DFT-Chemical Pressure Analysis: Visualizing the Role of Atomic Size in Shaping the Structures of Inorganic Materials

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.

Structural Analysis of the Gd-Au-Al 1/1 Quasicrystal Approximant Phase across Its Composition-Driven Magnetic Property Changes

Gd14AuxAl86-x Tsai-type 1/1 quasicrystal approximants (ACs) exhibit three magnetic orders that can be finely tuned by the valence electron concentration (e/a ratio). This parameter has been considered to be crucial for controlling the long-range magnetic order in quasicrystals (QCs) and ACs. However, the nonlinear trend of the lattice parameter as a function of Au concentration suggests that Gd14AuxAl86-x 1/1 ACs are not following a conventional solid solution behavior. We investigated Gd14AuxAl86-x samples with x values of 52, 53, 56, 61, 66, and 73 by single-crystal X-ray diffraction. Our analysis reveals that increasing Au/Al ordering with increasing x leads to distortions in the icosahedral shell built of the Gd atoms and that trends observed in the interatomic Gd-Gd distances closely correlate with the magnetic property changes across different x values. Our results demonstrate that the e/a ratio alone may be an oversimplified concept for investigating the long-range magnetic order in 1/1 ACs and QCs and that the mixing behavior of the nonmagnetic elements Au and Al plays a significant role in influencing the magnetic behavior of the Gd14AuxAl86-x 1/1 AC system. These findings will contribute to improved understanding towards tailoring magnetic properties in emerging materials.

Structures of LaH10, EuH9, and UH8 superhydrides rationalized by electron counting and Jahn-Teller distortions in a covalent cluster model

The superconducting hydrides LaH₁₀, EuH₉ and UH₈ are studied using chemically intuitive bonding analysis of periodic and molecular models. We find trends in the crystallographic and electronic structures of the materials by focusing on chemically meaningful building blocks in the predicted H sublattices. Atomic charge calculations, using two complementary techniques, allow us to assign oxidation states to the metals and divide the H sublattice into neutral and anionic components. Cubic [H₈]^q- clusters are an important structural motif, and molecular orbital analysis of this cluster in isolation shows the crystal structures to be consistent with our oxidation state assignments. Crystal orbital Hamilton population analysis confirms the applicability of the cluster model to the periodic electronic structure. A Jahn-Teller distortion predicted by MO analysis rationalises the distortion observed in a prior study of EuH₉. The impact of this distortion on superconductivity is determined, and implications for crystal structure prediction in other metal-hydrogen systems are discussed. Additionally, the performance of electronic structure analysis methods at high pressures are tested and recommendations for future studies are given. These results demonstrate the value of simple bonding models in rationalizing chemical structures under extreme 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 d_z² 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.

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, T_c, can be tuned by changing the average oxidation state of the metal atoms, with T_c being highest for an average valence of +1.5. KPbB₆C₆, with an ambient-pressure Eliashberg T_c of 88 K, is predicted to possess the highest T_c 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.

A Chemical-Pressure-Induced Phase Transition Controlled by Lone Electron Pair Activity

The chemical pressure approach offers a new paradigm for property control in functional materials. In this work, we disclose a correlation between the β → α pressure-induced phase transition in SnMoO₄ and the substitution process of Mo⁶⁺ by W⁶⁺ in SnMo_1-xW_xO₄ solid solutions (x = 0-1). Special attention is paid to discriminating the role of the lone pair Sn²⁺ cation from the structural distortive effect along the Mo/W substitution process, which is crucial to disentangle the driven force of the transition phase. Furthermore, the reverse α → β transition observed at high temperature in SnWO₄ is rationalized on the same basis as a negative pressure effect associated with a decreasing of W⁶⁺ percentage in the solid solution. This work opens a versatile chemical approach in which the types of interactions along the formation of solid solutions are clearly differentiated and can also be used to tune their properties, providing opportunities for the development of new materials.

