Al₂O₃ co-doped with Cr³⁺ and Mn⁴⁺, a dual-emitter probe for multimodal non-contact luminescence thermometry

Abstract

Luminescence probes that facilitate multimodal non-contact measurements of temperature are of particular interest due to the possibility of cross-referencing results across different readout techniques. This intrinsic referencing is an essential addition that enhances accuracy and reliability of the technique. A further enhancement of sensor performance can be achieved by using two luminescent ions acting as independent emitters, thereby adding in-built redundancy to non-contact temperature sensing, using a single readout technique. In this study we combine both approaches by engineering a material with two luminescent ions that can be independently probed through different readout modes of non-contact temperature sensing. The approach was tested using Al₂O₃ co-doped with Cr³⁺ and Mn⁴⁺, exhibiting sharp emission lines due to ²E → ⁴A₂ transitions. The temperature sensing performance was examined by measuring three characteristics: temperature-induced changes of the intensity ratio of the emission lines, their spectral position, and the luminescence decay time constant. The processes responsible for the changes with temperature of the measured luminescence characteristics are discussed in terms of relevant models. By comparing temperature resolutions achievable by different modes of temperature sensing it is established that in Al₂O₃-Cr,Mn spectroscopic methods provide the best measurement accuracy over a broad temperature range. A temperature resolution better than ±2.8 K can be achieved by monitoring the luminescence intensity ratio (40–145 K) and the spectral shift of the R-line of Mn⁴⁺ (145–300 K range).

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1. Introduction

When reliable temperature measurements are required in challenging applications, such as in harsh environments or with restricted access to an object of interest, non-contact probes with all their advantages are the temperature sensors of choice.^1–3 Examples include very hot or cold apparatus, aggressive chemicals, and strong electromagnetic and radiation fields where the necessity of isolation, shielding, or motion of the object would add complications. Many areas of science and technology benefit from using this method, such as aerospace,⁴ catalysis,⁵ life science,⁶ medicine⁷ and biology.^8,9 Importantly, it is one of the few methods capable of delivering temperature mapping with submicron spatial resolution.^10,11 Thus, the field of luminescence thermometry develops rapidly, as demonstrated by a steady stream of publications and reviews.^12–17

Temperature changes affect a range of luminescence characteristics, such as shapes of emission spectra, intensities, or luminescence decay time constants. Either of these observables can be used to monitor temperature.^16,18 The choice of detection scheme is often governed by the sensitivity to temperature changes that a sensor's specific luminescence characteristics exhibits. Most common are luminescence decay time and intensity ratio of two peaks.¹⁴ The intensity ratio method compares the emission intensities observed from two thermally coupled levels, obeying Boltzmann statistics. The energy difference between the two levels defines the range of temperatures where the method exhibits highest sensitivity.^12,19 The key advantage of this method is the ability to derive absolute temperature, without requiring sensor calibration.²⁰ In general, in luminescence decay time thermometry, it is the decay time of the excited state that is used for temperature monitoring. Depopulation of the excited level can proceed via the radiative and the non-radiative path for which the rate can be a strong function of temperature. Thus, a value for temperature can be derived by measuring the rate of photons emitted via the radiative process. The thermal depopulation of the excited state through a non-radiative decay channel is the dominant process that determines the sensitivity of a probe over a broad temperature range.^14,21,22 Given that both techniques rely on a change in population of the excited state, they are complementary by nature and can be adopted within the same material. This idea gave rise to the concept of dual-mode sensing that is gaining in popularity.^23–28 Dual-mode sensing benefits from the possibility of cross-referencing sensor readings by using two methods, thereby improving reliability and accuracy of measurements. This concept received a fresh impetus recently when the feasibility of multimodal temperature sensing using three different techniques, i.e. intensity ratio, decay time and peak shift, was demonstrated in Cr-doped oxides.²⁹ Materials doped with transition metal ions are well suited for multimodal sensing owing to a noticeable shift of the luminescence peaks with temperature, caused by electron–phonon interaction of impurity ions with the host lattice.^30–32

2. Concept of the multimodal dual-emitter sensor

A further performance enhancement of luminescence probes can be achieved by using a pair of emitters.³³ Combinations of different rare earth ions^34–37 as well as pairing rare-earth with transition metal ions^38–42 have been explored extensively and it has been shown that having two emitters in the same crystal enables a sensitivity enhancement and permits operation of the sensor over an extended temperature range. It is therefore important to assess this enhancement that a material with dual-emitters, multimodal sensor of temperature can bring, the topic of this feasibility study.

