Bond Order Potentials
The last few years have seen the development of the bond-order potentials (BOPs) in two areas:
(i) Accurate analytic BOPs have been derived for the sigma and pi bonds in open covalently-bonded structures by introducing the novel technique of constraining the intersite Green function to have the same poles as the corresponding on-site Green functions [1]. This leads to the sigma bonds in hydrocarbon systems being described on average to an accuracy of 1 % with information only about the second and fourth moments about the bond, thereby generating correct structural differentiation [2]. The analytic expression for the pi bond was derived using matrix recursion in order to handle the px and py orbitals on equal footing, so that the BOP depends only on bond and dihedral angles and not on the initial choice of coordinate axes. The pi bond potential is the first that can handle correctly the breaking of saturated pi bonds both on radical formation and under torsion. The use of matrix recursion has recently been shown to provide a convergent scheme for treating the vacancy formation energy in diamond structures that had until then eluded moments-based methods [3].
(ii) Applications of BOPs to metallic systems have yielded a good description of their defect behaviour [4,5,6,7]. In particular unlike the Embedded Atom or Finnis-Sinclair potentials, they have accounted for the prismatic rather than basal slip that is observed in hcp Ti [4,5] and the correct values of stacking fault energies in L1o TiAI [6]. To date BOP and other moments-based techniques are the only computationally viable order N methods for handling metals [8].
- D G Pettifor and I I Oleinik, Analytic bond-order potentials beyond TersofF Brenner. I. Theory, Phys. Rev. B59, 8487 (1999).
- I I Oleinik and D G Pettifor, Analytic bond-order potentials beyond TersofF Brenner. II. Application to the hydrocarbons, Phys. Rev. B59, 8500 (1999).
- T Ozaki, M Aoki and D G Pettifor, Block bond-order potential as a convergent moments-based method, Phys. Rev. (submitted).
- A Girshick, A M Bratkovsky, D G Pettifor and V Vitek, Atomistic simulation of titanium: I. A bond-order potential, Phil. Mag. A77, 981 (1998).
- A Girshick, D G Pettifor and V Vitek, Atomistic simulation of titanium: I. Structure of 1/3 <1210> screw dislocation, Phil. Mag. A77, 999 (1998).
- S Znam, D Nguyen-Manh, D G Pettifor and V Vitek, Bond-order potential for TiAl, 2nd International Alloy conference, Davos, Switzerland (1999).
- M Mrovec, V Vitek, D Nguyen-Manh, D G Pettifor, L G Wang and M Sob, Bond-order potentials for Mo and Nb: an assessment of their quality, MRS Symp. Proc. 538, 529 (1999).
- D R Bowler, M Aoki, M Goringe, A P Horsfield and D G Pettifor, A comparison of linear scaling tight-binding methods, Modelling Simul. Mater. Sci. Eng. 5, 199 (1997).
- D Nguyen-Manh, D G Pettifor and V Vitek, Analytic environmentally-dependent tight-binding parameters: application to the molybdenum silicides, (in preparation).
Future Goals
There are two immediate short-range goals for the future:
(i) The development of environmentally-dependent tight-binding (TB) parameters. This is important as the BOPs are derived as an exact many-atom expansion within the orthogonal two-centre TB approximation and, therefore, require an accurate TB description of the energetics of the given system. Nearest-neighbour TB parametrizations have been shown to provide a good description of the energetics about equilibrium bond lengths (see, for example, [2]), but they fail to describe correctly the activation barriers as the bonds are pulled apart. This requires the introduction of environmentally-dependent parameters. Very recently we have shown that we can derive analytic expressions for this environmental dependence by starting from a non-orthogonal TB representation and transforming it into an orthogonal representation, where the appropriate elements of the inverse non-orthogonality matrix can be evaluated using the formalism developed for finding the off-diagonal elements of the Green's function within BOP theory [9]. This novel theory of environmental dependence is currently being tested for the molybdenum silicides and will be extended to the hydrocarbons in order to model accurately the processes that take place at the diamond surface during CVD growth.
(ii) The extension of the BOPs to include ionic contributions. This is motivated by the importance of covalent interactions in determining the ferroelectric properties of transition metal perovskites and in modelling the oxidation of aluminium films when producing the insulating layer in spindependent tunnelling devices.
Future workshop
We intend to set up our Materials Modelling Laboratory (MML) workshops on a regular annual basis with hoped-for funding from the ESF. This year's workshop on 'Modelling across the length scales' was a great success.
