Origin of the deviation between the fluorescence intensity ratio of a thermally coupled level and the Boltzmann distribution law

¹ Condensed Matter Science and Technology Institute, Harbin Institute of Technology - 150080 Harbin, China
² School of Materials Science and Engineering, Harbin Institute of Technology - 150001 Harbin, China
³ Laboratory of Sono- and photo- theranostic Technology, Harbin Institute of Technology - 150001 Harbin, China
⁴ Department of Mathematics and Materials Research Institute, The Pennsylvania State University University Park, State College, 16082 PA, USA

^(a) zhangzhiguo@hit.edu.cn
^(b) dzk@psu.edu

Received: 10 November 2016
Accepted: 19 January 2017

Abstract

The temperature dependence of the fluorescence intensities of the thermally coupled pairs of some typical rare-earth ions was studied. The fluorescence intensity ratios (FIRs) of the thermally coupled pairs increased exponentially with increasing temperature. However, except for Er³⁺ and Nd³⁺, the FIRs of other rare-earth ions exhibited significant deviation from the Boltzmann distribution law. We suppose the deviation originates from the non-thermal population in the upper level of the coupled pairs. The temperature dependence of the deviation is discussed. Eliminating the deviation is beneficial for the development of FIR thermometry; only by clearly understanding the deviation can we eliminate it.