Orientational and crystallographic relationships in thin films of yttrium orthoferrite on sapphire substrates

An algorithm is proposed for determining the orientational relationships and crystal unit-cell parameters of thin films using a laboratory X-ray diffractometer and stereographic projections. It is illustrated by the treatment of experimental data obtained for yttrium orthoferrite YFeO3 films on single crystalline sapphire (Al2O3) substrates for film thicknesses in the range from 100 to 7000 angstrom. Precise determination of unit-cell constants and angles is possible by combining the results of X-ray measurements made in the in-plane and out-of-plane geometries. The unit-cell unit parameters and orientation relationships for thin films were determined. For the studied films, typical errors in determining unit-cell parameters and angles are better than 0.17 angstrom and 0.17 degrees, respectively.