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The question of material stability is of fundamental importance to any analysis of system properties in condensed matter physics and materials science. The ability to evaluate chemical stability, i.e., whether a stoichiometry will persist in some chemical environment, and structure selection, i.e. what crystal structure a stoichiometry will adopt, is critical to the prediction of materials synthesis, reactivity and properties. Here, we demonstrate that density functional theory, with the recently developed strongly constrained and appropriately normed (SCAN) functional, has advanced to a point where both facets of the stability problem can be reliably and efficiently predicted for main group compounds, while transition metal compounds are improved but remain a challenge. SCAN therefore offers a robust model for a significant portion of the periodic table, presenting an opportunity for the development of novel materials and the study of fine phase transformations even in largely unexplored systems with little to no experimental data.

Cation disorder is an important design criterion for technologically relevant transition-metal (TM) oxides, such as radiation-tolerant ceramics and Li-ion battery electrodes. In this Letter, we use a combination of first-principles calculations, normal mode analysis, and band-structure arguments to pinpoint a specific electronic-structure effect that influences the stability of disordered phases. We find that the electronic configuration of a TM ion determines to what extent the structural energy is affected by site distortions. This mechanism explains the stability of disordered phases with large ionic radius differences and provides a concrete guideline for the discovery of novel disordered compositions.

While control over crystal structure is one of the primary objectives in crystal growth, the present lack of predictive understanding of the mechanisms driving structure selection precludes the predictive synthesis of polymorphic materials. We address the formation of off-stoichiometric intermediates as one such handle driving polymorph selection in the diverse class of MnO2-framework structures. Specifically, we build on the recent benchmark of the SCAN functional for the ab initio modeling of MnO2 to examine the effect of alkali-insertion, protonation, and hydration to derive the thermodynamic conditions favoring the formation of the most common MnO2 phases-β, γ, R, α, δ, and λ-from aqueous solution. We explain the phase selection trends through the geometric and chemical compatibility of the alkali cations and the available phases, the interaction of water with the system, and the critical role of protons. Our results offer both a quantitative synthesis roadmap for this important class of functional oxides, and a description of the various structural phase transformations that may occur in this system.

The electrochemical properties of NaNi0.5Co0.5O2 and NaNi0.5Fe0.5O2 and their structural transitions as a function of Na extraction associated with redox reactions are investigated in this work. Synthesized in the O3-type layered structure, both materials show reasonable electrochemical activities at room temperature, delivering approximately 0.5 Na per formula unit at C/10 discharge. More Na can be reversibly cycled in NaNi0.5Co0.5O2 at elevated temperature and/or in an extended voltage window, while NaNi0.5Fe0.5O2 shows significant capacity fading at a high voltage cutoff which is likely due to Fe4+ migration. In situ X-ray diffraction shows that the structural changes in the two materials upon desodiation are very different. NaNi0.5Co0.5O2 goes through many different two-phase reactions including three different O3-type and three different P3-type structures during cycling, producing a voltage profile with multiple plateau-like features. In contrast, NaNi0.5Fe0.5O2 has a smooth voltage profile and shows the typical O3-P3 phase transition without lattice distortion seen in other materials. This different structural evolution upon desodiation and re-sodiation can be explained by the electronic structure of the mixed transition metals and how it perturbs the ordering between Na ions differently.

NaTi0.25Fe0.25Co0.25Ni0.25O2 is explored as a cathode material for Na-ion batteries. Synthesized by a solid-state reaction, the compound is phase-pure with the O3-type layered structure and consists of Ti4+, Fe3+, Co3+, and Ni2+ according to X-ray absorption spectroscopy. The cathode delivers 163 mAh/g and 504 Wh/kg at C/20 in the first discharge with 89% capacity retention after 20 cycles and demonstrates superior rate capability with micron sized particles, in which discharge capacity at 30 C is 80mAh/g. Our results indicate that the Ti-containing quaternary material can be a potential cathode composition for Na-ion batteries.

The space of metastable materials offers promising new design opportunities for next-generation technological materials, such as complex oxides, semiconductors, pharmaceuticals, steels, and beyond. Although metastable phases are ubiquitous in both nature and technology, only a heuristic understanding of their underlying thermodynamics exists. We report a large-scale data-mining study of the Materials Project, a high-throughput database of density functional theory-calculated energetics of Inorganic Crystal Structure Database structures, to explicitly quantify the thermodynamic scale of metastability for 29,902 observed inorganic crystalline phases. We reveal the influence of chemistry and composition on the accessible thermodynamic range of crystalline metastability for polymorphic and phase-separating compounds, yielding new physical insights that can guide the design of novel metastable materials. We further assert that not all low-energy metastable compounds can necessarily be synthesized, and propose a principle of 'remnant metastability'-that observable metastable crystalline phases are generally remnants of thermodynamic conditions where they were once the lowest free-energy phase.

