Luminescence Nanothermometry Based on Pr3+ : LaF3 Single Core and Pr3+ : LaF3/LaF3 Core/Shell Nanoparticles
Core Pr3+ : LaF3 (CPr = 1%) plate-like nanoparticles (nanoplates), core/shell Pr3+ : LaF3 (CPr = 1%)/LaF3 nanoplates, core Pr3+ : LaF3 (CPr = 1%) sphere-like nanoparticles (nanospheres), and core/shell Pr3+ : LaF3 (CPr = 1%)/LaF3 nanospheres were synthesized via the coprecipitation method of synthesis. The nanoparticles (NPs) were characterized by means of transmission electron microscopy, X-ray diffraction, and optical spectroscopy. The formation of the shell was proved by detecting the increase in physical sizes, sizes of coherent scattering regions, and luminescence lifetimes of core/shell NPs comparing with single core NPs. The average physical sizes of core nanoplates, core/shell nanoplates, core nanospheres, and core/shell nanospheres were 62.2 ± 0.9, 74.7 ± 1.2, 13.8 ± 0.9 and 22.0 ± 1.2 nm, respectively. The formation of the NP shell led to increasing of effective luminescence lifetime τeff of the 3P0 state of Pr3+ ions for the core nanoplates, core/shell nanoplates, core nanospheres, and core/shell nanospheres the values of τeff were 2.3, 3.6, 3.2, and 4.7 μsec, respectively (at 300 K). The values of absolute sensitivity Sa for fluorescence intensity ratio (FIR) thermometry was 0.01 K−1 at 300 K for all the samples. The FIR sensitivity can be attributed to the fact that 3P1 and 3P0 states share their electronic populations according to the Boltzmann process. The values of Sa for lifetime thermometry for core nanoplates, core/shell nanoplates, core nanospheres, and core/shell nanospheres were (36.4 ± 3.1) · 10−4, (70.7 ± 5.9) · 10−4, (40.7 ± 2.6) · 10−4, and (68.8 ± 2.4) · 10−4 K−1, respectively.
Nanothermometry aims to measure the local temperature of a studied system with submicrometric spatial resolution [1, 2]. Among different methods of nanothermometry such as using nanoscale thermocouples  and coulomb blockade nanothermometers , the luminescent nanothermometers hold a special place because of its high spatial and temporal resolution, accuracy, and contactlessness [1, 4–7]. Rare-earth-doped nanomaterials hold a special role in luminescent nanothermometry among other luminescent nanomaterials because of their excellent photostability [8, 9], long luminescent lifetimes [10, 11], sharp emission bands, high brightness [12, 13], high melting point, promising magnetic properties [14, 15], and good resistance to thermal and chemical attacks [16, 17]. More importantly, rare earth ions doped into fluoride nanoparticles demonstrate even better optical properties in comparison with some counterparts . Nanofuorides are chosen as the host not only because of their low phonon energy but also because of their desirable chemical stability and low toxicity [19–21].
Indeed, over the past decade, interest in nanothermometry based on rare-earth-doped fluoride nanoparticles has increased significantly [22–25]. On the one hand, nanosized dimensionality of the luminescent nanothermometers allows them to come into contact with the studied small system providing accurate and precise temperature measurement . The work in visible light provides high spatial resolution (∼λ/2). On the other hand, because of the high surface to volume ratio of nanosized objects the nanothermometer’s luminescence can significantly be reduced by surficial defects and high vibronic molecules which increase nonradiative decay probability [19, 26]. These adverse effects can be avoided or at least can be reduced by the formation of core/shell structure which prevents direct contact of surface ions with quenchers. Usually, the core serves as a scintillator, and the shell plays such screening “defensive” role although a set of functions of both core and shell can be more complicated [11, 26, 27]. In order to synthesize such core/shell NPs, the conventional coprecipitation  and hydrothermal methods  of synthesis have successfully been adopted during the last decade. The use of rare earth ions allows working into a broad range of wavelengths from ultraviolet (Dy3+ ) and visible light (Er3+  and Pr3+ ) to near-infrared light (Nd3+ ) for industrial, biological, and medical applications.
