. The Bell System technical journal . s vary as — 18e0 and that there is alsoone chlorine nucleus with charge +17e whose energy varies as -\-17ecj).This leaves a net effect of —ecj) for the Cl~ ions. Similarly a net effectof —e(f> comes from the electrons and nuclei of the Na+ ions. As inthe case of the ionic method the sum, — 2e, of these energies reallycontains each ionic energy twice and the total electrostatic energy perNaCl molecule is —ecf). So far as calculating energies is concerned,the two methods give equivalent results; the advantage, if any, lies ^ Phys., 75, 1 (1932).^^
. The Bell System technical journal . s vary as — 18e0 and that there is alsoone chlorine nucleus with charge +17e whose energy varies as -\-17ecj).This leaves a net effect of —ecj) for the Cl~ ions. Similarly a net effectof —e(f> comes from the electrons and nuclei of the Na+ ions. As inthe case of the ionic method the sum, — 2e, of these energies reallycontains each ionic energy twice and the total electrostatic energy perNaCl molecule is —ecf). So far as calculating energies is concerned,the two methods give equivalent results; the advantage, if any, lies ^ Phys., 75, 1 (1932).^^ Phys., 75, 19 (1932). 22 Jour. Chem. Phys., i, 643 (1933). 23 J, C. Slater and W. Shockley, Phys. Rev., 50, 705 (1936). 688 BELL SYSTEM TECHNICAL JOURNAL with the ionic method rather than the band method because of themore immediate physical interpretation of the former. We may remark that in the discussion of metalHc sodium, it was notnecessary to consider the potential energy of the nuclei and the closed. u ^ •« an^ ® ° 2 * ^ ^ 20 LATTICE CONSTANT IN ANGSTROMS Fig. 18—Energy bands for sodium chloride versus lattice constant. shell electrons as was done in NaCl. This is because sodium metal isnot ionic—although we think of it as consisting in part of Na+ ions,the electrostatic forces between them are suppressed by the shieldingeffect of the electron gas. In an ionic crystal, like NaCl, there is noelectron gas and the coulomb energy must be considered in the mannerdescribed above. Energy Bands for Other Crystals There are chemical compounds which lie between the homopolar and ionic types. For example in the sequence of compounds NaF, MgO, AIN, SiC the compounds are progressively less and less definitely ionic—the least ionic, SiC or carborundum, being homopolar. Simi- THE QUANTUM PHYSICS OF SOLIDS 689 larly there are compounds, in particular intermetallic compounds,which are more like metals than like either ionic crystals or valencecrystals. Thus
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