Date : September, 21st      Time : Thursday, 4-5pm      Place : Seminar room: Science 103

Title : Statistics of steps on crystal surfaces

Speaker : Dr. Howard Richards

Affiliation :Department of Physics, TAMU-Commerce

Abstract :

Modern techniques in microscopy make it possible to determine the positions of steps on vicinal crystal surfaces (surfaces which are cut at a small angle to a high-symmetry plane) to atomic precision. In principle, various histograms and correlation functions obtained from these experiments provide information about the total interaction between steps. These interactions may include contributions from elastic stress, surface electronic states, and free energy contributions from adsorbates. However, the precise experiments are of little value in accurately determining the interactions without a good theoretical model. For many purposes, the Pairwise Einstein Model (PEM) provides an excellent description of the statistics of steps. The PEM is similar to the Einstein model of a 1-dimensional crystal, with the steps mapped onto worldliness of spinless fermionic “atoms”; however, rather than placing only a single “atom” in a harmonic well, two “atoms” are placed in the same well, and the interactions between them are treated exactly. This approximation can be justified by considering the pair of steps confined by other steps in analogous fashion to the reptation tube which confines polymers. The PEM gives excellent agreement with Terrace Width Distributions calculated from Monte Carlo simulations for a surprisingly wide variety of physical circumstances.

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