Lattice models, also known as generalized Ising models or cluster expansions, are widely used in many areas of science and are routinely applied to the study of alloy thermodynamics, solid-solid phase transitions, magnetic and thermal properties of solids, fluid mechanics, and others. However, the problem of finding and proving the global ground state of a lattice model, which is essential for all of the aforementioned applications, has remained unresolved for relatively complex practical systems, with only a limited number of results for highly simplified systems known. In this paper, we present a practical and general algorithm that provides a provable periodically constrained ground state of a complex lattice model up to a given unit cell size and in many cases is able to prove global optimality over all other choices of unit cell. We transform the infinite-discrete-optimization problem into a pair of combinatorial optimization (MAX-SAT) and nonsmooth convex optimization (MAX-MIN) problems, which provide upper and lower bounds on the ground state energy, respectively. By systematically converging these bounds to each other, we may find and prove the exact ground state of realistic Hamiltonians whose exact solutions are difficult, if not impossible, to obtain via traditional methods. Considering that currently such practical Hamiltonians are solved using simulated annealing and genetic algorithms that are often unable to find the true global energy minimum and inherently cannot prove the optimality of their result, our paper opens the door to resolving longstanding uncertainties in lattice models of physical phenomena. An implementation of the algorithm is available at https://github.com/dkitch/maxsat-ising.

Cation disorder is a phenomenon that is becoming increasingly important for the design of high-energy lithium transition metal oxide cathodes (LiMO2) for Li-ion batteries. Disordered Li-excess rocksalts have recently been shown to achieve high reversible capacity, while in operando cation disorder has been observed in a large class of ordered compounds. The voltage slope (dVdxLi) is a critical quantity for the design of cation-disordered rocksalts, as it controls the Li capacity accessible at voltages below the stability limit of the electrolyte (∼4.5-4.7 V). In this study, we develop a lattice model based on first principles to understand and quantify the voltage slope of cation-disordered LiMO2. We show that cation disorder increases the voltage slope of Li transition metal oxides by creating a statistical distribution of transition metal environments around Li sites, as well as by allowing Li occupation of high-voltage tetrahedral sites. We further demonstrate that the voltage slope increase upon disorder is generally smaller for high-voltage transition metals than for low-voltage transition metals due to a more effective screening of Li-M interactions by oxygen electrons. Short-range order in practical disordered compounds is found to further mitigate the voltage slope increase upon disorder. Finally, our analysis shows that the additional high-voltage tetrahedral capacity induced by disorder is smaller in Li-excess compounds than in stoichiometric LiMO2 compounds.

Generalized Ising models, also known as cluster expansions, are an importanttool in many areas of condensed-matter physics and materials science, as theyare often used in the study of lattice thermodynamics, solid-solid phasetransitions, magnetic and thermal properties of solids, and fluid mechanics.However, the problem of finding the global ground state of generalized Isingmodel has remained unresolved, with only a limited number of results for simplesystems known. We propose a method to efficiently find the periodic groundstate of a generalized Ising model of arbitrary complexity by a new algorithmwhich we term cluster tree optimization. Importantly, we are able to show thateven in the case of an aperiodic ground state, our algorithm produces asequence of states with energy converging to the true ground state energy, witha provable bound on error. Compared to the current state-of-the-art polytopemethod, this algorithm eliminates the necessity of introducing an exponentialnumber of variables to counter frustration, and thus significantly improvestractability. We believe that the cluster tree algorithm offers an intuitiveand efficient approach to finding and proving ground states of generalizedIsing Hamiltonians of arbitrary complexity, which will help validateassumptions regarding local vs. global optimality in lattice models, as well asoffer insights into the low-energy behavior of highly frustrated systems.

Cation disorder is a phenomenon that is becoming increasingly important for the design of high-energy lithium transition-metal oxide positive electrodes (LiMO2) for Li-ion batteries. Disordered Li-excess rocksalts have recently been shown to achieve high reversible capacity, and in operando cation disorder (i.e., disorder induced by electrochemical cycling) has been observed in a large class of ordered materials. Despite the growing importance of cation disorder in the Li-ion battery field, very little is known about the effect of cation disorder on the average voltage (i.e., energy density) of lithium transition metal oxides. In this study, we use first-principles methods to demonstrate that, depending on the transition metal species, cation disorder can lead to an increase or a decrease of the average voltage of lithium transition metal oxides. We further demonstrate that the Ni3+/4+ redox can be high in disordered compounds, so that it may be preceded by oxygen activity. Finally, we establish rules for the voltage evolution of compounds that experience in operando disorder.