Generally, there are six parameters that define the luminescence emission of material: intensity, lifetime, band shape, bandwidth, polarization, and spectral position . Therefore, the luminescent nanothermometers can be grouped into six corresponding subclasses. The most widespread are the subclasses of luminescent nanothermometers based on the analysis of relative fluorescence intensity between the different emission bands corresponding to the suitable transitions and luminescent nanothermometers based on the analysis of luminescence lifetime. These methods cannot be affected by external conditions such as the fluctuation of the intensity of excitation light, the alteration of coupling degree, and the efficiency of optical fiber transmission electron microscopy (TEM). These facts make them very promising and highly developing.
In this case, the Pr3+ ion is very attractive for both methods. For the Pr3+ ions, the energy gap between 3P0 and the next-highest state, 3P1, is only a few hundred cm−1 for most host matrices. 3P1 becomes thermally populated following 3P0 excitation, and the luminescence spectrum contains both 3P0 and 3P1 emissions, with intensity ratios consistent with the predicted Boltzmann distribution among these states [22, 32–34]. The work  demonstrates the applicability of 5d⟶4f luminescence with the intra-f2 transitions of Pr3 covering a wide temperature range (10–1000 K). However, there are very few studies devoted to luminescence nanothermometry (especially lifetime thermometry) of rare-earth-doped nanoparticles of different morphology and structure including core/shell structure .
However, it should be noted that the lifetime thermometry is more complicated because of the complexity of lifetime curves and their interpretation for nanosized materials. Indeed, in bulk crystals, the lifetime curves of doping ions in the majority of cases can be described by exponential curves. However, the lifetime curves of doping ions in nanosized materials are more complicated. Indeed, in the nanoparticles, the role of the surface is increased, and the number of defects is higher. More importantly, the doping ions form clusters. These phenomena affect the crystal field around the doping ions which makes the shape of the lifetime curves more complicated in comparison with analogous bulk crystals [35, 36]. For these reasons, the modern theoretical approaches for some rare earth ions in some matrices are developed [36–38]. However, universal theories are still in the design phase. In order to estimate the luminescence lifetime values, the equation from  for an effective lifetime is used. Although this equation does not take into control the different abovementioned features of nanomaterials, it still allows obtaining a numerical value of luminescence lifetime.
The main goal of the paper is the demonstration of the applicability of Pr3+ : LaF3 NPs in luminescence thermometry based on both spectral ratio and luminescent lifetime. We analyze the temperature-dependent luminescence features of Pr3+ : LaF3 (CPr = 1%) spherical-like NPs (nanospheres) and Pr3+ : LaF3 (CPr = 1%) plate-like NPs (nanoplates) as well as Pr3+ : LaF3 (CPr = 1%)/LaF3 nanospheres and Pr3+ : LaF3 (CPr = 1%)/LaF3 nanoplates covered with undoped LaF3 shell in 80–320 K temperature range. We characterize the NPs by means of TEM, X-ray diffraction (XRD), and optical spectroscopy. The formation of the shell for both nanospheres and nanoplates is proved by detecting the increase in the NP size and luminescent lifetimes after the shell formation. The NP size is determined via TEM. Additionally, the size of the coherent scattering region of all the NPs is determined via Debye–Scherrer and Williamson–Hall methods.
2. Materials and Methods
2.1. Synthesis of the Nanoparticles
The single core NPs were synthesized via the coprecipitation method . In order to synthesize both Pr3+ : LaF3 (CPr = 1%) nanospheres and nanoplates, 0.04 g of Pr2O3 and 4.00 g of La2O3 were added to 85 mL of 10% nitric acid in a glass beaker. Both mixtures were heated to 50°С and stirred for 45 min until a transparent solution appeared. Then, the mixtures were filtered, poured into polypropylene glasses, and placed on magnetic mixers (400 revolutions per minute). The solutions of NaF were prepared by adding 3.8 g of NaF into 500 mL of deionized water. After filtration of the NaF solutions, the first one was swiftly poured for nanospheres and the second one was added dropwise for nanoplates. Then, the pH was adjusted to 4 by adding 25% solution of ammonium hydrate. Then both mixtures were stirring for 30 minutes (400 rpm), and finally, the NPs were washed by centrifugation (Janetski K24; 12000 rpm) using deionized water for several times.
