Cohesive alkali halides

Cortona P 1992 Direct determination of self-consistent total energies and charge densities of solids A study of the cohesive properties of the alkali halides Phys. Rev. B 46 2008... 

The ionic bond is the most obvious sort of electrostatic attraction between positive and negative charges. It is typified by cohesion in sodium chloride. Other alkali halides (such as lithium fluoride), oxides (magnesia, alumina) and components of cement (hydrated carbonates and oxides) are wholly or partly held together by ionic bonds. 

The simple theory of electronegativity fails in this discussion because it is based merely on electron transfer energies and determines only the approximate number of electrons transferred, and it does not consider the interactions which take place after transfer. Several calculations in the alkali halides of the cohesive energy (24), the elastic constants (24), the equilibrium spacing (24), and the NMR chemical shift 17, 18, 22) and its pressure dependence (15) have assumed complete ionicity. Because these calculations based on complete ionicity agree remarkably well with the experimental data, we are not surprised that the electronegativity concept of covalency fails completely for the alkali iodide isomer shifts. 

Table 1.3. Cohesive energy parameters of some alkali halides with NaCl structure ...

Repulsive interactions between ions farther apart than the next nearest neighbor distance are neglected. This is the usual assumption in calculating the cohesive energies of alkali halide crystals (4, 5, 9) and is based on the fact that the exponential forms representing these interactions die away rapidly. 

Strongly for the ionic crystals, yet the bulk modulus for the alkali halides varies as d. The cl trend for the bulk modulus will show up in the study of simple metals, and in terms of the pseudopotentials that will be used in the study of simple metals, d" -dependence takes on a particularly fundamental role. In Problem 15-3, the simple metal theory is used to give a good account of the bulk modulus in C, Si, and Gc. It should be noted also that the simple metal theory docs not give a good account of cohesive energy itself there is much cancellation between terms for that property, and there are important contributions (for example, that do not vary as... 

Let us then turn to the ionic solids themselves. Kim and Ciordon (1974) recalculated the total energy for the alkali halides that form rocksalt structures and thereby computed from first principles the lattice spacing, the separation energy (the energy per ion pair required to separate the solid into isolated ions -this comes from the theory more naturally than does the cohesive energy, which is relative to isolated neutral atoms), and the bulk modulus. For KCI, the agreement of the values for the three properties with experimental values is typical of the calculations. The calculated (and in parentheses, the experimental) values for KCI are 3.05 (3.15) A, 175 (166) kcal/mole, and 2.3 (1.9) x 10 dync/cmA Again we may say that the interactions are quite well understood in terms of the microscopic theory. We shall return to the interpretation of these properties in terms of simple models in Section 13-D. 

Although the simple model does give a semiquantitative account of bond length, cohesion, and compressibility for KCl, it is less useful to list the results of doing the arithmetic for the other alkali halides than merely to list the experimental parameters, as in Table 13-4. Predictions from the simple model will be approximately as accurate as the KCl results are, and more accurate models can be fitted to the experimental parameters if one wishes. Extension of the model to ions... 

Yamashita, J., and S. Asano (1983a). Cohesive properties of alkali halides and simple oxides in the local-density formalism. J. Phys. Soc. Jpn. 52, 3506-13. 

Table 5.3 shows the experimental values of the cohesive energies and the semi-theoretical values, calculated for pure ionic and pure covalent bonding. Table 5.3 includes most of the available data on AB solids. The omitted examples, mostly alkali halides and alkaline-earth chalcogenides, show no unexpected features. 

Our immediate concern is whether Eg, or possibly E, serves as a suitable measure of chemical hardness just as (/ — A) does for molecules. Examination of the data in Table 5.5 shows that it does. There is a good correlation btween Eg and the cohesive energy, as long as related solids are compared. That is, the 4-4 compounds show Eg falling just as AE coh does. The alkali halides also are correlated with each other, but not with the 4-4 cases. In the 2-6 examples, we can compare the CN6 compounds with each other, but not with the CN4 cases, which have their own relationship. The 3-5 solids form their own family for CN4, but there are no Eg data for the ionic 3-5 cases, which probably belong to a different family. 

Under elevated pressures, the rocksalt structure transforms into the CsCl structure. Changes in lattice constants and measurements of other physical properties have provided much quantitative information for empirical fits to equations of state. Modern theoretical tools are used for obtaining a deeper understanding of charge being transferred back from the anion towards the cation in the alkali halides. However, as can be seen from calculations of their cohesive properties, even nowadays there are problems to be solved for such simple structures. The data for the halide ions, in particular, are quite useful and may be transferred to other halide systems, and give good predictive values for more complex systems. 

The increase in cohesive energy in the 2-2 salts explains the generally lower solubility of these salts (for example, the sulfides, as compared with that of the alkali halides). The greater the cohesive energy, the more difficult it is for a solvent to break up the crystal. 

Traditionally, the classification of crystals includes an important category the ionic crystals. These crystals are composed of ions, and the cohesion arises from the balance between the attractive coulombian forces and short-distance repulsive interactions, which prevents the collapse of the crystal This category includes the alkali halides, all crystals possessing a similar structure (MgO, CaO), the oxy-salts (carbonates, nitrates, sulfates, silicates). Sometimes even corundum is included in this categoryI... 

Table 15.7 The properties of some alkali halides, ro is the distance between neighbor atoms S is bulk modulus coh is the cohesive energy.

The picture just painted is much too black. Models to be discussed in Section 3.1 do give very accurate accounts of the cohesive energies of most of the alkali halides, a good result obtained by allowing the ions to be less than rigid. The main feature of Figure 2— that most of the alkali halides have the sixfold-coordinated NaCl structure—comes out of those deformable-ion calculations as well. (Actually, the calculations predict that all alkali halides have the NaCl... 

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 isothermal compressibilities of halides of the alkali metals, alkaline earth metals, and divalent transition- and post-transition-metals are inversely correlated with their cohesive energies [221] in analogy with the expansibilities with a similar rationalization ... 

Fig. 3.4 The surface tension, a, of molten salts plotted against their cohesive energy density, ced. Equation (3.3) pertains to the red symbols alkali metal halides ( ), alkaline earth metal halides (A). other alkali metal salts with univalent anions ( ) Eq. (3.4) pertains to the alkali metal salts with divalent anions ( ) outliers from Eq. (3.3) (O), also post-transition metal halides and AgNOs [ ], and lanthanide chlorides ( ) (From Marcus [156] by permission of the publisher (Elsevier))...

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