Sublattice anion

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. 

A fraction x of the Mn4+ ions is missing in the manganese sublattice. For charge compensation, each Mn4+ vacancy is coordinated by four protons in the form of OH anions at the sites of the O ions. 

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... 

The compounds that are being reported here are mostly those with combined anions, such as BN anions in nitridoborates. On the other hand, we know of compounds with mixed anions, like the well-known Ti(N,C) in which anions share the same lattice site, or NbBN with separate B and N sublattices. How can these compounds be explained in comparison with compounds having C-N or B-N bonding Are there separate strategies for their synthesis, what are the differences in stability, what are their properties, and what are their structures like These and some other questions will be discussed, mainly for Ca-(B,C,N) and La-B-N systems. 

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). 

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... 

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). 

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. 

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... 

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

The favored defect type in strontium fluoride, which adopts the fluorite structure, are Frenkel defects on the anion sublattice. The enthalpy of formation of an anion Frenkel defect is estimated to be 167.88 kJ mol-1. Calculate the number of F- interstitials and vacancies due to anion Frenkel defects per cubic meter in SrF2 at 1000°C. The unit cell is cubic, with a cell edge of 0.57996 nm and contains four formula units of SrF2. It is reasonable to assume that the number of suitable interstitial sites is half that of the number of anion sites. 

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). 

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. 

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