Structurally Constrained Evolutionary Algorithm for the Discovery and Design of Metastable Phases.

Metastable materials are abundant in nature and technology, showcasing remarkable properties that inspire innovative materials design. However, traditional crystal structure prediction methods, which rely solely on energetic factors to determine a structure's fitness, are not suitable for predicting the vast number of potentially synthesizable phases that represent a local minimum corresponding to a state in thermodynamic equilibrium. Here, we present a new approach for the prediction of metastable phases with specific structural features and interface this method with the XtalOpt evolutionary algorithm. Our method relies on structural features that include the local crystalline order (e.g, the coordination number or chemical environment), and symmetry (e.g, Bravais lattice and space group) to filter the breeding pool of an evolutionary crystal structure search. The effectiveness of this approach is benchmarked on three known metastable systems: XeN8, with a two-dimensional polymeric nitrogen sublattice, brookite TiO2, and a high pressure BaH4 phase, which was recently characterized. Additionally, a newly predicted metastable melaminate salt, P1̅ WC3N6, was found to possess an energy that is lower than that of two phases proposed in a recent computational study. The method presented here could help in identifying the structures of compounds that have already been synthesized, and in developing new synthesis targets with desired properties.

Twists and Puckers: Tuning Crystal Chemistry in the La(AuxGe1-x)2 Compositional Series.

The physical properties of solid-state materials are closely tied to their crystal structure, yet our understanding of how competing structural arrangements energetically compare is limited. In this work, we explore how small differences in composition affect the structure in the La(AuxGe1-x)2 series of compounds, which comprises four unique structure types between LaGe2 and LaAu2. This family includes the previously unknown AlB2-type compound with stoichiometry La(Au0.375Ge0.625)2 as well as La(Au0.25Ge0.75)2, an intergrowth of the AlB2 and ThSi2 structure types. We then study the chemical forces driving the structure changes and use phonon band structure calculations and DFT-Chemical Pressure to evaluate atomic-size effects. These calculations show that the parent AlB2 structure type is disfavored in Au-rich compounds due to soft atomic motions along the c axis. The instability of AlB2-type LaAuGe is confirmed by the presence of imaginary modes in the phonon band structure that correspond to a "puckering" of the hexagonal AlB2-type lattice, resulting in the experimentally observed LiGaGe structure type. The impact of size effects is less clear for Au-poor compositions; instead, twisting the AlB2 structure type to form the ThSi2 type opens a pseudogap at the Fermi level in the electronic density of states. This investigation demonstrates how crystal structure in solid-state materials can be compositionally tuned based on balancing size and electronics when multiple structure types are in close thermodynamic competition.

Self-Consistent Chemical Pressure Analysis: Resolving Atomic Packing Effects through the Iterative Partitioning of Space and Energy.

While planewave DFT methods offer capabilities to calculate the relative stabilities and many physical properties exhibited by solid state structures, their detailed numerical output does not easily map onto the often empirical concepts and parameters used by synthetic chemists or materials scientists. The DFT-chemical pressure (CP) method is an approach to bridging this divide by explaining or anticipating a variety of structural phenomena in terms of atomic size and packing effects, but its reliance on adjustable parameters has limited the method's predictive potential. In this article, we present the self-consistent (sc)-DFT-CP analysis, in which the criterion of self-consistency is used to automatically solve these parameterization issues. We begin by illustrating the need for this improved method with the results for a series of CaCu5-type/MgCu2-type intergrowth structures, where unphysical trends emerge that have no clear structural origin. To address these challenges, we derive iterative treatments for assigning ionicity and for the partitioning of the EEwald + Eα terms in the DFT total energy into homogeneous and localized terms. In this method, self-consistency is achieved between the input and output charges from a variation of the Hirshfeld charge scheme, while the partitioning of the EEwald + Eα terms is adjusted to create equilibrium between the net atomic pressures calculated within atomic regions and from the interatomic interactions. The behavior of the sc-DFT-CP method is then tested using electronic structure data for several hundred compounds from the Intermetallic Reactivity Database. Finally, we return to the CaCu5-type/MgCu2-type intergrowth series with the sc-DFT-CP approach, showing that trends in the series are now easily traced to changes in the thicknesses of the CaCu5-type domains and lattice mismatch at the interface. Through this analysis and the complete update to the CP schemes in the IRD, the sc-DFT-CP method is demonstrated as a theoretical tool for the investigation of atomic packing issues across intermetallic chemistry.

