Theory of the Work Functions of Monovalent Metals
TL;DR: In this article, the work function of a metal is defined as the difference in energy between a lattice with an equal number of ions and electrons, and the lattice of the same number of ion and electron, but with one electron removed.
Abstract: The factors which determine the work function of a metal are described in a qualitative way The work function is defined as the difference in energy between a lattice with an equal number of ions and electrons, and the lattice with the same number of ions, but with one electron removed The work function is then found by first calculating the energy of a lattice with n i ions and n e electrons The final formula gives the work functions of monovalent metals in terms of the heats of sublimation This formula is approximate, and can claim validity only in a qualitative way, as one of the important factors, the electric double layer on the surface, is omitted entirely, and it is assumed that the Fermi energy is as great as if the electrons were entirely free The values obtained from this formula check very closely with the experimental values for the alkalis, so that it can be concluded that the double layer is probably small for these metals Finally, the deviations to be expected for other than monovalent metals are considered A more exact calculation of the work function of one substance (Na) will be given by one of us in an ensuing paper
Citations
More filters
TL;DR: In this paper, the work function of a monolayer of Mo, Ag, Au, Fe, Co, Ni, Nb, Li, N, and O was investigated and compared on W(100, W(110), W(211), and W(111) surfaces, showing that subtle details of the charge transfer can determine the sign and magnitude of surface dipole change.
Abstract: Local-density-functional calculations are used to study the change of work functions induced by a layer of adsorbates. We investigated and compared the work function of a monolayer of Mo, Ag, Au, Fe, Co, Ni, Nb, Li, N, and O on W(100), W(110), W(211), and W(111) surfaces. While many systems obey the commonly accepted rule that electronegative adsorbates increase the work function of the surface, we find some exceptions. For example, overlayers of Fe, Co, and Ni increase the work function of W(100), W(211), and W(111), but decrease the work function of the W(110) surface, although the charge transfer is the same in all orientations. We found that even a layer of oxygen can decrease the work function of W(100), although there are always electrons transferred from the W substrate to the oxygen adsorbates. In order to understand these results, we established the relationship between surface dipole density and work function within the framework of local-density formalism. It turns out that subtle details of the charge transfer can determine the sign and magnitude of surface dipole change, leading to a strong dependence on the orientation of the substrate, with the consequence that the work-function changes are not always governed by the sign and quantity of adsorbate induced charge transfer.
331 citations
TL;DR: In this article, the authors investigated the work functions of bare MXenes and their functionalized ones with F, OH, and O chemical groups using first-principles calculations and showed that the OH-terminated MXenes attain ultralow work functions between 1.6 and 2.8 eV.
Abstract: MXenes are a set of two-dimensional transition metal carbides and nitrides that offer many potential applications in energy storage and electronic devices. As an important parameter to design new electronic devices, we investigate the work functions of bare MXenes and their functionalized ones with F, OH, and O chemical groups using first-principles calculations. From our calculations, it turns out that the OH-terminated MXenes attain ultralow work functions between 1.6 and 2.8 eV. Moreover, depending on the type of the transition metal, the F or O functionalization affects increasing or decreasing the work functions. We show that the changes in the work functions upon functionalizations are linearly correlated with the changes in the surface dipole moments. It is shown that the work functions of the F- or O-terminated MXenes are controlled by two factors: the induced dipole moments by the charge transfers between F/O and the substrate, and the changes in the total surface dipole moments caused by surface relaxation upon the functionalization. However, in the cases of the OH-terminated MXenes, in addition to these two factors, the intrinsic dipole moments of the OH groups play an important role in determining the total dipole moments and consequently justify their ultralow work functions.
298 citations
IBM1
TL;DR: The density functional formalism was introduced by Hohenberg, Kohn, and Sham as mentioned in this paper to study strongly inhomogeneous electron gases in their ground state, which they referred to as the density-functional formalism.
Abstract: Publisher Summary A prerequisite to analysis of the electronic structure of metal surfaces is a procedure for studying large, strongly inhomogeneous systems of electrons. Two such procedures that have been widely used in the past are the Thomas–Fermi method and the Hartree method. Not long ago, a general theory of inhomogeneous electron gases in their ground state, which we shall refer to as the density-functional formalism, was introduced by Hohenberg, Kohn, and Sham. The central quantity in this theory is the electron density, whose basic role is established by the theorem that the properties of the system, in particular the groundstate energy, are functionals only of this density. With the density as the varied function, a variational principle is established for the energy. The associated Euler equation is formulated in two ways—both in principle exact—that are particularly convenient for the study of strongly inhomogeneous systems. One formulation is similar to the Thomas–Fermi method, the other to the Hartree method; in their various approximate versions, they represent systematic ways of extending the classic methods which they resemble. This chapter outlines the density-functional formalisms and discusses its application to two of the most basic static properties of a surface: the work function and the surface energy.
291 citations
TL;DR: The work function φ is a periodic function of atomic number, as shown clearly by a new compilation of published data for 57 elements as mentioned in this paper, and the progressive rise and fall of work function values throughout the table of the elements appears to be sufficiently regular to permit approximations to be made of values for the metallic and semimetallic elements on which no data has yet been published.
Abstract: Like the chemical properties of the elements, the work function φ is a periodic function of atomic number, as shown clearly by a new compilation of published data for 57 elements. The progressive rise and fall of work function values throughout the table of the elements appears to be sufficiently regular to permit approximations to be made of values for the metallic and semimetallic elements on which no data has yet been published. Since the first ionization potential Ei and electrode potential E0 exhibit a similar periodic function of atomic number, a striking resemblance exists among the respective plots of φ, Ei, and E0.
183 citations