Approximate energy gaps, dissimilar relative thermal sensitivities

In this field of luminescence ratiometric thermometry, it is long believed that those thermally coupled energy levels (TCELs) spaced by the approximate gaps own similar relative sensitivities (Sr), when the expression Sr = ΔE/kT² is taken into consideration, where ΔE is the gap between TCELs, k the Boltzmann constant, and T the absolute temperature. We demonstrate it is, however, inaccurate to some extent. The 653/678 nm emission bands and the 523/543 nm ones of Er³⁺, capable of enabling the thermal sensing over the temperature scope between 303 and 753 K, own similar practical gaps. However, the relative sensitivity for the 523/543 nm TCELs is much larger than that for the 653/678 nm ones. The former and the latter Sr are 0.88 and 0.18% K⁻¹ at 303 K, respectively, which largely differs from the conventional conception. The intense thermal quenching effect imposed on the ⁴F_9/2 state is verified to be responsible for this abnormal phenomenon. Due to the severe depopulation effect, the 653/678 nm TCELs’ emitting intensity ratio is confirmed to reflect more the thermal quenching mechanism but less the thermal effect. We then use the steady state rate equations to qualitatively show how the competition between the thermalization controlled by the Boltzmann distribution and the non-radiative relaxation mechanism plays a key role in determination of the final relative thermal sensitivity.