To employ all three schemes of temperature monitoring, including the shift of emission peaks as a function of temperature, hosts doped with two d³-type transition metal ions are deemed to be most suitable because of the narrow band emission (²E → ⁴A₂) which depends on the strength of the crystal field. The application of single ions of Cr³⁺ or Mn⁴⁺ for triple temperature readout has been recently demonstrated.^29,32 Here we test the multimodal dual-emitter approach by co-doping Al₂O₃ with both these ions. Aluminium oxide is a stable material with simple structure and is comprehensively characterised as temperature sensor based on luminescence (see ref. 29 and reference herein). Moreover, Al₂O₃ is capable of accommodating transition metal ions in different valence states.^43–45 The sharp emission peaks of chromium and manganese ions observed at around 700 nm are strongly influenced by the crystal field environment and sensitive to variation of temperature. Thus, Al₂O₃ co-doped with Cr³⁺ and Mn⁴⁺ (Al₂O₃-Cr,Mn) represents an attractive material for these investigations. Here we will demonstrate how these two ions can be harnessed to enhance the performance of Al₂O₃ in temperature sensing applications.

It is pertinent to highlight that the dual-emitter approach in combination with the multimodal readout may offer an easy way of cross-referencing the selected temperature sensing method by a simple switch between the emission peaks of the activators. This offers an innovative solution to the cross-referencing and has as further advantage in-built redundancy of temperature sensing. The latter could provide a vital cross-check in critical applications due to being able to derive temperature from two emitters simultaneously without having to change the method of detection. Thus, this study is an important step towards the development of effective multifunctional thermometers with intrinsic redundancy of temperature sensing.

3. Experimental

3.1. Sample preparation

In this study we used powder samples of Al₂O₃ with nominal concentration of Mn = 0.02 at% and Cr = 0.005 at%, prepared via the sol–gel citrate route. These concentrations were selected based on our prior knowledge of the luminescence properties of the material, aiming to ensure that no energy transfer between the impurity ions occurs. As the ionic radius of Mn⁴⁺ (0.54 Å, CN = 6) is almost identical to that of Al³⁺ (0.53 Å, CN = 6) when doped into α-Al₂O₃ it can replace the Al³⁺ ions in the AlO₆ octahedra but requires charge compensation. This is achieved by the admixture of other ions in a 2+ valence state (typically Mg²⁺).⁴⁶ Therefore Mg was added to the mixture in a concentration equal to that of Mn (0.02 at%). Water solutions of corresponding metal nitrates, taken in stoichiometric ratio according to nominal composition, were mixed together on a magnetic stirring device for 30 min. After that, the water solution of citric acid was added drop by drop to the reaction mixture, ensuring a molar ratio of metals to citric acid equal to 1 : 2. The solution prepared in this way was evaporated at a temperature of 80 °C and dried at 100 °C to form a polymer gel. The reaction occurs with intense release of NO₂ gas. The polymer gel was heat treated in several stages: at temperatures of 300 and 450 °C for 30 min to remove the organic component and at temperatures of 700, 800, 900 and 1000 °C with exposure at maximum temperature for 2 h. The final heat treatment of the product was performed at a temperature of 1200 °C for 4 h.

3.2. Luminescence characterisation

Photoluminescence characterization was performed using a Horiba/Jobin–Yvon Fluorolog-3 spectrofluorometer with a 450 W continuous spectrum xenon lamp for excitation. The emission was detected using a Hamamatsu R928P photomultiplier operating in photon counting mode. The luminescence decay kinetics were measured using the same Fluorolog-3 spectrofluorometer with the excitation light modulated by a mechanical modulator (chopper). The spectroscopic measurements in the temperature range between 4.4 and 330 K were carried out in a Janis continuous-flow liquid-helium cryostat using a Lake Shore 331 temperature controller. The spectra presented here are corrected for the instrumental response of the detection system.

