Determination of the structural parameters of an incommensurate phase from first principles: the case of Sc-II

We propose a procedure to accurately describe the structural parameters of an incommensurate phase using ab initio methods by approximating it with a set of analogous commensurate supercells. We apply this approach to obtain the structural parameters of the Sc-II phase, which has recently been identified as a complex incommensurate structure similar to Sr-V. The calculated incommensurate ratio gamma, lattice parameters, and Wyckoff positions of Sc-II are in excellent agreement with the available experimental data. Our results show that gamma increases with pressure up to 60 GPa approaching but never reaching the commensurate value 4/3. Hence calculations do not confirm the prediction made based on the reanalyzing of experimental data. When pressure exceeds 70 GPa, gamma shows a sharp decrease that might be considered as the precursor of a new structural phase transition.