Modelling extended systems is computationally very demanding, especially when accurate methods like DFT are used (cf. Section 2.1.2). These extended systems may be non-ordered, like amorphous or liquid materials, or ordered, like polymers, two-dimensional structures (e.g. graphene) or three-dimensional crystal structures. For the latter class of materials, translational symmetry is used to describe the periodic boundary conditions (PBC) in atomistic simulations. Therefore, a periodically repeated box that represents the smallest repeating unit in three-dimensional space, the unit cell, needs to be defined. This unit cell is defined by three lattice vectors, a, b and c. By multiplying these lattice vectors with integer constants, the system forms an infinite array of replicated cells. The introduction of the unit cell for calculations with PBC leads to a rapid decrease in computation time. However, this is mainly true for simulations of well-crystalline and highly symmetric materials. As soon as defects in realistic concentrations (less than 1-10 %) have to be considered, a supercell needs to be used, which leads to a rapid increase in computational time.