Surface Lattice Dynamics of Silver. II. Low-Energy Electron Thermal Diffuse Scattering

Abstract

Intensity measurements of the diffracted current in the low-energy electron diffraction from the (111) surface of silver show broad wings associated with the Bragg peaks. These wings have been identified as the thermal diffuse scattering. The observed intensity has been compared with model calculations for kinematic scattering of nonpenetrating radiation, using a Debye spectrum of vibrational modes. After the effects of the scattering factor and a temperature-independent background are accounted for, the data agree with the predictions of the model in the following ways: (i) Throughout nearly the entire Brillouin zone the intensity was inversely proportional to the distance to the nearest reciprocal-lattice rod. (ii) The ratio of the diffuse intensity to the peak intensity was proportional to temperature. (iii) The same ratio was proportional to the square of the length of the scattering vector. (iv) The ratio of the integrated intensities in the thermal diffuse scattering and in the peak was approximately equal to the exponent in the Debye-Waller factor. Refinements of the model to include qualitatively the penetration of the incident electrons and the free-surface elastic boundary conditions yield additional features that are only suggested in the data. However, to within the uncertainties in this analysis and the experiments, the results for the close-packed surface of silver can be understood in terms of an elastic continuum, and are consistent with the Debye-Waller factor for low-energy electrons.