Variational formulation of irreversible thermodynamics of surfaces and interfaces with grain-boundary triple-junction singularities under the capillary and electromigration forces in anisotropic two-dimensional space

Date

2006-06-01

Author

Ogurtani, TO

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

141
views

0
downloads

A variational irreversible thermodynamic method for curved surfaces and interfaces in a two-dimensional (2D) continuum, having anisotropic specific surface Gibbs free energy, is developed by utilizing the more realistic monolayer model of Verschaffelt and Guggenheim for the description of interfaces and surfaces in connection with the global entropy production hypothesis. This approach considers not only the asymmetric disposition of the grain-boundary triple junction, but also its dynamical effects on the morphological evolution of surfaces. The governing Euler equation and the associated boundary conditions (the strong solution) are derived rigorously by the variational technique applied on the positive definite rate of global internal entropy production; the results are in excellent accord with those deduced by the first-principles theory of irreversible thermodynamics of curved surfaces with triple junctions as formulated previously by the author, using the basic postulate of the local internal entropy production in connection with the microfinite-element method in discrete 2D space. At the final stage, the whole problem is converted into a variational extremum problem in order to obtain the weak solution in a class of smooth functions (i.e., Hermite functions) having continuous derivatives C-infinity(-infinity,+infinity) by transforming the displacement field into the particle-flux representation using the principle of conservation of particles, including the phase transition. As an application of the weak solution, which is converted into a compact matrix format in the normalized and scaled time and space domain, a set of computer simulation experiments is performed on symmetrically disposed bicrystal thin metallic films having fourfold anisotropic specific surface Gibbs free energy to demonstrate the breaching effects caused by grain-boundary grooving under the surface drift diffusion driven by the capillarity without electromigration forces.

Subject Keywords

Electronic, Optical and Magnetic Materials, Condensed Matter Physics

URI

https://hdl.handle.net/11511/63379

Journal

PHYSICAL REVIEW B

DOI

https://doi.org/10.1103/physrevb.73.235408

Collections

Department of Metallurgical and Materials Engineering, Article

Suggestions

OpenMETU
Core

Unified theory of linear instability of anisotropic surfaces and interfaces under capillary, electrostatic, and elastostatic forces: The regrowth of epitaxial amorphous silicon Ogurtani, Tarik Omer (American Physical Society (APS), 2006-10-01) The first-order unified linear instability analysis (LISA) of the governing equation for the evolution of surfaces and interfaces under capillary, electromigration (EM), and elastostatic forces is developed. A formal treatment of the thermomigration (Soret effect) driven by the nonuniform temperature distribution caused by exothermic phase transformation (growth) at the surface and interfacial layers is presented and its apparent influence on the capillary force in connection with the stability is also esta...
Modification of TiO2(001) surface electronic structure by Au impurity investigated with density functional theory METE, ERSEN; GÜLSEREN, Oğuz; Ellialtıoğlu, Süleyman Şinasi (American Physical Society (APS), 2009-07-01) We have used density functional theory calculations based on the projector augmented wave method to investigate the electronic structure of Au-incorporated anatase TiO2(001) surface. Due to the coordination with several level oxygens, Au atoms can be encapsulated inside TiO2 slab. Au is adsorbed over the surface Ti-O bond, so-called the bridge site on anatase TiO2(001) - 1 X 1 surface. However, for 0.25 monolayer coverage, Au atoms energetically prefer to stay at 0.64 angstrom above the midpoint of the two ...
Theoretical investigation of intersubband nonlinear optical rectification in AlxlGa1-xlAs/GaAs/AlxrGa1-xrAs asymmetric rectangular quantum wells Karabulut, Ibrahim; Atav, Uelfet; Safak, Haluk; Tomak, Mehmet (Wiley, 2007-09-01) In this study, a theoretical investigation of intersubband nonlinear optical rectification in Alx1Ga1-x1As/ GaAs/AlxrGa1-xrAs asymmetric rectangular quantum wells is presented. The electronic states in the asymmetric rectangular quantum well are described within the framework of the envelope function approach including the effects of band nonparabolicity and the effective mass mismatch. The nonlinear optical rectification is calculated using the density matrix formalism. It is found that the nonlinear optic...
Molecular-dynamics simulations of surface and bulk properties of Zn, Cd, and ZnCd systems Amirouche, L; Erkoç, Şakir (Wiley, 2004-02-01) Surface and bulk properties of Zn, Cd, and ZnCd systems have been investigated by performing molecular-dynamics simulations using a recently developed empirical many-body potential energy function for these systems, which comprices two- and three-body atomic interactions. Surface reconstruction and multilayer relaxation on clean surfaces, adatom on surface, substitutional atom on surface and bulk materials, and vacancy on surface and bulk materials have been studied extensively. (C) 2004 WILEY-VCH Verlag Gm...
Nonlinear intersubband optical absorption of Si delta-doped GaAs under an electric field Yildirim, Hasan; Tomak, Mehmet (Wiley, 2006-10-01) We study the nonlinear intersubband optical absorption of a single Si delta-doped GaAs sheet placed in the middle of a GaAs quantum well and subjected to an electric field. The Schrodinger and Poisson equations are solved self-consistently for various electric field strengths. The self-consistent solutions provide us with the correct confining potential, the wave functions, the corresponding subband energies and the subband occupations. The nonlinear optical intersubband absorption spectra are discussed wit...

Citation Formats

T. Ogurtani, “Variational formulation of irreversible thermodynamics of surfaces and interfaces with grain-boundary triple-junction singularities under the capillary and electromigration forces in anisotropic two-dimensional space,” PHYSICAL REVIEW B, pp. 0–0, 2006, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63379.