Mapping Temperature Heterogeneities during Catalytic CO2 Methanation with Operando Luminescence Thermometry

Controlling and understanding reaction temperature variations in catalytic processes are crucial for assessing the performance of a catalyst material. Local temperature measurements are challenging, however. Luminescence thermometry is a promising remote-sensing tool, but it is cross-sensitive to the optical properties of a sample and other external parameters. In this work, we measure spatial variations in the local temperature on the micrometer length scale during carbon dioxide (CO2) methanation over a TiO2-supported Ni catalyst and link them to variations in catalytic performance. We extract local temperatures from the temperature-dependent emission of Y2O3:Nd3+ particles, which are mixed with the CO2 methanation catalyst. Scanning, where a near-infrared laser locally excites the emitting Nd3+ ions, produces a temperature map with a micrometer pixel size. We first designed the Y2O3:Nd3+ particles for optimal temperature precision and characterized cross-sensitivity of the measured signal to parameters other than temperature, such as light absorption by the blackened sample due to coke deposition at elevated temperatures. Introducing reaction gases causes a local temperature increase of the catalyst of on average 6–25 K, increasing with the reactor set temperature in the range of 550–640 K. Pixel-to-pixel variations in the temperature increase show a standard deviation of up to 1.5 K, which are attributed to local variations in the catalytic reaction rate. Mapping and understanding such temperature variations are crucial for the optimization of overall catalyst performance on the nano- and macroscopic scale.


Calculating the LIR and constructing the calibration curve
The luminescence intensity ratio LIR at temperatures of T > 400 K was fitted to a Boltzmann model: 1

LIR = 𝐼
Here, Ii is the integrated intensity of emission line i, C is a prefactor including the spontaneous emission rates and degeneracies of the excited states, ∆ is the energy difference between the thermally coupled excited states, kB is the Boltzmann constant, and T the temperature.
Integration ranges of 795-860 nm and 860-960 nm were used for I2 and I1, respectively (Figure S2a).At temperatures above 963 K, the spectra were first corrected for black-body radiation (Figure S2b).The slope of ln(LIR) versus 1/T in the calibration curve (Figure 1c in the main text) is consistent with a value of ∆ = 996 cm -1 .
Figure S2.a) Emission spectrum of Y2O3 doped with 2% of neodymium at 993 K (corrected for black-body radiation), excited with the 785 nm laser of the Raman microscope.The luminescence intensity ratio is calculated by dividing the red area (I2, 4 F5/2 to 4 I9/2 electronic transition) over the blue area (I1, 4 F3/2 to 4 I9/2 electronic transition).b) Black-body radiation measured using the same settings as in a), but without laser excitation.The spectra were collected from 963 K (blue) to 1173 K (red), with intervals of 30 K.

Calculating the cross-relaxation strength
The cross-relaxation rate kx scales strongly with the distance R between a Nd 3+ ion in the excited state and a Nd 3+ in the ground state (as shown in Figure 1f), as kx = Cx R -6 .Substitutional doping (Nd 3+ for Y 3+ ) introduces optically active dopants at discrete lattice sites, but with varying numbers of neighboring dopants in the nearest neighbor shell, next-nearest neighbor shell, etc.
To model the photoluminescence decay curve at a particular Nd 3+ concentration, we assume random substitutional doping. 2 We take into account all distances to neighbors from the two types of lattice sites in the Y2O3 crystal, and assume equal rate constants for radiative decay kr and cross-relaxation Cx for Nd 3+ on either site.This produces the following model function for the photoluminescence decay I(t) as a function of the doping concentration : () =  0 (  , , )e -() +  0 with ( 2) Here, I0 is the amplitude of the curve, k is the intrinsic decay rate of a Nd 3+ dopant (i.e., excluding ion-ion interactions) and y0 is the background intensity.Ni is the number of cations at a discrete distance Ri from a C2 site (24d in Wyckoff notation) of the Y2O3 host crystal, and ni * , Ri * are and the same but for an S6 site (8b) (Figure S3).Our global fit procedure optimizes k and Cx simultaneously.Since the rates of cross-relaxation are approximately constant over the whole temperature range, the Cx from the global fit approach on the room-temperature data can be used to describe the cross-relaxation interactions between Nd 3+ ions at all temperatures.

