Lanthanide-doped nanoparticles based on fluoride hosts have potential uses in nextgeneration biomedical imaging modalities. Isomorphic β-NaYF₄ : 18%Yb³⁺, 2%Er³⁺ and β-KYF₄ : 18%Yb³⁺, 2%Er³⁺ nanoparticles have been synthesised by hydrothermal methods and were characterised using X-ray diffraction, scanning electron microscopy, and infrared absorption spectroscopy.

For each nanoparticle species, upconversion fluorescence spectra have been used to investigate how green and red upconversion fluorescence intensities can be tuned by optically stimulating the (Yb) ²F₇/₂ → ²F₅/₂ transition with various excitation pulse widths. The green-to-red upconversion fluorescence intensity ratio for both nanoparticle species decreased with increasing excitation pulse width, indicating that multiple initial pathways populate the red fluorescing (Er) ⁴F₉/₂ state.

Upconversion fluorescence transients have been used to monitor the time-dependent population of the (Er) ⁴F₉/₂ state in each nanoparticle species, along with the green fluorescing (Er) ²H₁₁/₂ and (Er) ⁴S₃/₂ states. Such time-dependent populations have been used to understand the behaviour of the green-to-red upconversion fluorescence intensity ratio with increasing excitation pulse width. It was determined that the dominant populating pathways of the (Er) ⁴F₉/₂ state vary between the nanoparticle species.

A system of rate equations has been used to simulate these upconversion fluorescence transients to quantitatively understand the dynamics of the upconversion mechanisms in each nanoparticle species. The rate equations were computationally solved using the finite element method, and the simulations were fit to data using the Nelder-Mead algorithm. It has been inferred by simulating the upconversion fluorescence transients that upconversion mechanisms may be present in both nanoparticle species, which have previously not been accounted for by the rate equations.

Upconversion mechanism rate constants have been obtained for each nanoparticle species, indicating that the populating pathway to the (Er) ⁴F₉/₂ state through the (Er) ⁴I₁₃/₂ state may be dominant in β-KYF4: 18%Yb³⁺, 2%Er³⁺ nanoparticles but not in β- NaYF₄: 18%Yb³⁺, 2%Er³⁺ nanoparticles. These differences contribute to understanding the discrepancies in the fluorescence behaviour of each nanoparticle species.