The Quantum Physics of Solids, I. The Energies of Electrons in Crystals

ff I V HE parts of all homogeneal hard Bodies which fully touch one A another, stick together very strongly . . . I . . . infer from their Cohesion, that their Particles attract one another by some Force, which in immediate Contact is exceeding strong, at small distances 645 646 ' BELL SYSTEM TECHNICAL JOURNAL performs the chymical Operations above mention'd, and reaches not far from the Particles with any sensible Effect. . . . There are therefore Agents in Nature able to make the Particles of Bodies stick together by very strong Attractions. And it is the Business of experimental Philosophy to find them out." But it was not destined for experimental philosophy to finish the business which Sir Isaac Newton set for it in the above words 1 until two centuries had elapsed. Only since the advent of quantum mechanics have scientists had laws capable of explaining the cohesive forces of solid bodies and predicting their numerical magnitudes. The new laws were developed first in order to explain the behaviors of independently acting atoms but, as we shall see, they are laws capable of extension to systems containing large numbers of atoms and thus to solid bodies. The fact that a solid body remains a solid body, resists being pulled apart, and exerts the cohesive forces of which Newton wrote, is explained by showing from theory that atoms packed together in a solid are in a state of low energy, and to change the state requires the expenditure of work. In this paper we shall describe how the quantum mechanical concepts developed for isolated atoms are applied to interacting atoms and lead to methods of calculating the energies and forces binding atoms together in crystals.