4. Results

4.1. X-ray diffraction and structure determination

Heat treatment of sol–gel derived precursors at 700 °C for 2 h leads to the formation of an X-ray amorphous product. Crystallization of the nanocrystalline γ-Al₂O₃ phase occurs after additional heating to 800 °C and this structure is preserved after further treatment at 900 °C. A well-crystallized α-Al₂O₃ corundum phase appears after further annealing of the material at 1000 °C for 2 h. Thus, the material heated to 1000 °C consists of two alumina polymorphs – nanocrystalline γ-Al₂O₃ and rhombohedral (sub)microcrystalline α-Al₂O₃ (Fig. 1). A practically pure corundum α-Al₂O₃ phase was obtained after additional heat treatment of the powder at 1200 °C for 4 h (see (Fig. 2)). Only few extra peaks with relative intensity less than 1% could be detected in the XRD pattern (i.e. at 27.6, 30.43, 31.88 and 44.65 deg. 2 theta), which, however, could not be identified among the phases containing Al–O–Mn–Mg.

Fig. 1 X-ray diffraction patterns of sol–gel derived powders of Al₂O₃, subsequently heat treated in air at 800 °C, 900 °C and 1000 °C for 2 h.

Fig. 2 Graphical results of Rietveld refinement of structure of Al₂O₃ annealed at 1200 °C in space group R3̄c. Experimental and calculated XRD patterns (blue circles and black line, respectively) are shown together with corresponding Miller indices for Bragg maxima of the corundum structure. The inset shows the enlarged high-angle part of the pattern.

The precise structural parameters of Al₂O₃ annealed at 1200 °C were derived by full profile Rietveld refinement from experimental XRD data collected over a wide 2Θ range, spanning 10 to 155° using an XPERT-PRO diffractometer. Unit cell dimensions, coordinates and isotropic displacement parameters of atoms in the rhombohedral Al₂O₃ structure were refined together with profile parameters, applying corrections for absorption and instrumental sample shift. As the final stage of the refinement procedure, anisotropic displacement parameters of Al and O species were refined. As a result, an excellent fit between calculated and experimental profiles was achieved (Fig. 2). Refined structural parameters of the final product and corresponding residuals are presented in Table 1.

Table 1 Crystallographic data for Al₂O₃ annealed at 1200 °C: space group R3̄c, a = 4.75931(6) Å, c = 12.9933(1) Å

Atoms, sites	x/a	y/b	z/c	B iso/eq ^a, Å^2	B 11	B 22	B 33	B 12	B 13	B 23
a B iso/eq = 1/3(B11(a*)^2a^2 + … 2B23b*c*bc cos α); T = exp(−1/4(B11(a*)^2h^2 + … 2B23b*c*kl)).
Al, 12c	0	0	0.3524(1)	0.64(3)	0.61(3)	B 11	0.70(5)	1/2B11	0	0
O, 18e	0.3080(4)	0	1/4	0.72(8)	0.70(8)	0.83(11)	0.66(10)	1/2B22	−0.04(5)	2B13
R I = 0.028, RP = 0.078

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4.2. Luminescence and crystal field analysis

Aluminium oxide doped with Cr³⁺ is an extensively studied material used as solid-state laser,⁴⁷ pressure sensor in diamond anvil cells⁴⁸ and sensor of temperature.^49,50 Therefore, the luminescence properties of this material and their temperature evolution are well documented (see e.g. ref. 29, 51, 52 and reference there). The studies of luminescence properties of Al₂O₃ doped with isoelectronic Mn⁴⁺ ions are, however, scarce. The low-temperature (T = 77 K) spectra due to ²E → ⁴A₂ transitions in Al₂O₃-Mn⁴⁺ have been first reported by Geschwind et al.⁴⁴ and later the temperature changes of the luminescence were measured over the 2.5 to 295 K range.⁵³ It is worth commenting that the narrow band emission at 694 nm due to Cr³⁺ has been identified occasionally in samples of Mn⁴⁺-doped Al₂O₃ ^45,54 as such due to unintended contamination of the material.

The application of Al₂O₃-Cr,Mn as a dual-emitter probe for temperature sensing relies on a holistic understanding of processes governing the temperature changes of luminescence characteristics of the material. Therefore, we begin the study from measurements of the temperature-dependent spectroscopic characteristics. The luminescence excitation and emission spectra of Al₂O₃-Cr,Mn are shown in Fig. 3 while the positions of the main excitation bands and emission peaks of Cr³⁺ and Mn⁴⁺ are listed in Table 2.

