Ionic arrangement

Fig. 7. Ionic arrangements on different (a) < 100 >, (b) < 110 >, and (c) < 111 > crystallographic surfaces. The interionic separations are given in nanometers for AgBr and in parentheses for AgCl. Values are larger for AgBr because of the relative ionic radii of bromide and chloride.

Fig. 43. Fragments of X-ray powder diffraction patterns of compounds with rock-salt structures that underwent modification to a state of disordered ionic arrangement. 1 - Li3Ta04 2 - LiflbO 3 - Li4Ta04F 4 - Li3Ti03F 5 -LiiFeOiF 6 - LiNiOF (Reflections attributed to LiF are marked by an asterisk).

Fig. 44. IR absorption spectra of Li3Ta04 (1), Li4Ta04F (2), LiJJbOfr (3), Li3Ti03F (4)- rock-salt-type structures with disordered ionic arrangement and high-temperature modifications of Li3Ta04 (5), Li4Ta04F (6), Li3Nb04 (7), LiMO.F (8).

Based on the ionic radii, nine of the alkali halides should not have the sodium chloride structure. However, only three, CsCl, CsBr, and Csl, do not have the sodium chloride structure. This means that the hard sphere approach to ionic arrangement is inadequate. It should be mentioned that it does predict the correct arrangement of ions in the majority of cases. It is a guide, not an infallible rule. One of the factors that is not included is related to the fact that the electron clouds of ions have some ability to be deformed. This electronic polarizability leads to additional forces of the types that were discussed in the previous chapter. Distorting the electron cloud of an anion leads to part of its electron density being drawn toward the cations surrounding it. In essence, there is some sharing of electron density as a result. Thus the bond has become partially covalent. 

Hence, two phases in contact can only be at a difference of electric potential V when the electrical distribution in the interfacial layer gives rise to the necessary moment. Thus, although the equilibrium value of V is determined solely by the chemical composition of the two homogeneous phases, a particular molecular and ionic arrangement must be established in the intervening non-homogeneous layer in order that the conditions of chemical and electrical equilibrium may be simultaneously obeyed. 

This calculation is still hypothetical, in that the actual substance formed when sodium metal reacts with difluorine is solid sodium fluoride, and the standard enthalpy of its formation is -569 kJ mol-1. The actual substance is 311 kJ mol-1 more stable than the hypothetical substance consisting of ion pairs, Na+F (g), described above. The added stability of the observed solid compound arises from the long-range interactions of all the positive Na+ ions and negative F ions in the solid lattice which forms the structure of crystalline sodium fluoride. The ionic arrangement is shown in Figure 7.5. Each Na+ ion is octahedrally surrounded (i.e. coordinated) by six fluoride ions, and the fluoride ions are similarly coordinated by six sodium ions. The coordination numbers of both kinds of ion are six. 

However, many such imaginable microstates would correspond to ionic arrangements that are inconsistent with the ice rule constraints of two covalent O—H bonds and two O H hydrogen bonds to each oxygen atom. To evaluate the fraction of allowed microstates that are consistent with the ice rules, let us consider a chosen O atom and its four tetrahedrally... 

Markov et al. [60,61] proposed an equation for the equivalent electrical conductivity of simple binary molten salt mixtures. In binary systems (MjX + M2X or MXj + MX2) there is the possibility of the following ionic arrangements MjX — MjX M2X — M2X MjX — M2X. The probabilities of forming the combinations MjX - MjX M2X - M2X and MjX - M2X are proportional to X, x2 and 2xxx2, respectively, where Xt and x2 are the molar fractions of the two salts. For monovalent molten salts, the equivalent electrical conductivity of a mixture of these salts, Am, can be written as... 

The cubic fluorite crystal structure (space group Fm3 m) can be described as an fee array of cations in which all the tet interstices are filled with anions and the oet sites are empty. Alternatively, as shown in Figure 2.3, the ionic arrangement can be viewed as a simple cubic array of anions with cations occupying alternate cube centers. 

The bending of the O-H- - -O angle is indeed observed in the structures, where the H-atom becomes disordered [16, 21]. Although this property has been discussed here for the OH-O bond, analogous interdependence between the H-site and molecular/ionic arrangement is also observed for other hydrogen bonds, for example NH- - -N [23]. 

Acid-oxidized SWCNTs were also reacted with lanthanide salts containing Eu, La, and Tb [88], In this study it was found that the lanthanide ions were linked to CNTs through the surface oxygen atoms, forming predominantly ionic arrangements, and thus the oxidized nanotubes acted as primary ligands for these metal ions. The adducts were analyzed using spectroscopic techniques (ETIR, Raman, and photoluminescence) and were characterized structurally by AEM and TEM. 

Table 2 Limiting Radius Ratios, Cation Coordination Numbers, and Ionic Arrangements in Ionic Solids...

The alert reader will have realized that almost all examples given in this chapter are from Na. Of course this was on purpose two of the most important conditions to be fulfilled for the excellent validity of the jellium model, namely (a) that the pseudopotential is local and (b) that the geometrical parts of the ionic arrangement are weak, are best met in NaA. In trying other elements we found only one other material that works comparably well — potassium. But the important point to note is that this simple model serves as a guideline for more complex cases. After electronic shells and plasmons have been found in Na, they have been found in almost all metal clusters. In order to get the same quantitative agreement as in the case of Na one has either to do all-electron calculations or to use non-local pseudopotentials, as has been done in the case of Li [39, 40]. But in these... 

Consider the formation of a saltwater solution. Earlier we pointed out (Section 4.2) that solid ionic compounds are collections of ions held together by attractions between the opposite ionic charges. When an ionic compound dissolves, the orderly ionic arrangement is destroyed as the interionic attractions are overcome. Thus, the attractive forces between water molecules and ions must be stronger than the interionic attractions within the crystal. 

The Fermi wave vector kp = Ep/h is a meaningful quantity (k is a good quantum number ) as long as the scattering is weak, that is, Ak 1/A << l/ kp/2 tr. In this limit, the electronic wave function retains phase coherence over many interatomic distances as illustrated in Fig. 2.9(a). In the integral of Eq. 2.7, the ionic arrangement is described by S Q), the liquid structure factor which we discuss in detail in later chapters. The scattering characteristics of the ions are represented by the so-called form factor v(Q)... 

The lattice energy results from electrostatic interactions among ions, so its magnitude depends on ionic size, ionic charge, and ionic arrangement in the solid. Therefore, we expect to see periodic trends in lattice energy. 

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