Determination of single-crystal elastic moduli of Li RE F₄(RE = Y, Gd, and Tb) by resonant ultrasound spectroscopy

The tetragonal fluoro-scheelite Li R E F 4 compounds (R E = rare earth) have been shown to exhibit a variety of useful optical and magnetic properties. While LiYF 4 has been widely studied, many of the fundamental thermodynamic properties of other members of this family remain unknown. Here, we report the complete elastic tensors (C ij) of single-crystalline LiYF 4, LiTbF 4, and LiGdF 4 using resonant ultrasound spectroscopy and density functional theory (DFT). We compare the results for LiYF 4 with prior experimental results using time-of-flight ultrasound methods. This is the first report, however, of the experimental elastic tensors of LiTbF 4 and LiGdF 4. The present results point to a softening of the elastic moduli of the Li R E F 4 system when Y is replaced by the larger ionic radius of Tb or Gd. Furthermore, we find that just 0.3% doping with Nd on the Y site also leads to a slight softening of the moduli. The variation of the elastic moduli as a function of temperature up to 216 ° C was also measured. A nearly linear softening of all seven independent elastic moduli was observed with increasing temperature. Phonon dispersions and phonon density of states obtained by DFT support the experimental finding of a significantly higher sound velocity due to lighter Y atoms in LiYF 4, as compared to heavier LiTbF 4 and LiGdF 4.