Fig. 3 Luminescence (left) and luminescence excitation spectra (right) of Al₂O₃-Cr,Mn measured at T = 40 K (emission) and 4.4 K (excitation).

Table 2 Position of Mn⁴⁺ and Cr³⁺ emission and excitation peaks in Al₂O₃ co-doped with Cr and Mn

Ion	Ē → ^4A2 (R1-line), nm (cm^−1)	→ ^4A2 (R2-line), nm (cm^−1)	R1–R2 gap, meV (cm^−1)	^4A2 → ^4T1g nm (cm^−1)	^4A2 → ^4T2g, nm (cm^−1)	Ref.
a Tentative assignment due to overlap with the charge-transfer band.
Mn^4+	676.3 (14 786)	672.6 (14 868)	10.1 (81.5)	390 (25 641)	472 (21 186)	This work
	676.3 (14 786)	672.7 (14 865)	10.2 (82.3)	320^a (31 250)	470 (21 277)	44
Cr^3+	693.3 (14 424)	691.9 (14 453)	3.6 (29)	405 (24 691)	557 (17 953)	This work
	693.3 nm/(14 424)	691.9 (14 453)	3.6 (29)	411 (24 330)	568 (17 606)	29

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The unfilled 3d states of Mn⁴⁺ and Cr³⁺ are strongly influenced by the immediate environment of the ions in the crystals. The crystal field causes a splitting of the electron states into several energy levels. The luminescence excitation bands due to ⁴A₂ → ⁴T_2g, ⁴T_1g transitions of Cr³⁺ are clearly identified at 557 and 405 nm. The luminescence excitation spectrum of Mn⁴⁺ consists of only two bands in the examined region. The band with a maximum at about 472 nm is related to the ⁴A₂ → ⁴T_2g transition and it is blue-shifted compared to the band associated with the same transitions for Cr³⁺ ions. The second band with a maximum at 390 nm is likely to be related to a mixture of ⁴A₂ → ⁴T_1g and charge-transfer transitions. We therefore assume that these two types of transitions spectrally overlap.

Through knowing the positions of the bands it is possible to calculate the strength of the crystal field D_q and Racah parameters B and C, using the following formulas.⁵⁵

E(⁴T_2g) = 10D_q (1)

ΔE = E(⁴T_1g) − E(⁴T_2g) (4)

For the calculations of crystal field parameters for Cr³⁺ we used band maxima positions. However, for Mn⁴⁺ reasonable values of crystal field and nephelauxetic parameter are obtained if, instead of band peaks, the expected positions of electronic levels (zero-phonon lines) are used. The overlap between the ⁴A₂ → ⁴T_1g and charge-transfer transitions for Mn⁴⁺ is responsible for difficulties in establishing the exact position of the ⁴A₂ → ⁴T_1g band. We assume that the positions of zero-phonon lines are located at the low-energy side of the appropriate bands. Parameters D_q, B, and C, calculated in this way, are listed in Table 3.

Table 3 Crystal field and nephelauxetic β₁ parameters for Cr³⁺ and Mn⁴⁺ in Al₂O₃

Parameter	Value (cm^−1)
	Cr^3+	Mn^4+
D q	1786	1905
B	714	762
C	3041	3038
β 1	1.0997	0.9573

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The results obtained also allow to calculate the nephelauxetic parameter β₁, defined in ref. 56 as:

Having established the values of crystal field and Racah parameters, it is possible to construct Tanabe–Sugano diagrams for both ions. They are presented together in one figure (Fig. 4). The analysis of excitation spectra of Mn⁴⁺ and Cr³⁺ emission shows that the excitation bands of the two ions are well separated. No emission of Mn⁴⁺ is detected at the excitation in the range of the ⁴A₂ → ⁴T_2g band of Cr³⁺, while the excitation spectrum of Cr³⁺ is similar to the one measured earlier in Al₂O₃-Cr²⁹ and exhibits no changes that could be attributed to the influence of other ions. This enables us to conclude that due to low concentration there is no energy transfer between dopant ions in the material under study that can markedly alter the luminescence characteristics.⁴¹ Consequently, emission of Mn⁴⁺ and Cr³⁺ can be treated independently. This is an important condition that allows to analyse the changes of their luminescence characteristics with temperature within the framework of models developed for the emission of individual ions. The spectra also allowed to select a single wavelength for the excitation of both activators with the aim to achieve similar intensity of the R₁-lines.

