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 Å. 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 Å and 0.17°, respectively.