Mat. Res. Bull. Vol. 2, pp. 37-48, 1967. Pergamon Press, Inc. Printed in the United States. CHARACTERIZATION OF d ELECTRONS IN SOLIDS BY STRUCTURE I. LOCALIZED vs COLLECTIVE ELECTRONS John B. Goodenough Lincoln Laboratory,* Massachusetts Institute of Technology Lexington~ Massachusetts 02173 (Received November 25, 1966; Communicated by the author) ABSTRACT Outer ~ electrons in solids may be either localized or collective~ depending upon the magnitudes of the over- lap integrals ~ for crystal-field orbitals on neighbor- ing atoms. If ~ < Ac~ they are localized; and if > Ac~ they are col1-~ctive. At Ac there is a change from--6ne electronic phase to the o---~her. This change may be first-order. The crystal-field orbitals contain covalent mixing into atomic _d orbitals of _s and orbitals of nearest-neighbor anions and cations~ so that there are two types of overlap integrals: cation- cation Acc and cation-anion-cation Acac. If Acc > Ac and Acac < Ac~ the d orbitals form cation-subl-~tic~-- band states?- If Acc < A c and Aca c > Ac~ they form crystalline band ~%--~tes__ In t~-~ case--~f heavy atoms in a low valence state~ such as Pb 2+ or Bi 3+, anion-vacancy trap orbitals may mix with heavy-atom core orbitals to produce partially filled band orbitals that must be distinguished from collective d orbitals. Collective electrons in partially filled bands have a well defined Fermi surface~ localized electrons do not. Therefore a Fermi-surface-dependent property that is enhanced as the band narrows and is different for localized electrons~ where the Fermi surface is not well defined~ is particularly useful for characterizing the state of the d electrons. Spontaneous crystallographic distortions To lower symmetry at lower temperatures represent such a property. *Operated with support from the U. S. Air Force. This paper was presented at the International Conference on the Characterization of Materials, State College, Pa., U.S.A., November 16-18, 1966. 37