Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-19T13:07:00.920Z Has data issue: false hasContentIssue false
  • English
  • Français

Tight-Binding Theory and Computational Materials Synthesis

Published online by Cambridge University Press:  29 November 2013

A.P. Sutton ,
P.D. Godwin  and
A.P. Horsfield
Get access

Extract

At the heart of any atomistic simulation is a description of the atomic interactions. A whole hierarchy of models of atomic interactions has been developed over the last twenty years or so, ranging from ab initio density-functional techniques, to simple empirical potentials such as the embedded-atom method and Finnis-Sinclair potentials in metals, valence force fields in covalently bonded materials, and the somewhat older shell model in ionic systems. Between the ab initio formulations and empirical potentials lies the tight-binding approximation: It involves the solution of equations that take into account the electronic structure of the system, but at a small fraction of the cost of an ab initio simulation, because those equations contain simplifying approximations and parameters that are usually fitted empirically.

Tight binding may be characterized as the simplest formulation of atomic interactions that incorporates the quantum-mechanical nature of bonding. The particular features that it captures are as follows: (1) the strength of a bond being dependent not only on the interatomic separation but also on the angles it forms with respect to other bonds, which arises fundamentally from the spatially directed characters of p and d atomic orbitals, (2) the filling of bonding (and possibly antibonding) states with electrons, which controls the bond strengths, and (3) changes in the energy distribution of bonding and antibonding states as a result of atomic displacements. These features enable one to obtain considerable improvements in accuracy compared to the simple “glue models” of bonding since use is made of the physics and chemistry of bonding.

Type
Interatomic Potentials for Atomistic Simulations
Information
MRS Bulletin , Volume 21 , Issue 2 , February 1996 , pp. 42 - 48
Copyright
Copyright © Materials Research Society 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Sutton, A.P. and Balluffi, R.W., Interfaces in Crystalline Materials (Oxford University Press, New York, 1995), Chapter 3.Google Scholar
2.Car, R. and Parrinello, M., Phys. Rev. Lett. 55 (1985) p. 2471.CrossRefGoogle Scholar
3.Daw, M.S. and Baskes, M.I., Phys. Rev. B 29 (1984) p. 6443. S.M. Foiles, M.I. Baskes, and M.S. Daw, Phys. Rev. B 33 (1986) p. 7983.CrossRefGoogle Scholar
4.Finnis, M.W. and Sinclair, J.E., Philos. Mag. A 50 (1984) p. 45; G.J. Ackland and R. Thetford, Philos. Mag. A 56 (1987) p. 15.CrossRefGoogle Scholar
5.Altmann, S.L., Lapiccirella, A., Lodge, K.W., and Tomassini, N., J. Phys. C 15 (1982) p. 5581.Google Scholar
6.Dick, B.G. and Overhauser, A.W., Phys. Rev. 112 (1958) p. 90. U. Schröder, Sol. Stat. Commun. 4 (1966) p. 347.CrossRefGoogle Scholar
7.Ercolessi, F., Parrinello, M., and Tossatti, E., Philos. Mag. A 58 (1988) p. 213.CrossRefGoogle Scholar
8.Tersoff, J., Phys. Rev. B 38 (1988) p. 9902.CrossRefGoogle Scholar
9.Sutton, A.P., Electronic Structure of Materials (Oxford University Press, New York, 1993); D.G. Pettifor, Bonding and Structure of Molecules and Solids (Oxford University Press, New York, 1995).Google Scholar
10.Friedel, J., in The Physics of Metals, edited by Ziman, J.M. (Cambridge University Press, New York, 1969) p. 494.Google Scholar
11.Chadi, D.J., Phys. Rev. B 19 (1979) p. 2074; D.J. Chadi, Phys. Rev. B 29 (1984) p. 785.CrossRefGoogle Scholar
12.Sutton, A.P., Finnis, M.W., Pettifor, D.G., and Ohta, Y., J. Phys. C 21 (1988) p. 35.Google Scholar
13.Slater, J.C. and Koster, G.F., Phys. Rev. 94 (1954) p. 1498.CrossRefGoogle Scholar
14.Horsfield, A.P., Godwin, P.D., Pettifor, D.G., and Sutton, A.P., in preparation.Google Scholar
15.Xu, C.H., Wang, C.Z., Chan, C.T., and Ho, K.M., J. Phys.: Condens. Matter 4 (1992) p. 6047.Google Scholar
16.Davidson, B.N. and Pickett, W.E., Phys. Rev. 49 (1994) p. 11,253.CrossRefGoogle Scholar
17.Sykes, P., A Guide to Mechanism in Organic Chemistry, 6th ed. (Longman, London, 1986).Google Scholar
18.McCabe, A.R.et al., in Surface Engineering III: Process Technology and Surface Analysis, edited by Datta, P.K. and Gray, J.S. (Royal Society of Chemistry, London, 1993) p. 163.Google Scholar
19.Godwin, P.D., Horsfield, A.P., Pettifor, D.G., and Sutton, A.P., in preparation.Google Scholar
20.Kohyama, M., Kose, S., Kinoshita, M., and Yamamoto, R., J. Phys.: Condens. Matter 2 (1990) p. 7791.Google Scholar
21.Pettifor, D.G., Phys. Rev. Lett. 63 (1989) p. 2480; G. Galli and M. Parrinello, Phys. Rev. Lett. 69 (1992) p. 3547; X.P. Li, W. Nunes, and D. Vanderbilt, Phys. Rev. B 47 (1993) p. 10,891; M.S. Daw, Phys. Rev. B 47 (1993) p. 10,895; S. Goedecker and L. Colombo, Phys. Rev. Lett. 73 (1994) p. 122; E.B. Stechel, A.R. Williams, and P.J. Feibelman, Phys. Rev. B 49 (1994) p. 10,088; P. Ordejon, D.A. Drabold, R.M. Martin, and M.P. Grumbac, Phys. Rev. B 51 (1995) p. 1456.CrossRefGoogle Scholar