chain length, morphology, or Φ c , allowing us to calculate t + 0 for any SEO/LiTFSI or PEO/LiTFSI mixture when κ and D are known. Finally, the framework developed in this paper enables predicting the performance of any block copolymer electrolyte in a rechargeable battery.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Critical Assessment of the Thermodynamics of Vacancy Formation in Fe 2 O 3 Using Hybrid Density Functional Theory

Fe 2 O 3 hematite is a technologically important material with applications in energy storage as well as being the key phase formed in the rust of iron-based materials. Despite this central importance, there is much that is still unknown regarding the properties of defects in Fe 2 O 3 and consequently oxide growth. In this work, using screened hybrid density functional theory (HSE06), we consider the thermodynamics of vacancies in Fe 2 O 3 , considering the effects of ionic and electronic chemical potentials on both iron and oxygen vacancy formation. We find that, in the oxygen-rich limit, iron vacancies are easier to form, though the difference in formation energy between the two vacancies is only about 1 eV. In contrast, in the Fe-rich limit, oxygen vacancies have an extremely low formation energy, only 0.07 eV at mid-gap, and would spontaneously form as the Fermi level is reduced, while Fe vacancies require over 5 eV to form. Consistent with experiment, this indicates that Fe 2 O 3 is relatively easily reduced but not oxidized. However, the theoretical picture is very different when considering other exchange–correlation functionals (GGA + U or SCAN), emphasizing the critical role of the exchange–correlation functional in describing this system accurately.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