Calculating the efficiencies
To estimate the Nd 3+ emission efficiencies as a function of temperature and doping concentration, we first characterize the temperature-independent radiative decay rate kr and the temperature-dependent nonradiative decay rate knr. Figure S4a shows the decay traces of the thermometer at a low Nd 3+ concentration (0.2%) at 293 K and 1023 K.These decay curves and those at a range of other temperature between 293 and 1173 K were fitted to a single exponent.
The inset of Figure S4a shows the increase of the total decay rate with temperature, which is caused by thermal quenching. 3,4This increase in the non-radiative rate at constant radiative rate leads to a lowered signal intensity of the lanthanide emission at temperatures above 900 K, which is undesired for precise temperature readouts. 5,6We exclude that this quenching is due to multi-phonon relaxation, which is the coupling of host lattice phonons leading to relaxation from the thermally coupled excited states to the underlying energy level ( 4 F3/2 → 4 I15/2). 5Multiphonon relaxation is highly improbable as a non-radiative decay pathway in Y2O3, since the energy gap between the 4 F3/2 and 4 I15/2 levels is ~5500 cm -1 , requiring nine maximum energy phonons to bridge that gap (maximum phonon energy of Y2O3 is around 600 cm -1 ). 5,7,8Indeed, thermal quenching sets in at different temperatures for three similar rare earth oxides: Gd2O3, Y2O3, and Sc2O3 (Figure S4b).These host materials have comparable phonon energies (Figure S4c), so similar multi-photon relaxation rates are expected.The quenching temperatures are different, so the quenching process is not multi-phonon relaxation.The ionic radius order is (coordination number = 6): Gd 3+ (0.938 Å) > Y 3+ (0.9 Å) > Sc 3+ (0.745 Å), which follows the inverse trend of the onset temperature at which non-radiative decay rates become dominant.Multi-phonon relaxation can be excluded as the dominant non-radiative decay pathway based on this data, since the onset temperature would be equal in all host crystal lattices (phonon energy is comparable in all oxide lattices.c) Phonon energies for the crystal oxide lattices, measured with the Raman microscope (λ = 638 nm).The phonon energies with the highest intensities are at 360, 376 and 416 cm -1 for Gd2O3, Y2O3 and Sc2O3, respectively. 9 fit the temperature-dependent decay rates to a constant term plus a model of non-radiative decay via cross-over to the ground state via a charge-transfer state: We estimate the radiative decay rate  r by multiplying the constant decay term  const with the radiative efficiency of 0.2% Nd 3+ doping at room temperature (Figure S5a).This value of  r is used in the global fit of Figure 1d of the main text to find the cross-relaxation strength Cx.The results from the global fit can be used to calculate the probabilities of radiative decay ( r ), nonradiative decay ( nr ) and cross-relaxation ( x ) from the emitting levels of Nd 3+ , as a function of temperature T and doping concentration : nr =  nr () ∫ e −[ r + nr ()] ( x , , )d ∞ 0 (5) Figure S5 shows the calculated probabilities of the different decay pathways.The efficiency of radiative decay and the probability of cross-relaxation decrease with temperature, while the probability of nonradiative decay increases.The increase in concentration results in an increased probability of cross-relaxation, while the probabilities of the radiative and nonradiative pathways decrease.

Calculating the relative temperature uncertainty
The expected uncertainty in temperature   for a Boltzmann thermometer with Poissonian counting noise on the number of photon counts in the two emission bands is: 3 which depends on the Boltzmann populations   of the emitting states i = 1,2: Here, gi is the degeneracy of level i,  r is the rate of radiative transition from emitting level i to the ground state, and A is a prefactor that depends on detection efficiency, measurement duration, etc.Any effect of wavelength-dependent scattering could be taken into account by adjusting  r , but for our calculations we assume that  r2 / r1 = , where  is the prefactor in the calibration curve (Eq.S1).
The normalization of the temperature uncertainty, yielding the graph in Figure 1g, was performed by dividing all the calculated temperature uncertainties at a specific temperature (e.g., 300 K) by the minimum temperature uncertainty at that temperature.We could therefore determine the optimal doping concentration at every temperature.
Introducing CO 2 into the gas atmosphere

Color change of the studied material before and after CO 2 methanation
Upon reducing the nickel hydroxide to nickel oxide/metallic nickel, the catalyst material changes color from green to black (Figure S8).During the CO2 methanation experiment (after reduction), the sample remains black.

