DFT-Chemical Pressure Research Articles

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 YNi3Cx 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.

Putting ScTGa5(T = Fe, Co, Ni) on the Map: How Electron Counts and Chemical Pressure Shape the Stability Range of the HoCoGa5Type

We explore the factors stabilizing one member of the diverse structures encountered in Ln–T–E systems (Ln = lanthanide or similar early d-block element, T = transition metal, E = p-block element): the HoCoGa5 type, an arrangement of atoms associated with unconventional superconductivity. We first probe the boundaries of its stability range through the growth and characterization of ScTGa5 crystals (T = Fe, Co, Ni). After confirming that these compounds adopt the HoCoGa5 type, we analyze their electronic structure using density functional theory (DFT) and DFT-calibrated Hückel calculations. The observed valence electron count range of the HoCoGa5 type is explained in terms of the 18-n rule, with n = 6 for the Ln atoms and n = 2 for the T sites. The role of atomic sizes is investigated with DFT-chemical pressure (DFT-CP) analysis of ScNiGa5, which reveals negative pressures within the Ga sublattice as it stretches to accommodate the Sc and T atoms. This CP scheme is consistent with HoCoGa5-type gallides only being observed for relatively small Ln and T atoms. These conclusions account for the relative positions of the HoCoGa5, BaMg4Si3, and Ce2NiGa10 types in a structure map, demonstrating how combining the 18-n and CP schemes can guide our understanding of Ln–T–E systems.

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.

Structural plasticity: how intermetallics deform themselves in response to chemical pressure, and the complex structures that result.

Interfaces between periodic domains play a crucial role in the properties of metallic materials, as is vividly illustrated by the way in which the familiar malleability of many metals arises from the formation and migration of dislocations. In complex intermetallics, such interfaces can occur as an integral part of the ground-state crystal structure, rather than as defects, resulting in such marvels as the NaCd2 structure (whose giant cubic unit cell contains more than 1000 atoms). However, the sources of the periodic interfaces in intermetallics remain mysterious, unlike the dislocations in simple metals, which can be associated with the exertion of physical stresses. In this Article, we propose and explore the concept of structural plasticity, the hypothesis that interfaces in complex intermetallic structures similarly result from stresses, but ones that are inherent in a defect-free parent structure, rather than being externally applied. Using DFT-chemical pressure analysis, we show how the complex structures of Ca2Ag7 (Yb2Ag7 type), Ca14Cd51 (Gd14Ag51 type), and the 1/1 Tsai-type quasicrystal approximant CaCd6 (YCd6 type) can all be traced to large negative pressures around the Ca atoms of a common progenitor structure, the CaCu5 type with its simple hexagonal 6-atom unit cell. Two structural paths are found by which the compounds provide relief to the Ca atoms' negative pressures: a Ca-rich pathway, where lower coordination numbers are achieved through defects eliminating transition metal (TM) atoms from the structure; and a TM-rich path, along which the addition of spacer Cd atoms provides the Ca coordination environments greater independence from each other as they contract. The common origins of these structures in the presence of stresses within a single parent structure highlights the diverse paths by which intermetallics can cope with competing interactions, and the role that structural plasticity may play in navigating this diversity.

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.

Filling in the Holes: Structural and Magnetic Properties of the Chemical Pressure Stabilized LnMnxGa3 (Ln = Ho–Tm; x < 0.15)

Single crystals of LnMnxGa3 (Ln = Ho–Tm; x < 0.15) were grown from a Ga self-flux. These compounds crystallize in a variant of the AuCu3 structure type where Mn partially occupies the Ga6 octahedral holes. Introduction of the Mn guest atoms allows for modulation of the structures and magnetic properties of their hosts: While TmGa3 orders antiferromagnetically at ∼4.2 K, TmMnxGa3 (x = 0.05, 0.10) remains paramagnetic down to 1.8 K. Ho and Er analogs order antiferromagnetically, with effective moments and Neel temperatures, respectively, decreasing and increasing as a function of Mn concentration. DFT–chemical pressure analysis elucidates the trends in the stability of LnGa3 AuCu3-type phases and their stuffed derivatives. Guest atom insertion supports expansion of the filled octahedra, allowing the relief of negative chemical pressures in the surrounding Ga–Ga contacts.