Fig. 4 Tanabe–Sugano diagrams for Cr³⁺ (black lines) and Mn⁴⁺ (red lines) in Al₂O₃. Positions of energy levels are slightly dependent on both B and C Racah parameters, therefore it is necessary to distinguish between Cr³⁺ and Mn⁴⁺. The effect of the stronger crystal field for Mn⁴⁺ compared with that for Cr³⁺ is clearly visible on the graph.

The luminescence spectrum of Al₂O₃-Cr,Mn features two pairs of narrow peaks that correspond to the characteristic transitions of Mn⁴⁺ and Cr³⁺ (see (Fig. 3)). The peaks referred to as R₁ and R₂ lines are due to spin-forbidden transitions from the lowest excited ²E level split into two levels (Ē and ) to the ground state ⁴A₂. The splitting is due to the lowering of the octahedral symmetry of the local crystal field surrounding the ions.⁵² The magnitude of the splitting is proportional to the strength of the crystal field. The energy of the emission lines is further influenced by the nephelauxetic effect. The covalence increases with the charge of the ions,⁵⁶ resulting in an increase of the energy of the emitted photons. Consequently, the R-lines of Mn⁴⁺ are shifted to shorter wavelength with respect to the emission of Cr³⁺. Notably, the correlation between the calculated nephelauxetic parameters β₁ and the position of the ²E levels of the two ions fits the established trend.⁵⁶

4.3. Temperature dependent luminescence characteristics

The high sensitivity of the outer 3d shells of Cr³⁺ and Mn⁴⁺ to changes of the crystal field environment and their coupling with lattice vibrations are the main factors that control the changes with temperature of the luminescence characteristics of ions in different hosts. Due to the very narrow emission peaks, a small change in the population of the emitting levels as wll as their energy is clearly visible in Fig. 5.

Fig. 5 Luminescence spectra of Al₂O₃ co-doped by Cr³⁺ and Mn⁴⁺ in the wavelength region of the R-lines, measured at 505 nm excitation and various temperatures. The spectra are shifted vertically for clarity.

These changes are exploited by two methods of luminescence thermometry based on measurements of spectroscopic characteristics. Since the population of two emitting levels obeys Boltzmann statistics, the emission spectra exhibit a rapid decrease of the intensity of the R₂ lines with respect to R₁ at cooling due to an increase in the population of the lower exited state. In the framework of a statistical model, the ratio of intensities F = I_R2/I_R1 can be derived from the population of the levels in thermal equilibrium, resulting in the following expression:

where A is a constant depending on the spontaneous emission rate, its frequency and degeneracy of the two levels,²⁰D is the energy difference between the two emitting levels, k is the Boltzmann constant, and T is the absolute temperature. It should be noted that in some cases the background signal due to other emission processes can cause an offset, usually expressed through adding a constant to eqn (6).¹⁹ The potential of a material as luminescence sensor of temperature can be assessed using the ratio of luminescence intensities of two lines. The Arrhenius plots displayed in Fig. 6 show good linearity above 30 K, evidencing thermal equilibrium between excited states in Mn⁴⁺ and Cr³⁺. The deviation from linearity at high temperatures is due to thermalisation via phonon interaction not accounted for by the model. The values of energy gaps derived from a linear fit of the data are 3.67 ± 0.03 meV for Cr³⁺ and 10.2 ± 0.2 meV for Mn⁴⁺. They correlate very well with the parameters obtained from spectroscopic measurements, confirming the validity of the underlying models. It is worthwhile noting that a factor of three difference in the energy gap is observed for the two ions, translating into different sensitivity of the intensity ratio to changes of temperature.

Fig. 6 Arrhenius plot for the intensity ratio of the R₂- and R₁-lines of Cr³⁺ and Mn⁴⁺ in Al₂O₃-Cr,Mn and linear fits of the dependences.

The temperature dependence of the spectral position of the R₁ and R₂-lines are displayed in Fig. 7. The thermal shift of the lines, Δν, resulting from the interaction of electronic states of impurity ions with acoustic phonons can be described by the Debye theory:⁵⁷

where α is the coupling coefficient for the electron–phonon interactions and T_D is the Debye temperature. We carried out a correlated fit of the R-line wave numbers for different temperatures to find the optimal values for the parameter α, individually for the two lines, and for the Debye temperature T_D, common to both datasets.