In order to synthesize either Pr3+ : LaF3 (CPr = 1%)/LaF3 core/shell nanospheres or nanoplates, 2.00 g of synthesized core NPs were suspended into 250 mL of deionized water at 50°C. The suspension was placed on magnetic mixers (400 rpm). The temperature of 50°С was maintained during the synthesis procedure. Then, the solution of 2.10 g/L of NaF was added into 100 m/L of deionized water dropwise to the NPs suspension. Then, the mixture was stirred for 2 hours. After that, the solution of 7.00 g/L of La(NO3)3.6H2O was added into 150 m/L of deionized water dropwise. Then, the mixture was stirred for 2 hours. Finally, it was washed by centrifugation (Janetski K24; 12000 rpm) using the deionized water for several times similarly to core NPs. All the samples were dried on air in dust—free box.
2.2. X-Ray Diffraction and Transmission Electron Microscopy
The phase composition of the samples was characterized by an XRD method with the Shimadzu XRD-7000S X-ray diffractometer. Analysis of samples was carried out in a transmission electron microscope Hitachi HT7700 Exalens. Sample preparation is as follows: 10 microliters of the suspension were placed on a formvar/carbon lacey 3 mm copper grid; drying was performed at room temperature. After drying, the grid was placed in a transmission electron microscope using a special holder for microanalysis. The analysis was held at an accelerating voltage of 100 kV in the TEM mode. The additional control of the amount of nitrates in a colloidal solution of the NPs after each stage of centrifugation was performed by the identification test using diphenylamine (the diphenylamine test).
2.3. Optical Spectroscopy
The luminescence spectra were recorded using the CCD spectrometer (StellarNet), which detects the emission in 200–1100 nm spectral range with a spectral resolution of 0.5 nm. The optical parametric oscillator laser system (420–1200 nm) from JV LOTIS TII was used for excitation of the luminescence of the samples. The pulse width and the pulse-repetition rate were 10 ns and 10 Hz, respectively. The spectral width of laser radiation was less than 0.15 nm. The experiments were carried out in 80–320 K temperature range. The luminescent lifetimes of Pr3+ ions were detected using BORDO 211A (10 bit and 200 MHz bandwidth) digital oscillograph and MDR-3 monochromator.
3. Results and Discussion
3.1. Transmission Electron Microscopy
In order to prove the formation of core/shell structured NPs, we demonstrate the increase in physical sizes, coherent scattering regions (CSR), and luminescent lifetimes of core/shell NPs comparing with single core ones. The increase in physical size and CSR of the NPs was estimated via TEM and XRD methods, respectively. The XRD data were analyzed using the well-known Debye–Scherrer  and Williamson–Hall  methods.
According to the TEM data (Figures 1 and 2), nanoplates and nanospheres differ between each other by size and shape. In order to build a size distribution for the nanoplates, the length of the nanoplates was measured.
According to Figures 1(a) and 1(b), both core and core/shell nanoplates form agglomerates consisting of the thin plates (∼6 nm in thickness) on the formvar/carbon lacey copper grid. For both core and core/shell nanoplates, the interlayer distance between two fringes which are parallel to the upper and lower pedestals of the plate was measured to be ∼0.35 nm which corresponds to the  plane of the LaF3 crystal. Hence, it can be suggested that the preferred growth of the nanoplates takes place along both  and  planes under the existing conditions of synthesis . The average lengths of the core and core/shell nanoplates are 62.2 ± 0.9 and 74.7 ± 1.2 nm, respectively. The irregularity in the shape of the core/shell nanoplates seems to be less in comparison with the core ones.
On the one hand, both core and core/shell nanospheres are not perfectly spherical (Figures 2(a) and 2(b), respectively). Some of the nanospheres have an irregular shape. On the other hand, there is no preferential direction of growth unlike the nanoplates described above. For this reason, we classified these NPs as spherical just for the sake of simplicity. The average diameters of the core and core/shell nanospheres are 13.8 ± 0.9 and .22.0 ± 1.2 nm, respectively, which proves the increase in the size of the particles after the shell formation.
