Correlation of Electron Work Function and Surface-Atomic Structure of Some d Transition Metals

Abstract

The correlation between the atomic structure of semi-infinite plane surfaces and the electron work function j of crystalline metals is investigated for nine d transition metals. An (hkl)-dependent scalar parameter Dt, expressed in terms of the linear atomic and broken-bond densities, for metal surfaces treated as a plasma of free electrons and atomic cores, is used to linearly approximate j. A linear regression procedure employed yields a high correlation with mean values of experimental j for different planes of a given metal. Two structural ranges of j linearity are found. The trend of work-function variation known from theory and experiment is confirmed. A high correlation is also found for 2nd, 3rd, 4th, 1/2 and 3/2 powers of Dt. Polycrystalline j range from ca. 5.40 (Pt) through 4.90 (Re) and 4.52 (W) to ca. 4.13 eV (Ta), and the dipole term varies from 0.23 (W) to ca. 0.38 (Cu) or 0.17 eV (Re). Values of j for crystal planes which lack reported data are predicted.

Two-extremum electrostatic potential of metal-lattice plasma and the work function of an electron

“…Physical and chemical potentials and potential energies refer to an electron with zero chosen at infinity in the vacuum. Calculations are made for tungsten with its intensive parameter of MLP the chemical potential found by employing the linear regression method for the hard-sphere system [16].…”

“…Metal's average surface (MS) skin was defined for a conventional polycrystal [16]. For bcc metals, the MS of a metal can best be illustrated with the (111) plane as shown in Fig.…”

“…The e∆Φ is face dependent, while the internal intensive parameter µ is homogeneous, which was proved by Smoluchowski [19]. Magnitudes of the chemical potential µ were found for several d transition metals based on a great number of existing experimental WF values [16]; there was also the effective WF change ∆ϕ (hkl) determined using the Helmholtz 2D-gas dipole formula.…”

“…Since the 3D metal inside exhibits isotropic electronic properties, while its 2D surface skin of 2 or 3 atomic layers and the WF display clearly anisotropic ones, we treat a crystal of metal (Me) as a thermodynamic two-phase two-component system of free electrons and lattice ions. The characteristic length d s (hkl) which determines the phase boundary position between the Me surface and the bulk, was determined [16] in terms of the crystalline (atomic) lattice. The novel potential Ψ ES with its two extremes has the form similar to theoretical pseudopotentials, such as the Tavares-Prausnitz double minimum potential [8,17].…”

“…where B is a constant numerically equal to the slope of the linear regression [16]; henceforth, we omit subscript MS. The radius R d is related to the average MS electron density by:…”