Room temperature measurement of variations in LIR
At evelated temperatures, preferential paths for the (colder) gas flow through the catalyst powder, which could lead to variations in the cooling of the sample and result in variations in LIR.We therefore performed a measurement at room temperature on the reduced (blackened) sample, without a gas flow.The result of the measurement at room temperature is shown in Figure S11, which shows that even without a gas flow and without heating, there are still variations in LIR.The uncertainty in LIR due to random noise was more than an order of magnitude smaller than the measured variations in LIR (compare 10 -3 variations in Figure S11a versus 10 -5 -10 -4 errors in Figure S11b).

Theoretical background on ∆E and prefactor C
In our experiments Nd 3+ acts as a "Boltzmann thermometer", because the populations of the emitting levels are in a thermal quasi-equilibrium. 10The equation often quoted for the theoretical luminescence intensity ratio (LIR) from a single-ion Boltzmann thermometer is: ) should be the same for ions in a specific crystalline material where the ∆ 21 is fixed and will not vary in different sample environments, perhaps apart from minor differences in ∆ 21 due to strain and/or external pressure. 12 contrast, the factor in Eq.S8 does not describe an intrinsic property of the thermometer.
Einstein A coefficients are not constants but instead depend on the density of optical states as described by Fermi's golden rule. 13This dependence gives rise to "local-field factors" in expressions for excited-state lifetime. 14Also, scattering particles or reflective interfaces affect the density of optical states and, hence, the LIR. 15Experiments record only a fraction of emitted light, namely the fraction that reaches the detector and is subsequently recorded. 16This fraction may be affected by several factors, such as scattering, reflection, absorption, losses induced by the collection optics, and/or a limited efficiency of the detector.Any of these factors affect the LIR if and only if they affect the light emitted by states 1 and 2 differently.In practice, they often will.
Eq. S8 could be adapted to include the external factors on photon emission and recording.The influences of scattering and reflection could be described by the concept of a collected density of optical states, only considering emission into those photon states that reach the detector. 15e influences of absorption, such as by biological tissue, could be described by a transmission factor. 16Finally, the finite efficiency of the collection and detection system could be described by another efficiency factor.Taking all these effects into account, an adapted version of Eq.S8 would read: Here,  0 (0) is the Einstein A coefficient for spontaneous emission from level  to 0 in vacuum,   is the density of optical states at the emission wavelength of level  into the direction of the detector normalized to corresponding the density of optical states in vacuum,   is the transmission of the sample for light emitted by level , and   is the collection and detection efficiency for light emitted by level  to 0.
We observe spatial variations in LIR in a reference measurement at a homogeneous constant temperature.We ascribe these to spatial variations in the factors described above.As our samples are both colored and scattering, we are not sure of the relative contributions from variations in  2 / 1 (absorption) or from variations in  2 / 1 (local-field effects).The relative contributions are not so relevant, because only the product of these contributions appears in Eq.S9.Our reference measurement at a homogeneous constant temperature calibrates the spatial dependence of the entire prefactor , which is lumped together into parameter ′(, ) in Eq. 3 in the main text.This strategy of using a reference measurement at a known temperature is one of the solutions to avoid photonic artifacts proposed in Ref. [15].
Eq. S9 must be further adapted to account for background fluorescence from our samples.We arrive at a simple model equation if we assume that the background fluorescence has a fixed intensity relative to  1 -the intensity from the lower-energy thermometer level-and has a temperature-independent spectrum.This yields a recorded LIR of Here  is the ratio between background fluorescence intensity and  1 . 1 and  2 are the fractions of background fluorescence that overlap with  1 and  2 , respectively.Eq.S10 can be rewritten to where the background-corrected prefactor  ′ is smaller than the background-free  of Eq.S9, because  > 0 for a positive background signal, and  is a constant that scales with the background intensity.
Different background characteristics than assumed in the derivation (e.g., a temperaturedependent intensity or spectrum) would yield a slightly different Eq.S10.Our derivation has the advantages of simplicity and some available interpretation of  ′ and .