3.2. X-Ray Diffraction
The XRD patterns of the core, core/shell nanoplates, and core, core/shell nanospheres are shown in Figures 3(a) and 3(b), respectively. According to the XRD data, all the NPs are hexagonal-structured nanocrystals that correspond to the structure of matrices of LaF3 and PrF3. Sharp peaks and lack of peaks from impurities are observed, suggesting the high purity of these samples. For all the samples, the lattice parameters a and c were calculated. The lattice constants a and c are listed in Table 1. The lattice parameters for LaF3 (JCPDS–32–0483) are a = 0.7186 and c = 0.7352 nm. It is clearly seen that the lattice constants of the obtained samples are slightly bigger. Probably this difference can be explained by a larger number of defects, including water molecules in comparison with etalon bulk crystals. In turn, the lattice constants for both core and core/shell nanospheres are slightly larger than lattice constants of core and core/shell nanospheres. It can be related to the presence of captured water in nanospheres and/or other defects appearing due to the spontaneous character of the chemical reaction.
It is clearly seen from Figures 3(a) and 3(b) that the XRD peaks of the nanoplates are narrower than the XRD peaks of the nanospheres. Moreover, the nanospheres demonstrate a hint of an amorphous phase halo over the baseline unlike the nanoplates demonstrating lack of amorphous phase and consequently better crystallinity. Additionally, the signal-to-noise ratio for the nanoplates is higher than that for the nanospheres. It can be concluded that the slow dropwise addition of NaF solution provides better crystallinity comparing with a swift addition of NaF solution. Probably such relatively low crystallinity is a result of spontaneous character of the reaction in the coprecipitation method .
It is well known that nanoscale dimensionality of the crystalline particles leads to XRD peak broadening. Hence, the core/shell NPs should demonstrate narrower XRD peaks comparing with core ones. This phenomenon is clearly seen in Figures 3(c) and 3(d) showing normalized XRD patterns.
In order to additionally estimate the increase in the size of the NPs after the shell formation, the calculations of the size of the CSR via Debye–Scherrer and Williamson–Hall methods were carried out. It should be noted that the CSR is not a physical size of the NPs.
The following Debye–Scherrer formula is used :where D is the size of the CSR, K is a shape factor (we used K = 0.9), λ is the X-ray wavelength (0.15418 nm), βD is the line broadening at half the maximum intensity (FWHM) in radians, and θ is the Bragg angle in degrees. The distinguishable diffraction peaks having the lowest values of the signal-to-noise ratio are chosen. The CSR at different crystallographic orientations (hkl) for nanoplates and nanospheres are shown in Figures 4(a) and 4(b), respectively.
It is clearly seen in Figures 4(a) and 4(b) that the CSR of both nanoplates and nanospheres increases after the shell formation for all the chosen crystallographic orientations. For example, D002 for core and core/shell nanoplates are 13.6 and 16.7 nm, respectively. D002 for core and core/shell nanospheres are 9.1 and 12.0 nm, respectively. Moreover, the Debye–Scherrer calculations qualitatively prove the preferred direction of growth of the nanoplates along  and  planes. Indeed, D110 is 2 times higher than D002 for nanoplates (Figure 4(a)). Unlike Dhkl of the nanospheres does not demonstrate such a significant difference. This difference can be related to not perfectly spherical shape. The comparison of CSR of core nanoplates and core nanospheres for all the chosen crystallographic orientations is shown in Figure 4(c). It is additionally seen that the values of CSR of the nanoplates strongly depend on crystallographic orientations. In the case of nanospheres, such dependence is not clear. It additionally confirms that the shape of the nanoplates is more irregular comparing with nanospheres.
Additionally, the XRD patterns were analyzed via the Williamson–Hall method . This method allows obtaining values of CSR taking into control the contribution of strains to XRD peak broadening as follows:where D is also the size of the CSR, K is the shape factor (we used K = 0.9), λ is the X-ray wavelength (0.15418 nm), βhlk is the line broadening at half the maximum intensity (FWHM) in radians, and θ is the Bragg angle in degrees. A plot (equation 2) is drawn with along the x-axis and along the y-axis. From the linear fit to the data, the CSR was estimated from the y intercept, and the strain ε from the slope of the fit.
The Williamson–Hall plots for the nanoplates and nanospheres are shown on Figures 5(a) and 5(b), respectively. For core and core/shell nanoplates, the values of the CSR are 23.1 and 37.4 nm, respectively. For core and core/shell nanospheres, the values of the CSR are 13.9 and 17.1 nm, respectively. According to both Debye–Scherrer and Williamson–Hall methods, the CSR of both core nanoplates and core increases with shell formation. Based on the conclusion that CSR is increased, it can be suggested that the shell grows around the core according to the core crystal structure instead of chaotic formation.