Current state-of-the-art Na-ion battery cathodes are selected from the broad chemical space of layered first-row transition-metal (TM) oxides. Unlike their lithium-ion counterparts, seven first-row layered TM oxides can intercalate Na ions reversibly. Their voltage curves indicate significant and numerous reversible phase transformations during electrochemical cycling. These transformations are not yet fully understood but arise from Na-ion vacancy ordering and metal oxide slab glide. In this study, we investigate the nature of vacancy ordering within the O3 host lattice framework. We generate predicted electrochemical voltage curves for each of the Na-ion intercalating layered TM oxides by using a high-throughput framework of density-functional-theory calculations. We determine a set of vacancy-ordered phases appearing as ground states in all NaxMO2 systems and investigate the energy effect of the stacking of adjacent layers.

Accelerating the discovery of advanced materials is essential for human welfare and sustainable, clean energy. In this paper, we introduce the Materials Project (www.materialsproject.org), a core program of the Materials Genome Initiative that uses high-throughput computing to uncover the properties of all known inorganic materials. This open dataset can be accessed through multiple channels for both interactive exploration and data mining. The Materials Project also seeks to create open-source platforms for developing robust, sophisticated materials analyses. Future efforts will enable users to perform ''rapid-prototyping'' of new materials in silico, and provide researchers with new avenues for cost-effective, data-driven materials design. © 2013 Author(s).

Abstract: Fluorination of Li‐ion cathode materials is of significant interest as it is claimed to lead to significant improvements in long‐term reversible capacity. However, the mechanism by which LiF incorporates and improves performance remains uncertain. Indeed, recent evidence suggests that fluorine is often present as a coating layer rather than incorporated into the bulk of the material. In this work, first‐principles calculations are used to investigate the thermodynamics of fluorination in transition metal oxide cathodes to determine the conditions under which bulk fluorination is possible. It is found that unlike classic well‐ordered cathodes, which cannot incorporate fluorine, disordered rock salt‐structured materials achieve significant fluorination levels due to the presence of locally metal‐poor, lithium‐rich environments that are highly preferred for fluorine. As well as explaining the fluorination process in known materials, this finding is encouraging for the development of new disordered rock salt lithium‐excess transition metal oxides, a promising new class of Li‐ion battery cathode materials that offer superior practical capacity to traditional layered oxides. In particular, it is found that bulk fluorination may serve as an alternative source of Li‐excess in these compounds that can replace the conventional substitution of a heavy redox‐inactive element on the transition metal sublattice. [ABSTRACT FROM AUTHOR]

While control over crystal structure is one of the primary objectives in crystal growth, the present lack of predictive understanding of the mechanisms driving structure selection precludes the predictive synthesis of polymorphic materials. We address the formation of off-stoichiometric intermediates as one such handle driving polymorph selection in the diverse class of MnO2-framework structures. Specifically, we build on the recent benchmark of the SCAN functional for the ab initio modeling of MnO2 to examine the effect of alkali-insertion, protonation, and hydration to derive the thermodynamic conditions favoring the formation of the most common MnO2 phases β, γ, R, α, δ, and λ from aqueous solution. We explain the phase selection trends through the geometric and chemical compatibility of the alkali cations and the available phases, the interaction of water with the system, and the critical role of protons. Our results offer both a quantitative synthesis roadmap for this important class of functional oxides, and a description of the various structural phase transformations that may occur in this system. [ABSTRACT FROM AUTHOR]

Fluorophosphate cathodes with the chemical formula NaxV2(PO4)2O2yF3-2y (0 ≤ x ≤ 4, 0 ≤ y ≤ 1) are some of the few known sodium-ion cathode materials with the potential to be competitive with conventional lithium-ion cathodes. However, the experimentally accessible performance of the fluorophosphates remains limited, primarily due to the fact that only half of the theoretical capacity has been reversibly cycled. In this article, we review the extensive body of literature on the fluorophosphate class of sodium-ion cathodes and, in combination with our own ab initio model of the material, investigate the mechanisms underlying the sodium-extraction limitations in the NaxV2(PO4)2F3 (y = 0) fluorophosphate. Specifically, we focus on the potential to reversibly extract sodium beyond the 1 ≤ x ≤ 3 range. We find that this limitation arises from a combination of the high voltage of the V4+/5+ oxidation reaction associated with sodium extraction in the 0 ≤ x ≤ 1 region and a precipitous drop in sodium diffusivity near the x = 1 composition due to the presence of a strong ordering, which prevents the formation of mobile defects in the structure. We conclude that the accessible capacity of NaxV2(PO4)2F3 can potentially be expanded to 0 ≤ x ≤ 3 by introducing defects into the material and reducing the voltage of the transition metal redox couple, both of which can likely be achieved via transition metal substitution and aliovalent anion doping. [ABSTRACT FROM AUTHOR]

