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

2021 ◽  
Vol 22 (3) ◽  
pp. 522-528
Author(s):  
Yu.V. Syrovatko ◽  
Ye.P. Shtapenko
Keyword(s):  
Activation Energy ◽  
Surface Diffusion ◽  
Substrate Surface ◽  
Geometric Mean ◽  
Harmonic Oscillators ◽  
Energy Calculation ◽  
Potential Well ◽  
Negative Part ◽  
Potential Wells ◽  
Thermal Oscillations

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.

ON THE OPTICAL POTENTIAL OF AN ATTRACTIVE NONRELATIVISTIC DEGENERATE ELECTRON GAS INTERACTING WITH NUCLEAR MATTER

2012 ◽  
Vol 26 (31) ◽  
pp. 1250210 ◽  
Author(s):  
M. A. GRADO-CAFFARO ◽  
M. GRADO-CAFFARO
Keyword(s):  
Nuclear Matter ◽  
Optical Potential ◽  
Electron Gas ◽  
Three Dimensional ◽  
Harmonic Oscillators ◽  
Fermi Velocity ◽  
Potential Well ◽  
Schwinger Model ◽  
Degenerate Fermi Gas ◽  
Degenerate Electron Gas

The optical potential of an attractive nonrelativistic electron gas interacting with nuclear matter is determined on the basis of the concept of degenerate Fermi gas. In fact, the involved electrons are treated as three-dimensional quantum harmonic oscillators confined at the surface of a spherical (approximately ideal) potential well. Within this picture, the Fermi velocity is calculated as well as the spatial electron density at the surface of the potential well and the attractive force between the electron gas and the nuclear matter. In addition, considerations related to the Lippmann–Schwinger model are made.

scholarly journals Thermally stimulated oxygen desorption in Sr2FeMoO6-δ

2018 ◽  
Vol 4 (1) ◽  
pp. 1-5 ◽  
Author(s):  
Nikolay A. Kalanda
Keyword(s):  
Activation Energy ◽  
Oxygen Diffusion ◽  
Gas Flow ◽  
Oxygen Vacancies ◽  
Early Stage ◽  
Diffusion Activation Energy ◽  
Energy Calculation ◽  
Heating Rates ◽  
Oxygen Desorption ◽  
Diffusion Activation

Polycrystalline Sr2FeMoO6-δ specimens have been obtained by solid state synthesis from partially reduced SrFeO2,52 and SrMoO4 precursors. It has been shown that during oxygen desorption from the Sr2FeMoO6-δ compound in polythermal mode in a 5%H2/Ar gas flow at different heating rates, the oxygen index 6-δ depends on the heating rate and does not achieve saturation at T = 1420 K. Oxygen diffusion activation energy calculation using the Merzhanov method has shown that at an early stage of oxygen desorption from the Sr2FeMoO6-δ compound the oxygen diffusion activation energy is the lowest Еа = 76.7 kJ/mole at δ = 0.005. With an increase in the concentration of oxygen vacancies, the oxygen diffusion activation energy grows to Еа = 156.3 kJ/mole at δ = 0.06. It has been found that the dδ/dt = f (Т) and dδ/dt = f (δ) functions have a typical break which allows one to divide oxygen desorption in two process stages. It is hypothesized that an increase in the concentration of oxygen vacancies Vo•• leads to their mutual interaction followed by ordering in the Fe/Mo-01 crystallographic planes with the formation of various types of associations.

Surface Energy and Wettability Study of Flip Chip Packaging Materials

2011 ◽  
Vol 2011 (1) ◽  
pp. 000961-000970
Author(s):  
Jinlin Wang
Keyword(s):  
Surface Energy ◽  
Flip Chip ◽  
Substrate Surface ◽  
Solid Surfaces ◽  
Energy Calculation ◽  
Assembly Process ◽  
Flip Chip Packaging ◽  
Materials Used ◽  
Lead Free Solders ◽  
Ic Package

The surface energy of solid surfaces and surface tension of liquids are important parameters in the IC package assembly process. Wettability analyses have been completed for various materials used in the assembly process of flip chip packages, including underfills, substrates, fluxes, and lead free solders. We will highlight some of these results in this paper. We will focus our discussion on substrate surface energy analysis. A brief discussion of different surface energy methods and the liquid selection criteria will be given. The advantage and limitation of the surface energy calculation methods will be discussed. The data from several case studies will be presented. Our results show that contact angle and surface energy measurements are very useful for quality control and product development where interfacial properties are important.

scholarly journals Non-equilibrium adatom thermal state enables rapid additive nanomanufacturing

2019 ◽  
Vol 21 (20) ◽  
pp. 10449-10456 ◽  
Author(s):  
Matthew R. Henry ◽  
Songkil Kim ◽  
Andrei G. Fedorov
Keyword(s):  
Surface Temperature ◽  
Surface Diffusion ◽  
Thermal State ◽  
Substrate Surface ◽  
Negligible Effect ◽  
Adsorbed Molecules ◽  
Non Equilibrium

A new state of radical thermal non-equilibrium in surface adsorbed molecules is discovered that enables rapid surface diffusion of energized adatoms with a negligible effect on the substrate surface temperature.