Buffering Octahedra in Mo4Zr9P: Intergrowth as a Solution to the Frustrated Packing of Tricapped Trigonal Prisms and Icosahedra

Atomic packings based on icosahedra and tricapped trigonal prisms are prone to frustration─indeed, these polyhedra represent common configurations in metallic glasses. In this Article, we illustrate how these packing issues can serve as a driving force for the formation of modular intermetallic structures. Using Density Functional Theory-Chemical Pressure (DFT-CP) analysis, we relate the Hf₉Mo₄B-type structure of Mo₄Zr₉P to interatomic pressures experienced by the atoms in two parent structures: Zr₃P, whose structure is built from tricapped trigonal prisms, and ZrMo₂, a Laves phase containing icosahedra. CP analysis of Zr₃P reveals that it has particularly frustrated packing because of the entangling of its tricapped trigonal prisms. In the ternary phase, the frustration is significantly relieved as the units become isolated from each other. Further analysis points to the stabilizing effect of a face-sharing network of octahedra in Mo₄Zr₉P that largely separates the structure into Zr-Mo and Zr-P domains and serves as a buffering region for the relaxation of interatomic distances. These conclusions are generalized to the broader members of this structure type with the examination of the CP schemes for the isostructural Mo₄Zr₉B, Al₅Co₂, and Mg₅Pd₂ phases. Finally, we screen the structural literature using the ToposPro software to identify three additional structure types that have similar intergrowth patterns: the Dy₄CoCd, La₂₃Ni₇Mg₄, and Gd₁₄Co₃In₃ types. An analysis of the interatomic distances within the octahedral networks of these structures suggests that these networks commonly facilitate the reconciliation of packing incompatibilities in intermetallic chemistry.

Tutorial on Chemical Pressure Analysis: How Atomic Packing Drives Laves/Zintl Intergrowth in K3Au5Tl

The tight atomic packing generally exhibited by alloys and intermetallics can create the impression of their being composed of hard spheres arranged to maximize their density. As such, the atomic size factor has historically been central to explanations of the structural chemistry of these systems. However, the role atomic size plays structurally has traditionally been inferred from empirical considerations. The recently developed DFT-Chemical Pressure (CP) analysis has opened a path to investigating these effects with theory. In this article, we provide a step-by-step tutorial on the DFT-CP method for non-specialists, along with advances in the approach that broaden its applicability. A new version of the CP software package is introduced, which features an interactive system that guides the user in preparing the necessary electronic structure data and generating the CP scheme, with the results being readily visualized with a web browser (and easily incorporated into websites). For demonstration purposes, we investigate the origins of the crystal structure of K3Au5Tl, which represents an intergrowth of Laves and Zintl phase domains. Here, CP analysis reveals that the intergrowth is supported by complementary CP features of NaTl-type KTl and MgCu2-type KAu2 phases. In this way, K3Au5Tl exemplifies how CP effects can drive the merging for geometrical motifs derived from different families of intermetallics through a mechanism referred to as epitaxial stabilization.

Varying Electronic Configurations in Compressed Atoms: From the Role of the Spatial Extension of Atomic Orbitals to the Change of Electronic Configuration as an Isobaric Transformation

A quantum chemical model for the study of the electronic structure of compressed atoms lends itself to a perturbation-theoretic analysis. It is shown, both analytically and numerically, that the increase of the electronic energy with increasing compression depends on the electronic configuration, as a result of the variable spatial extent of the atomic orbitals involved. The different destabilization of the electronic states may lead to an isobaric change of the ground-state electronic configuration, and the same first-order model paves the way to a simple thermodynamical interpretation of this process.

Frustrated and Allowed Structural Transitions: The Theory-Guided Discovery of the Modulated Structure of IrSi

To the experienced molecular chemist, predicting the geometries and reactivities of a system is an exercise in balancing simple concepts such as sterics and electronics. In this Article, we illustrate how recent theoretical developments can give this combination of concepts a similar predictive power in intermetallic chemistry through the anticipation and discovery of structural complexity in the nominally MnP-type compound IrSi. Analysis of the bonding scheme and DFT-Chemical Pressure (CP) distribution of the reported MnP-type structure exposes issues pointing toward new structural behavior. The placement of the Fermi energy below an electronic pseudogap indicates that this structure is electron-poor, an observation that can be traced via the 18-n rule to the structure's Ir-Ir connectivity. In parallel with this, the structure's CP scheme highlights facile paths of atomic motion that could enable a structural response to this electronic deficiency. Combined, these analyses suggest that IrSi may adopt a more complex structure than previously recognized. Through synthesis and detailed structural investigation of this phase, we confirm this prediction: single-crystal X-ray diffraction reveals an incommensurately modulated structure with the (3+1)D superspace group P2₁/n(0βγ)00 and q ≈ -0.22b* + 0.29c*. The structural modulations increase the average number of Ir-Ir bonds to nearly match the 18-n expectations of the phase through Ir-Ir trimerization along negative CPs with the incommensurability arising from the difficulty of contracting and stretching the Ir-Ir contacts in a regular pattern without expanding the structure along directions of negative Si-Si CP. Integrating these results with prior analyses of related systems points to a simple guideline for materials design, the Frustrated and Allowed Structural Transitions (FAST) principle: the ease with which competing structural phenomena can be experimentally realized is governed by the degree to which they are supported by the coordination of the atomic packing and electronic factors.

