Inversion anti-phase domains in Cu-rich γ-brasses. II. Defects in the domain structure

Structure and stability of γ1-AuZn2.1: a γ-brass-related complex phase in the Au-Zn System

γ₁-AuZn_2.1 in the Au-Zn binary system has been synthesized and its structure analyzed by single-crystal X-ray diffraction. It crystallizes in the trigonal space group P31m (No. 157) with ∼227 atoms per unit cell and represents a \surd3a × \surd3a × c superstructure of rhombohedrally distorted γ-Au_5-xZn_8+y. The structure is largely tetrahedrally closed packed. The formation of γ₁-AuZn_2.1 can be understood within the framework of a Hume-Rothery stabilization mechanism with a valence electron concentration of 1.68 e/a (valence electrons per atom).

Structural impact of platinum on the incommensurably modulated γ-brass related composite structure Pd15Zn54

The crystal structure of three incommensurately modulated γ-brass related composite structures in the Pd-Zn-Pt system has been solved from X-ray single crystal diffraction data using a 3 + 1-dimensional super space description. The compounds Pt(x)Pd(15-x)Zn(54) (x ≈ 6, 7, 10) crystallize in orthorhombic superspace group Fmmm(α00)0s0 (F = [(1/2, 1/2, 0, 0); (1/2, 0, 1/2, 0); (0, 1/2, 1/2, 0)] with the following fundamental cell dimensions: a = 4.265(1) Å, b = 9.132(1) Å, c = 12.928(2) Å, q ≈ 0.629a*; a = 4.284(1) Å, b = 9.151(2) Å, c = 12.948(4) Å, q ≈ 0.628a*; and a = 4.288(1) Å, b = 9.140(4) Å, c = 12.926(7) Å, q ≈ 0.627a*. Each structure is built by two sub-lattices-pentagonal antiprismatic columns parallel to [100] and a zigzag chain of Zn atoms running along the center of the column.

Pd0.213Cd0.787 and Pd0.235Cd0.765 Structures: Their Longc Axis and Composite Crystals, Chemical Twinning, and Atomic Site Preferences

We present single-crystal studies of Pd(0.213)Cd(0.787) and Pd(0.235)Cd(0.765), synchrotron powder studies of Pd(1-x)Cd(x), 0.755> or =x> or =0.800, and LDA-DFT and extended Hückel (eH) calculations on these or related phases. The two single-crystal structures have a, b, and c axis lengths of 9.9013(7), 14.0033(10), 37.063(24) and 9.9251(3), 14.0212(7), 60.181(3) A, respectively and they crystallize in the space groups Ccme and F2mm, respectively (solved as (3+1)-dimensional crystals their most convenient superspace group is Xmmm(00gamma)s00). The structures have two different structural components each with their own separate axis parameters. Powder data shows that the ratio of these separate axes (S/L) varies from 1.615 to 1.64, values near the golden mean (1.618). For Pd(0.213)Cd(0.787), different Pd and Cd site occupancies lead to variation in the R factor from 2.6-3.6 %. The site occupancy pattern with the lowest R factor (among the 26 820 variants studied) is the exact site occupancy pattern predicted by LDA-DFT parameterized eH Mulliken charge populations. The phases can be understood through a chemical twinning principle found in gamma-brass, the parent structure for the above phases (a relation with the MgCu(2) Laves phase is also noted). This twinning principle can be used to account for Cd and Pd site preferences. At the same time there is a clean separation among the Cd and Pd atoms for the two separate chain types at height b=0 and 1/2. These results indicate that Cd:Pd stoichiometry plays a role in phase stability.

STRUCTURAL DIVERSITY IN SOLID STATE CHEMISTRY:A Story of Squares and Triangles

▪ Abstract  A simple method for calculating the electronic energy of extended solids is discussed in this review. This method is based on the Hückel or tight-binding theory in which an explicit pairwise repulsion is added to the generally attractive forces of the partially filled valence electron bands. An expansion based on the power moments of the electronic density of states is discussed, and the structural energy difference theorem is reviewed. The repulsive energy is found to vary linearly with the second power moment of the electronic density of states. These results are then used to show why there is such a diversity of structure in the solid state. The elemental structures of the main group are rationalized by the above methods. It is the third and fourth power moments (which correspond in part to triangles and squares of bonded atoms) that account for much of the elemental structures of the main group elements of the periodic table. This serves as an introduction to further rationalizations of transition for noble metal alloy, binary and ternary telluride and selenide, and other intermetallic structures.Thus a cohesive picture of both covalent and metallic bonding is presented in this review, illustrating the importance of atomic orbitals and their overlap integrals.