An Accelerated Coordinate Gradient Descent Algorithm for Non-separable Composite Optimization

Journal of Optimization Theory and Applications - Coordinate descent algorithms are popular in machine learning and large-scale data analysis problems due to their low computational cost iterative...     

An auger electron spectroscopy study of low temperature segregation of silicon at aluminum surface

Low temperature surface segregation of silicon out of refined aluminum samples is studied by AES. The analysis of kinetics data gives an Arrhenius type diffusivity with an activation energy equal to 65 kJ mol^?1 (0.68 eV atom^?1). The pre-exponential factor is of the order of 3 × 10^?6 m² s^?1. These results fit well within the limits of grain boundaries and dislocation diffusivities, as compiled from the literature by Hwang and Balluffi, and show that the segregation proceeds from distorted sites in grain boundaries and dislocations, rather than from bulk undistorted sites. The analysis of data obtained from a slow-cooling-rate experiment gives a segregation energy of ?60 kJ mol^?1 (?0.63 eV atom^?1) and shows that the silicon surface concentration limit is not a monolayer, but rather unexpectedly about 8%. This may be related to LEED observation of silicon adsorption on various faces of aluminum by Jona and suggests that long range repulsive forces are effective to saturate silicon condensation on aluminum at a low coverage value.     

Medium energy electron diffraction on aluminum

Measurements of the specular beam intensity in the medium range of energy (645 eV and 980 eV) are presented for the aluminum (001) and (110) surfaces. They have been performed with a LEED goniometer allowing to achieve high accuracy in the determination of the angular parameters of the diffraction experiment. The experimental results are displayed in the form of iso-intensity maps in (θ, φ) coordinates at a constant primary beam energy. θ denotes the colatitude angle of incidence and is varied in the range 30° to 80°. φ denotes the azimuth and is varied between 0° and 360°. Sections of the maps at constant angle of incidence are known as rotation diagrams. A model calculation ignoring intra-layer multiple scattering, but incorporating inter-layer multiple scattering processes shows the prominent role of the latter, in many cases, and the non-negligible contribution of the former in other cases. Sections of the maps at constant azimuth are called incidence-profiles. They are very sensitive to the azimuth and very hard to compute. Using the preceding model calculation, average incidence profiles have been computed, using as input parameters the refractive and absorptive potentials and the surface normal relaxation parameter obtained by a pseudo-kinematic analysis of experimental average incidence profiles as explained in another paper. The peak position and width have been compared to those obtained from the pseudo-kinematic calculation. From the result, it is shown that if averaging is performed according to a specific set of restrictive rules, the pseudokinematic analysis of the data has a semi-quantitative meaning.     

Reduction of Leed data for surface crystallography

We present two methods for reducing Leed intensities, starting from rotation diagrams as basic data. Results are given for the specular reflection on the (001) surface of aluminium in the form of ‘averaged’ and ‘maxima’ rocking curves at three representative energies (50, 150 and 380 eV). Both methods are compared to previous work and found to present several advantages. Possible application to surface crystallography is discussed.     

New theoretical results about the anisotropy of the secondary emission of Al(001) and Al(110)

The source function giving the number of electrons acquiring the energy E and the direction of propagation Ω at the depth z in a target of aluminium submitted to a bombardment of electrons of an energy of 350 eV is evaluated by a Monte Carlo calculation. This source function is used to study the anisotropy of the secondary electron emission. The influences of the depth dependence and of the anisotropy of the source function on the anisotropy of the secondary electron emission on Al(001) and Al(110) are negligible. These results are considered as an evidence that the observed anisotropy in the emitted beam is due to electron final state effects.     

Experimental contribution to the relaxation problem on the (100) and (110) surfaces of aluminum by LEED data reduction

It is shown that low-energy electron diffraction intensities off crystal surfaces can, despite their apparent complexity, be fully understood with such simple and familiar concepts as Bragg reflections, zero-angle scattering phase shifts, electron penetration depth, and intdermediate beams in multiple scattering. Our emphasis is on direct physical understanding rather than on calculational methods.