Study of Boundary Structures.

Abstract

The project extends previous studies on structures of a 2-D grain boundary (g.b.). The basic analytical tool is the cluster variation method (CVM) and the path probability method (PPM), both developed by the author. In the CVM, the free energy is minimized with respect to a large number of variables using a linear iteration method called the natural iteration method (NIM). A square lattice is chosen as the basic lattice (called the DSC lattice) of the analysis. The first, second, and third nearest neighbor pairs are excluded due to a large repulsion. The fourth and fifth neighbors contribute interaction potentials E(4,AB) and E(5,AB), and so on. In the DSC lattice the CVM is formulated using a cluster made of nine lattice points in the form of a quadruple square. The QS formulation leads to numerical results that are reliable compared with the MC method. In low temperatures, atoms hardly deviate from the skeletal stable crystalline structure. The pair method is found to give reliable numerical results practically the same as those of QS for low temperatures including the entire ordered phase in the work D. This result is significant because when the pair method is used, the two sides of the g.b. do not need to be oriented symmetrically as were done in the present report. Applications of this point of view for g.b. of different angle combinations and the 3-D cases are now planned.

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Document Details

Document Type
Technical Report
Publication Date
Jul 31, 1987
Accession Number
ADA184808

Entities

People

  • Ryoichi Kikuchi

Organizations

  • University of Washington

Tags

DTIC Thesaurus Topics

  • Classification
  • Coefficients
  • Contracts
  • Crystal Structure
  • Diffusion Coefficient
  • Energy
  • Free Energy
  • Grain Boundaries
  • Iterations
  • Low Temperature
  • Materials
  • Materials Science
  • Mechanics
  • Security
  • Statistical Mechanics
  • Transitions
  • Two Dimensional

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