Interatomic Potentials

  Interatomic potentials consist of sets of two- and three-body interaction terms of varying complexity, which are parameterised using a variety of experimental and ab initio data to fit to. Due to their high speed compared to ab initio calculations they can be routinely used with large supercells, and many molecular dynamics timesteps can be calculated. For example, recent studies of VO diffusion in Si used a 512 atom supercell under the Jiang-Brown (JB) potential, with multiple time steps and diffusion constraints [31].

We use a Musgrave-Pople (MP) potential fitted to results from AIMPRO calculations when determining LVMs. The potential can be used to calculate bulk phonon dispersion curves (see Section 4.3). However it is primarily used by our group to determine the energy double derivative terms in the dynamical matrix for bulk Si atoms, since to calculate all of these from first principles would be too time consuming. For this reason I describe here the MP potential, although `stand-alone' O in Si calculations are normally performed using either the Jiang-Brown[30] or Stillinger-Weber[33] potentials.

The Musgrave-Pople potential [34] is a three- and four- body potential made up of bond stretch and bond bending terms. It is given for atom i by the formula

Here $\Delta r_{ij}$ and $\Delta \theta_{jik}$ are the changes in the length of the i-j bond and angle between the i-j and i-k bond respectively (see Figure 2.3), and the summation is over the nearest neighbours j, k, and l. r₀ is the equilibrium bond length and is often set to be the experimental value. The coefficients k_r, $k_\theta$, $k_{r\theta}$, k_rr, and $k_{\theta \theta}$ are defined in Table 2.8.2.

  

Figure 2.3: Schematic diagram showing terms included in the Musgrave Pople potential

 

Coefficient Description

k_r bond stretch

$$k_\theta$$ bond bending

$$k_{r\theta}$$ stretch-bend interaction

k_rr stretch-stretch interaction

$$k_{\theta \theta}$$ bend-bend interaction