Fig. 7 Temperature shift of the R-lines of Mn⁴⁺ (top) and Cr³⁺ (bottom) in Al₂O₃-Cr,Mn measured at 505 nm excitation. The dots are the experimental data points and the solid lines show the best fit of experimental results to eqn (7), using parameters shown in Table 4.

The applied fitting procedure resulted in very good fits throughout the entire measurement range. The fit parameters, summarised in Table 4, are in very good agreement with our recent results for Al₂O₃-Cr.²⁹ The value of the Debye temperature derived from the wavelength shift of Mn⁴⁺ is closer to earlier results for Al₂O₃-Cr, T_D = 750 K.⁵⁷ It should be noted that the R-lines of both ions exhibit a very similar pattern regarding the spectral shift with temperature. The shift is negligible below 100 K while it can be detected at temperature above that, thus confining this temperature monitoring method to temperatures above 100 K.

Table 4 Parameters of fits obtained from the temperature dependence of the luminescence wavelength shift eqn (3) for Cr³⁺ and Mn⁴⁺ emission in Al₂O₃-Cr,Mn

Parameter	Cr^3+ in Al2O3-Cr	Cr^3+ in Al2O3-Cr,Mn	Mn^4+ in Al2O3-Cr,Mn
α R1, cm^−1	−518.0	−515.2	−1048.5
α R2, cm^−1	−507.5	−500.0	−972.0
T D, K	867	856	736
Ref.	29	This work	This work

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One more method of temperature monitoring that can be implemented with materials doped with transition metal ions uses the luminescence decay time of the R-lines. To evaluate the merit of the dual-emitter concept of temperature sensing further we investigated the changes of the luminescence decay time with temperature of Cr³⁺ and Mn⁴⁺ in Al₂O₃. Fig. 8 shows the decay curves recorded at 694 and 676 nm peaks and temperature dependence of respective decay time constants.

Fig. 8 Left – Decay curves measured at the peak of Mn⁴⁺ and Cr⁴⁺ emission at different temperatures. Right – Temperature dependence of the luminescence decay time constant of Mn⁴⁺ (top) and Cr³⁺ emission (bottom) in Al₂O₃-Cr,Mn. The solid lines show the best fit of eqn (8) to the experimental results (dots) using the parameters summarised in Table 5.

Qualitatively the measured dependences are very similar for both ions. The initial increase of the decay time constant with cooling can be readily explained by the decrease of the probability for non-radiative de-excitation of the emitting level. This is a typical behaviour observed in luminescence materials.^58,59 The decay time constant reaches a maximum value at ca. 100 K but below this temperature it decreases with further cooling. Such drop of τ = f(T) at very low temperatures is not very common. It has been discussed so far in few materials doped with Cr³⁺ (ref. 29, 60 and 61) while it is the first time that the effect is explicitly observed for Mn⁴⁺ emission. This behaviour is explained assuming different radiative transition probability from the Ē and levels, constituting the emitting ²E state. The probability of radiative decay from the upper level is lower in comparison with that for Ē, leading to an increase of the measured radiative decay time constant of the R-line emission. However, a decrease of temperature leads to depopulation of the upper level, thereby reducing its contribution to the emission process in favour of transitions from the low-lying level Ē with a higher radiative decay rate. This is then manifested as decrease of the measured decay time constant of the R-lines with further cooling.

The observed behaviour of the decay time constant for the Cr³⁺ and Mn⁴⁺ emissions in Al₂O₃ over the examined temperature range reflects the dynamic of temperature changes in the population of the excited states and probabilities of transitions between them. Recently we demonstrated that this convoluted phenomenon can be comprehensively described by taking into account the main processes affecting the population and radiative rates of the ²E state, i.e. thermalisation, phonon-assisted interaction with lattice vibrations and thermally induced depopulation.²⁹ Under the assumption of thermal equilibrium between the states Ē, and ⁴T₂ involved in the transitions and considering interactions with lattice vibrations we obtained the following expression for τ(T):

Here 1/τ_i (i = 1, 2 and 3) are the radiative decay rates of the Ē, , and ⁴T₂ levels respectively. ΔE is the energy difference between the ²E and ⁴T₂ levels, E_p stands for “effective energy” of the phonons responsible for the exchange with the sidebands while other notations are explained above. This equation explicitly describes the thermalisation process occurring between the Ē and levels, phonon-assisted relaxation and depopulation of the levels due to thermally induced ²E → ⁴T₂ transitions.

