Exploring the structural complexity of intermetallic compounds by an adaptive genetic algorithm

Interface Nucleus Complementarity: An Iterative Process for the Discovery of Modular Intermetallics Guided by Chemical Pressure

We present an iterative process for the discovery of modular intermetallic structures based on a recently developed interface nucleus approach. The process begins with the proposal of a suitable geometric motif that may serve as an interface nucleus. We then screen crystallographic databases for structures containing this motif as potential intergrowth partners. The extent to which pairs of these structures are likely to combine into more complicated assembles is then assessed with a new chemical pressure-based metric, interface nucleus complementarity (INC). Promising combinations of structures are translated into systems for synthesis, with new compounds providing either support for the importance of the original interface nucleus or new geometrical motifs for the next round of analysis. We demonstrate this process using a fragment derived from the σ-phase structure as a starting point, leading to the synthesis of PrMg4.13Zn10.20 and a new motif to seed the next cycle.

Interface Nuclei in the Y-Ag-Zn System: Three Chemical Pressure-Templated Phases with Lamellar Mg2Zn11- and CaPd5+x-Type Domains

The interface nucleus approach was recently presented as a framework for understanding and predicting the emergence of modular intermetallic phases, i.e., complex structures derived from the assembly of units from simpler parent structures. Here, we present the synthesis and crystal structures of three new modular intermetallics in the Y-Ag-Zn system that support this strategy: YAg2.79Zn2.80 (I), YAg2.44Zn3.17 (II), and YAg2.71Zn2.71 (III). Each of these structures is derived from an intergrowth of slabs of the Mg2Zn11 and CaPd5+x types, with the chief differences being in the thickness and degree of disorder within the CaPd5+x-type domains. The merging of the parent structure domains is facilitated by their sharing a common geometrical unit, a double hexagonal antiprism. The use of this motif as an interface nucleus mirrors its role in another family of structures: an intergrowth series combining the CaCu5 and Laves phase structure types, as in the PuNi3-type phase YNi3. However, there is a key difference between the two series. While in the CaCu5/Laves intergrowths, the interface between the parent structures arises perpendicular to the interface nucleus's unique (hexagonal) axis, in the Mg2Zn11/CaPd5+x-type intergrowths revealed here, the interfaces run parallel to this axis. Using CP analysis of the Mg2Zn11/CaPd5+x-type parent structures, we trace this behavior to the different directions of high-CP compatibility of the interface nuclei in the Mg2Zn11/CaPd5+x and CaCu5/Laves structure type pairs. In this way, the Y(Ag/Zn)5+x phases highlight the role that interface nuclei play in directing the domain morphologies of modular intermetallic phases.

Toward Predicting the Assembly of Modular Intermetallics from Chemical Pressure Analysis: The Interface Nucleus Approach

Complex intermetallic phases are often constructed from domains derived from simpler structures arranged into hierarchical assemblies. These modular arrangements offer intriguing prospects, such as the integration of the properties of distinct compounds into a single material or for the emergence of new properties from the interactions among different domains. In this article, we develop a strategy for the design of such complex structures, which we term the interface nucleus approach. Within this framework, the assembly of complex structures is facilitated by interface nuclei: geometrical motifs shared by two parent structures that serve as a region of overlap to nucleate or seed the formation of a combined structure. Our central hypothesis is that the formation of an interface between structures at these motifs creates opportunities for the relief of atomic packing stresses, as revealed by Density Functional Theory-Chemical Pressure (DFT-CP) analysis: when corresponding interatomic contacts in two structures exhibit complementarity─negative CP with positive CP or intense CP with mild CP─the intergrowth allows for a more balanced packing arrangement. To illustrate the application of the interface nucleus concept, we analyze three modular intermetallic structures, the σ-phase (FeCr), PuNi3, and Ca6Cu6Al5 types. In each case, the assembly of the structure can be connected to complementary CP features in an interface nucleus shared by its parent structures, while the distribution of the interface nuclei in the parents serves to template the geometry of the overall framework. In this way, the interface nucleus approach points toward avenues for the design of modular intermetallics from the CP schemes of potential partner structures.

