E.G. McRae

Surface studies by electron diffraction

Abstract The problems in the analysis of surface structures by means of electron diffraction, particularly at low energy, are reviewed. A brief introduction is given to the basic scattering and diffraction phenomena occurring at a solid surface after which the nature of the experimental diffraction data is described. The theoretical interpretation of the diffracted intensity by various kinematical and dynamical methods is outlined and the present difficulties in obtaining a complete surface structure determination are examined. The different types of ordered and disordered layers which may be formed on a surface—usually by adsorption of foreign species—are discussed and the interpretation of the corresponding diffraction patterns is illustrated by some examples.

Electron diffraction at crystal surfaces: I. Generalization of Darwin's dynamical theory

Abstract The dynamical diffraction theory put forward originally by C.G. Darwin in his treatment of X-ray reflection is developed in a more general form suitable for the treatment of electron diffraction at crystal surfaces. The theory applies to a model crystal consisting of two parts: a selvedge with two-dimensional periodicity but otherwise arbitrary structure and a semi-infinite substrate composed of identical and equally-spaced atom layers. In the treatment of this model, the wave field in a region of locally-constant scattering potential between neighboring layers is expressed as a superposition of all possible diffracted (propagating) waves and an arbitrary number of evanescent waves. The diffraction problem is formulated in terms of “transfer” matrices involving the scattering properties of individual atom layers parallel to the crystal surface. It is shown that the diffraction problem and the corresponding band-structure problem for the substrate may be reduced to a matrix eigenvalue problem involving the transfer matrix for a substrate layer. The diffraction amplitudes are expressed in terms of the eigenvectors of this transfer matrix.

Low-energy electron diffraction study of lithium fluoride (100) surface

Abstract The diffraction of electrons by a LiF (100) surface formed by cleavage has been studied in the electron energy range 2–200 eV. The experimental arrangement was of the postdiffraction acceleration type, in which the diffraction pattern is displayed on a fluorescent screen. By heating to ∼ 300° C, the conductivity of the crystal was increased sufficiently to prevent charging in the electron beam. The diffraction pattern indicates that the LiF surface does not rearrange upon cleavage followed by annealing. The dependence of diffracted beam intensity on energy has been studied in detail. The gross structure of intensity vs. energy is attributed to single scattering events (Bragg reflections) and the superimposed fine structure which was also observed is interpreted as an effect of multiple scattering. From the Bragg reflection maxima it is inferred that the LiF crystal is distorted in the neighborhood of the surface. The results are consistent with a theoretical prediction of surface distortion by Benson, Freeman and Dempsey: near the (100) surface of an alkali halide MX, an alternation of M + spacing is superposed on an overall expansion of the crystal in the direction normal to the surface. In the energy range 90–200 eV, the background to the diffraction pattern exhibits a banded structure. The dark regions in the background are interpreted as Kikuchi deficiency lines, deriving from inelastic scattering followed by elastic scattering. The inelastic process is probably phonon scattering.

Electron diffraction at crystal surfaces: II. The double-diffraction picture

A highly simplified theoretical picture of electron diffraction at crystal surfaces previously proposed on intuitive grounds by Bauer and others, is here developed systematically on the basis of the dynamical theory given in I. It is shown that the application of nondegenerate second-order perturbation theory to the matrix eigenvalue problem in I leads to an expression for the diffraction amplitude, b, of the form b=b(1)+b(2) , where b(1) denotes the contribution from single-diffraction processes at different atom layers, summed over all atom layers and b(2) denotes the contribution from sequences of double-diffraction processes at different atom layers, summed over all pairs of atom layers. The term double-diffraction as used here includes processes involving an evanescent intermediate wave. The term b(1) represents a modified kinematical description. The description including both b(1) and b(2) is called the “double-diffraction” picture. Explicit expressions are given for b(1) and b(2), for a model crystal with a one-layer selvedge. The physical meaning and limits of validity of the double-diffraction picture are discussed. Applications to the following three topics in the field of low-energy electron diffraction are commented on briefly: secondary peaks, fractional-order beams and satellite beams.

Observation of multiple scattering resonance effects in low energy electron diffraction studies of LiF, NaF and graphite

Abstract The predicted effects associated with the resonances that occur in a multiple scattering theory of electron diffraction by crystals 2 ) are (a) a peak in the 00 beam intensity at an electron energy below that of the lowest-energy resonance, and (b) minima in all beam intensities at the energy of each resonance. According to the theory for crystals made up of identical atom layers, with one atom per unit mesh in each layer, there is a resonance associated with the emergence of each diffracted beam parallel to the surface. The theory is extended to the case of two atoms per unit mesh in each layer. In specific applications to alkali halide (001) and graphite (0001) surfaces, it is shown that the theory leads to the same result as for the case of one atom per unit mesh-layer, except in that for alkali halides there is no resonance associated with the emergence of beams whose index sum is odd. The theory indicates that both the energy interval between the resonance and the emergence energy of the associated beam, and the energy interval between the resonance peak and the resonance, are approximately independent of beam orientation. It is proposed that an identification of resonance effects can be based on these properties. Sets of experimental 00 reflectivity curves, showing the effects of varying the primary beam orientation, are presented for NaF and graphite crystals. In each set of curves, and in the corresponding sets for LiF crystal 4 ), series of resonance peaks are identified on the basis of a correlation with the emergence energies of the relevant diffracted beams. It is shown that in the case of LiF crystal the resonance minimum in the 00 intensity, associated with the emergence of the 11 beam, may be displayed by defocussing the diffraction pattern. The display consists of a dark line that crosses the 00 spot. In experiments at different angles of incidence, the energy at which the line crosses the spot center differs by a fixed amount from the 11 emergence energy. The observation is explained in detail on the basis of the resonance mechanism. The resonance minimum is displayed in another way in multiple exposure photographs of the diffraction pattern of a stress-annealed pyrolytic (rotationally disordered) graphite sample in which successive exposures correspond to small increments in the angle of incidence. The photographs are criss-crossed by dark lines, which is identified with the loci of resonance conditions. The observation of resonance effects is interpreted as evidence for long-range dynamical interactions involving ≳ 10 4 atoms per atom layer in the crystal.

