Beyond the Energy Gap Law: The Influence of Selection Rules and Host Compound Effects on Nonradiative Transition Rates in Boltzmann Thermometers

Abstract

range from biothermal imaging, [5,6] temperature monitoring in catalysis, [7][8][9][10] microelectronics, [11] or molecular logics [12] to the investigation of fundamental thermodynamic phenomena [13] at the micro-and nanoscale. One of the conceptually simplest ways of optical temperature sensing, also in terms of the required setup, is the exploitation of the luminescence intensity ratio (LIR) of two emission bands due to radiative transitions from two thermally coupled excited levels of an ensemble of non-interacting ions. In case of efficient thermal coupling between these levels by (multi) phonon transitions, the LIR follows Boltzmann's law. [14] Trivalent lanthanoid ions with the rich energy level structure arising from their partially filled 4f n (n = 1-13) configuration are primary representatives for this type of luminescence thermometry, with Er 3+ and its green-emitting 2 H 11/2 and 4 S 3/2 levels being the most prominent examples. [7,15] Boltzmann-type equilibrium between the two excited levels critically depends on the interplay between the depopulating radiative decay and the nonradiative multiphonon thermalization pathways. [14,16] The rate-determining step is the Apart from the energy gap law, control parameters over nonradiative transitions are so far only scarcely regarded. In this work, the impact of both covalence of the lanthanoid-ligand bond and varying bond distance on the magnitude of the intrinsic nonradiative decay rate between the excited 6 P 5/2 and 6 P 7/2 spin-orbit levels of Gd 3+ is investigated in the chemically related compounds Y 2 [B 2 (SO 4 ) 6 ] and LaBO 3 . Analysis of the temperature-dependent luminescence spectra reveals that the intrinsic nonradiative transition rates between the excited 6 P J ( J = 5/2, 7/2) levels are of the order of only 10 ms −1 (Y 2 [B 2 (SO 4 ) 6 ]:Gd 3+ : 8.9 ms −1 ; LaBO 3 :Gd 3+ : 10.5 ms −1 ) and differ due to the different degree of covalence of the GdO bonds in the two compounds. Comparison to the established luminescent Boltzmann thermometer Er 3+ reveals, however, that the nonradiative transition rates between the excited levels of Gd 3+ are over three orders of magnitude slower despite a similar energy gap and the presence of a single resonant phonon mode. This hints to a fundamental magnetic dipolar character of the nonradiative coupling in Gd 3+ . These findings can pave a way to control nonradiative transition rates and how to tune the dynamic range of luminescent Boltzmann thermometers.

A Cr3+ luminescence based ratiometric optical laser power meter

“…The luminescence spectra of materials doped with Cr 3+ ions result from the d-d electronic transitions. In the case of the transition metal ions of 3d 3 electronic configuration observed for Cr 3+ ions, depending on the crystal field strength of the host material the spectrum is dominated either by narrow band 2 E (g) -4 A 2g emission (strong crystal field) or broad emission band 4 T 2(g) -4 A 2(g) for the weak crystal field. However, in order to develop a ratiometric optical excitation density sensor based on the emission intensity ratio from the 2 E (g) level to that from the 4 T 2(g) level, one should use materials with an intermediate crystal field for which both bands are observed in the spectrum simultaneously (Fig.…”

“…As the Cr 3+ content increases, the intensity of the broad 4 T 2(g) -4 A 2(g) band increases relative to the 2 E (g) -4 A 2(g) one. Although such a change may suggest a modification in the crystal field strength with increasing dopant ion concentrations, 42 a careful analysis of the excitation spectra clearly indicates that the positions of the 4 A 2(g) -4 T 2(g) and 4 A 2(g) -4 T 1(g) absorption bands of Cr 3+ ions are independent of the dopant ion concentration. The determined strength of the crystal field (based on eqn (S1)-(S3), ESI †) confirms this observation and Dq/B B 2.48 is obtained for all analyzed dopant concentrations (Fig.…”

“…citric acid) and further polymerization Fig. 1 Schematic representation of the principle of operation of Cr 3+ based ratiometric laser power meter: the luminescence spectra of Cr 3+ ions in GdAl 3 (BO 3 ) 4 consist of two emission bands associated with the radiative transitions from both 2 E (g) and 4 T 2(g) states. Upon low excitation density (top), low heat is generated, hence the 2 E (g) -4 A 2(g) emission band dominates in the spectrum, whereas upon high excitation density (bottom), high heat generated in the system leads to the thermalization of the 4 T 2(g) state and thus a relative increase of the 4 T 2(g) -4 A 2(g) band intensity with respect to the 2 E (g) -4 A 2(g) is observed.…”

“…Nonradiative relaxation is typically considered as detrimental for luminescence and many efforts have been undertaken to prevent it. [1][2][3][4][5] In the case of materials doped with lanthanide ions, low phonon energy matrices and low dopant concentrations were proposed, mostly to eliminate multiphonon relaxation processes. 6,7 On the other hand, for transition metal ions, the preservation of a small shift between the parabolas of the excited and ground levels and a small electron-phonon coupling were found to reduce the probability of nonradiative processes.…”

“…[36][37][38] Besides, GdAl 3 (BO 3 ) 4 is highly mechanically and thermally stable which enables developing a laser beam power meter operating even in the high excitation power density range without any degradation or decomposition of the material. The spectrally broad absorption bands of Cr 3+ ions in the visible range associated with the 4 A 2(g) -4 T 1(g) and 4 A 2(g) -4 T 2(g) electronic transitions allow for extending the useful spectral range for which the luminescence response of the developed power meter will be recorded. Understanding the photophysics and materials sciences, let us propose a new method to measure the laser beam power as a simple proof-of-concept demonstration of multi-functional luminescent nanoparticles.…”