MAGUS: machine learning and graph theory assisted universal structure searcher

Crystal structure predictions based on first-principles calculations have gained great success in materials science and solid state physics. However, the remaining challenges still limit their applications in systems with a large number of atoms, especially the complexity of conformational space and the cost of local optimizations for big systems. Here, we introduce a crystal structure prediction method, MAGUS, based on the evolutionary algorithm, which addresses the above challenges with machine learning and graph theory. Techniques used in the program are summarized in detail and benchmark tests are provided. With intensive tests, we demonstrate that on-the-fly machine-learning potentials can be used to significantly reduce the number of expensive first-principles calculations, and the crystal decomposition based on graph theory can efficiently decrease the required configurations in order to find the target structures. We also summarized the representative applications of this method on several research topics, including unexpected compounds in the interior of planets and their exotic states at high pressure and high temperature (superionic, plastic, partially diffusive state, etc.); new functional materials (superhard, high-energy-density, superconducting, photoelectric materials), etc. These successful applications demonstrated that MAGUS code can help to accelerate the discovery of interesting materials and phenomena, as well as the significant value of crystal structure predictions in general.

Machine Learning-Guided Discovery of Ternary Compounds Containing La, P, and Group 14 Elements

We integrate a deep machine learning (ML) method with first-principles calculations to efficiently search for the energetically favorable ternary compounds. Using La-Si-P as a prototype system, we demonstrate that ML-guided first-principles calculations can efficiently explore crystal structures and their relative energetic stabilities, thus greatly accelerate the pace of material discovery. A number of new La-Si-P ternary compounds with formation energies less than 30 meV/atom above the known ternary convex hull are discovered. Among them, the formation energies of La₅SiP₃ and La₂SiP phases are only 2 and 10 meV/atom, respectively, above the convex hull. These two compounds are dynamically stable with no imaginary phonon modes. Moreover, by replacing Si with heavier-group 14 elements in the eight lowest-energy La-Si-P structures from our ML-guided predictions, a number of low-energy La-X-P phases (X = Ge, Sn, Pb) are predicted.

Computational prediction of new magnetic materials

The discovery of new magnetic materials is a big challenge in the field of modern materials science. We report the development of a new extension of the evolutionary algorithm USPEX, enabling the search for half-metals (materials that are metallic only in one spin channel) and hard magnetic materials. First, we enabled the simultaneous optimization of stoichiometries, crystal structures, and magnetic structures of stable phases. Second, we developed a new fitness function for half-metallic materials that can be used for predicting half-metals through an evolutionary algorithm. We used this extended technique to predict new, potentially hard magnets and rediscover known half-metals. In total, we report five promising hard magnets with high energy product (|BH|_MAX), anisotropy field (H_a), and magnetic hardness (κ) and a few half-metal phases in the Cr-O system. A comparison of our predictions with experimental results, including the synthesis of a newly predicted antiferromagnetic material (WMnB₂), shows the robustness of our technique.

Quantum spin Hall effect in tilted penta silicene and its isoelectronic substitutions

Silicene, a competitive two-dimensional (2D) material for future electronic devices, has attracted intensive attention in condensed matter physics. Utilizing an adaptive genetic algorithm (AGA), we identify a topological allotrope of silicene, named tilted penta (tPenta) silicene. Based on first-principles calculations, the geometric and electronic properties of tPenta silicene and its isoelectronic substitutions (Ge, Sn) are investigated. Our results indicate that tPenta silicene exhibits a semimetallic state with distorted Dirac cones in the absence of spin-orbit coupling (SOC). When SOC is considered, it shows semiconducting behavior with a gap opening of 2.4 meV at the Dirac point. Based on the results of invariant ( = 1) and the helical edge states, we demonstrate that tPenta silicene is a topological insulator. Furthermore, the effect of isoelectronic substitutions on tPenta silicene is studied. Two stoichiometric phases, i.e., tPenta Si_0.333Ge_0.667 and tPenta Si_0.333Sn_0.667 are found to retain the geometric framework of tPenta silicene and exhibit high stabilities. Our calculations show that both tPenta Si_0.333Ge_0.667 and tPenta Si_0.333Sn_0.667 are QSH insulators with enlarged band gaps of 32.5 meV and 94.3 meV, respectively, at the HSE06 level, offering great potential for practical applications at room temperature.