Generalized Stress-Redox Equivalence: A Chemical Link between Pressure and Electronegativity in Inorganic Crystals

The crystal structure of many inorganic compounds can be understood as a metallic matrix playing the role of a host lattice in which the nonmetallic atomic constituents are located, the Anions in Metallic Matrices (AMM) model stated. The power and utility of this model lie in its capacity to anticipate the actual positions of the guest atoms in inorganic crystals using only the information known from the metal lattice structure. As a pertinent test-bed for the AMM model, we choose a set of common metallic phases along with other nonconventional or more complex structures (face-centered cubic (fcc) and simple cubic Ca, CsCl-type BaSn, hP4-K, and fcc-Na) and perform density functional theory electronic structure calculations. Our topological analysis of the chemical pressure (CP) scalar field, easily derived from these standard first-principles electronic computations, reveals that CP minima appear just at the precise positions of the nonmetallic elements in typical inorganic crystals presenting the above metallic subarrays: CaF₂, rock-salt and CsCl-type phases of CaX (X = O, S, Se, Te), BaSnO₃, K₂S, and NaX (X = F, Cl, Br, I). A theoretical basis for this correlation is provided by exploring the equivalence between hydrostatic pressure and the oxidation (or reduction) effect induced by the nonmetallic element on the metal structure. Indeed, our CP analysis leads us to propose a generalized stress-redox equivalence that is able to account for the two main observed phenomena in solid inorganic compounds upon crystal formation: (i) the expansion or contraction experienced by the metal structure after hosting the nonmetallic element while its topology is maintained and (ii) the increasing or decreasing of the effective charge associated with the anions in inorganic compounds with respect to the charge already present in the interstices of the metal network. We demonstrate that a rational explanation of this rich behavior is provided by means of Pearson-Parr's electronegativity equalization principle.

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.

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.

Paths to Stabilizing Electronically Aberrant Compounds: A Defect-Stabilized Polymorph and Constrained Atomic Motion in PtGa2

The structures and properties of intermetallic phases are intimately connected to electron count; unfavorable electron counts can result in structural rearrangements or new electrical or magnetic behavior when no such transformation is available. The compound PtGa₂ appears to teeter on the border between these two scenarios with its two polymorphs: a cubic fluorite type form (c-PtGa₂) and a complex tetragonal superstructure (t-PtGa₂) whose Pt-Pt connectivity aligns with the 18- n electron counting rule. Here, we investigate the factors underlying this polymorphism. Electronic structure calculations show that the transition to t-PtGa₂ opens a pseudogap at the Fermi energy that can be traced to Pt-Pt isolobal bond formation, in line with the 18- n bonding scheme. Conversely, DFT-chemical pressure (CP) analysis reveals a network of positive local pressures along Pt-Ga contacts, requiring that the c-PtGa₂ to t-PtGa₂ transition follows tightly concerted atomic motions. Experimentally, a series of samples with varying Pt:Ga ratios were synthesized to examine the stability ranges of the polymorphs. Ga-poor samples yield exclusively the cubic polymorph over the full range of temperatures studied, which can be correlated to the enhanced incorporation of interstitial Pt atoms (at points of negative pressure in the CP scheme). At more Ga-rich compositions, however, t-PtGa₂ emerges as a low-temperature form. In these samples, the t-PtGa₂ to c-PtGa₂ transition is found to be reversible, but with a large hysteresis that in single crystals can exceed 100 °C. Together, the theoretical and experimental results indicate that the c-PtGa₂ phase is buttressed at its unfavorable electron count by the interstitial atoms and networks of positive CPs that restrict atomic motion, suggesting more general strategies for achieving exotic electronic structures in intermetallic materials.

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, E_α, 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.

