28. Finite-Element-Based Electronic Structure Calculation in Metal/Ceramic Interface Problems

  1. Manuel E. Brito,
  2. Peter Filip,
  3. Charles Lewinsohn,
  4. Ali Sayir,
  5. Mark Opeka and
  6. William M. Mullins
  1. Yoshinori Shiihara1,
  2. Osamu Kuwazuru2 and
  3. Nobuhiro Yoshikawa3

Published Online: 26 MAR 2008

DOI: 10.1002/9780470291283.ch28

Developments in Advanced Ceramics and Composites: Ceramic Engineering and Science Proceedings, Volume 26, Number 8

Developments in Advanced Ceramics and Composites: Ceramic Engineering and Science Proceedings, Volume 26, Number 8

How to Cite

Shiihara, Y., Kuwazuru, O. and Yoshikawa, N. (2005) Finite-Element-Based Electronic Structure Calculation in Metal/Ceramic Interface Problems, in Developments in Advanced Ceramics and Composites: Ceramic Engineering and Science Proceedings, Volume 26, Number 8 (eds M. E. Brito, P. Filip, C. Lewinsohn, A. Sayir, M. Opeka and W. M. Mullins), John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470291283.ch28

Author Information

  1. 1

    The University of Tokyo 4–6–1, Komaba Meguro-Ku, Tokyo, 153–8505 Japan

  2. 2

    Institute of Industrial Science, The University of Tokyo 4–6–1, Komaba Meguro-Ku, Tokyo, 153–8505 Japan

  3. 3

    Institute of Industrial Science, The University of Tokyo 4–6–1, Komaba Meguro-Ku, Tokyo, 153–8505 Japan

Publication History

  1. Published Online: 26 MAR 2008
  2. Published Print: 1 JAN 2005

ISBN Information

Print ISBN: 9781574982619

Online ISBN: 9780470291283

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Keywords:

  • ceramic;
  • element;
  • experiments;
  • technology;
  • titanium

Summary

The Finite Element Method (FEM) is implemented for atomic-scale analyses oi metal/ceramic interface problems based on the Density Functional Theory (DFT), which is indispensable to prediction of ultimate bond strength in various combinations of metals and ceramics. The DFT simulation contributes much for the design of the new breed of functional materials without laborious trial and error experiments. For interface problems, an inconvenientl) large number of atoms should be included in a unit cell. The traditional DFT scheme of the plane- wave basis is not effective for such a large-scale calculation, since its scheme requires quadratic-scaling operation for matrix-vector product. We propose to reduce inherently prolonged computational time by employing finite discretization of real space to perform the DFT scheme. The sparseness of the Hamiltonian matrix improves computational efficiency so effectively as to increase the matrix-vector product linearly in proportion to number of atoms. Additional merit of the DFT by the FEM is in parallel computation caused by real space discretization, which makes decomposition of the matrix systematic. This is not the case with the traditional DFT using Fourier transforms. The finite element formulation is summarized and a trial computation with a Si dimer is demonstrated to verify the applicability of the FEM.