## 5 Conclusions  
Yb:LLF crystals with a scheelite structure (space group \(I4_{1}/a\)) have been synthesized through a safe and scalable PEG-assisted hydrothermal approach. We show that size and morphology can be finely controlled by changing reaction conditions such as temperature, time, fluoride source, and precursor amount. The results show that higher temperature and prolonged reaction time facilitate the formation of more stable LiLuF\({}_{4}\) crystals. The substitution of PEG for NH\({}_{4}\)HF\({}_{2}\) changes the morphology of the product, as shown by the appearance of crystal facets (101) and (112) in the PEG-assisted crystals. The average size of the crystals can be controlled by the concentration of precursors in an aqueous solution. We demonstrate solid-state laser refrigeration of the Yb:LLF crystals using a focused near-infrared laser excitation source (\(\lambda\) = 1020 nm). A calibrated ratiometric Boltzmann analysis of the Yb\({}^{3+}\) luminescence reveals laser cooling in air by more than 15 K below room temperature and in water by more than 5 K below room temperature. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app12020774/s1](https://www.mdpi.com/article/10.3390/app12020774/s1)]([https://www.mdpi.com/article/10.3390/app12020774/s1](https://www.mdpi.com/article/10.3390/app12020774/s1)), Figure S1: Scanning electron microscope images of crystals following PEG-assisted hydrothermal synthesis at: (a) 100 \({}^{\circ}\)C (scale bar is 1 \(\upmu\)m), (b) 120 \({}^{\circ}\)C (scale bar is 1 \(\upmu\)m), (c) 130 \({}^{\circ}\)C (scale bar is 1 \(\upmu\)m), (d) 180 \({}^{\circ}\)C (scale bar is 2 \(\upmu\)m), (e) 200 \({}^{\circ}\)C (scale bar is 2 \(\upmu\)m) and (f) 220 \({}^{\circ}\)C (scale bar is 5 \(\upmu\)m), for 24 h, Figure S2: Powder XRD pattern of crystals following PEG-assisted hydrothermal synthesis at 130 \({}^{\circ}\)C for: (a) 3 h, (b) 5 h, (c) 14 h, (d) 24 h, Figure S3: Scanning electron microscope images of crystals following PEG-assisted hydrothermal synthesis at 130 \({}^{\circ}\)C for: (a) 3 h (scale bar is 1 \(\upmu\)m), (b) 5 h (500 nm), (c) 14 h (1 \(\upmu\)m), (d) 24 h (1 \(\upmu\)m), Figure S4: Temperature-calibrated PL spectra of Yb\({}^{3+}\):LLF, Figure S5: ATR-FTIR spectra of Yb\({}^{3+}\):LLF synthesized under following conditions: (a) at 130 \({}^{\circ}\)C for 14 h; (b) at 150 \({}^{\circ}\)C for 5 h; (c) at 200 \({}^{\circ}\)C for 24 h; (d) at 200 \({}^{\circ}\)C for 72 h; (e) at 220 \({}^{\circ}\)C for 5 h; (f) at 220 \({}^{\circ}\)C for 48 h, Figure S6: Powder XRD pattern of crystals following PEG-assisted hydrothermal synthesis at 220 \({}^{\circ}\)C for 2 h (a) without calcination and calcination at: (b) 300 \({}^{\circ}\)C, (c) 500 \({}^{\circ}\)C, (d) 600 \({}^{\circ}\)C, Figure S7: Scanning electron microscope images of crystals following PEG-assisted hydrothermal synthesis at 220 \({}^{\circ}\)C for 2 h (a) without calcination and calcination at: (b) 300 \({}^{\circ}\)C, (c) 500 \({}^{\circ}\)C h, (d) 600 \({}^{\circ}\)C. Scale bar is 1 \(\upmu\)m, Figure S8: Scanning electron microscope images of LLF crystals following PEG-assisted hydrothermal synthesis at 200 \({}^{\circ}\)C for 24 h. (a) RE nitrate precursor amount is 4 mmol. Scale bar is 5 \(\upmu\)m. (b) RE nitrate precursor amount is 16 mmol. Scale bar is 20 \(\upmu\)m.  
Conceptualization, E.A.D. and P.J.P. ; methodology, E.A.D. and P.J.P. ; software, E.A.D., A.P. and X.X. ; validation, R.E.G. ; formal analysis, E.A.D., A.P. and X.X. ; investigation, E.A.D., A.P., X.X. and R.E.G. ; resources, P.J.P. ; data curation, E.A.D., X.X., A.P. and R.E.G. ; writing--original draft preparation, E.A.D. ; writing--review and editing, E.A.D., A.P., X.X., R.E.G. and P.J.P. ; visualization, E.A.D., A.P. and X.X. ; supervision, E.A.D. and P.J.P. ; project administration, E.A.D. and P.J.P. ; funding acquisition, P.J.P. All authors have read and agreed to the published version of the manuscript. **Funding:** E.A.D., R.E.G. and P.J.P.