On the Functionality of Complex Intermetallics: Frustration, Chemical Pressure Relief, and Potential Rattling Atoms in Y11Ni60C6

Intermetallic carbides provide excellent model systems for exploring how frustration can shape the structures and properties of inorganic materials. Combinations of several metals with carbon can be designed in which the formation of tetrahedrally close-packed (TCP) intermetallics conflicts with the C atoms' requirement of trigonal prismatic or octahedral coordination environments, as offered by the simple close-packings (SCP) of equally sized spheres. In this Article, we explore the driving forces that lead to the coexistence of these incompatible arrangements in the Yb₁₁Ni₆₀C₆-type compound Y₁₁Ni₆₀C₆ (cI154), as well as potential consequences of this intergrowth for the phase's physical properties. Our focus begins on the structure's SCP regions, which appear as C-stuffed versions of a AuCu₃-type YNi₃ phase that is not observed on its own in the Y-Ni system. DFT-Chemical Pressure (DFT-CP) calculations on this hypothetical YNi₃ phase reveal large negative pressures within the Ni sublattice, as it is stretched to accommodate the size requirements of the Y atoms. In the Y₁₁Ni₆₀C₆ structure, two structural mechanisms for addressing these CP issues appear: the incorporation of interstitial C atoms, and the presence of interfaces with CaCu₅-type domains. The relative roles of these two mechanisms are investigated with the CP analysis on a hypothetical YNi₃C_x series of C-stuffed AuCu₃-type phases, the Y-Ni sublattice of Y₁₁Ni₆₀C₆, and finally the full Y₁₁Ni₆₀C₆ structure. Through these calculations, the C atoms appear to play the roles of relieving positive Y CPs and supporting relaxation at the AuCu₃-type/CaCu₅-type interfaces, where the cancellation occurs between opposite CPs experienced by the Y atoms in the two parent structures (following the epitaxial stabilization mechanism). The CP analysis of Y₁₁Ni₆₀C₆ also highlights a sublattice of Y and Ni atoms with large negative CPs (and thus the potential for soft vibrational modes), illustrating how frustrated structures could lead to the full realization of the phonon glass-electron crystal concept.

First principles investigation on how site preference and entropy affect the stability of (EuxM1–x)2Ge2Pb (M = Ca, Sr, Ba) polar intermetallics

Density functional theory calculations have been carried out to analyze the factors contributing to the stabilities of a set of recently synthesized quaternary polar intermetallic compounds, (EuxM1–x)2Ge2Pb with M = Ca, Sr, and Ba. Experiments showed that these preferentially crystallized with Pbam (M = Ca) or Cmmm (M = Sr, Ba) symmetry. We systematically explored how the electronic energies of these structures depended on how they were “colored” by the europium/M ions for a wide composition range. It was found that whereas there was very little site preference in the Cmmm structure, the “B” site in the Pbam structure strongly preferred smaller cations. The configurational entropy was also found to play a role in determining which structures might be preferred. However, the experimentally obtained product ratios could only be fully rationalized by the Gibbs free energies of structures containing M:Eu ratios resembling those that were synthesized experimentally. Our results highlight the importance of calculating vibrational contributions to the entropy for realistic structure models (in terms of coloring and composition) to explain product ratios for syntheses carried out at high temperatures.

Epitaxial Stabilization between Intermetallic and Carbide Domains in the Structures of Mn16SiC4 and Mn17Si2C4

The concept of frustration between competing geometrical or bonding motifs is frequently evoked in explaining complex phenomena in the structures and properties of materials. This idea is of particular importance for metallic systems, where frustration forms the basis for the design of metallic glasses, a source of diverse magnetic phenomena, and a rationale for the existence of intermetallics with giant unit cells containing thousands of atoms. Unlike soft materials, however, where conflicts can be synthetically encoded in the molecular structure, staging frustration in the metallic state is challenging due to the ease of macroscopic segregation of incompatible components. In this Article, we illustrate one approach for inducing the intergrowth of incompatible bonding motifs with the synthesis and characterization of two new intermetallic carbides: Mn16SiC4 (mC42) and Mn17Si2C4 (mP46). Similar to the phases Mn5SiC and Mn8Si2C in the Mn-Si-C system, these compounds appear as intergrowths of Mn3C and tetrahedrally close-packed (TCP) regions reminiscent of Mn-rich Mn-Si phases. The nearly complete spatial segregation of Mn-Si (intermetallic) and Mn-C (carbide) interactions in these structures can be understood from the differing geometrical requirements of C and Si. Rather than macroscopically separating into distinct phases, though, the two bonding types are tightly interwoven, with most Mn atoms being on the interfaces. DFT chemical pressure analysis reveals a driving force stabilizing these interfaces: the major local pressures acting between the Mn atoms in the Mn-Si and Mn-C systems are of opposite signs. Joining the intermetallic and carbide domains together then provides substantial relief to these local pressures, an effect we term epitaxial stabilization.

