The electronic-structure origin of cation disorder in transition-metal oxides

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 which 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.Comment: 12 pages, 9 figures, 4 table

Proposed definition of crystal substructure and substructural similarity

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.National Science Foundation (U.S.) (SI2-SSI Collaborative Research program Award OCI-1147503)United States. Dept. of Energy. Office of Basic Energy Sciences (Grant EDCBEE

Vacancy Ordering in O3-Type Layered Metal Oxide Sodium-Ion Battery Cathodes

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 Na[subscript x]MO[subscript 2] systems and investigate the energy effect of the stacking of adjacent layers.Samsung Advanced Institute of Technolog

Constructing and proving the ground state of a generalized Ising model by the cluster tree optimization algorithm

Generalized Ising models, also known as cluster expansions, are an important tool in many areas of condensed-matter physics and materials science, as they are often used in the study of lattice thermodynamics, solid-solid phase transitions, magnetic and thermal properties of solids, and fluid mechanics. However, the problem of finding the global ground state of generalized Ising model has remained unresolved, with only a limited number of results for simple systems known. We propose a method to efficiently find the periodic ground state of a generalized Ising model of arbitrary complexity by a new algorithm which we term cluster tree optimization. Importantly, we are able to show that even in the case of an aperiodic ground state, our algorithm produces a sequence of states with energy converging to the true ground state energy, with a provable bound on error. Compared to the current state-of-the-art polytope method, this algorithm eliminates the necessity of introducing an exponential number of variables to counter frustration, and thus significantly improves tractability. We believe that the cluster tree algorithm offers an intuitive and efficient approach to finding and proving ground states of generalized Ising Hamiltonians of arbitrary complexity, which will help validate assumptions regarding local vs. global optimality in lattice models, as well as offer insights into the low-energy behavior of highly frustrated systems

Finding and proving the exact ground state of a generalized Ising model by convex optimization and MAX-SAT

This paper was supported primarily by the US Department of Energy (DOE) under Contract No. DE-FG02-96ER45571. In addition, some of the test cases for ground states were supported by the Office of Naval Research under contract N00014-14-1-0444.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-isingPublisher PDFPeer reviewe

The thermodynamic scale of inorganic crystalline metastability

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.United States. Dept. of Energy. Office of Basic Energy Sciences (DE-AC02-05CH11231)United States. Dept. of Energy. Office of Basic Energy Sciences (contract UGA-0-41029-16/ER392000