Anion sub-lattice

It is not necessary for a compound to depart from stoichiometry in order to contain point defects such as vacant sites on the cation sub-lattice. All compounds contain such iirndirsic defects even at the precisely stoichiometric ratio. The Schottky defects, in which an equal number of vacant sites are present on both cation and anion sub-lattices, may occur at a given tempe-ramre in such a large concentration drat die effects of small departures from stoichiometry are masked. Thus, in MnOi+ it is thought that the intrinsic concentration of defects (Mn + ions) is so large that when there are only small departures from stoichiometry, the additional concentration of Mn + ions which arises from these deparmres is negligibly small. The non-stoichiometry then varies as in this region. When the departure from non-stoichio-... 

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. 

Typical examples of compounds with a coordination-type structure are Nb02F and Ta02F, which crystallize in a Re03 type structure [233, 243]. Oxygen and fluorine ions are statistically distributed in the anionic sub-lattice. The compounds are characterized by X Me = 3 and can be described as MeX3 type compounds. 

A Cubic Lattice Showing the Cation and Anion Sub-Lattices... 

Cation Sub-Lattice Anion Sub-Lattice Combined Lattice... 

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). 

In the case of the Frenkel defect, the "square" represents where the cation was supposed to reside in the lattice before it moved to its interstitial position in the cation sub-lattice. Additionally, "Anti-Frenkel" defects can exist in the anion sub-lattice. The substitutional defects axe shown as the same size as the cation or anion it displaced. Note that if they were not, the lattice structure would be disrupted from regularity at the points of ins tlon of the foreign ion. 

All of these point defects are intrinsic to the heterogeneous solid, and cirise due to the presence of both cation and anion sub-lattices. The factors responsible for their formation are entropy effects (stacking faults) and impurity effects. At the present time, the highest-purity materials available stiU contain about 0.1 part per billion of various impurities, yet are 99.9999999 % pure. Such a solid will still contain about IQi impurity atoms per mole. So it is safe to say that all solids contain impurity atoms, and that it is unlikely that we shall ever be able to obtain a solid which is completdy pure and does not contain defects. 

Draw a heterogeneous lattice, using circles and squares to indicate atom positions in a simple cubic lattice. Indicate both Schottky and Frenkel defects, plus the simple lattice defects. Hint- use both cation and anion sub-lattices. 

Temkin was the first to derive the ideal solution model for an ionic solution consisting of more than one sub-lattice [13]. An ionic solution, molten or solid, is considered as completely ionized and to consist of charged atoms anions and cations. These anions and cations are distributed on separate sub-lattices. There are strong Coulombic interactions between the ions, and in the solid state the positively charged cations are surrounded by negatively charged anions and vice versa. In the Temkin model, the local chemical order present in the solid state is assumed to be present also in the molten state, and an ionic liquid is considered using a quasi-lattice approach. If the different anions and the different cations have similar physical properties, it is assumed that the cations mix randomly at the cation sub-lattice and the anions randomly at the anion sub-lattice. 

Let us now look at this slightly more complex case where the Gibbs energy of the components are needed. Until now we have mixed one salt like AC with another like BD. This implies that the fraction of A atoms on the cation sub-lattice has been equal to the fraction of C atoms on the anion sub-lattice. Let us consider a composition like that marked with a cross in Figure 9.8. There are several possible... 

The closely similar reactivities and values measured for the decompositions of KMn04, RbMn04 and CsMn04 [29,41] are consistent with control by the same step (probably electron transfer in the anionic sub-lattice) within very similar reactant... 

Decomposition as discussed in this section has been studied by optical methods, X-ray diffraction, X-ray photoelectron spectroscopy, and infrared absorption. Although this section is concerned to a large extent with disorder resulting from decomposition of the metal sublattice, i.e., metal colloids, all types of disorder remaining after irradiation are considered, and some attention is given to the decomposition of the anion sub lattice. The decomposition of the anion sublattice of small band gap azides is considered in much greater detail in Section E dealing with gas evolution (primarily N2). 

