In metallic crystals

The atom radius of an element is the shortest distance between like atoms. It is the distance of the centers of the atoms from one another in metallic crystals and for these materials the atom radius is often called the metal radius. Except for the lanthanides (CN = 6), CN = 12 for the elements. The atom radii listed in Table 4.6 are taken mostly from A. Kelly and G. W. Groves, Crystallography and Crystal Defects, Addison-Wesley, Reading, Mass., 1970. 

The smallest imperfections in metal crystals are point defects, in particular vacant lattice sites (vacancies) and interstitial atoms. As illustrated in Fig. 20.21a, a vacancy occurs where an atom is missing from the crystal structure... 

Metallic bonding The bonding present in metallic crystals composed of a lattice of positively charged atoms in a sea of delocalized electrons. 

A naturally occurring chiral metal structure is a screw dislocation (Fig. 3.4),11 which is a chiral arrangement observed in metal crystals but never resolved and tested for enantioselective heterogeneous catalysis. A possible method of making chiral arrangements like screw dislocations is by the glancing angle deposition technique, which can produce chiral sculptured thin films.12... 

Inelastic shearing of atoms relative to one another is the mechanism that determines hardness. The shearing is localized at dislocation lines and at kinks along these lines. The kinks are very sharp in covalent crystals where they encompass only individual chemical bonds. On the other hand, in metal crystals they are often very extended. In metallic glasses they are localized in configurations that have a variety of shapes. In ionic crystals the kinks are localized in order to minimize the electrostatic energy. 

Fig. 1-2. Energy distribution of electrons near the Fermi level, cf> in metal crystals c = electron energy f(.i) s distribution function (probability density) ZXe) = electron state density, = occupied...

In semicrystalline polymers such as polyethylene, yielding involves significant disruption of the crystal structure. Slip occurs between the crystal lamellae, which slide by each other, and within the individual lamellae by a process comparable to glide in metallic crystals. The slip within the individual lamellae is the dominant process, and leads to molecular orientation, since the slip direction within the crystal is along the axis of the polymer molecule. As plastic flow continues, the slip direction rotates toward the tensile axis. Ultimately, the slip direction (molecular axis) coincides with the tensile axis, and the polymer is then oriented and resists further flow. The two slip processes continue to occur during plastic flow, but the lamellae and spherullites increasingly lose their identity and a new fibrillar structure is formed (see Figure 5.69). 

The suggestion that in metal crystals the atoms are arranged in closest packing was made by Barlow before the development of the x-ray technique, in order to account for the observations that many metals crystallize with cubic or hexagonal symmetry and that in the latter case many of the observed values of the axial ratio lie near the ideal value 2y/2/ v 3 = 1.633 for hexagonal closest packing. 

Molecular orbital (MO) theory has been used to explain the bonding in metallic crystals, such as pure sodium or pure aluminum. Each MO, instead of dealing with a few atoms in a typical molecule, must cover the entire crystal (might be 1020 or more atoms ). Following the rule that the number of MOs must equal the number of atomic orbitals (AOs) combined, this many MOs must be so close on an energy level diagram that they form a continuous band of energies. Because of this factor, the theory is known as band theory. 

It is well-known that it is more difficult to etch dislocations in metal crystals than in ionic and covalent ones. The cause might be poor techniques, but a relatively low energy increment for metal atoms near a dislocation core could also be... 

Metals are characterized by high thermal and electrical conductivity, malleability, and ductility. As we will see, these properties can be traced to the nondirectional covalent bonding found in metallic crystals. 

The structure of metallic crystals— Of the characteristic properties of metals which distinguish them from non-metals, the high thermal and electrical conductivities are perhaps the most significant. We shall, however, be concerned here mainly with the problem of the nature of the bond between two atoms in metallic crystals and we must refer those who are... 

The most obvious evidence of radiation damage in metallic crystals is decrease in electrical and thermal conductivity. This is attributable to scattering of electrons and phonons by vacancies and interstitials that destroy the order of the lattice necessary for high conductivity. 

The obvious effects of radiation damage in metallic crystals can be reversed by annealing. Heating the irradiated materials supplies the energy required to push an interstitial back into a vacancy. 

Bonding in metallic crystals is explained as a sea of delocalized electrons around positively charged ions located at the lattice sites. The number density of electrons is equal to the number density of positive ions, so the metal is electrically neutral. The bonds are quite strong, evidenced by the high boiling points of metals. Metals are malleable and ductile because the highly mobile electrons can rapidly adjust when lattice ions are pushed to new locations by external mechanical forces. Metals are good conductors of heat and electricity because the delocalized electrons respond easily to applied external fields. 

A simple explanation for the many characteristic features of the metallic state is given by free-electron theory. In metallic crystals the atoms are assumed to take part collectively in bonding, where each atom provides electrons from outer electron energy levels to the bond. The crystal... 

Electron Energy Zones in Metal Crystals. Before leaving the subject of the nature of the binding forces in crystals it might... 

ATOM PLANES, ATOM DIRECTIONS AND INTERATOMIC DISTANCES IN METAL CRYSTALS... 

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