Mn39Si9Nx: Epitaxial Stabilization as a Pathway to the Formation of Intermetallic Nitrides.

The realization of the full potential of nitrogen-containing solid-state materials is limited by the inert and gaseous nature of N2. In this Communication, we describe the simple synthesis yet complex structure of the new phase Mn39Si9Nx (x = 0.84). The formation of this intermetallic subnitride appears to be facilitated by the high solubility of nitrogen in manganese metal, while its structural features are guided by the complementary internal packing strains of Mn-Si and Mn-N domains, an effect known as epitaxial stabilization. These domains intergrow into a composite structure based on the interpenetration of tetrahedrally close-packed (TCP) and Mackay cluster-like modules. We anticipate that other systems combining nitrogen with the TCP packing of metals will be similarly driven toward intergrowth, opening a path to a broader family of intermetallic nitrides.

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.

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.