On the Relaxation Energy of Vacancy Formation and the Jellium Model for the Alkali Metals

Abstract

Within the jellium model we write the vacancy formation energy E' as the sum of several terms:E' = AT + AExc + BE, + E,, where AT is the change in kinetic energy of the electrons, AExc is the change in exchange and correlation energy, AEc is the change in electrostatic energy, and E , is thc contribution because of lattice relaxation. Each term in this equation, except E,, is calculated using the density functional formalism for Li, Na, K, Rb, and Cs, respectively. To obtain E, we used the corresponding experimental values of E' and subtracted from each of them the corresponding calculated values of the other terms. The resulting values for E , are all positive and relatively large, varying from about 0.1 to 0.23 eV. lntroductionThe formation energy for a vacancy E' is obtained by subtracting the energy of a metal with a perfect lattice consisting of N ions in a volume Q from the total ground state energy of a similar system in which one atomic cell has been removed from the bulk and placed on the surface. The vacancy formation energy can be written as the sum of several terms [l, 21,where AT is the change in kinetic energy of the electrons, AExc is the change in exchange and correlation energy, AEc is the change in electrostatic energy, and E, is the relaxation energy.Within the density functional formalism and the local density approximation, the vacancy formation energy can be expressed for a monovalent metal [l, 21 aswhere BEcigcn is the change in the energy eigenvalues of the electrons when the vacancy is formed and it is given by (see, for example, [l, 3, 41)where k , is the Fermi wave vector, ?il(k) is the corresponding phase shift of wave vector k and angular momentum 1 produced by the vacancy. The term U , , is the electrostatic energy,. ~-' ) Apartado Postal 20-364, Codigo Postal 01000, Mexico D.F., Mexico.