18 BELL SYSTEM TECHNICAL JOURNAL 



In the solid structure neighboring atoms influence the motion and 

 distribution of electrons, particularly in the third part of the third shell 

 {M shell) and the first part of the fourth shell (4^ shell). In Fig. 10 

 the difference between a free atom and one that is part of a metal is 

 illustrated. Each of the ten places for electrons in the 2)d shell is 

 represented by an area which is shaded if that place is occupied. The 

 distribution corresponds in (a) to an isolated atom of nickel, in (&) 

 to a nickel atom in a metal ; in the latter situation there is on the average 

 0.6 electron per atom in the 45 shell (these electrons are loosely bound 

 and are the free electrons responsible for electric conduction) and a 

 vacancy or hole of 0.6 electron per atom in the 3J-shell.^ In the 4^ 

 shell the number of electrons with + and with — spin are almost 

 exactly equal, but in the Zd shell all of the spaces for + spin are filled. 

 The difference between the numbers of + and — spins is equal to the 

 net magnetic moment per atom. Experimentally the difference in 

 the number of + spins and — spins in an atom is determined from the 

 saturation intensity of magnetization at absolute zero. When this 

 difference is one the atom has a moment of one Bohr magneton, 



MB = 9.2 X 10"^^ erg/gauss 



consequently the number of Bohr magnetons can be calculated from 

 the atomic weight, A , and the density, d : 



Bohr magnetons/atom = |S = — ■-, • 



IXBd 



In Fig. 10 (/) the diagram for nickel is repeated, this time with the 

 tops of the unfilled positions on the same level to bring out an analogy 

 with the filling of vessels with water. Diagrams for manganese, iron, 

 cobalt, nickel and copper are shown in parts {c) to (g). In each case 

 the 18 electrons in closed shells are not shown. In iron the situation is 

 somewhat different from that in nickel, neither the 3d-\- nor the M — 

 shell is filled. This follows from the relative constancy of the number 

 of electrons in 45, from the excess of holes in Zd-{- over those in Zd — 

 (jS = 2.2), and from the total number, 26, of extra-nuclear electrons. 



The distribution in space of electrons belonging to the Zd and 4^ 

 shells is known approximately ^ and is depicted in Fig. 11. In (a) the 

 ordinate shows the number of electrons there are at various distances 

 from the nucleus. The 3d shell is thus seen to be a rather dense ring 



6E. C. Stoner, Phil. Mag., 15, 1018-1034 (1933); N. F. Mott, Proc. Phys. Soc, 

 47, 571-588 (1935); L. Pauling, Phys. Rev., 54, 899-904 (1938). 



^ Calculations were based on the equation given by J. C. Slater, Phys. Rev., 36, 

 57-64 (1930). 



