Cohesion in Solids

In addition to symmetry, the nature of the bonding forces between atoms provides a useful way to classify solids. This classification does indeed lead to an understanding of the remarkable differences in the chemical and physical properties of different materials. We now consider crystals held together through ionic, metallic, or covalent bonding interactions, and the one class of solids held together by intermolecular forces. 

FIGURE 21.16 The sodium chloride, or rock-salt, structure. On the left, the sizes of the Na ions (purplish pink) and the Cr ions (green) are drawn to scale. On the right, the ions are reduced in size to allow a unit cell (shown by red lines) to be outlined clearly. 

FIGURE 21.18 Two ionic lattices in the fee system. A single (nonprimitive) cubic unit cell of each is shown. 

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So far, our quantum mechanics examples have been rather far afield from questions of immediate interest to our study of solids. In particular, we aim to see what light quantum mechanics sheds on the origin of bonding and cohesion in solids. To do so, in this introductory chapter we consider two opposite extremes. Presently, we consider the limit in which each atom is imagined to donate one or more electrons to the solid which are then distributed throughout the solid. The resulting model is the so-called electron gas model and will be returned to repeatedly in coming... 

From a quantum mechanical perspective, the starting point for any analysis of the total energy is the relevant Hamiltonian for the system of interest. In the present setting, it is cohesion in solids that is our concern and hence it is the Hamiltonian characterizing the motions and interactions of all of the nuclei and electrons in the system that must be considered. On qualitative grounds, our intuition coaches us to expect not only the kinetic energy terms for both the electrons and nuclei, but also their mutual interactions via the Coulomb potential. In particular, the Hamiltonian may be written as... 

From the standpoint of cohesion in solids, we have seen that the Fermi energy... 

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