Progress in Visualizing Atomic Size Effects with DFT-Chemical Pressure Analysis: From Isolated Atoms to Trends in AB5 Intermetallics

The notion of atomic size poses an important challenge to chemical theory: empirical evidence has long established that atoms have spatial requirements, which are summarized in tables of covalent, ionic, metallic, and van der Waals radii. Considerations based on these radii play a central role in the design and interpretation of experiments, but few methods are available to directly support arguments based on atomic size using electronic structure methods. Recently, we described an approach to elucidating atomic size effects using theoretical calculations: the DFT-Chemical Pressure analysis, which visualizes the local pressures arising in crystal structures from the interactions of atomic size and electronic effects. Using this approach, a variety of structural phenomena in intermetallic phases have already been understood in terms that provide guidance to new synthetic experiments. However, the applicability of the DFT-CP method to the broad range of the structures encountered in the solid state is limited by two issues: (1) the difficulty of interpreting the intense pressure features that appear in atomic core regions and (2) the need to divide space among pairs of interacting atoms in a meaningful way. In this article, we describe general solutions to these issues. In addressing the first issue, we explore the CP analysis of a test case in which no core pressures would be expected to arise: isolated atoms in large boxes. Our calculations reveal that intense core pressures do indeed arise in these virtually pressure-less model systems and allow us to trace the issue to the shifts in the voxel positions relative to atomic centers upon expanding and contracting the unit cell. A compensatory grid unwarping procedure is introduced to remedy this artifact. The second issue revolves around the difficulty of interpreting the pressure map in terms of interatomic interactions in a way that respects the size differences of the atoms and avoids artificial geometrical constraints. In approaching this challenge, we have developed a scheme for allocating the grid pressures to contacts inspired by the Hirshfeld charge analysis. Here, each voxel is allocated to the contact between the two atoms whose free atom electron densities show the largest values at that position. In this way, the differing sizes of atoms are naturally included in the division of space without resorting to empirical radii. The use of the improved DFT-CP method is illustrated through analyses of the applicability of radius ratio arguments to Laves phase structures and the structural preferences of AB5 intermetallics between the CaCu5 and AuBe5 structure types.

Targeted crystal growth of rare Earth intermetallics with synergistic magnetic and electrical properties: structural complexity to simplicity

The single-crystal growth of extended solids is an active area of solid-state chemistry driven by the discovery of new physical phenomena. Although many solid-state compounds have been discovered over the last several decades, single-crystal growth of these materials in particular enables the determination of physical properties with respect to crystallographic orientation and the determination of properties without possible secondary inclusions. The synthesis and discovery of new classes of materials is necessary to drive the science forward, in particular materials properties such as superconductivity, magnetism, thermoelectrics, and magnetocalorics. Our research is focused on structural characterization and determination of physical properties of intermetallics, culminating in an understanding of the structure-property relationships of single-crystalline phases. We have prepared and studied compounds with layered motifs, three-dimensional magnetic compounds exhibiting anisotropic magnetic and transport behavior, and complex crystal structures leading to intrinsically low lattice thermal conductivity. In this Account, we present the structural characteristics and properties that are important for understanding the magnetic properties of rare earth transition metal intermetallics grown with group 13 and 14 metals. We present phases adopting the HoCoGa5 structure type and the homologous series. We also discuss the insertion of transition metals into the cuboctahedra of the AuCu3 structure type, leading to the synthetic strategy of selecting binaries to relate to ternary intermetallics adopting the Y4PdGa12 structure type. We provide examples of compounds adopting the ThMn12, NaZn13, SmZn11, CeCr2Al20, Ho6Mo4Al43, CeRu2Al10, and CeRu4Al16-x structure types grown with main-group-rich self-flux methods. We also discuss the phase stability of three related crystal structures containing atoms in similar chemical environments: ThMn12, CaCr2Al10, and YbFe2Al10. In addition to dimensionality and chemical environment, complexity is also important in materials design. From relatively common and well-studied intermetallic structure types, we present our motivation to work with complex stannides adopting the Dy117Co57Sn112 structure type for thermoelectric applications and describe a strategy for the design of new magnetic intermetallics with low lattice thermal conductivity. Our quest to grow single crystals of rare-earth-rich complex stannides possessing low lattice thermal conductivity led us to discover the new structure type Ln30Ru4+xSn31-y (Ln = Gd, Dy), thus allowing the correlation of primitive volumes with lattice thermal conductivities. We highlight the observation that Ln30Ru4+xSn31-y gives rise to highly anisotropic magnetic and transport behavior, which is unexpected, illustrating the need to measure properties on single crystals.