An embedded-atom-method study of diffusion of an Ag adatom on (111) Ag

1990 ◽  
Vol 68 (9) ◽  
pp. 1035-1040 ◽  
Author(s):  
W. K. Rilling ◽  
C. M. Gilmore ◽  
T. D. Andreadis ◽  
J. A. Sprague
Keyword(s):  
Activation Energy ◽  
Saddle Point ◽  
Surface Diffusion ◽  
Minimum Energy ◽  
Dynamics Simulation ◽  
Embedded Atom Method ◽  
Fixed Position ◽  
Embedded Atom ◽  
Minimization Procedure ◽  
Gradient Energy

The activation energy, vibrational frequency, and surface-diffusion jumps of a single adatom on a perfect (111) surface were studied using the embedded-atom method. The activation energy was determined with a conjugate gradient energy-minimization procedure. The surface adatom was moved in steps across the (111) plane through a saddle point. The adatom position was fixed within (parallel to) the (111) plane; but, the Ag adatom was free to relax, normal to the (111) plane. In this way the adatom was free to ride up over the saddle point; so that at each fixed position within the (111) plane the Ag adatom was free to move to its minimum energy. Also all of the atoms within the Ag crystal were free to relax to minimum-energy positions as the Ag adatom was moved across the surface. The minimum activation energy calculated for adatom diffusion was 0.058 eV. The embedded-atom method was also combined with a molecular dynamics simulation to observe the vibrations of the surface atoms and the adatom and to observe surface-diffusion jumps of the adatom. The adatom jumped to new surface sites at a frequency of approximately 1 × 1012 jumps s−1 at a temperature of 700 K.

scholarly journals Escape time from potential wells of strongly nonlinear oscillators with slowly varying parameters

2005 ◽  
Vol 2005 (3) ◽  
pp. 365-375 ◽  
Author(s):  
Jianping Cai ◽  
Y. P. Li ◽  
Xiaofeng Wu
Keyword(s):  
Elliptic Function ◽  
Nonlinear Oscillators ◽  
Oscillatory System ◽  
Escape Time ◽  
Potential Well ◽  
Jacobian Elliptic Function ◽  
Potential Wells ◽  
Varying Parameters ◽  
Strongly Nonlinear ◽  
Strongly Nonlinear Oscillators

The effect of negative damping to an oscillatory system is to force the amplitude to increase gradually and the motion will be out of the potential well of the oscillatory system eventually. In order to deduce the escape time from the potential well of quadratic or cubic nonlinear oscillator, the multiple scales method is firstly used to obtain the asymptotic solutions of strongly nonlinear oscillators with slowly varying parameters, and secondly the character of modulus of Jacobian elliptic function is applied to derive the equations governing the escape time. The approximate potential method, instead of Taylor series expansion, is used to approximate the potential of an oscillation system such that the asymptotic solution can be expressed in terms of Jacobian elliptic function. Numerical examples verify the efficiency of the present method.

The Escape of Particles from a Confining Potential well

1992 ◽  
Vol 290 ◽  
Author(s):  
James P. Lavine ◽  
Edmund K. Banghart ◽  
Joseph M. Pimbley
Keyword(s):  
Diffusion Coefficient ◽  
Chemical Reactions ◽  
Smoluchowski Equation ◽  
Escape Rate ◽  
Potential Well ◽  
Potential Wells ◽  
Confining Potential ◽  
Potential Shape ◽  
Well Depth ◽  
Electron Devices

AbstractMany electron devices and chemical reactions depend on the escape rate of particles confined by potential wells. When the diffusion coefficient of the particle is small, the carrier continuity or the Smoluchowski equation is used to study the escape rate. This equation includes diffusion and field-aided drift. In this work solutions to the Smoluchowski equation are probed to show how the escape rate depends on the potential well shape and well depth. It is found that the escape rate varies by up to two orders of magnitude when the potential shape differs for a fixed well depth.

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