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Quantum mechanical predictions in intermetallics modelling

  • D. Nguyen Manh
  • A. M. Bratkovsky
  • D. G. Pettifor

Abstract

Materials modelling involves research that spans the very broad spectrum of length scales from quantum mechanical calculations at the A level all the way through to finite-element or finite-difference modelling at the continuum level. This paper reviews the role that quantum mechanics plays in the modelling hierarchy with particular reference to the titanium and nickel aluminides.

Keywords

Bond Order Nickel Aluminide Quantum Mechanical Prediction Bond Order Potential Binding Energy Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Aoki, M. 1993 Rapidly convergent bond order expansion for atomistic simulations. Phys. Rev. Lett. 71, 3842–3845.CrossRefGoogle Scholar
  2. Bratkovsky, A. M., Aoki, M., Horsfield, A. & Pettifor, D. G. 1994 Tight-binding calculations in real space: towards the bond-order potentials. Workshop on Bond-Order Potentials for Atomistic Simulations, University of Oxford, Oxford, 26–27 September.Google Scholar
  3. Coulson, C. A. 1939 The electronic structure of some polyelenes and aromatic molecules. VII Bonds of fractional order by molecular orbital method. Proc. R. Soc. Lond. A 169, 413–428.CrossRefGoogle Scholar
  4. Darolia, R. 1991 NiAl alloys for high-temperature structural appications. J. Metals 43, 44–49.Google Scholar
  5. Dimiduk, D. M., Miracle, D. B. & Ward, C. H. 1992 Development of intermetallic materials for aerospace systems. Mater. Sci. Technol . 8, 367–375.CrossRefGoogle Scholar
  6. Finnis, M. W. & Sinclair, J. E. 1984 A simple empirical N-body potential for transition metals. Phil. Mag. A 85, 45–55.Google Scholar
  7. Goodwin, L., Skinner, A. J. & Pettifor, D. G. 1989 Generating transferable tight-binding parameters: application to silicon. Europhys. Lett. 9, 701–706.CrossRefGoogle Scholar
  8. Hohenberg, P. & Kohn, W. 1964 Inhomogeneous electron gas. Phys. Rev. 136B, 864–871.CrossRefGoogle Scholar
  9. Kohn, W. & Sham, L. 1965 Self-consistent equations including exchange and correlation effect. Phys. Rev. 140A, 1133–1138.CrossRefGoogle Scholar
  10. Methfessel, M. 1988 Elastic constants and phonon frequencies of Si calculated by a fast full-potential linear-muffin-tin-method. Phys. Rev. 38B, 1537–1540.Google Scholar
  11. Nguyen Manh, D., Paxton, A. T., Pettifor, D. G. & Pasturel, A. 1995 On the phase stability of transition metal trialuminides compounds. Intermetallics 3, 9–14.CrossRefGoogle Scholar
  12. Nguyen Manh, D., Trambly de Lassardiere, J. J. P., Mayou, D. & Cyrot-Lackmann, F. 1992 Electronic structure and hybridization effect in the compounds Al2Ru and Ga2Ru. Solid St. Commun. 82, 329–334.CrossRefGoogle Scholar
  13. Pettifor, D. G. 1989 New many-body potential for the bond order. Phys. Rev. Lett. 63, 2480–2843.CrossRefGoogle Scholar
  14. Pettifor, D. G. 1992 Theoretical predictions of structure and related properties of intermetallics. Mater. Sci. Technol. 8, 345–349.CrossRefGoogle Scholar
  15. Pettifor, D. G., Aoki, M., Gumbsh, P., Horsfield, A., Nguyen Manh, D. & Vitek, V. 1995 Defect modelling: the need for angularly-dependent potentials. Mater. Sci. Engrg A 192/193, 24–30.CrossRefGoogle Scholar
  16. Pettifor, D. G. & Podloucky, R. 1986 The structure of binary compounds. II. Theory of the pd-bonded AB compounds. J. Phys. C 19, 315–330.CrossRefGoogle Scholar
  17. Pierce, F. S., Poon, S. J. & Biggs, B. D. 1993 Band-structure gap and lectronic transport in metallic quasicrystals and crystals. Phys. Rev. Lett. 70, 3919–3922.CrossRefGoogle Scholar
  18. Yamaguchi, M. & Inui, H. 1993 TiAl compounds for structural applications. Structural intermetallics (ed. R. Darolia, J. J. Lewandowski, C. T. Liu, P. L. Martin, D. B. Miracle & M. V. Nathal), pp. 127–142. The Minerals, Metals and Materials Society.Google Scholar
  19. Zhang, B. & Soffa, W. A. 1994 The structure and properties of Llo ordered ferromagnets: Co—Pt, Fe—Pt, Fe—Pd and Mn—Al. Scr. metall. Mater. 30, 683–688.CrossRefGoogle Scholar
  20. A. R. C. Westwood (Sandia National Laboratories,USA). What are the prospects for extending this approach to ternary and quaternary alloys with the ultimate objective of developing, from first principles, an intermetallic that exhibits significant ductility?Google Scholar
  21. D. G. Pettifor. The approach of modelling defects using bond order potential is easily extendable to a treatment of ternary and quaternary alloys provided the appropriate tight binding parameters between the different chemical constituents are known. These calculations at the electronic and atomistic level would have to be linked to simulation of dislocation behaviour at the microstructural level before we have a truly `first principles’ modelling capability of ductile behaviour.Google Scholar
  22. K. S. Kumar (Martin Marietta Laboratories,Baltimore, USA). Given that the mechanical properties of intermetallic compounds are particularly sensitive to mi-nor stoichiometric deviations as well as minor alloying additions, how realistically can we expect atomistic modelling to serve as a predictive tool, since the number of atoms/cells that can be included is limited? Further, can defect population be included in the calculations?Google Scholar
  23. D. G. Pettifor. The sensitivity of planar fault energies to alloying additions is already being modelled. As the interatomic potentials become more realistic and computers ever more powerful, we can expect that modelling will be able to provide new insight into the role of alloying additions and non-stoichiometry on mechanical properties.Google Scholar
  24. R. W. Cahn (University of Cambridge, UK). Professor Pettifor showed, for certain intermetallic phases, that the energy differences between the stable and the next-most-favourable crystal structures are exceedingly small. Can he reliably predict which of such phases will exhibit stacking faults (polytypism), like SiC or Co?Google Scholar
  25. D. G. Pettifor. Yes, even though the absolute energy may show sizeable error, relative energies are usually very reliable. The polytypism in SiC or Co has been successfully predicted by groups in the Cavendish Laboratory and the Techniche Hochschule in Darmstadt.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • D. Nguyen Manh
  • A. M. Bratkovsky
  • D. G. Pettifor

There are no affiliations available

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