Substitutional Impurities: Introduction and Exploration

NetLogo model 6.5.1 above is a molecular dynamics model, like the one in the previous chapter (Section 5.3), but now there is a substitutional atom (the purple one in the middle). You can increase and decrease its size, and its relative size compared to the atoms of the host lattice is displayed next to it (it starts with a size of 1, i.e., the same as the other atoms).

The way this is modeled is that instead of a single $\sigma$ parameter in the Lennard-Jones potential (Eq. 4.5.1), each atom $i$ has its own $\sigma_i$ and the interatomic potential between two atoms, $i$ and $j$ is calculated using the average: $\sigma = \frac{\sigma_i + \sigma_j}{2}$.

Note also, in this model, temperature (and therefore kinetic energy) is held constant at the value of the temp slider. This means that the velocities of the atoms are scaled each time step so that the average kinetic energy of the atoms results in the set temperature.