Sublattice metal

The vacant sites will be distributed among the N lattice sites, and the interstitial defects on the N interstitial sites in the lattice, leaving a conesponding number of vacancies on die N lattice sites. In the case of ionic species, it is necessaty to differentiate between cationic sites and anionic sites, because in any particular substance tire defects will occur mainly on one of the sublattices that are formed by each of these species. In the case of vacant-site point defects in a metal, Schottky defects, if the number of these is n, tire random distribution of the n vacancies on the N lattice sites cair be achieved in... 

The isomorphous diiodides of Ce, Pr and Gd stand apart from all the other, salt-like, dihalides. These three, like LaH, are notable for their metallic lustre and very high conductivities and are best formulated as (Ln ,2I",e", the electron being in a delocalized conduction band. Besides the dihalides, other reduced species have been obtained such as LnsCln (Ln = Sm, Gd, Ho). They have fluorite-related structures (p. 118) in which the anionic sublattice is partially rearranged to accommodate additional anions. 

One of the most important parameters that defines the structure and stability of inorganic crystals is their stoichiometry - the quantitative relationship between the anions and the cations [134]. Oxygen and fluorine ions, O2 and F, have very similar ionic radii of 1.36 and 1.33 A, respectively. The steric similarity enables isomorphic substitution of oxygen and fluorine ions in the anionic sub-lattice as well as the combination of complex fluoride, oxyfluoride and some oxide compounds in the same system. On the other hand, tantalum or niobium, which are the central atoms in the fluoride and oxyfluoride complexes, have identical ionic radii equal to 0.66 A. Several other cations of transition metals are also sterically similar or even identical to tantalum and niobium, which allows for certain isomorphic substitutions in the cation sublattice. 

The radius of the second cation in known MuNbOFs, MU2Nb03F3 and Mul2Nb05F compounds containing bi- and trivalent metals, is usually similar to that of niobium s ionic radius. Such compounds cannot be considered as having an island-type structure and will be discussed later on. Only bismuth-containing compounds (Bi3+) display the presence of different cationic sublattices in their crystal structure. 

Solution behavior and phase equilibria are published for ternary and higher order t phases and for the mixed interstitial r-carboborides (boro-carbides) with extended substitution on both the metal and nonmetal sublattices ... 

Figure 1. Crystallographic relation (schematic) between the structure types of RhB (anti-NiAs type), TaFeB (ordered Fe2P type) and ZrIrjB4 type. Numbers given indicate heights in projection along [001]. Large circles are metal atoms, small circles are B atoms. Metal sublattice of RhB and different modes of filling the voids (squares) generate the different structure types (see text).

Table 2. Crystal Structures and Boron Coordination of Platinum Metal Borides WITH Isolated B Atoms (Owing to Defect Boron Sublattice)...

In the crystal structure of these phases with tetragonal symmetry (P4/mbm, D h) the boron covalent sublattice is formed by chains of octahedra, developing along the c axis and by pairs of B atoms, bonding the octahedra in the xOy plane (see Fig. 1). The resulting three-dimensional skeleton contains tunnels parallel to the c axis that are filled by metal atoms . ... 

The thermal behavior of tetraborides is based on two factors the saturation vapor pressure of the metal, an increase of which increases the dissociation, and the stability of the B—B bonds within the boron sublattice, the strength of the B—B bonds decreasing as the size of the cubic lattice parameter increases. 

The structure of CaB contains bonding bands typical of the boron sublattice and capable of accommodating 20 electrons per CaB formula, and separated from antibonding bands by a relatively narrow gap (from 1.5 to 4.4 eV) . The B atoms of the B(, octahedron yield only 18 electrons thus a transfer of two electrons from the metal to the boron sublattice is necessary to stabilize the crystalline framework. The semiconducting properties of M B phases (M = Ca, Sr ", Ba, Eu, Yb ) and the metallic ones of M B or M B5 phases (Y, La, Ce, Pr, Nd ", Gd , Tb , Dy and Th ) are directly explained by this model . The validity of these models may be questionable because of the existence and stability of Na,Ba, Bft solid solutions and of KB, since they prove that the CaB -type structure is still stable when the electron contribution of the inserted atom is less than two . A detailed description of physical properties of hexaborides involves not only the bonding and antibonding B bands, but also bonds originating in the atomic orbitals of the inserted metal . ... 

Mixed compounds, e.g., in the M-B-N system, where M is a transition metal, are well known with separate B and N sublattices or atoms. Prominent examples are NbBN [22] containing kinked B-chains and isolated nitride ions or Ti(N,C) with a NaCl-like structure containing disordered C and N ions sharing... 

Figure 13 Metal sublattice in Co2TaTe2. Large black circles - Ta, small gray circles -Co. Te atoms not shown...

Turning to pure compounds, such as CaO, MgAl2C>4, or FeS, the same intrinsic defects as described above can occur, but in these cases there is more than one set of atoms that can be affected. For example, in a crystal of formula MX, vacancies might occur on metal atom positions, written VM, or on nonmetal atom positions, given the symbol Vx, or both. Similarly, it is possible to imagine that interstitial metal atoms, written Mi or nonmetal atoms, written X might occur (Fig. 1.3). The different sets of atom types are frequently called a sublattice, so that one might speak of vacancies on the metal sublattice or on the nonmetal sublattice. 

No material is completely pure, and some foreign atoms will invariably be present. If these are undesirable or accidental, they are termed impurities, but if they have been added deliberately, to change the properties of the material on purpose, they are called dopant atoms. Impurities can form point defects when present in low concentrations, the simplest of which are analogs of vacancies and interstitials. For example, an impurity atom A in a crystal of a metal M can occupy atom sites normally occupied by the parent atoms, to form substitutional point defects, written AM, or can occupy interstitial sites, to form interstitial point defects, written Aj (Fig. 1.4). The doping of aluminum into silicon creates substitutional point defects as the aluminum atoms occupy sites normally filled by silicon atoms. In compounds, the impurities can affect one or all sublattices. For instance, natural sodium chloride often contains... 

Across the phase range of all of these systems the metal atoms La, Y, and the like substitute for calcium on the cation sublattice. Charge balance is ensured by the incorporation of additional F ions into the crystals, which, to a first approximation, can be regarded as F interstitials that occupy the unoccupied (F8) coordination polyhedra (Fig. 4.7) ... 

Figure 1. 7-LiJV[02 (layered) and 5-LiM204 (spinel) structures (M = 3d transition metal). M occupy octahedral sites in both structures. In 7-LiJV[02, M and Li (and/or vacancies) alternately occupy (111) planes of the ccp oxygen sublattice. The (111) plane parallel to the M layers is indicated by the black line between the layered and spinel structures. The [111] direction is shown as well. In s-Lii/2Mn02, (111) planes with three-fourths of the Mn alternate with (111) planes with one-fourth of the Mn. Li ions occupy tetrahedral sites in the planes with one-fourth of the Mn. The planes with three-fourths of the Mn are free of Li. In fully lithiated spinel-like 5-Li2Mn204, the Li move into octahedral sites. Three-fourths of the Li are in the (111) plane with one-fourth of the Mn, and one-fourth of the Li are in the plane with three-fourths of the Mn.

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