Crystal structure prediction by combining graph network and optimization algorithm

Crystal structure prediction is a long-standing challenge in condensed matter and chemical science. Here we report a machine-learning approach for crystal structure prediction, in which a graph network (GN) is employed to establish a correlation model between the crystal structure and formation enthalpies at the given database, and an optimization algorithm (OA) is used to accelerate the search for crystal structure with lowest formation enthalpy. The framework of the utilized approach (a database + a GN model + an optimization algorithm) is flexible. We implemented two benchmark databases, i.e., the open quantum materials database (OQMD) and Matbench (MatB), and three OAs, i.e., random searching (RAS), particle-swarm optimization (PSO) and Bayesian optimization (BO), that can predict crystal structures at a given number of atoms in a periodic cell. The comparative studies show that the GN model trained on MatB combined with BO, i.e., GN(MatB)-BO, exhibit the best performance for predicting crystal structures of 29 typical compounds with a computational cost three orders of magnitude less than that required for conventional approaches screening structures through density functional theory calculation. The flexible framework in combination with a materials database, a graph network, and an optimization algorithm may open new avenues for data-driven crystal structural predictions.

Controlling the nucleation and growth of ultrasmall metal nanoclusters with MoS2 grain boundaries

The stabilization of supported nanoclusters is critical for different applications, including catalysis and plasmonics. Herein we investigate the impact of MoS₂ grain boundaries (GBs) on the nucleation and growth of Pt NCs. The optimum atomic structure of the metal clusters is obtained using an adaptive genetic algorithm that employs a hybrid approach based on atomistic force fields and density functional theory. Our findings show that GBs stabilize the NCs up to a cluster size of nearly ten atoms, and with larger clusters having a similar binding to the pristine system. Notably, Pt monomers are found to be attracted to GB cores achieving 60% more stabilization compared to the pristine surface. Furthermore, we show that the nucleation and growth of the metal seeds are facile with low kinetic barriers, which are of similar magnitude to the diffusion barriers of metals on the pristine surface. The findings highlight the need to engineer ultrasmall NCs to take advantage of enhanced stabilization imparted by the GB region, particularly to circumvent sintering behavior for high-temperature applications.

How to Look for Compounds: Predictive Screening and in situ Studies in Na-Zn-Bi System

Here, the combination of theoretical computations followed by rapid experimental screening and in situ diffraction studies is demonstrated as a powerful strategy for novel compounds discovery. When applied for the previously “empty” Na−Zn−Bi system, such an approach led to four novel phases. The compositional space of this system was rapidly screened via the hydride route method and the theoretically predicted NaZnBi (PbClF type, P4/nmm) and Na₁₁Zn₂Bi₅ (Na₁₁Cd₂Sb₅ type, P1‾ ) phases were successfully synthesized, while other computationally generated compounds on the list were rejected. In addition, single crystal X‐ray diffraction studies of NaZnBi indicate minor deviations from the stoichiometric 1 : 1 : 1 molar ratio. As a result, two isostructural (PbClF type, P4/nmm) Zn‐deficient phases with similar compositions, but distinctly different unit cell parameters were discovered. The vacancies on Zn sites and unit cell expansion were rationalized from bonding analysis using electronic structure calculations on stoichiometric “NaZnBi”. In‐situ synchrotron powder X‐ray diffraction studies shed light on complex equilibria in the Na−Zn−Bi system at elevated temperatures. In particular, the high‐temperature polymorph HT‐Na₃Bi (BiF₃ type, Fm3‾m) was obtained as a product of Na₁₁Zn₂Bi₅ decomposition above 611 K. HT‐Na₃Bi cannot be stabilized at room temperature by quenching, and this type of structure was earlier observed in the high‐pressure polymorph HP‐Na₃Bi above 0.5 GPa. The aforementioned approach of predictive synthesis can be extended to other multinary systems.