Temperature maps at the other reactor set temperatures
The measurements were performed at three different reactor temperatures: 550, 595 and 640 K.
The temperature maps from the measurement at 550 K are shown in Figure 3b for (, ).Here  tot,ref is the total intensity (integrated over all wavelengths) in the reference experiment and  tot is the linearly interpolated map of the total intensity in the measurement.
The summation runs over all integer pixel values (, ) of the reference experiments except for the pixels on the edge of the map.The pixels on the edge of the map are however used for the linear interpolation of  tot .We find typical values of  and  of 100-500 nm, i.e., 10-50% of a pixel (Figure S13).The drift (, ) is then used to define drift-corrected maps of  1 ,  2 , and between local-calibration model and the experimental LIR in calibration experiments (Figure 3a) is minimized for ′ and .The estimated errors on ′ and  are calculated as: = √2 2 ( −1 ) 22 (17) and the covariance: where  is the Hessian matrix for  2 ( ′ , ).Both and the uncertainty in the temperature is estimated at: For the experiments under reaction atmosphere, we find  = 556.3± 1.4 K and   = 0.35 ± 0.15 (mean ± standard deviation over 28 × 28 pixels, excluding the pixels on the edge) at a reactor temperature of 550 K;  = 608.6 ± 1.3 K and   = 0.32 ± 0.10 at a reactor temperature of 595 K; and  = 665.7 ± 1.4 K and   = 0.45 ± 0.21 at a reactor temperature of 640 K.
For the experiments under inert atmosphere (measured after the reaction), we find  = 550.1 ± 0.3 K and   = 0.37 ± 0.17

Temperature deviation of Harrick HVC cell
The Harrick cell consists of an internal thermocouple at position X in Figure S15a.This thermocouple is placed closer to the heating rod than the sample and it therefore overestimates the temperature of the sample.We placed an extra thermocouple through the gas outlet, ending up at position Y in Figure S15a.We measured the temperatures at both position in a temperature range between room temperature and 873 K.The deviation from the blue dotted line in Figure S14b shows that the sample temperature is deviating from the readout temperature at position X.We used the temperature values at position Y for our calculations.

Laser heating due to sample blackening
The blackening of the sample could lead to heating of the sample due to laser absorption.We checked whether the laser power used for the thermometry experiments (1% relative to the maximum power) was sufficient to facilitate this heating.Figure S16 shows the results of this measurement, where the LIR is constant below 10%, indicating that the 1% laser power used in the experiments is safe to prevent laser heating.

Figure S3 .
Figure S3.Schematic representation of the unit cell of Y2O3 (space group Ia-3), obtained from the VESTA software.The oxygen (red), 8b (grey/green) and 24d (green) sites are highlighted.

Figure S4 .
Figure S4.a) Photoluminescence decay curves (measured at 822-831 nm, upon excitation at 579-581 nm) of the thermally coupled 4 F5/2/ 4 F3/2 energy levels of the 0.2%-doped Nd 3+ sample at 323 K (blue) and 1023 K (red).The solid black lines are fitted to a single-exponential decay model.The inset shows the decay rates obtained from fits between 293 K and 1173 K.The black line is a fit to a model for the temperature-dependent cross-over via a charge transfer state.b) Decay rates of the 4 F3/2 level for 0.2% of neodymium in different host crystal lattices, gadolinium oxide (green), yttrium oxide (light blue) and scandium oxide (dark blue) at temperatures of 300-1200 K.The ionic radius order is (coordination number = 6): Gd 3+ (0.938 Å) > Y 3+ (0.9 Å) > Sc 3+ (0.745 Å), which follows the inverse trend of the onset temperature at which non-radiative decay rates become dominant.Multi-phonon relaxation can be excluded as the dominant non-radiative decay pathway based on this data, since the onset temperature would be equal in all host crystal lattices (phonon energy is comparable in all oxide lattices.c) Phonon energies for the crystal oxide lattices, measured with the Raman microscope (λ = 638 nm).The phonon energies with the highest intensities are at 360, 376 and 416 cm -1 for Gd2O3, Y2O3 and Sc2O3, respectively.9

Figure S5 .
Figure S5.The probabilities of a) radiative decay (ηr), b) non-radiative decay (ηnr) and c) cross-relaxation (ηx) from the thermally coupled energy levels of Nd 3+ as a function of T. Differently colored lines denote calculations for different Nd 3+ doping concentrations of 0.2, 1.1, 3.4, and 4.9%, as indicated in panel b.

