How to calibrate luminescent crossover thermometers: a note on “quasi”-Boltzmann systems

Abstract

Luminescent thermometers are potential material candidates for remote and non-invasive temperature sensing by means of a temperature-dependent optical signal. A particularly well-known class of luminescent thermometers are Boltzmann thermometers that rely on thermal coupling between two excited levels from the same configuration. Their thermal coupling kinetics is then governed by multiphonon transitions. A substantial part of potential luminescent thermometers does, however, rely on an interconfigurational crossover between two excited state potentials with differing equilibrium metal-ligand distances such as Cr³⁺ or Pr³⁺. These thermometers are often characterized by much higher intrinsic non-radiative coupling rates that allow exploiting a much higher energy gap for high relative sensitivities at appreciably low temperatures. For this class of luminescent thermometers, fitting models are often merely effective and no clear guidelines on how to tune them or how to verify the physical reliability of the fit are available. In this work, we derive a generalized fitting model for luminescent crossover thermometers and demonstrate that they generally follow a “quasi”-Boltzmann law. We explicitly demonstrate the concepts on the established phosphor SrB₄O₇ : 0.5% Sm²⁺. In this compound, Sm²⁺ can be efficiently excited with blue light and shows intense red ⁵D₀ → ⁷F_J (J = 0…6) luminescence above 680 nm and broad-banded 4f⁵5d¹ → 4f⁶-related luminescence peaking at 585 nm. By additional time-resolved measurements, it is possible to independently assess the expected order of magnitude of the fitting parameters and thus, judge the physical content of the calibration model of a luminescent crossover thermometer. It is finally shown that crossover thermometers are characterized by high relative sensitivities and low-temperature measurement uncertainty at elevated temperatures but their liability toward thermal quenching poses a serious limitation to the dynamic working range of this class of thermometers.