Interatomic distance alkali halides

The Alkali Halides.—In Table V are given the experimental interatomic distances for the alkali halides with the sodium chloride structure, together with the sum of the radii of Table II. 

A more direct link with molecular volumes holds for alkali halides, because the lattice energy (IT) is inversely proportional to interatomic distance or the cube root of molecular volume (MV). The latter has been approximated by a logarithmic function which gives a superior data fit. Plots of AH against log(MV) are linear for alkali halides 37a). Presumably, U and AH can be equated because AH M, ) is a constant in a series, and AH (halide )) is approximately constant when the anion is referred to the dihalogen as the standard state. 

Figure 13 Interatomic distances in alkali halides, arranged in cationic and anionic series.

The concept that the ionic radius is relatively independent of the structure of the solid arose intuitively from experimental observations carried out on alkali halides, which are ionic solids par excellence. Figure 1.3 shows the evolution of interatomic distances in alkali halides as a function of the types of anion and cation, respectively. Significant parallelism within each of the two families of curves may be noted. This parallelism intuitively generates the concept of constancy of the ionic radius. 

TABLE 1.8 Interatomic distances of some alkali halides, TMx/pm... 

For the alkali metal halides for which vapor interatomic-distance data and heat-of-sublimation data are available, the M+—X distances computed... 

Table LXIII. Interatomic Distances in Gaseous Alkali Halides (A)...

The vibrational frequency was estimated from those of Til(g), TlCl(g), ZrCl(g), and the alkali halides. The ground state configuration was assumed to be analogous to the ground term of TiCl(g) as given by Shenyavskaya et al. ( ). The interatomic distance was estlamted from those of TiBr(g), Til (g) and Zrl (g). 

It is clear that from the observed interionic distances we can deduce only the sum of two ionic radii, but that if any one radius is known then other radii may be found. Various independent methods are available for estimating the radii of certain ions, and the values so determined, taken in conjunction with data from the crystal structures not only of the alkali halides but also of many other compounds, lead to the semi-empirical ionic crystal radii shown in table 3.02 and in fig. 3.05. The interpretation of the radii given in this table is subject to a number of qualifications which will be discussed below. For the present, however, it is sufficient to treat the radii as constant and characteristic of the ions concerned. For the alkali halides with the sodium chloride structure it will be seen that the interatomic distances quoted in table 3.01 are given with fair accuracy as the sum of the corresponding radii from table 3.02. 

Expressions for the force constant, i.r. absorption frequency, Debye temperature, cohesive energy, and atomization energy of alkali-metal halide crystals have been obtained. Gaussian and modified Gaussian interatomic functions were used as a basis the potential parameters were evaluated, using molecular force constants and interatomic distances. A linear dependence between spectroscopically determined values of crystal ionicity and crystal parameters (e.g. interatomic distances, atomic vibrations) has been observed. Such a correlation permits quantitative prediction of coefficients of thermal expansion and amplitude of thermal vibrations of the atoms. The temperature dependence (295—773 K) of the atomic vibrations for NaF, NaCl, KCl, and KBr has been determined, and molecular dynamics calculations have been performed on Lil and NaCl. Empirical values for free ion polarizabilities of alkali-metal, alkaline-earth-metal, and halide ions have been obtained from static crystal polarizabilities the results for the cations are in agreement with recent experimental and theoretical work. 

The ionization potentials in the halides of hydrogen and alkali metals indicate that the electron is removed from the halogen atom their values also depend on the interatomic distances (Table SI.2). As the bond distance (d) and the negative charge iq) of the halogen atom increase, /(MX) decreases and ultimately approaches the electron affinity of the corresponding halogen atom A, see below) when q = -. Therefore the ionization potentials of MX molecules (M = H, Li, Na, K, Rb, Cs X = F, Cl, Br, I) can be estimated similarly to Eq. 1.5, as... 

The first theoretical estimate of ionic radii has been made by Pauling [172] who partitioned interatomic distances in the crystals of alkali halides comprising iso-electronic ions (i.e. Na+ F , K+CP, Rb+Br" and Cs+P) in an inverse relation to their effective nuclear charges, in accordance with Eq. 1.23, and obtained the following radii K+ 1.33, CP 1.81, Rb+ 1.48, Br 1.95, Cs+ 1.69 and P 2.13 A the radii of F (1.36 A) and 0 (1.40 A) were derived by additivity. These values agree with the empirical radii, especially the latest system of Brown [173]. Batsanov [174] applied Pauling s idea to molecular and crystalline halides MX (with iso-electronic M"+ and X ions) and calculated the halide radii for different Ac. This approach was applied also to the molecular and crystalline iso-electronic oxides and chalcogenides (Table 1.14). 

There are several methods for determining ionic radii from physical characteristics of atoms and crystals. Thus, Fumi and Tosi [209] derived ionic radii (similar to the bonded ones) for alkali halides, using the Born model of crystal lattice energy with experimental interatomic distances, compressibilities and polarizabilities. Rossein-sky [210] calculated ionic radii from ionization potentials and electron affinities of atoms, his results were close to Pauling s. Important conclusions can also be drawn from the behaviour of solids under pressure. Considering metal as an assembly of cations immersed into electron gas, its compressibility at extremely high pressures... 

In Table 5.4 there are listed interatomic distances in MX solids of the structure type NaCl (Bl), where atoms have octahedral coordination. These compounds contain metal atoms with low ENs, forming bonds of an essentially ionic character. Therefore compounds with the B1 structure are usually considered as typically ionic. Comparison of interatomic distances in structures of the B3 and Bl types (Tables 5.3 and 5.4) shows that such increase in coordination of atoms is accompanied by an increase of the bond lengths by a factor of 1.080(9). Interatomic distances in crystal of this type are additive. Differences of the bond lengths in halides MX are Afi Na-Li = (f(Na—X) — (f(Li—X) = 0.28 A, Ai K-Na = 0.34 A, Ai Rb-K = 0.015 A, Afi Cs-Rb = 0.18 A, A /cs-NH4 = 0-17 A, A /NH4 Ag = 0.52 A, A fxi-Ag = 0.41 A. This principle works very well because of similar character of chemical bonds (for example, for halides K, Rb and Cs the deviation is ca. 5 %). On the contrary, if we compare hydrides and fluorides of alkali metals where the bond character is different, we get Ad = /(M-H)- /(M-F) = 0.15 A 35 %. In the case of oxides and chalco-genides of the MX type, the additive principle is correct within 8 %. Comparison of data in Tables 3.2, S3.1 and 5.4 shows, that the ratio of the bond lengths for = 1 to... 

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