3.3. Optical Spectroscopy
Room-temperature luminescence spectra of both core nanoplates and core/shell nanoplates excited by a laser beam at 444 nm are presented in Figure 6(a). The luminescent spectra have the emission bands at about 487, 523, 537, 580, 601, and 672 nm which are interpreted as the result of the transition from 3Pj (j = 0, 1, 2) excited states to 3H4, 3H5, 3H5, 3H6, and 3F4 states of Pr3+ ions, respectively . The emission from the 1D2 state was not found under the excitation condition and in the studied temperature range. Probably the emission from 1D2 is not observed because of the lack of nonradiative relaxation of 3Pj to 1D2 due to low cutoff phonon frequency in LaF3 (350–400 cm−1), which is 2 times less than one for YAG (700–865 cm−1). Indeed, to bridge the 3P0–1D2 energy gap, the 9 phonons are required in case of LaF3 and only 4 or 5 ones for YAG; thus, the multiphonon relaxation is expected to be negligible .
The lifetime curves of the samples are shown in Figures 6(b) and 6(c). All the lifetime curves are not single or double exponential. The shape of the lifetime curves is more complicated obviously due to a set of different physical processes taking place in the NPs. In , the complicated shape of lifetime curves of Nd3+ : LaF3 NPs synthesized via the coprecipitation method is explained by the presence of defects such as water molecules in the NPs core as well as on the NPs surface and by inhomogeneous distribution of doping ions. For these reasons, the effective luminescence lifetimes (τeff) were calculated using equation (3)  in order to compare the lifetimes of the samples:
For the core nanoplates, core/shell nanoplates, core nanospheres, and core/shell nanospheres, the values of τeff are 2.3, 3.6, 3.2, and 4.7 μsec, respectively (at 300 K). It is clearly seen that the luminescence lifetime increases after shell formation for both nanoplates and nanospheres. It can be suggested that the shell reduces the amount of surface defects as well as prevents the surface Pr3+ ions from contacting with surface quenchers. It should be noted that the values of τeff are less than the lifetime for Pr3+ : LaF3 (CPr = 1%) crystal which additionally confirms the presence of quenchers.
3.4. Intensity Ratio Thermometry
Figure 7 exhibits the emission spectra of the core nanospheres as a function of temperature in 80–320 K range. The luminescence spectra of all the compounds do not present any change in the peak positions with the temperature increase. Herewith, the intensity of 3P0 emission decreases as the intensity of 3P1 increases in the whole 80–320 K temperature range. In the experimental set up, the NPs were excited by 444 pulse laser irradiation which corresponds to excitation from the 3H4 ground state to the 3P2 exited state. In our case after excitation of the 3P2 state, the 3P2-3P0 nonradiative relaxation takes place. Then, the decrease in the intensity of the emission from 3P0 (at 487 nm or 537 nm) and simultaneous increase in the intensity of the emission from 3P1 (at 523 nm) can be attributed to the fact that 3P1 and 3P0 states share their electronic populations according to the Boltzmann process . Thermalization of the 3P1 state begins at around 80 K and operates more and more efficiently upon warming. A fluorescence intensity ratio (FIR) arising from the 3P1 state to that arising from the 3P0 state can be described as where B is a constant, ΔE is the effective energy difference between the 3P1 and 3P0 states, kB is the Boltzmann constant, and T is the absolute temperature. Two distinct emission bands at 523 and 532 nm, corresponding to the 3P1⟶3H5 and 3P0⟶3H5 transitions, respectively, were chosen for intensity ratio calculations. The FIR plots for all the samples are shown in Figure 8. As expected, the FIR for all the samples does not differ between each other and can be fitted by using the following formula:
ΔE = 554 ± 9 cm−1 is in good agreement with the literature data .
