Packings of Spheres. Metal Structures

This bismuth-III structure is also observed for antimony from 10 to 28 GPa and for bismuth from 2.8 to 8 GPa. At even higher pressures antimony and bismuth adopt the body-centered cubic packing of spheres which is typical for metals. Bi-III has a peculiar incommensurate composite crystal structure. It can be described by two intergrown partial structures that are not compatible metrically with one another (Fig. 11.11). The partial structure 1 consists of square antiprisms which share faces along c and which are connected by tetrahedral building blocks. The partial structure 2 forms linear chains of atoms that run along c in the midst of the square antiprisms. In addition, to compensate for the... 

The cluster condensation can be carried on the chains of octahedra sharing edges can be joined to double-strands and finally to layers of octahedra (Fig. 13.18). Every layer consists of metal atoms in two planes arranged in the same way as two adjacent layers of atoms in a closest-packing of spheres. This is simply a section from a metal structure. The X atoms occupy positions between the metal layers and act as insulating layers. Substances like ZrCl that have this structure have metallic properties in two dimensions. 

It is not surprising that often a crystalline substance is a rather closely packed aggregate of atoms or ions, since the van der W ata interactions, Coulomb interactions, and interactions involving metallic valence tend to stabilise structures in which the atoms have large liganeies. It has been found that the structures of many crystals can be profitably discussed in terms of the packing of spheres, to which we now direct our attention. 

The characteristic line sequences for cubic lattices are shown graphically in Fig. 10-2, in the form of calculated diffraction patterns. The calculations are made for Cu Kol radiation and a lattice parameter a of 3.50 A. The positions of all the diffraction lines which would be formed under these conditions are indicated as they would appear on a film or chart of the length shown. (For comparative purposes, the pattern of a hexagonal close-packed structure is also illustrated, since this structure is frequently encountered among metals and alloys. The line positions are calculated for Cu Kol radiation, a = 2.50 A, and cja = 1.633, which corresponds to the close packing of spheres.)... 

Describe the three types of cubic unit cells and explain how to find the number of particles in each and how packing of spheres gives rise to each calculate the atomic radius of an element from its density and crystal structure distinguish the types of crystalline solids explain how the electron-sea model and band theory account for the properties of metals and how the size of the energy gap explains the conductivity of substances ( 12.6) (SP 12.4) (EPs 12.57-12.75)... 

It is evident that event the simplest model for the packing of spheres of equivalent size permits the possibility of polymorphism. Most of the metals of the lanthanide series exist in the hexagonal close-packed structure at room temperature but transform into the body-centered cubic from at temperatures exceeding 800°C [9]. For the most part, these transitions appear to be enantiotropic in nature. 

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