648 BELL SYSTEM TECHNICAL JOURNAL 



primarily of importance as an aid in classifying and identifying min- 

 erals; and although they do give some information about the arrange- 

 ment of the atoms in planes within the crystal, the information is 

 too meager to permit a determination of the microscopic structure. 

 The latter can be deduced by the methods of x-ray diffraction. X-rays 

 are light waves of very short wave-length and they are diffracted from 

 crystals in much the same way as light is diffracted from a ruled grating. 

 From studies of x-ray diffraction patterns, the arrangements of atoms 

 in a large number of crystals have been determined. Exceedingly 

 strong forces act to hold the atoms in these arrangements and, by appli- 

 cation of the laws of quantum mechanics, we shall try to find them out. 



There is now no question that the elementary building blocks of 

 the material world are primarily electrical and of two sorts.^ The 

 negative particles, electrons, are all alike and have the same charge 

 — e and the same mass m\ the positive particles, atomic nuclei, are 

 not all alike and may differ in charge and mass from one another. 

 The positive charge is always some integral multiple, Z, of the funda- 

 mental charge e and we shall not be concerned with the mass except 

 to say that it varies upwards from about 2,000 times the electron mass. 

 An atom of a chemical element consists of one nucleus surrounded by 

 enough electrons to neutralize its charge ; all atoms of a given chemical 

 element have the same nuclear charge, Z, which is appropriately 

 known as the "atomic number"; atoms having the same nuclear 

 charge but different masses are called "isotopes"; their chemical be- 

 haviors are slightly different, so that it is possible by chemical processes 

 to separate one isotope of a chemical element from the others, but this 

 difference is so slight that we can neglect it here. An atom, then, 

 consists of a number of electrons circulating about and attracted by 

 the nucleus, which, by virtue of its relatively great mass, is effectively 

 an immobile center for their motions. A simple molecule consists of 

 an assemblage of a few such atomic systems and a crystal of an 

 immense number. The fundamental problem of atomic mechanics — 

 which is now solved quite satisfactorily but not yet perfectly— is to 

 find the laws governing the motion of these particles. 



The necessity of finding such laws is made most apparent by con- 

 sidering the failure of the older laws of "classical mechanics," Newton's 

 laws. These laws were satisfactory for dealing with large bodies — 

 but not perfect; for, as is well known, they are approximations to the 

 more adequate laws of relativity — and they were successfully applied 



" Since we are here concerned with problems of a chemical nature, we may disre- 

 gard those particles such as positrons, mesotrons, neutrons, etc., which are concerned 

 with cosmic rays and nuclear processes but not with ordinary atomic behavior. 



