Fractiecoördinaten

Fractiecoördinaten, also known as fractional coordinates or fractional atomic coordinates, are a way to describe the positions of atoms within a crystal lattice. Instead of using absolute Cartesian coordinates (x, y, z), which depend on the origin and orientation of the chosen coordinate system, fractional coordinates express atom positions as fractions of the unit cell vectors.

To determine the fractional coordinates of an atom, one takes the real-space coordinates of the atom and projects them onto the three basis vectors of the unit cell. The resulting values are then divided by the lengths of these basis vectors. This results in a set of three numbers (u, v, w), where each number represents a fraction of the unit cell length along the corresponding basis vector. For example, a position of (0.5, 0, 0) would mean the atom is located halfway along the first basis vector, and at the origin along the other two.

The advantage of using fractional coordinates is that they are invariant under translations of the unit cell. This means that if you shift the origin of your coordinate system, the fractional coordinates of the atoms within the unit cell remain the same. This property is crucial in crystallography and solid-state physics, as it simplifies the analysis of crystal structures and their properties, independent of the arbitrary placement of the unit cell in space. They are commonly used in crystallographic databases and software for representing and manipulating atomic positions.