Conventional High-Temperature Superconductivity in Metallic, Covalently Bonded, Binary-Guest C-B Clathrates.

Inspired by the synthesis of XB3C3 (X = Sr, La) compounds in the bipartite sodalite clathrate structure, density functional theory (DFT) calculations are performed on members of this family containing up to two different metal atoms. A DFT-chemical pressure analysis on systems with X = Mg, Ca, Sr, Ba reveals that the size of the metal cation, which can be tuned to stabilize the B-C framework, is key for their ambient-pressure dynamic stability. High-throughput density functional theory calculations on 105 Pm3̅ symmetry XYB6C6 binary-guest compounds (where X, Y are electropositive metal atoms) find 22 that are dynamically stable at 1 atm, expanding the number of potentially synthesizable phases by 19 (18 metals and 1 insulator). The density of states at the Fermi level and superconducting critical temperature, Tc, can be tuned by changing the average oxidation state of the metal atoms, with Tc being highest for an average valence of +1.5. KPbB6C6, with an ambient-pressure Eliashberg Tc of 88 K, is predicted to possess the highest Tc among the studied Pm3̅n XB3C3 or Pm3̅ XYB6C6 phases, and calculations suggest it may be synthesized using high-pressure high-temperature techniques and then quenched to ambient conditions.

Emergent Transitions: Discord between Electronic and Chemical Pressure Effects in the REAl3 (RE = Sc, Y, Lanthanides) Series.

Atomic packing and electronic structure are key factors underlying the crystal structures adopted by solid-state compounds. In cases where these factors conflict, structural complexity often arises. Such is born in the series of REAl3 (RE = Sc, Y, lanthanides), which adopt structures with varied stacking patterns of face-centered cubic close packed (FCC, AuCu3 type) and hexagonal close packed (HCP, Ni3Sn type) layers. The percentage of the hexagonal stacking in the structures is correlated with the size of the rare earth atom, but the mechanism by which changes in atomic size drive these large-scale shifts is unclear. In this Article, we reveal this mechanism through DFT-Chemical Pressure (CP) and reversed approximation Molecular Orbital (raMO) analyses. CP analysis illustrates that the Ni3Sn structure type is preferable from the viewpoint of atomic packing as it offers relief to packing issues in the AuCu3 type by consolidating Al octahedra into columns, which shortens Al-Al contacts while simultaneously expanding the RE atom's coordination environment. On the other hand, the AuCu3 type offers more electronic stability with an 18-n closed-shell configuration that is not available in the Ni3Sn type (due to electron transfer from the RE dz2 atomic orbitals into Al-based states). Based on these results, we then turn to a schematic analysis of how the energetic contributions from atomic packing and the electronic structure vary as a function of the ratio of FCC and HCP stacking configurations within the structure and the RE atomic radius. The minima on the atomic packing and electronic surfaces are non-overlapping, creating frustration. However, when their contributions are added, new minima can emerge from their combination for specific RE radii representing intergrowth structures in the REAl3 series. Based on this picture, we propose the concept of emergent transitions, within the framework of the Frustrated and Allowed Structural Transitions principle, for tracing the connection between competing energetic factors and complexity in intermetallic structures.

Rational Design of Superconducting Metal Hydrides via Chemical Pressure Tuning.