Electron diffraction at crystal surfaces: IV. Computation of LEED intensities for “muffin-tin” models with application to tungsten (001)

Low energy electron diffraction intensities have been computed for “muffin-tin” models representing atomically-clean crystal surfaces and surfaces formed by the adsorption of foreign atoms. Computational results are reported for specific model potentials corresponding to tungsten crystal with a (001) surface and hydrogen adsorbed on tungsten (001) to form various surface structures of centered (2 × 2) periodicity. No attempt has been made to optimize the model potentials or to allow for inelastic scattering processes. The computational method is a combination of the generalized Darwin method (Part I in the series) with Kambes method for simple monolayers. The scattering ability of tungsten and hydrogen atom layers and the appropriate band-structure section for tungsten are determined at intermediate stages in the intensity computation. Results are reported for the energy range 0–4 ryd (0–54 eV). The main features of the computed intensity curve for tungsten appear to be related more directly to scattering resonances of a single layer of atoms than to the Bragg conditions referring to the free-electron description. The presence of a surface potential barrier has a substantial effect on intensity curves. The computational results are compared with the observed intensity versus energy curve for tungsten (001) in the energy range 0–20 eV. The computation accurately locates two peaks observed at 8 and 17 eV, but the model cannot account for a third peak observed at 4 eV. An interpretation as a displaced resonance of the surface monolayer is suggested. The computations for hydrogen on tungsten indicate that integral-order beam intensities are only slightly affected by a hydrogen layer. The computed intensities for fractional-order beams are comparable with the intensities for neighboring integral-order beams, and are extremely structure-sensitive. The chief mechanism for the appearance of fractional-order beams is inter-layer multiple scattering.

Structure of Si(111)-7×7

Abstract A model of the Si(111)−7 × 7 surface atomic arrangement is put forward on the basis of results already established for Si(111) and Si(100) surfaces. The unit mesh contains a triangular double-layer island with 21 first-layer atoms. The island is laterally expanded and is bounded by [112] steps with second-layer edge atoms forming asymmetric dimers. It is shown that salient features of low energy electron diffraction (LEED) patterns for Si(111)−7 × 7 can be explained by the model. The LEED patterns are interpreted qualitatively by a double-diffraction mechanism involving forward diffraction in the selvedge. It is shown that the patterns contain characteristic formations of fractional-order spots attributable to the dimers at the island boundaries. The best agreement with observed patterns is obtained with the following parameter values: dimer bond length 2.5 ± 0.2 A, island lateral expansion 3 ± 2%. Some of the implications of the model for the chemical reactivity and electronic properties of the Si(111)−7 × 7 surface are discussed.

Very low energy electron reflection at Cu(001) surfaces

Abstract Measurements of the coefficient of elastic reflection of very low energy electrons at Cu(001), Cu(001) (2 × 4)45° O and Cu (001) c (2 × 2) N surfaces are reported. The measurements refer to normally-incident electrons with kinetic energies E in the range 0.5–22 eV. The elastic reflection coefficient R el was determined from separate observations of the total reflection coefficient and of the energy distribution of reflected electrons. For Cu(001) R el is 0.55 at E = 0.5 eV and drops monotonically to 0.03 with increasing E , the maximum slope being at E = 3 eV . Theoretical calculations of R el are reported. The reflection amplitude of the substrate crystal was parameterized using existing results of accurate band structure calculations, and the surface scattering matrix was evaluated for assumed surface scattering potentials. It is shown that to fit the observed R el it is necessary to take account of both the image potential and the extension of the imaginary part of the crystal scattering potential into vacuum. From the fit, the range of the imaginary potential is 1.0 A. For Cu(001) (2 × 4)45° O and Cu (001) c (2 × 2) N the values of R el at E = 0.5 eV were 0.35 and 0.15, respectively. The effect of adsorption in reducing R el is especially marked for E eV . Adsorption of either O or N results in an additional peak in R el near E = 12 eV .

Ordering and layer composition at the Cu3Au(110) surface

Low energy electron diffraction and low energy ion scattering observations on Cu3Au(110) reveal a correlation between surface compositional ordering and the average compositions in the first and second surface atom layers. The surface undergoes a broadened, discontinuous 2 × 1 → 1 × 1 transition at least 6 K below the bulk compositional-disordering transition at 660 K, while near 660 K the values of Au atom fractions in the first (second) atom layers approach 0.35 (0.35) starting from 0.45 (0.20) below 400 K.

Diffraction effects in low-energy electron emission

Abstract The origin of diffraction peaks in the energy distribution of intensity of low-energy (