Lithium nickel borides: evolution of [NiB] layers driven by Li pressure

Insertion of additional Li atoms into the Li-monolayer in the structures of layered LiNiB polymorphs induces the deformation of [NiB] layers and alters their stacking, however, does not affect magnetic properties.

"Teamwork Makes the Dream Work": Tribal Competition Evolutionary Search as a Surrogate for Free-Energy-Based Structural Predictions

Crystal structure prediction has been a grand challenge in material science owing to the large configurational space that one must explore. Evolutionary (genetic) algorithms coupled with first principles calculations are commonly used in crystal structure prediction to sample the ground and metastable states of materials based on configurational energies. However, crystal structure predictions at finite temperature ( T), pressure ( P), and composition ( X) require a free-energy-based search that is often computationally expensive and tedious. Here, we introduce a new machine-learning workflow for structure prediction that is based on a concept inspired by the evolution of human tribes in primitive society. Our tribal genetic algorithm (GA) combines configurational sampling with evolutionary optimization to accurately predict entropically stabilized phases at finite ( T, P, X), at a computational cost that is an order of magnitude smaller than that required for a free-energy-based search. In a departure from standard GA techniques, the populations of individuals are divided into multiple tribes based on a bond-order fingerprint, and genetic operations are modified to ensure that cluster configurations are sampled adequately to capture entropic contributions. Team competition introduced into the evolutionary process allows winning teams (representing a better set of individuals) to expand their sizes; this translates into a more expanded search of the phase space allowing us to explore solutions near possible global minimum. Each team explores a specific section of the structural phase space and avoids bias on solutions arising from the use of individual populations in a purely energy-based search. We demonstrate the efficacy of our approach by performing the structural prediction of a representative two-dimensional two-body system as well as Lennard-Jones clusters over a range of temperatures up to its melting point. Our approach outperforms the standard GA approaches and enables structural search under "real nonambient conditions" on both bulk systems and finite-sized clusters.

Templating Structural Progessions in Intermetallics: How Chemical Pressure Directs Helix Formation in the Nowotny Chimney Ladders

In the structural diversity of intermetallic phases, hierarchies can be perceived relating complex structures to relatively simple parent structures. One example is the Nowotny Chimney Ladder (NCL) series, a family of transition metal-main group (T-E) compounds in which the T sublattices trace out helical channels populated by E-atom helices. A sequence of structures emerges from this arrangement because the spacing along the channels of the E atoms smoothly varies relative to that of the T framework, dictated largely by optimization of the valence-electron concentration. In this Communication, we show how this behavior is anticipated and explained by the Density Functional Theory-Chemical Pressure (DFT-CP) schemes of the NCLs. A CP analysis of the RuGa₂ parent structure reveals CP quadrupoles on the Ga atoms (telltale signs of soft atomic motion) that arise from overly short Ru-Ga contacts along one axis and underutilized spaces in the perpendicular directions. In their placement and orientation, the CP quadrupoles highlight a helical path of facile movement for the Ga atoms that avoids further compression of the already strained Ru-Ga contacts. The E atoms of a series of NCLs (in their DFT-optimized geometries) are all found to lie along this helix, with the CP quadrupole character being a persistent feature. In this way, the T sublattice common to the NCLs encodes helical paths by which the E-atom spacing can be varied, creating a mechanism to accommodate electronically driven compositional changes. These results illustrate how CP schemes can be combined with electron-counting rules to create well-defined structural sequences, potentially guiding the discovery of new intermetallic phases.