The high critical superconducting temperatures (Tc s) of metal hydride phases with clathrate-like hydrogen networks have generated great interest. Herein, we employ the Density Functional Theory-Chemical Pressure (DFT-CP) method to explain why certain electropositive elements adopt these structure types, whereas others distort the hydrogenic lattice, thereby decreasing the Tc . The progressive opening of the H24 polyhedra in MH6 phases is shown to arise from internal pressures exerted by large metal atoms, some of which may favor an even higher hydrogen content that loosens the metal atom coordination environments. The stability of the LaH10 and LaBH8 phases is tied to stuffing of their shared hydrogen network with either additional hydrogen or boron atoms. The predictive capabilities of DFT-CP are finally applied to the Y-X-H system to identify possible ternary additions yielding a superconducting phase stable to low pressures.

Principles of weakly ordered domains in intermetallics: the cooperative effects of atomic packing and electronics in Fe2Al5.

Many complex intermetallic structures feature a curious juxtaposition of domains with strict 3D periodicity and regions of much weaker order or incommensurability. This article explores the basic principles leading to such arrangements through an investigation of the weakly ordered channels of Fe2Al5. It starts by experimentally confirming the earlier crystallographic model of the high-temperature form, in which nearly continuous columns of electron density corresponding to disordered Al atoms emerge. Then electronic structure calculations on ordered models are used to determine the factors leading to the formation of these columns. These calculations reveal electronic pseudogaps near 16 electrons/Fe atom, an electron concentration close to the Al-rich side of the phase's homogeneity range. Through a reversed approximation Molecular Orbital (raMO) analysis, these pseudogaps are correlated with the filling of 18-electron configurations on the Fe atoms with the support of isolobal σ Fe-Fe bonds. The resulting preference for 16 electrons/Fe requires a fractional number of Al atoms in the Fe2Al5 unit cell. Density functional theory-chemical pressure (DFT-CP) analysis is then applied to investigate how this nonstoichiometry is accommodated. The CP schemes reveal strong quadrupolar distributions on the Al atoms of the channels, suggestive of soft atomic motions along the undulating electron density observed in the Fourier map that allow the Al positions to shift easily in response to compositional changes. Such a combination of preferred electron counts tied to stoichiometry and continuous paths of CP quadrupoles could provide predictive indicators for the emergence of channels of disordered or incommensurately spaced atoms in intermetallic structures.

Discerning Chemical Pressure amidst Weak Potentials: Vibrational Modes and Dumbbell/Atom Substitution in Intermetallic Aluminides.

The space requirements of atoms are generally regarded as key constraints in the structures, reactivity, and physical properties of chemical systems. However, the empirical nature of such considerations renders the elucidation of these size effects with first-principles calculations challenging. DFT-chemical pressure (DFT-CP) analysis, in which the output of DFT calculations is used to construct maps of the local pressures acting between atoms due to lattice constraints, is one productive approach to extracting the role of atomic size in the crystal structures of materials. While in principle this method should be applicable to any system for which DFT is deemed an appropriate treatment, so far it has worked most successfully when semicore electrons are included in the valence set of each atom to supply an explicit repulsive response to compression. In this Article, we address this limiting factor, using as model systems intermetallics based on aluminum, a key component in many structurally interesting phases that is not amenable to modeling with a semicore pseudopotential. Beginning with the Laves phase CaAl2, we illustrate the difficulties of creating a CP scheme that reflects the compound's phonon band structure with the original method due to minimal core responses on the Al atoms. These deficiencies are resolved through a spatial mapping of three energetic terms that were previously treated as homogeneous background effects: the Ewald, Eα, and nonlocal pseudopotential components. When charge transfer is factored into the integration scheme, CP schemes consistent with the phonon band structure are obtainable for CaAl2, regardless of whether Ca is modeled with a semicore or valence-only pseudopotential. Finally, we demonstrate the utility of the revised method through its application to the La3Al11 structure, which is shown to soothe CPs that would be encountered in a hypothetical BaAl4-type parent phase through the substitution of selected Al2 pairs with single Al atoms. La3Al11 then emerges as an example of a more general phenomenon, CP-driven substitutions of simple motifs.