The true atomistic structure of a disordered crystal: a computational study on the photon upconverting material...

Hexagonal (β-) NaYF₄ and LiYF₄ doped with trivalent lanthanide ions (Ln³⁺, e.g., Er³⁺, Tm³⁺, and Yb³⁺) are well-known photon upconverting materials. This property is crucially determined by the precise location of the Ln³⁺ 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-NaYF₄ is not unambiguously provided by X-ray diffraction techniques. Here, theoretical estimates for the true structure of the material are obtained via periodic density functional theory (DFT) calculations of large supercells. Our results reveal that Ln³⁺ doping of β-NaYF₄ 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 Y³⁺ 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 LiYF₄ and by comparison with available experimental and theoretical data. Similar results are expected for other disordered crystalline host materials such as β-NaGdF₄ or cubic (α-) NaYF₄. 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.