Characterizing modulated structures with first-principles calculations: a unified superspace scheme of ordering in mullite

The benefit of computational methods applying density functional theory for the description and understanding of modulated crystal structures is investigated. A method is presented which allows one to establish, improve and test superspace models including displacive and occupational modulation functions from first-principles calculations on commensurate structures. The total energies of different configurations allow one to distinguish stable and less stable structure models. The study is based on a series of geometrically optimized superstructures of mullite (Al4+2xSi2-2xO10-x) derived from the superspace group Pbam(α0½)0ss. Despite the disordered and structurally complex nature of mullite, the calculations on ordered superstructures are very useful for determining the ideal Al/Si ordering in mullite, extracting atomic modulation functions as well as understanding the SiO2-Al2O3 phase diagram. The results are compared with experimentally established models which confirm the validity and utility of the presented method.

Magnetism of new metastable cobalt-nitride compounds

The search for new magnetic materials with high magnetization and magnetocrystalline anisotropy is important for a wide range of applications including information and energy processing. There is only a limited number of naturally occurring magnetic compounds that are suitable. This situation stimulates an exploration of new phases that occur far from thermal-equilibrium conditions, but their stabilization is generally inhibited due to high positive formation energies. Here a nanocluster-deposition method has enabled the discovery of a set of new non-equilibrium Co-N intermetallic compounds. The experimental search was assisted by computational methods including adaptive-genetic-algorithm and electronic-structure calculations. Conventional wisdom is that the interstitial or substitutional solubility of N in Co is much lower than that in Fe and that N in Co in equilibrium alloys does not produce materials with significant magnetization and anisotropy. By contrast, our experiments identify new Co-N compounds with favorable magnetic properties including hexagonal Co3N nanoparticles with a high saturation magnetic polarization (Js = 1.28 T or 12.8 kG) and an appreciable uniaxial magnetocrystalline anisotropy (K1 = 1.01 MJ m-3 or 10.1 Mergs per cm3). This research provides a pathway for uncovering new magnetic compounds with computational efficiency beyond the existing materials database, which is significant for future technologies.

Fe-Cluster Compounds of Chalcogenides: Candidates for Rare-Earth-Free Permanent Magnet and Magnetic Nodal-Line Topological Material

Fe-cluster-based crystal structures are predicted for chalcogenides Fe₃X₄ (X = S, Se, Te) using an adaptive genetic algorithm. Topologically different from the well-studied layered structures of iron chalcogenides, the newly predicted structures consist of Fe clusters that are either separated by the chalcogen atoms or connected via sharing of the vertex Fe atoms. Using first-principles calculations, we demonstrate that these structures have competitive or even lower formation energies than the experimentally synthesized Fe₃X₄ compounds and exhibit interesting magnetic and electronic properties. In particular, we show that Fe₃Te₄ can be a good candidate as a rare-earth-free permanent magnet and Fe₃S₄ can be a magnetic nodal-line topological material.

Structures of defects on anatase TiO2(001) surfaces

Defects on oxide surfaces play a crucial role in surface reactivity and thus it is crucial to understand their atomic and electronic structures. The defects on anatase TiO₂(001)-(1 × 4) surfaces are found to be highly reactive; however, due to the surface reconstruction, the defects exhibit a complicated character in different experiments that make it very challenging to determine their atomic structures. Here we present a systematic first-principles investigation of the defects on anatase TiO₂(001)-(1 × 4) surfaces based on a global-search adaptive genetic algorithm (AGA) and density functional theory (DFT). For different Ti-O ratios, we identify the low energy defect structures, investigate their electronic structure using a hybrid functional, and map their regions of stability under realistic conditions. We successfully find novel oxygen vacancy (O_V) and Ti interstitial (Ti_ini) structures that are different from the conventional ones in terms of their charge localization, magnetic state, and their scanning-tunneling-microscopy bright-dark image signature. This provides an insight into the complex geometric and electronic structure of the surface defects, and resolves several experimental discrepancies.

