A reciprocal lattice model to study the crystallography of epitaxial films

Abstract

A modified reciprocal lattice based model is proposed to study orientation relationship between a film and a substrate. The model is derived from a 3D version applicable to study precipitation crystallography in materials. The proposed geometric model was used to study the suitability of the model to predict the crystallography during film growth. The model requires data on crystal structure, lattice parameters, atomic positions, and substrate plane as input and calculates the reciprocal lattice vectors weighted by their respective diffraction intensity. The preferred orientation is then selected based on coincident or near-coincidence of maximum number of reciprocal lattice vectors assuming this provides minimum lattice misfit orientation. The model was implemented in 'MATLAB' and was used to study material systems with well-known orientation relationship experimentally obtained and have been reported in literature. The systems studied were FCC on BCC, BCC on FCC, FCC on FCC, FCC on Halite, BCC on Halite, FCC on Diamond cubic, BCC on Diamond cubic, and Diamond cubic on Diamond cubic. Finally, the obtained theoretical epitaxial relationships were compared with the reported experimental results. The model was found to be quite effective in predicting the orientation relationship for BCC on FCC, FCC on Halite, BCC on Halite and DC on DC and found limited success in case of FCC on BCC, FCC on FCC.