Determination of Activation Energy of Surface Diffusion Based on Thermal Oscillations of Atoms

Yu.V. Syrovatko,Ye.P. Shtapenko

doi:10.15330/pcss.22.3.522-528

Abstract

This paper covers calculations of the activation energy of surface diffusion of ad-atoms on the substrate surface from the point of view of thermal oscillations of substrate atoms and ad-atoms. The main characteristic of oscillations of atoms and geometric mean frequency was calculated based on statistical approximation of the Debye model using the reference values of entropy and heat capacity of metals. The basic principle of the model of activation energy calculation presented in the paper is the formation of potential wells and barriers during oscillations of atoms localized in the sites of the lattice. Oscillations of atoms were considered in the framework of quasiclassical quantum approximation as the oscillations of harmonic oscillators in the potential parabolic wells. Dimensions of the negative part of values of the potential well energy were determined by the amplitude of thermal oscillations of atoms. Positive values constituted a significant part of the potential well energy values. Barriers were formed owing to interaction of positive values of the energy of parabolic wells of adjacent atoms. Therefore, in order to make the ad-atom jump, it is necessary to get out of the potential well having the negative values, and to overcome the potential barrier. The energy required for the ad-atom jump on the substrate surface was the activation energy of surface diffusion. The results obtained in this paper agree satisfactorily with the results of another method, which is based on determining the energy of ad-atom binding with the substrate atoms.

Highlights

Surface diffusion, which consists in the transfer of a substance on the surface of the solid-state body, plays an important role in many surface processes and chemical reactions, such as adsorption, desorption, crystallization, wetting, thin-film growth, and formation of nanostructures [1,2,3]
The important characteristic of surface diffusion, which determines the rate of thermoactive process at a given surface temperature, is the activation energy of surface diffusion Ea
Existing theoretical methods for Ea calculation are mostly based on the energy of ad-atom binding with the atoms of the substrate surface [7]

Summary

Vasyl Stefanyk Precarpathian National University

Determination of Activation Energy of Surface Diffusion Based on Thermal Oscillations of Atoms. This paper covers calculations of the activation energy of surface diffusion of ad-atoms on the substrate surface from the point of view of thermal oscillations of substrate atoms and ad-atoms. The basic principle of the model of activation energy calculation presented in the paper is the formation of potential wells and barriers during oscillations of atoms localized in the sites of the lattice. Dimensions of the negative part of values of the potential well energy were determined by the amplitude of thermal oscillations of atoms. Barriers were formed owing to interaction of positive values of the energy of parabolic wells of adjacent atoms. The energy required for the ad-atom jump on the substrate surface was the activation energy of surface diffusion.

Introduction

Results and discussion

Conclusions