Alkali metals, cohesive energies

It is certain, however, that the 3d electrons contribute to an important extent to the cohesion of the transition metals with their very low volatility, in contrast to the idea of Mott and Jones who, on the basis of the band theory, assumed that the bonding is determined essentially by the 4s electrons and even by less than one. This would make them comparable to the alkali metals in lattice energy and volatility. 

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... 

PW91 appears to improve the properties of both simple[43,110] and transition metals[lll]. For example, LSD tends to underestimate bond lengths of molecules and solids, including metals. Even in the alkali metals Li and Na, which are often compared with the uniform electron gas, this error is about 4%. PW91 expands the lattice, producing lattice constants in better agreement with experiment, as seen in Table 8. GGA s also improve cohesive energies, just as they improve atomization en-... 

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 experimental lattice energy at the static limit can also be evaluated with respect to the isolated ions, and it is easily obtained by including the ionization energy of the alkali metal (Na) and the electron affinity of the halogen (Cl). According to The Handbook of Chemistry and Fhysics the ionization energy of sodium is —495.8 kj/mol and the electron affinity of chlorine is 348.7 kj/mol. Then, the experimental cohesive energy from ions is 791.3 kj/ mol at the static limit. 

Table 5.2 Cohesive energies and their components (in tydberg per atom) of alkali metals. Cj and mefF are given in atomic units.

In Table 5.2, the results of calculations of the cohesive energy and the experimental data are presented. The agreement is satisfactory for aU alkali metals except for lithium (the discrepancy between calculated and measured values is 18%) and rubidium (23%). For other metals the fit is good (from 5 to 8%). The cohesive energies are small varying from 0.83 to 1.59 eV/atom, so that the alkah metals are not strongly bound. Indeed, the metals are mechanically soft. 

Interest in clusters of the IIA (Mg, Ca, Sr, Ba and Ra) and IIB (Zn, Cd and Hg) elements has been motivated mainly by the fact that these systems may undergo a nonmetal-to-metal transition in their electronic structure as a function of size. The basis for this expectation is simple. On the one hand, bulk samples of these elements are clearly metallic, although, not surprisingly, key properties such as conductivity and plasma frequencies show that their electronic structure (and the Fermi surface in particular) deviates from the ideal free-electron picture much more than in the case of alkali metals [50]. On the other hand, experimental data show that the cohesive energy, equilibrium distances, vibrational frequencies and excitation energies for the homonuclear dimers of these elements are close to those expected for weakly bound van der Waals systems. 

The first two columns are the alkali metals with only s electrons forming a weak metallic bond. The bond energies rise rapidly in the transition metals, peak, and then fall to a minimum at column 12. But something funny seems to be going on in columns 4-9 in the atoms with 3d electrons. Then another rise and fall in the cohesive energies is seen with a peak occurring at column 14. How do we account for this behavior ... 

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))...

The meaning of the B parameters is rather obscure. It is expected that the larger the attractive forces between the ions, the less ready would they be to move in an external force gradient, hence the smaller the fluidity. This expectation is borne out only for the alkali metal fluorides, for which B decreases linearly with their cohesive energy densities. For 51 other molten salts of the 1 1, 1 2, and 1 3 types the B parameters increase linearly with the cohesive energy (that is, with ceti. z ), but with cOTisiderable scatter [256]. 

Fig. 4. Trends in cohesive energies (heats of atomization) for alkali metals (column lA) and tetravalent nontransition metalloids (column IVB) of the periodic table. The abscissa is the mean inter-electronic spacing of the valence electrons expressed in units of the Bohr radius aQ.

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