High-precision determination of atomic positions in crystals: The case of $6H$- and $4H$-SiC

The atomic structures of the hexagonal $6H$ and $4H$ polytypes of SiC are determined by means of high-precision x-ray-diffraction measurements and first-principles calculations. The cell-internal relaxations which conform with the space-group symmetry are fully taken into account. Since the tetrahedra are distorted along the [0001] direction, an analysis of “quasiforbidden” reflections is possible. The measured and calculated data are compared and discussed in detail especially for $6H$-SiC. We find an almost perfect agreement for the ratio $c/a$ of the lattice constants. A comparison of the measured structure factors with those for calculated geometries is given. The atomic relaxations within the unit cell are derived.