Representation of system structure
The graphite crystal 'system' is represented in the code by a three dimensional integer array that is mapped onto real space. The integer values held in the array correspond to the occupancy, or state, of defined lattice positions located at Cartesian coordinates that are mapped onto the array indices. This mapping is shown in below for the basal (x-y) plane, where two consecutive array indices in the x direction are separated by 1.22 A in real space, and two consecutive array indices in the y direction are separated by 0.71 A in real space.
Mapping of lattice sites onto the system array. Black circles are lattice sites in the A plane, white circles are b atoms in the B plane.
In this geometry, all lattice positions in AB graphite can be mapped into the array (with 2/3 of the array redundant). A third dimension and array index maps to the c-direction and multiple layers.
The grafted and spiro interstitial positions are mapped onto a separate array which interweaves the lattice array. In this array, interstitials can occupy the sites between a atoms in the layers above and below, in one of 6 different orientations.
Non-zero integers in the lattice array denote lattice positions in different allowed states. 1 denotes an in-plane lattice atom (occupied site), and 2 denotes a lattice vacancy (un-occupied site). 5 denotes a two-coordinated lattice atom bonded to a two-coordinated atom in the plane above, and 6 denotes a two-coordinated lattice atom bonded to a two-coordinated atom in the plane below. 7 denotes a split interstitial at an occupied lattice site.
In the interstitial plane, all un-occupied a sites are denoted with 8. Spiro interstitials can occupy these a sites and are denoted with an integer between 1 and 6 which corresponds to the orientation of the spiro interstitial relative to the crystallographic directions, as shown below.
Left: Integer mapping for spiro orientations about a sites. Right: Integer mapping for grafted orientations about a sites (+10 bonded to the lower plane, +20 bonded to the upper plane).
The grafted interstitial can be bonded to any two nearest-neighbour (a-b) atoms, however its position can be defined again by an orientation about a atoms. If the grafted is bonded to the lower plane, it is denoted with an integer 11-16, if it is bonded to the upper plane it is denoted with an integer 21-26.