Sublattice cation

In theory, the III-V compound semiconductors and their alloys are made from a one to one proportion of elements of the III and V columns of the periodic table. Most of them crystallize in the sphalerite (zinc-blende ZnS) structure. This structure is very similar to that of diamond but in the III-V compounds, the two cfc sublattices are different the anion sublattice contains the group V atoms and the cation sublattice the group III atoms. An excess of one of the constituents in the melt or in the growing atmosphere can induce excess atoms of one type (group V for instance) to occupy sites of the opposite sublattice (cation sublattice). Such atoms are said to be in an antisite configuration. Other possibilities related with deviations from stoichiometry are the existence of vacancies (absence of atoms on atomic sites) on the sublattice of the less abundant constituent and/or of interstitial atoms of the most abundant one. 

The appearance of cation vacancies in carbides and nitrides is much less characteristic than vacancies in nonmetal sublattices. Cation defects were... 

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... 

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. 

Agl above 149 °C, the design of multinary compounds by adding cations or anions to form a suitable sublattice for fast ionic motion is necessary. 

Ha. Transfer occurs within anionic or cationic sublattice... 

AgsSBr, /3-AgsSI, and a-AgsSI are cationic conductors due to the structural disorder of the cation sublattices. AgsSI (see Fig. 5) has been discussed for use in solid-electrolyte cells (209,371, 374,414-416) because of its high silver ionic conductivity at rather low temperatures (see Section II,D,1). The practical use seems to be limited, however, by an electronic part of the conductivity that is not negligible (370), and by the instability of the material with respect to loss of iodine (415). 

Note that, in general, anions are larger in size than cations due to the extra electrons present in the former. A hexagonal lattice is shown in 3.1.6. with both Frenkel and Schottky defects, as well as substitutional defects. Thus, if a cation is missing (cation vacancy) in the cation sublattice, a like anion will be missing in the anion sub-lattice. This is known as a Schottky defect (after the first investigator to note its existence). 

Extrinsic Defects Extrinsic defects occur when an impurity atom or ion is incorporated into the lattice either by substitution onto the normal lattice site or by insertion into interstitial positions. Where the impurity is aliovalent with the host sublattice, a compensating charge must be found within the lattice to pre-serve elec-troneutality. For example, inclusion of Ca in the NaCl crystal lattice results in the creation of an equal number of cation vacancies. These defects therefore alter the composition of the solid. In many systems the concentration of the dopant ion can vary enormously and can be used to tailor specific properties. These systems are termed solid solutions and are discussed in more detail in Section 25.1.2. 

Cation Vacancies If the cation of the host structure has a lower charge than the cation that is replacing it, cation vacancies may be introduced for the preservation of electroneutrality. Alternatively, the substitution of an anion by one of lower charge may also achieve this in certain systems. For example, NaCl is able to dissolve a small amount of CaCl2, and the mechanism of solid-solution formation involves the replacement of two Na+ ions by one Ca ion, leaving one vacancy on the Na" sublattice, Nai 2xCa Cl (where x denotes a vacancy). 

Anion Vacancies If the cation of the host structure has a higher charge than the replacing cation, electroneutrality may be maintained by introducing vacancies into the anion sublattice. The best-known examples of anion vacancies occur in the stabilized zirconia, such as calcium- or yttrium-stabilized zirconia. The high-temperature... 

In ferrites, the magnetization of the B-sublattice with octahedrally coordinated cations is usually parallel to the applied field whereas the magnetization of the /l-sublattice with tetrahedrally coordinated cations is in the opposite direction. 

Every ionic crystal can formally be regarded as a mutually interconnected composite of two distinct structures cationic sublattice and anionic sublattice, which may or may not have identical symmetry. Silver iodide exhibits two structures thermodynamically stable below 146°C sphalerite (below 137°C) and wurtzite (137-146°C), with a plane-centred I- sublattice. This changes into a body-centred one at 146°C, and it persists up to the melting point of Agl (555°C). On the other hand, the Ag+ sub-lattice is much less stable it collapses at the phase transition temperature (146°C) into a highly disordered, liquid-like system, in which the Ag+ ions are easily mobile over all the 42 theoretically available interstitial sites in the I-sub-lattice. This system shows an Ag+ conductivity of 1.31 S/cm at 146°C (the regular wurtzite modification of Agl has an ionic conductivity of about 10-3 S/cm at this temperature). 

Group II acceptors in III-V compounds normally occupy an atomic site of the cation sublattice (group III atoms). We will discuss spectroscopic results obtained on hydrogenated GaAs doped with zinc and beryllium and on InP doped with zinc. 

In crystals of more complex formula, such as titanium dioxide, TiC>2, a Schottky defect will consist of two anion vacancies and one cation vacancy. This is because it is necessary to counterbalance the loss of one Ti4+ ion from the crystal by the absence of two O2- ions in order to maintain composition and electroneutrality. This ratio of two anion vacancies per one cation vacancy will hold in all ionic compounds of formula MX2. In crystals like A1203, two Al3+ vacancies must be balanced by three O2- vacancies. Thus, in crystals with a formula M2X3, a Schottky defect will consist of two vacancies on the cation sublattice and three vacancies on the anion sublattice. These vacancies are not considered to be clustered together but are distributed... 

The estimation of the number of Frenkel defects in a crystal can proceed along lines parallel to those for Schottky defects by estimating the configurational entropy (Supplementary Material S4). This approach confirms that Frenkel defects are thermodynamically stable intrinsic defects that cannot be removed by thermal treatment. Because of this, the defect population can be treated as a chemical equilibrium. For a crystal of composition MX, the appropriate chemical equilibrium for Frenkel defects on the cation sublattice is... 

Frenkel defects on the cation sublattice of a sodium chloride structure compound. Frenkel defects on the anion sublattice of a fluorite structure compound. 

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) ... 

When Schottky defects are present in a crystal, vacancies occur on both the cation and anion sublattices, allowing both cation and anion vacancy diffusion to occur (Fig. 5.12a). In the case of Frenkel defects interstitial, interstitialcy, and vacancy diffusion can take place in the same crystal with respect to the atoms forming the Frenkel defect population (Fig. 5.12b). 

In densely packed solids without obvious open channels, the transport number depends upon the defects present, a feature well illustrated by the mostly ionic halides. Lithium halides are characterized by small mobile Li+ ions that usually migrate via vacancies due to Schottky defects and have tc for Li+ close to 1. Similarly, silver halides with Frenkel defects on the cation sublattice have lc for Ag+ close to 1. Barium and lead halides, with very large cations and that contain... 

Frenkel defects on the anion sublattice show only anion migration and hence have fa close to 1. The alkali halides NaF, NaCl, NaBr, and KC1 in which Schottky defects prevail and in which the cations and anions are of similar sizes have both cation and anion contributions to ionic conductivity and show intermediate values of both anion and cation transport number. 

The introduction of an impurity cation onto one sublattice of perovskite structure oxides can change the defects on the other cation sublattice, on the oxygen sublattice,... 

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