Role of Surface Stress on the Reactivity of Anatase TiO2(001)

In contrast with theoretical predictions in which anatase TiO₂(001) and its (1 × 4) reconstructed surfaces are highly reactive, recent experimental results show this surface to be inert except for the defect sites. In this report, based on a systematic study of anatase TiO₂(001)-(1 × 4) surface using first-principles calculations, the tensile stress is shown to play a crucial role on the surface reactivity. The predicted high reactivity based on add-molecule model is due to the large surface tensile stress, which can be easily suppressed by a stress-release mechanism. We show that various surface defects can induce stress release concomitantly with surface passivation. Thus the synthesis of anatase(001) surface with few defects is essential to improve the reactivity, which can be achieved, for example, via H₂O adsorption. Our study provides a uniform interpretation of controversial experimental observations and theoretical predictions on anatase TiO₂(001) surface and further proposes new insights into the origin of surface reactivity.

Effect of boron doping on nanostructure and magnetism of rapidly quenched Zr2Co11-based alloys

The role of B on the microstructure and magnetism of Zr₁₆Co_82.5-x Mo_1.5B _x ribbons prepared by arc melting and melt spinning is investigated. Microstructure analysis show that the ribbons consist of a hard-magnetic rhombohedral Zr₂Co₁₁ phase and a minor amount of soft-magnetic Co. We show that the addition of B increases the amount of hard-magnetic phase, reduces the amount of soft-magnetic Co and coarsens the grain size from about 35 nm to 110 nm. There is a monotonic increase in the volume of the rhombohedral Zr₂Co₁₁ unit cell with increasing B concentration. This is consistent with a previous theoretical prediction that B may occupy a special type of large interstitial sites, called interruption sites. The optimum magnetic properties, obtained for x = 1, are a saturation magnetization of 7.8 kG, a coercivity of 5.4 kOe, and a maximum energy product of 4.1 MGOe.

'Crystal Genes' in Metallic Liquids and Glasses

We analyze the underlying structural order that transcends liquid, glass and crystalline states in metallic systems. A genetic algorithm is applied to search for the most common energetically favorable packing motifs in crystalline structures. These motifs are in turn compared to the observed packing motifs in the actual liquid or glass structures using a cluster-alignment method. Using this method, we have revealed the nature of the short-range order in Cu64Zr36 glasses. More importantly, we identified a novel structural order in the Al90Sm10 system. In addition, our approach brings new insight into understanding the origin of vitrification and describing mesoscopic order-disorder transitions in condensed matter systems.

Metastable cobalt nitride structures with high magnetic anisotropy for rare-earth free magnets

Cobalt nitride can exhibit a tetragonal structure and large magnetocrystalline anisotropy energy, which make it a promising material for rare-earth free magnets.

Adaptive cluster expansion approach for predicting the structure evolution of graphene oxide

An adaptive cluster expansion (CE) method is used to explore surface adsorption and growth processes. Unlike the traditional CE method, suitable effective cluster interaction (ECI) parameters are determined, and then the selected fixed number of ECIs is continually optimized to predict the stable configurations with gradual increase of adatom coverage. Comparing with traditional CE method, the efficiency of the adaptive CE method could be greatly enhanced. As an application, the adsorption and growth of oxygen atoms on one side of pristine graphene was carefully investigated using this method in combination with first-principles calculations. The calculated results successfully uncover the structural evolution of graphene oxide for the different numbers of oxygen adatoms on graphene. The aggregation behavior of the stable configurations for different oxygen adatom coverages is revealed for increasing coverages of oxygen atoms. As a targeted method, adaptive CE can also be applied to understand the evolution of other surface adsorption and growth processes.