The Electronic and the Ionic Contribution to the Free Energy of Alkali Metals in Intercalation Compounds

Abstract

The process of intercalation is thermodynamically analyzed. It is shown that an ionic and an electronic component of the intercalation free energy can be distinguished. A prediction of the electronic contribution is possible if the electronic band structure of the host material in the energy range above the Fermi energy is known. An experimental way for measuring the electronic contribution is suggested.The cell voltage of a battery in which one electrode is an intercalation compound varies with the concentration of the intercalated species. If they are metal atoms, they are usually present in the form of ions while their charge compensating electrons are incorporated into the electronic system of the host material. We show that a distinction between the ionic and the electronic contribution to the driving force of intercalation can be made in principle. While the ionic contribution is difficult to predict, the electronic contribution is correlated closely to the electronic band structure of the host material. For an experimental determination of the electronic contribution a correlation with work function measurements is suggested. Thermodynamics of the Cell VoltageThe voltage of a galvanic cell of the type M + zZ~ M (metal) in a substrate-S) (electrolyte) (intercalated phase I II III is controlled at open circuit by the free energy difference between the metal atoms in the intercalation compound and the pure metal '-3In this formulation, p~ represents the chemical potential per atom, AGM refers to the transfer of one metal atom from phase I to III, and AV is the cell voltage. The process of intercalation consists in the uptake of one M ~+ ion from the electrolyte (phase II) and the compensation of this charge by z electrons coming from phase I. There are two contributions to the free-energy difference: one comes from the chemical interaction of the ions with the host lattice, the other from the chemical binding of the electrons when they are transferred from the metal to the host compound. These two components can be separated as shown in the following way. The measured cell voltage corresponds to the difference of the electrochemical potential of electrons between phases III and I. The electrochemical potential ~ of a species with a charge Zeo contains two componentswhere z, is the valence of the species and eo the elementary electric charge. Consequently for the electrons 1 -eoAV = m~--~-= ~iP~--~--eo(~m -~) =z AG~ [3] This relationship shows that h Vhas two components, one from the difference of the chemical potential of the electrons between the intercalation compound and the metal, * Electrochemical Society Active Member.In the scheme of the galvanic cell shown above, the interfaces between phases I and II and equally between H and III can only be passed by the metal ions. Their free energies must at equilibrium be equal in all three phases. For simplicity and because metals of higher valency may not be fully ionized, we shall in the following discuss only metal ions with the charge z = 1. The free energ...

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