High voltage and high thermal safety are desirable characteristics of cathode materials, but difficult to achieve simultaneously. This work uses high-throughput density functional theory computations to evaluate the link between voltage and safety (as estimated by thermodynamic O2 release temperatures) for over 1400 cathode materials. Our study indicates that a strong inverse relationship exists between voltage and safety: just over half the variance in O2 release temperature can be explained by voltage alone. We examine the effect of polyanion group, redox couple, and ratio of oxygen to counter-cation on both voltage and safety. As expected, our data demonstrates that polyanion groups improve safety when comparing compounds with similar voltages. However, a counterintuitive result of our study is that polyanion groups produce either no benefit or reduce safety when comparing compounds with the same redox couple. Using our data set, we tabulate voltages and oxidation potentials for over 105 combinations of redox couple/anion, which can be used towards the design and rationalization of new cathode materials. Overall, only a few compounds in our study, representing limited redox couple/polyanion combinations, exhibit both high voltage and high safety. We discuss these compounds in more detail as well as the opportunities for designing safe, high-voltage cathodes. [ABSTRACT FROM AUTHOR]

NaTi0.25Fe0.25Co0.25Ni0.25O2 is explored as a cathode material for Na-ion batteries. Synthesized by a solid-state reaction, the compound is phase-pure with the O3-type layered structure and consists of Ti4+, Fe3+, Co3+, and Ni2+ according to X-ray absorption spectroscopy. The cathode delivers 163 mAh/g and 504 Wh/kg at C/20 in the first discharge with 89% capacity retention after 20 cycles and demonstrates superior rate capability with micron sized particles, in which discharge capacity at 30 C is 80 mAh/g. Our results indicate that the Ti-containing quaternary material can be a potential cathode composition for Na-ion batteries. [ABSTRACT FROM AUTHOR]

There is a clear need for a practical and mathematically rigorous description of local structure in inorganic compounds so that structures and chemistries can be easily compared across large data sets. Here a method for decomposing crystal structures into substructures is given, and a similarity function between those substructures is defined. The similarity function is based on both geometric and chemical similarity. This construction allows for large-scale data mining of substructural properties, and the analysis of substructures and void spaces within crystal structures. The method is validated via the prediction of Li-ion intercalation sites for the oxides. Tested on databases of known Li-ion-containing oxides, the method reproduces all Li-ion sites in an oxide with a maximum of 4 incorrect guesses 80% of the time. [ABSTRACT FROM AUTHOR]

Lattice models, also known as generalized Ising models or cluster expansions, are widely used in many areas of science and are routinely applied to the study of alloy thermodynamics, solid-solid phase transitions, magnetic and thermal properties of solids, fluid mechanics, and others. However, the problem of finding and proving the global ground state of a lattice model, which is essential for all of the aforementioned applications, has remained unresolved for relatively complex practical systems, with only a limited number of results for highly simplified systems known. In this paper, we present a practical and general algorithm that provides a provable periodically constrained ground state of a complex lattice model up to a given unit cell size and in many cases is able to prove global optimality over all other choices of unit cell. We transform the infinite-discrete-optimization problem into a pair of combinatorial optimization (MAX-SAT) and nonsmooth convex optimization (MAX-MIN) problems, which provide upper and lower bounds on the ground state energy, respectively. By systematically converging these bounds to each other, we may find and prove the exact ground state of realistic Hamiltonians whose exact solutions are difficult, if not impossible, to obtain via traditional methods. Considering that currently such practical Hamiltonians are solved using simulated annealing and genetic algorithms that are often unable to find the true global energy minimum and inherently cannot prove the optimality of their result, our paper opens the door to resolving longstanding uncertainties in lattice models of physical phenomena. [ABSTRACT FROM AUTHOR]

While control over crystal structure is one of the primary objectives in crystal growth, the present lack of predictive understanding of the mechanisms driving structure selection precludes the predictive synthesis of polymorphic materials. We address the formation of off-stoichiometric intermediates as one such handle driving polymorph selection in the diverse class of MnO 2 -framework structures. Specifically, we build on the recent benchmark of the SCAN functional for the ab initio modeling of MnO 2 to examine the effect of alkali-insertion, protonation, and hydration to derive the thermodynamic conditions favoring the formation of the most common MnO 2 phases-β, γ, R, α, δ, and λ-from aqueous solution. We explain the phase selection trends through the geometric and chemical compatibility of the alkali cations and the available phases, the interaction of water with the system, and the critical role of protons. Our results offer both a quantitative synthesis roadmap for this important class of functional oxides, and a description of the various structural phase transformations that may occur in this system.