Void lattices

There are certain unusual types of defects in metal systems that are noteworthy. It has been found (Taylor Doyle, 1972) that in NiAl alloys A1 atoms on the Al-rich side do not substitute on the Ni sublattice instead there are vacancies in the Ni sites. For example, at 55 at.% Al, 18% of Ni sites are vacant while the A1 sites are filled. Such vacancies determined by composition are referred to as constitutional vacancies. Other alloys have since been found to exhibit such vacancies, typical of these being NiGa and CoGA. Another rather curious aspect of defects is the formation of void lattices when metals such as Mo are irradiated with neutrons or more massive projectiles (Gleiter, 1983). Void lattices arise from agglomeration of vacancies and are akin to superlattices. Typically, neighbouring voids in Mo are separated by 200 A. An explanation for the stability of void lattices on the basis of the continuum theory of elasticity has been proposed (Stoneham, 1971 Tewary Bullough, 1972). 

Long-range periodicity based on extended defects is not, however, confined to shear-plane structures. Indeed the occurrence of extended defect super-lattices is widespread. The adaptive structures discussed by Anderson have already been referred to in the Introduction. A further illustration of the phenomenon, which strikingly illustrates its generality, is provided by the void lattice observed in certain irradiated metals, e.g., Mo, where voids, typically of diameters 50 A, formed by the aggregation of irradiation induced vacancies, order to give a stable f.c.c. lattice in which the voids are separated by 300 A. 

Figure 7.18 (a) Phase field modeling of void lattice formation due to ID interstitial diffusion [77]. (b) Phase field modeling of radiation-induced homogeneous precipitation in an unsaturated AgB92 model alloy at 40 dpa [100],... 

Not all fracture is by crack propagation. Highly ductile materials stressed at high temperature will eventually break by the growth, through absorption of lattice vacancies, of plastic voids. This shades into the phenomenon of superplasticity, which was examined in Section 4.2.5. 

Figure 6.1 The icosahedron and some of its symmetry elements, (a) An icosahedron has 12 vertices and 20 triangular faces defined by 30 edges, (b) The preferred pentagonal pyramidal coordination polyhedron for 6-coordinate boron in icosahedral structures as it is not possible to generate an infinite three-dimensional lattice on the basis of fivefold symmetry, various distortions, translations and voids occur in the actual crystal structures, (c) The distortion angle 0, which varies from 0° to 25°, for various boron atoms in crystalline boron and metal borides.

Gitter-konstante, /. lattice constant grating constant, -loch, n. (Cryst.) lattice hole, lattice void, -masche, /. grid mesh, -span-nung, /. (Elec.) grid voltage, -spektrograph,... 

In practice, thermal cycling rather than isothermal conditions more frequently occurs, leading to a deviation from steady state thermodynamic conditions and introducing kinetic modifications. Lattice expansion and contraction, the development of stresses and the production of voids at the alloy-oxide interface, as well as temperature-induced compositional changes, can all give rise to further complications. The resulting loss of scale adhesion and spalling may lead to breakaway oxidation " in which linear oxidation replaces parabolic oxidation (see Section 1.10). 

Returning to the observed values for these cesium salts, plotted as dark circles in Fig. 57, we must conclude that the position of the experimental points—nearer the diagonal than any salt of Rb, K, or Na—does not indicate anything unusual about the aqueous solution of the cesium salts, but merely arises from the fact that these cesium salts happen to crystallize in a more compact lattice structure, with less void space between the ions. We cannot make a similar remark about the points for the lithium salts, which lie astride the diagonal the interpretation of these values will be discussed later. 

The stabilizing influence of small amounts of B (M/B > 0.25) in the voids of the metal host lattice varies with the mode of filling (partial or complete) of the interstitial, mostly O, sites and whether the compounds develop from the binary-intermetallic host lattice. The structures of B-rich compounds (M/B < 4) are mainly determined by the formation of regular, covalent B polyhedra (O, icosahedron) and the connections between them (B frame structures). Typical metal (M) borides therefore are found within a characteristic ratio of metal to boron 0.125 < M/B < 4. 

Interstitial metal-rich borides are found among typical elemental or binary eompound types, stabilized by filling the voids of the metal host lattice with isolated B atoms. 

Phase Trigonal prismatic void in 2c Metal host lattice atoms in 12k -f- 6h(l) -1- 6h(2) Icosahedral center in 2a Octahedral void in 6g ... 

Compounds isotypic with the k phases arc found among intcrmetallics, borides, carbides and oxides and also with silicides, germanides, arsenides, sulfides and sclcnides no nitrides, however, are found. The mode of filling the various voids in the metal host lattice of the k phases follows the schemein Ref. 4 and is presented in Table 1 for all those compounds for which the atom distribution is well known from x-ray or neutron diffraction. Accordingly, B atoms in tc-borides, Zr, Mo, W, Re)4B and Hfy(Mo, W, Re, Os)4B , occupy the trigonal prismatic interstices within the parent metal framework of a Mn, Aln,-type structure (see Table 1 see also ref. 48). Extended solid solutions are found for (Hf, Al)[Pg.140]

Phase Octahedral void I in 16c Octahedral void 11 in 8a Icosahedral center in 16d Metal host lattice atoms in 48f + 32e... 

Many of the diamondoids can be brought to macroscopic crystalline forms with some special properties. For example, in its crystalline lattice, the pyramidal-shaped [l(2,3)4]pentamantane (see Table I) has a large void in comparison to similar crystals. Although it has a diamond-like macroscopic structure, it possesses the weak, noncovalent, intermolecular van der Waals... 

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