Bond energy crystals

The fluoride ion is the least polarizable anion. It is small, having a diameter of 0.136 nm, 0.045 nm smaller than the chloride ion. The isoelectronic E and ions are the only anions of comparable size to many cations. These anions are about the same size as K" and Ba " and smaller than Rb" and Cs". The small size of E allows for high coordination numbers and leads to different crystal forms and solubiUties, and higher bond energies than are evidenced by the other haUdes. Bonds between fluorine and other elements are strong whereas the fluorine—fluorine bond is much weaker, 158.8 kj/mol (37.95 kcal/mol), than the chlorine—chlorine bond which is 242.58 kJ/mol (57.98 kcal/mol). This bond weakness relative to the second-row elements is also seen ia 0-0 and N—N single bonds and results from electronic repulsion. 

This qualitative description of the interactions in the metal is compatible with quantum mechanical treatments which have been given the problem,6 and it leads to an understanding of such properties as the ratio of about 1.5 of crystal energy of alkali metals to bond energy of their diatomic molecules (the increase being the contribution of the resonance energy), and the increase in interatomic distance by about 15 percent from the diatomic molecule to the crystal. 

The gaps in the bonding energy spectra of the corresponding molecules (diatoms in the case of the elements) get carried over into the crystals where they are called band-gaps. They determine the stabilities of the bonds, and the crystals. As Chapter 5 discusses, they also determine hardnesses. 

Since chemical hardness is related to the gaps in the bonding energy spectra of covalent molecules and solids, the band gap density (Eg/Vm) may be substituted for it. When the shear moduli of the III-V compound crystals (isoelec-tronic with the Group IV elements) are plotted versus the gap density there is again a simple linear correlation. 

It is shown that the stabilities of solids can be related to Parr s physical hardness parameter for solids, and that this is proportional to Pearson s chemical hardness parameter for molecules. For sp-bonded metals, the bulk moduli correlate with the chemical hardness density (CffD), and for covalently bonded crystals, the octahedral shear moduli correlate with CHD. By analogy with molecules, the chemical hardness is related to the gap in the spectrum of bonding energies. This is verified for the Group IV elements and the isoelec-tronic III-V compounds. Since polarization requires excitation of the valence electrons, polarizability is related to band-gaps, and thence to chemical hardness and elastic moduli. Another measure of stability is indentation hardness, and it is shown that this correlates linearly with reciprocal polarizability. Finally, it is shown that theoretical values of critical transformation pressures correlate linearly with indentation hardness numbers, so the latter are a good measure of phase stability. 

With the atom C strongly bound not only to B but also to the other atoms of a solid-state matrix (i.e., when C fB) the above ratio is small in the parameter mc/mB 1, so that the dominant contribution to the interaction with phonons is provided by the deformation potential. Reorientation probabilities were calculated, with the deformation term only taken into consideration, in Refs. 209, 210. For a diatomic group BC, c A Uv 0.1 eV, whereas eb 10 eV (a typical bond energy for ionic and covalent crystals). A strong binding of the atom C only to the atom B results in the dominant contribution from inertial forces.211 For OH groups, as an example, the second term in Eq. (A2.13) is more than 6 times as large as the first one. 

Here a0 is the lattice parameter of the crystal. An approximate value for the bond energy, e, for this structure where the co-ordination number, Z, equals twelve is given by... 

In the gas phase, ions may be isolated, and properties such as stability, metal-ligand bond energy, or reactivity determined, full structural characterization is not yet possible. There are no complications due to solvent or crystal packing forces and so the intrinsic properties of the ions may be investigated. The effects of solvation may be probed by studying ions such as [M(solvent) ]+. The spectroscopic investigation of ions has been limited to the photoelectron spectroscopy of anions but other methods such as infrared (IR) photodissociation spectroscopy are now available. 

Similar studies have been made on isomerization about C=C double bonds. Careful crystallization of the p-diphenoquinone 21 gives material containing only one of the two isomers. However, in solution isomerization occurs, albeit with an appreciable activation energy. Rapid quenching of a solution in acetic acid gives almost equal amounts of crystals of the two isomers (63). 

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