Figure
Figure S6.a) Mass Spectrometry (MS) traces for CO2 (red, m/z = 44) and CH4 (blue, m/z = 15) at a reactor temperature of 640 K, after the introduction of CO2 and H2 into the Harrick cell.b) MS traces for CH4 at reactor temperatures of 550, 595 and 640 K, respectively.

Figure S11 .
Figure S11.a) LIR values measured on the reduced sample at room temperature (294 K), without a gas flow.The measured area was 40x40 µm, to allow for more statistics.b) Calculated uncertainty in LIR due to random noise, using Eq.S7.

)
Our model as well as other model equations yield approximately straight lines on the small temperature interval considered in our experiments, i.e., 25% change in absolute temperature between 540 and 680 K. Some previous studies used LIR =  ′′ exp (as an approximate model, with an adapted energy gap between emitting levels ∆ 21 ′ .Similar to our model, this yields an approximate straight line of a small temperature interval, but variations of the value ∆ 21 ′ have no good physical interpretation as lanthanide ions in the same host crystals experience the same local coordination. /c, while the temperature maps for the other measurements are shown in Figure S12.At each temperature, the measurements were performed sequentially: (1) a measurement under Ar atmosphere, used for calibration (Figure 3a in the main text); (2) a measurement under CO2/H2/Ar flow, used to characterize local reaction-induced temperatures (Figure 3c); (3) a measurement under Ar atmosphere, used to confirm the uniform temperatures under inert conditions (Figure 3b).

Figure S12 .
Figure S12.a) 2D map of the measured temperatures, calculated using the local calibration, in only Ar at a reactor temperature of 595 K. b) Same as in a), but after the introduction of CO2 and H2.c) 2D map of the measured temperatures, calculated using the local calibration, in only Ar at a reactor temperature of 640 K. d) Same as in c), but after the introduction of CO2 and H2.

1 ′
Figure 3a of the main text to calibrate the local values of ′(, ) and (, ).The driftcorrected measurements at different reactor temperatures under different gas environments are used in Figure 3b-f to calculate local temperatures.

Figure S13 .
Figure S13.a) 2D map of the total Nd 3+ emission intensity Itot, integrated over all wavelengths between 795 and 980 nm, of the frame-of-reference experiment (reactor temperature 550 K; inert atmosphere).b) Same as in a), but in the CO2/H2/Ar gas atmosphere.The map in b) must be shifted by a small amount for the highest correlation with the map in a), as indicated in the inset.

Figure S15 .
Figure S15.a) Drawing of the Harrick HVC cell, with a zoom in on the reaction chamber.The self-supporting wafer is placed at position Y, while the heating element and the internal thermocouple are placed at position X. b) Measured temperatures with an external thermocouple placed at position Y, compared to the readout values of the internal thermocouple at position X.

Figure S16 .
Figure S16.The effect of the laser power of the Horiba Raman spectrometer on the LIR, measured at room temperature on the blackened sample.The laser power of 1% (relative to the maximum power) used in the thermometry experiments during CO2 methanation does not influence the measured LIR, while laser powers > 10% affect the LIR in a way consistent with illumination-induced heating.
0 is the Einstein A coefficient for spontaneous emission from emitting level  (= 1,2) to the ground state,   is the degeneracy of level , and ∆ 21 is the energy difference between excited-state levels 1 and 2. Sometimes the energies ℎ  of emitted photons are included in the fraction, depending on whether the LIR is defined in terms of intensity (= energy per unit of time) or photon count rate (= number of photons per unit of time).
) in Eq.S8 describes intrinsic properties of the thermometer, due to the energy-level structure of the emitting ions.The energy-level structure of lanthanide ions depends only weakly on any external influence and is determined by the local coordination of lanthanide ions in (nano)crystallites.Hence, if the luminescence thermometer is based on lanthanide emission, the factor