As shown in Fig. 8 the measured temperature dependences of the decay time constants of Cr³⁺ and Mn⁴⁺ perfectly fit the equation confirming agreement of experimental results with theory over the entire temperature range. The parameters of the fit for Cr³⁺ summarised in Table 5 show good agreement with the results published earlier while the effective energy of phonons, E_p, is comparable with the mean value of the phonon energy of Al₂O₃.⁶²

Table 5 Fit parameters obtained from the temperature dependence of the luminescence decay time constant eqn (5) for Cr³⁺ and Mn⁴⁺ emission in Al₂O₃-Cr,Mn

Parameter	Cr^3+ in Al2O3-Cr	Cr^3+ in Al2O3-Cr,Mn	Mn^4+ in Al2O3-Cr,Mn
a The value of D is fixed to be equal to the energy splitting of the ^2E level.
τ 1, ms	3.98 ± 0.01	4.04 ± 0.01	0.83 ± 0.01
τ 2, ms	4.46 ± 0.01	5.43 ± 0.02	1.16 ± 0.01
E p, meV	60.9 ± 0.4	61.2 ± 0.1	55.7 ± 0.1
D , meV	3.6	3.6	10.2
τ 3, μs	33 ± 25	86 ± 41	139 ± 94
ΔE, meV	237 ± 23	281 ± 15	213 ± 25
Ref.	29	This work	This work

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It should be noted that from the standpoint of temperature monitoring the observed change in the slope of the τ = f(T) curve is worse in comparison with temperature dependences of other luminescence characteristics that exhibit a monotonous trend. This change is caused by a lower sensitivity of the method around the peak of the curve. The consequences and implication of this feature for the dual-emitter sensing will be discussed in the next section.

4.4. Thermometric performance

To estimate the merit of a dual-emitter Al₂O₃-Cr,Mn probe in different modes of temperature sensing we adopted as metrics the temperature uncertainty δT. This parameter calculated by converting the uncertainty of the parameter that is measured, δQ, by dividing it by the responsivity of the sensor, |dQ/dT|.^18,63,64

This approach allows a direct comparison of the different temperature measurement methods.²⁹

The absolute sensitivity can be readily calculated from the measured temperature dependence of the parameter of interest. The uncertainty of the measurements of decay time and intensity ratio over the examined temperature range were estimated to be 0.5% and 2% respectively. The absolute error in determining the wavelength shift is taken as a constant value of 0.02 nm. These data were used to calculate the uncertainty of temperature measurements δT = f(T) for different modes of sensing (see Fig. 9).

Fig. 9 The temperature resolution of Al₂O₃-Cr,Mn in different modes of temperature sensing: F – luminescence intensity ratio, Δν – spectral shift and τ – decay time constant.

Analysis of the plots allows to assess the potential of the multimodal dual-emitter concept as non-contact luminescence sensor of temperature. The plot clearly demonstrates the significant difference in the achievable resolution depending on the measurement technique, luminescence ion and temperature range of operation. The lowest temperature uncertainty (±0.1 K at 10 K) can be reached by using the intensity ratio of R-lines of Cr³⁺ while for Mn⁴⁺ emission this value is three times higher. The sensitivity of the method is proportional to the energy gap between the R-levels involved in the transitions^19,20 translating to better temperature resolution achievable with Cr³⁺ ions in comparison with Mn⁴⁺. However, a smaller gap also implies a narrow temperature range for a ratiometric sensor.²⁰ This shortcoming of the intensity ratio method using Cr³⁺ emission is clearly visible in Fig. 9. The measurement uncertainty increases very rapidly; it is more than ±1 K above 50 K. In this regard the intensity ratio of the R-lines of Mn⁴⁺ is superior in comparison with other techniques as such, permitting to achieve lowest uncertainty of temperature measurements over the 40–145 K range.