New Roles for Icosahedral Clusters in Intermetallic Phases: Micelle-like Segregation of Ca–Cd and Cu–Cd Interactions in Ca10Cd27Cu2

Despite significant progress in the structural characterization of the quasicrystalline state, the chemical origins of long- and short-range icosahedral order remain mysterious and a subject of debate. In this Article, we present the crystal structure of a new complex intermetallic phase, Ca10Cd27Cu2 (mC234.24), whose geometrical features offer clues to the driving forces underlying the icosahedral clusters that occur in Bergman-type quasicrystals. Ca10Cd27Cu2 adopts a C-centered monoclinic superstructure of the 1/1 Bergman approximant structure, in which [110] layers of Bergman clusters in the 1/1 structure are separated through the insertion of additional atoms (accompanied by substantial positional disorder). An examination of the coordination environments of Ca and Cu (in the ordered regions) reveals that the structure can be viewed as a combination of coordination polyhedra present in the nearest binary phases in the Ca-Cd-Cu compositional space. A notable feature is the separation of Ca-Cd and Cu-Cd interactions, with Bergman clusters emerging as Ca-Cd Friauf polyhedra (derived from the MgZn2-type CaCd2 phase) encapsulate a Cu-Cd icosahedron similar to those appearing in Cu2Cd5. DFT chemical pressure calculations on nearby binary phases point to the importance of this segregation of Ca-Cd and Cu-Cd interactions. The mismatch in atomic size between Cu and Cd leads to an inability to satisfy Ca-Cu and Ca-Cd interactions simultaneously in the Friauf polyhedra of the nearby Laves phase CaCd2. The relegation of the Cu atoms to icosahedra prevents this frustration while nucleating the formation of Bergman clusters.

Problem Solving with Pentagons: Tsai-Type Quasicrystal as a Structural Response to Chemical Pressure

Even after significant advances in the structural characterization of quasicrystals--phases whose diffraction patterns combine the sharp peaks normally associated with lattice periodicity and rotational symmetries antithetical to such periodicity--this new form of long-range order remains enigmatic. Here, we present DFT-chemical pressure calculations on the Tsai-type quasicrystal approximant CaCd6, which reveal how its icosahedral clusters can be traced to simple CaCu5-type (hP6) intermetallics. The results indicate that the Tsai-type clusters emerge from an atomic-size-driven transformation from planar arrangements to spherical clusters, recalling the relationship between graphene and C60.

First-Principles Elucidation of Atomic Size Effects Using DFT-Chemical Pressure Analysis: Origins of Ca36Sn23's Long-Period Superstructure.

The space requirements of atoms are empirically known to play key roles in determining structure and reactivity across compounds ranging from simple molecules to extended solid state phases. Despite the importance of this concept, the effects of atomic size on stability remain difficult to extract from quantum mechanical calculations. Recently, we outlined a quantitative yet visual and intuitive approach to the theoretical analysis of atomic size in periodic structures: the DFT-Chemical Pressure (DFT-CP) analysis. In this Article, we describe the methodological details of this DFT-CP procedure, with a particular emphasis on refinements of the method to make it useful for a wider variety of systems. A central improvement is a new integration scheme with broader applicability than our earlier Voronoi cell method: contact volume space-partitioning. In this approach, we make explicit our assumption that the pressure at each voxel is most strongly influenced by its two closest atoms. The unit cell is divided into regions corresponding to individual interatomic contacts, with each region containing all points that share the same two closest atoms. The voxel pressures within each contact region are then averaged, resulting in effective interatomic pressures. The method is illustrated through the verification of the role of Ca-Ca repulsion (deduced earlier from empirical considerations by Corbett and co-workers) in the long-period superstructure of the W5Si3 type exhibited by Ca36Sn23.

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

Atomic size effects have long played a role in our empirical understanding of inorganic crystal structures. At the level of electronic structure calculations, however, the contribution of atomic size remains difficult to analyze, both alone and relative to other influences. In this paper, we extend the concepts outlined in a recent communication to develop a theoretical method for revealing the impact of the space requirements of atoms: the density functional theory-chemical pressure (DFT-CP) analysis. The influence of atomic size is most pronounced when the optimization of bonding contacts is impeded by steric repulsion at other contacts, resulting in nonideal interatomic distances. Such contacts are associated with chemical pressures (CPs) acting upon the atoms involved. The DFT-CP analysis allows for the calculation and interpretation of the CP distributions within crystal structures using DFT results. The method is demonstrated using the stability of the Ca(2)Ag(7) structure over the simpler CaCu(5)-type alternative adopted by its Sr-analogue, SrAg(5). A hypothetical CaCu(5)-type CaAg(5) phase is found to exhibit large negative pressures on each Ca atom, which are concentrated in two symmetry-related interstitial spaces on opposite sides of the Ca nucleus. In moving to the Ca(2)Ag(7) structure, relief comes to each Ca atom as a defect plane is introduced into one of these two negative-pressure regions, breaking the symmetry equivalence of the two sides and yielding a more compact Ca coordination environment. These results illustrate how the DFT-CP analysis can visually and intuitively portray how atomic size interacts with electronics in determining structure, and bridge theoretical and experimental approaches toward understanding the structural chemistry of inorganic materials.