Layer intercalation compounds of ZrSj and HfSj with NH3, N2H4, and RNHNHMe (R = H or Me) have been obtained and the corresponding layer expansions determined. The non-stoicheiometric zirconium and hafnium ditelluride phases ZrTe, (x = 1.74—1.45) and HfTei 94 have been characterized by X-ray diffraction studies. The non-stoicheiometry of the latter compound appears to be in the anion sub-lattice. ... 

Schottky defects. Ionic mobility is explained by the existence of ionic vacancies. In order to maintain electroneutrality, it is necessary to postulate an equivalent number, or concentration, of vacancies on both cationic and anionic sub-lattices. This type of defect occurs in the alkali halides and is shown for KCl in Figure 3.1. Since vacancies exist on both sub-lattices, it is to be expected that both anions and cations will be mobile. 

In contrast to the sulphides of most of the transition metals, sulphides of the refractory metals have quite tight stoichiometry, similar to Cr203, although, in the cases of the refractory-metal sulfides and oxides, the defects appear on the anion sub-lattice. Figure 6.1 compares the rates of oxidation and sulphidation for several of the transition and refractory metals. The low rates of sulphidation of the refractory metals are thought to be due to the low concentrations of defects in the sulphide structures. 

Let us consider vacancy diffusion in an elemental solid or a cation or an anion sub-lattice. The number of jumps per unit time, F, depends on several factors. First, it depends on the jump frequency co towards an adjacent site. Furthermore, it is also proportional to the number of sites to which the atom may jump, i.e., the number of nearest neighbour positions of the atom, Z. Finally, the atom may only jump if a vacancy is located on an adjacent site, and this probability is given by the fraction (concentration) of vacancies in the crystal, N. Thus, r is in this case given by... 

Consider an atom on a normal lattice site of a cation or anion sub-lattice. If this atom is to move by the interstitialcy mechanism, an atom on a nearest neighbour interstitial site has to push the atom on the normal site to a neighbouring interstitial site. Thus for this diffusion mechanism an atom may only diffuse when it has an interstitial atom on a neighbouring site, and as for vacancy diffusion the diffusion coefficient of the atoms is proportional to the fraction (concentration) of interstitial atoms or ions in the sub-lattice. 

As a consequence of the electrostatic forces between the ions in a molten salt there will, at ordinary temperatures, be no mutual randomization of the cations and anions. This led TemkinT to postulate that in an ideal molten salt mixture the different types of anions will be randomly distributed among the anions (i.e., on the anion "sub-lattice"), while similarly the different types of cations will be randomly distributed among the cations. 

To obtain information on the valence band states, one has to start from an approximate expression of M(F). The simplest form is a delta function peaked at the energy F of its first moment, with a weight equal to no (defined p. 26). Due to the quadratic relationship between and Fjj, the first moment of M(F) on the anion sub-lattice is equal to the covalent contribution to the second moment of Na(F), i.e. 

The concentrations of the surface species obey the following equalities in the anion sub-lattice and in adsorbed phase ... 

In view of this, some reference state for the cation distribution needs to be defined to serve as a bench mark to which observed low-temperature states can be referred. Summerville (1973) has coined the phrase operational equilibrium to describe the state achieved after a low-temperature anneal when the anion sub-lattice adjusts to a random cation distribution this should be reproducible. Operational equilibrium will be achieved in principle with samples that have been melted initially, or in practice perhaps with those which have been heated above, say, 2000°C. Any tendency for changes in the random cation distribution thus achieved, which might stem from the stable existence below, say, 1600 C of some intermediate compound of defined composition, would only be revealed if the sample were annealed at close to this temperature for sufficient time for the diffusion-controlled reaction to take place. So it is that for the Zr02-Sc203 system, arc-nlelted samples of compositions between those of the y- and S-phases appear optically, to X-rays, but not to electrons as monophasic. However, after a week s annealing at 1600°C and subsequent quenching, phase separation does occur on a sub-microscopic scale, and is clearly shown in X-ray diffraction. 

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