Inspecting Fig. 9 shows that the temperature monitoring techniques based on intensity ratio and wavelength shift of the Mn⁴⁺ emission exhibit the same uncertainty of ±2.8 K at about T = 145 K. This defines a cross-over point between the two methods. It is worthwhile noting that for Cr³⁺ emission the measurement uncertainty at the cross-over point (T = 135 K) is larger by a factor three. At higher temperatures (145–300 K) the best temperature resolution can be achieved by monitoring the wavelength shift of the R-lines of the Mn⁴⁺ luminescence. This gives more accurate readings in comparison with the shift of Cr³⁺ lines and methods based on the changes of decay time constants of Cr³⁺ or Mn⁴⁺ emission. The R-lines of Mn⁴⁺ exhibit a larger shift with temperature in comparison to Cr³⁺ lines (see also Fig. 5), translating into better accuracy. It is also evident that the temperature resolution of decay time thermometry in this case is inferior when compared with spectroscopic methods of temperature monitoring. Finally, it should be noted that temperature resolution obtained for Al₂O₃ co-doped with Cr³⁺ and Mn⁴⁺ is very compatible with the typical values reported for other oxides doped with transition metal ions (see Table 6).

Table 6 Thermometric resolution of Cr³⁺ and Mn⁴⁺ doped oxides

Material	Method	Temperature, K	Temperature resolution, K	Ref.
α-Al2O3-Cr	Intensity ratio	30	0.45	63
α-Ga2O3-Cr	Intensity ratio	300	0.25	65
β-Ga2O3-Cr	Intensity ratio	300	0.42	65
β-Ga2O3-Cr	Line shift	300	2	29
β-Ga2O3-Cr	Decay time	165	0.3	29
YAlO3-Cr	Intensity ratio	20	0.2	29
Bi2Al4O9-Cr	Intensity ratio	300	0.23	66
Mg2SiO4-Cr	Line shift	310	7.9	32
Mg2SiO4-Cr	Decay time	310	0.2	32
Li2TiO3-Mn	Decay time	332	0.032	67
Zn2GeO4-Mn	Decay time	360	0.64	26
MgTiO3-Mn	Intensity ratio	93	0.42	24
MgTiO3-Mn	Decay time	278	0.025	24

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5. Conclusion

The concept of multimodal dual-emitter luminescence sensors of temperature was put to the test using Al₂O₃ co-doped with transition metal ions of Cr³⁺ and Mn⁴⁺. To assess the feasibility of non-contact temperature measurements through monitoring the intensity ratio, wavelength shift, and decay time constant of R-lines emitted by both ions, we examined the evolution of the luminescence spectra and decay time constant of Al₂O₃-Cr,Mn over the 4–350 K temperature range. Detailed analysis of spectroscopic results allowed to determine the energy level diagram and establish that the crystal field acting upon each ion governs the luminescence properties of the material. The investigations were conducted by comparing experiments with relevant theoretical models. It is shown that the models provide adequate interpretation of the emission processes, evidenced by the high quality of fits obtained for the measured temperature dependences of the luminescence intensity ratio, wavelength shift and decay time constant for both emitting ions.

The thermometric performance of Al₂O₃-Cr,Mn was assessed by analysing the temperature resolution achievable by different methods. The comparison shows that in this material the resolution obtained through measuring the luminescence decay time constant is not adequate for monitoring temperature over 4–300 K range. In contrast, the intensity ratio method is superior at very low temperature as it allows to attain a temperature uncertainty as low as ±0.1 K at 10 K by monitoring Cr³⁺ emission. As temperature increases, measurements of the intensity ratio of the R-lines of Mn⁴⁺ is preferable as such, giving better accuracy in comparison with that of Cr³⁺ emission. Though the accuracy of the method gradually decreases it remains the most accurate up to the cross-over point at 145 K when the measurement uncertainty reaches ±2.8 K. Above this point monitoring the wavelength shift of Mn⁴⁺ lines allows the temperature to be determined with better uncertainty.

The significance of these findings is two-fold. First, they demonstrated the viability of the dual-emitter multimodal concept for non-contact luminescence measurements of temperature. The luminescence characteristics of transition metal ions co-doped in Al₂O₃ exhibit measurable changes with temperature, laying the foundation for future designs of novel materials and read-out configurations with improved accuracy and reliability. Second, the results of this study highlighted the advantage of Mn⁴⁺ emission in aluminium oxide for thermometric application. It is very competitive in comparison with Cr-doped Al₂O₃ and consequently this material holds a considerable promise for the technology of non-contact sensing.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The work was partially supported by the Polish National Science Centre (project no. 2018/31/B/ST8/00774) and by the National Research Foundation of Ukraine (grant no. 2020.02/0373).

Notes and references

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