The true atomistic structure of a disordered crystal: a computational study on the photon upconverting material β-NaYF and its Er-, Tm-, and Yb-doped derivates.

Hexagonal (β-) NaYF and LiYF doped with trivalent lanthanide ions (Ln, , Er, Tm, and Yb) are well-known photon upconverting materials. This property is crucially determined by the precise location of the Ln dopant ions and their closest neighbouring ions in the host material. However, due to the inherent disorder of the crystal structures the atomistic structure of a disordered crystal such as β-NaYF is not unambiguously provided by X-ray diffraction techniques. Here, theoretical estimates for the true structure of the material are obtained periodic density functional theory (DFT) calculations of large supercells. Our results reveal that Ln doping of β-NaYF occurs in a variety of low-symmetry sites, which are significantly altered by the occupational disorder of the crystal structure. Mainly, the distribution of Na and Y around a doping site significantly influences the positions of the F closest to the dopant. The results of this study are substantiated by applying the same method on the well-ordered host crystal LiYF and by comparison with available experimental and theoretical data. Similar results are expected for other disordered crystalline host materials such as β-NaGdF or cubic (α-) NaYF. The obtained structural information is a prerequisite for future accurate simulations and prediction of key parameters for the upconversion process in bulk materials and nanoparticles.