. The Bell System technical journal . th lattice constant a Angstroms, Oo = a^l2. Substituting the expressionfor N{E) into the equation for Ep gives Ef = \ Sraax. = (v) Expressing Ef in atomic units and fto in terms of the lattice constant, we find Ef = (vi) This is the equation of the curve for Figure 15. The values of Emax. calculated fromthe above equations for a series of metals are Metal Li Na K Rb Cs Cu Ag Au £max.(ev) H. M. Krutter, Phys. Rev., 48, 664 (1935). THE QUANTUM PHYSICS OF SOLIDS 683 we should expect encroachment
. The Bell System technical journal . th lattice constant a Angstroms, Oo = a^l2. Substituting the expressionfor N{E) into the equation for Ep gives Ef = \ Sraax. = (v) Expressing Ef in atomic units and fto in terms of the lattice constant, we find Ef = (vi) This is the equation of the curve for Figure 15. The values of Emax. calculated fromthe above equations for a series of metals are Metal Li Na K Rb Cs Cu Ag Au £max.(ev) H. M. Krutter, Phys. Rev., 48, 664 (1935). THE QUANTUM PHYSICS OF SOLIDS 683 we should expect encroachment repulsions between these Ions whentheir wave functions begin to overlap. In the band picture this repul-sion results from the spreading of the 3d band; since the band spreadsmore to higher energies than to lower energies and since it is full, theaverage energy of an electron in it increases as the lattice constantdecreases. Thus the same result, repulsion between closed shells, is 0 3d I 2 - O 5 , --0,8 0 I 2 3ao4 5 6 7 8 9 10 II LATTICE CONSTANT IN ANGSTROMS Fig. 16—Energy bands for copper versus lattice constant. found for the ions in a metal as for the rare gas atoms. For elementswhose atoms have partially filled 3d levels the situation is quite differ-ent. For them only part of the levels of the 3d band will be filledand there will be a decrease in the energy of the 3d electrons in themetal as compared to the atom. This has been proposed by Seitz andJohnson as an explanation of the fact that the highest binding energiesfor the metals of a transition series occur for those that have approxi-mately half-filled 3d bands and for which consequently nearly all ofthe 3d electrons have lower energies than in the atomic state. ^^ Thevery high melting point metals—columbium, molybdenum, tantalum,and tungsten—come approximately at the middle of their transitionseries. In Table II we give the binding energies for a number of thetransition elements.
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