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 there- 

 fore Agents in Nature able to make the Particles of Bodies stick to- 

 gether by very strong Attractions. And it is the Business of experi- 

 mental 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 i 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 to- 

 gether in crystals. 



A crystal is a regular array of atoms. The regularity of this atomic 

 array is frequently exhibited in the macroscopic appearance of the 

 crystal. A crystal of potassium chloride — sylvine — is a good ex- 

 ample (Fig. lA). The natural growth faces of the crystal are parallel 

 to planes passing through the atoms, which are arranged in the micro- 

 scopic array pictured in Fig. IB. It is evident that the microscopic 

 arrangement of the atoms in the crystal is one of its most basic features. 

 In sylvine the atoms are arranged on the corners of cubes in an alter- 

 nating fashion. The arrangement of the atoms in the crystal is called 

 a "lattice." Sodium chloride— rock salt — has the same arrangement 

 as sylvine and the type lattice pictured in Fig. IB is known as a "sodium 

 chloride lattice." The distance between atoms in a given lattice is 

 specified by giving the value of the "lattice constant," which for a cubic 

 crystal is defined as the distance between like atoms along a line 

 parallel to a cube edge. Lattice constants are usually expressed in 

 angstroms; 1 angstrom = lA = 10~^ cm. The lattice constant of 

 sylvine, designated by "a" in Fig. IB, is 6.28A. Figure IC suggests 

 how a large number of atoms, arranged as in Fig. IB, produce the 

 shape of the crystal photographed for Fig. lA. Studies of the direc- 

 tions of the natural growth faces and cleavage faces of crystals are 



1 "Opticks" 3rd ed., 1721, p. 363. 



