Recent developments and simulations utilizing bond-order potentials

Judith A. Harrison, US Naval Accademy, Annapolis, USA

Covalent materials, e.g., Si and C, form strong directional bonds. This poses a challenge for potential development for this important class of materials. Tersoff was the first to attempt to incorporate the structural chemistry of covalently bonded systems into an empirical potential energy function. The development of bond-order potentials (BOP) for C, Si, and Ge has spawned other potentials that utilize the bond-order approach [Tersoff, Phys. Rev. B, 39 (1989) 5566]. Using Tersoff’s BOP for C, Brenner created the reactive empirical bond-order (REBO) potential for hydrocarbons and used it to model diamond growth [Brenner, Phys. Rev. B, 42 (1990) 9458]. The first attempts to construct bond-order potentials capable of modeling 3 different atom types were two independently developed C-Si-H potentials, based on the REBO formalism [Beardmore & Smith, Phil. Mag. A, 74 (1996) 1439; Dyson & Smith, Surf. Sci., 355 (1996) 140]. These potentials inherit the strengths and weaknesses of the underlying potentials. Because the REBO potential is unable to reproduce the elastic constants of diamond and graphite, the C-Si-H potentials also have poor elastic properties. Thus, the functional form of the REBO was updated to create the second-generation REBO, or REBO2, potential [Brenner, et al., J. Phys. C., 14 (2002) 783]. The functional form and expanded fitting database resulted in significantly better descriptions of bond energies, lengths, force constants for hydrocarbon molecules. In addition, the zero-Kelvin elastic properties, interstitial defect energies, and surface energies for diamond are fairly well reproduced. However, the elastic constants as a function of temperature [Gao, et al. J. Chem. Phys., 125 (2006) 144506] and the force required to break covalent bonds were subsequently shown to be incorrectly reproduced [Pastewka, et al. Phys. Rev. B, 78 (2008) 161402(R)].

We recently developed a new bond-order potential for systems containing Si, C, and H, such as organosilicon molecules, solid Si, solid C, and alloys. This potential is based on the REBO2 potential [Brenner et al., J. Phys. C, 14 (2002) 783] for hydrocarbons and REBO for Si [Schall et al., Phys. Rev. B, 77 (2008) 115209]. Modifications to the hydrocarbon REBO potential were made to improve the description of three-atom type systems. The widespread use of Brenner’s REBO potential, its ability to model a wide range of hydrocarbon materials, and the existence of parameters for several atom types were the motivating factors for obtaining the Si-C-H (2B-SiCH) parameterization. We will briefly outline the 2B-SiCH potential and present recent simulations that examined adhesion and friction between Si and SiC tips and diamond surfaces.

The adaptive intermolecular REBO, or AIREBO, potential includes intermolecular interactions between non-bonded atoms and torsional interactions associated with a connected sequence of 3 bonds [Stuart, et al. J. Chem. Phys. 112, 6472 (2000)]. This makes the AIREBO potential capable of studying interfacial/tribological systems where chemical reactions take place. A method for extending charge transfer to BOPs, known as the bond-order potential/split-charge equilibration (BOP/SQE) method [Mikulski, et al. J. Chem. Phys. 131, 241105 (2009)], was recently integrated into a new BOP for interactions between O, C, and H. This qAIREBO potential [Knippenberg et al., J. Chem. Phys. 136, 164701 (2012)] is able to model chemical reactions where partial charges change in gas- and condensed-phase systems containing O, C, and H. The BOP/SQE method prevents the unrestricted growth of charges, without adding significant computational time, because it makes use of a quantity which is calculated as part of the underlying covalent portion of the potential, namely, the bond order. We will outline some of our recent work that uses the qAIREBO potential to examine the humidity dependence of friction in carbon-based solid lubricants.