Gemischte Tristannide der Reihe CaSn3 - SrSn3 - BaSn3: Synthesen, Kristallstrukturen, Chemische Bindung

Alkaline-earth tri-mercurides A IIHg3 (A II=Ca, Sr, Ba): binary intermetallic compounds with a common and a new structure type

The alkaline-earth tri-mercurides AHg3 (A=Ca, Sr, Ba) were yielded from stoichiometric melts of the elements in pure phase (in the case of Sr with Sr11Hg54 as a by-product) and their structures were determined by means of single crystal X-ray data. As reported long ago from powder data, CaHg3 and SrHg3 crystallize in the Ni3Sn-type (P63/mmc, a=662.26(2)/689.39(3), c=501.64(2)/510.38(3) pm, Z=2, R1=0.0233/0.0306 for A=Ca/Sr). The structure consists of a hexagonal close packing of ordered layers AHg3 or a dense packing of anti-cuboctahedra [AHg12] (as cation coordination polyhedra, CCP) and [Hg6] octahedra fused via opposite faces to form columns along c. BaHg3 crystallizes in a unique structure type (P4/ncc, a=1193.04(3), c=958.02(5) pm, Z=12, R1=0.0461). It contains three crystallographically different Hg atoms, which form layers of distorted flat square pyramids. In contrast to the layers of the BaAl4-type, 1 5 ${1 \over 5}$ of the pyramids are missing. Due to the 45 degree rotation of adjacent layers, the connection between the layers is not a ‘apical-to-apical’ one like in BaAl4, but is established by ‘apical-to-basal’ bonds. Compared to the Ca and Sr compound, the CCPs of the two different Ba atoms, which are embedded between the pyramid layers, are increased to 12+4 and 14+2 (for Hg+Ba). For all title compounds and the Li phase LiHg3, which is isotypic to CaHg3, the electronic band structures were calculated within the framework of the FP-LAPW DFT method. Even though the compounds are metals and exhibit only very slight minima of the tDOS at the Fermi level, the electron transfer from the alkali/alkaline-earth element towards mercury is almost complete. Thus, Coulomb interactions and the optimized size and arrangement of the A CCPs, besides the flexible Hg–Hg bonding within the polyanion, determine the structure formation.

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.