For temperature sensing applications, the absolute temperature sensitivity Sa and the relative temperature sensitivity Sr are the two very important parameters, corresponding to the absolute change and the relative change of the ratio R with respect to temperature variation, respectively. According to equation 1, Sa and Sr can be written as 
Sa plot of the samples is shown in Figure 9. For all the samples, Sa = 0.01 K−1 at 300 K. As it is proved, Sa does not depend on the structure of the NPs. Even the core/shell nanospheres having the highest lifetime demonstrate the same intensity ratio temperature sensing. Hence, we studied the lifetime thermometry. The result is also superior to the Sa value of 0.0034 K−1 for the Y2O3 : Tm3+/Yb3+ sample  and that of 0.0075 K−1 for the LiNbO3 : Er3+/Yb3+ sample  at 310 K.
3.5. Luminescence Lifetime Thermometry
Luminescence decay curves of the 3P0 state of Pr3+ ions for core nanoplates, core/shell nanoplates, core nanospheres, and core/shell nanospheres recorded at different temperatures upon 444 nm pulse laser excitation are shown in Figures 10(a)–10(d), respectively. All the curves keep their sophisticated shape in the whole temperature range. In order to estimate the influence of different processes on luminescence lifetime, the experimental lifetime texp can be defined as a sum of different terms that contribute into it :where τrad is the radiative contribution, τNR is the nonradiative or multiphonon contribution, and τQ is a term linked to the contribution of other quenching mechanisms, such as energy transfer to other lanthanide ions or additional quenchers. τrad expressing the radiative transition rate has almost no temperature dependence [42, 48]. τNR expressing the nonradiative or multiphonon rate behaves in the opposite way. As it was mentioned above, the 1D2 emission was not found or seems to be negligible for Pr3+ : LaF3. Hence, the lifetime of the 3P0 state is not influenced by multiphonon relaxation from 3P0 to 1D2 although this process is temperature dependent [49, 50]. As was discussed above, the rapid thermalization of the 3P1 level by 3P0 upon warming contributes to the temperature dependence of luminescence lifetime of the 3P0 state . In particular, in , the temperature dependence of 3P0 state luminescence lifetime of Pr3+ in Pr3+ : LaF3 (CPr = 0.01–0.03%) is explained by this rapid thermalization of 3P1 only. Therefore, 3P1 and 3P0 states share their electronic populations according to the Boltzmann process and thermalization of the 3P1 state takes place. Hence, the Boltzmann process has significant contribution to the temperature dependence of luminescence lifetime of the 3P0 state. However, there are probably more temperature-dependent processes.
Indeed, the lifetime curves of the samples demonstrate a complicated shape (Figures 6(a) and 6(b)). It can be suggested that there are several physical processes which can be responsible for luminescence quenching . Some of these processes can be temperature dependent. Hence, the τQ term seems to have a contribution into the temperature dependence of luminescence lifetime . However, due to different morphology and structure of the samples, the real contribution of the τQ term to temperature sensitivity of 3P0 state luminescence lifetime can be different. In particular, for system Pr3+ : LaF3, concentration quenching at high Pr3+ concentration takes place. It happens via cross-relaxation . The energy migration between Pr3+ ions and final quenching by a defect is also possible. This quenching can be temperature dependent . Indeed, at 1% concentration of Pr3+ ions, the quenching processes may take place.. On the one hand, at the concentration of 0.01%, it is considered that the Pr3+ ions do not interact with each other in crystals. On the other hand, concentration such as 12% is very convenient for observing the cross-relaxation processes of Pr3+ ions. However, as it was mentioned above, in the NPs synthesized via the coprecipitation method, the inhomogeneity in concentrations of doping ions may take place. It means that the local concentration of the doping ions can be more than 1%. Doping ions form clusters where interaction between doping ions and subsequent luminescence quenching is more effective. Thus, it can be suggested that this inhomogeneity of Pr3+ distribution can lead to energy migration process which is temperature dependent [52, 53]. The nature of defects in the samples is not well known. The samples can differ from each other by the nature of defects and their concentrations. Finally, it can be concluded that there are several temperature-dependent processes including thermalization of 3P1, as well as temperature-dependent luminescence quenching processes.
As it was mentioned above, the shape of the lifetime curves is not single exponential or double exponential. The shape is complicated and it cannot be easily described. Hence, in order to estimate the lifetimes, equation 3 was used. τeff temperature dependence plot should reflect the contributions of these processes without the specificity of each process. Figure 11 represents the temperature evolution of τeff for all the samples. Surprisingly, τeff temperature dependence can be fitted linearly. It is noteworthy that, in the case of linear fitting, the Pearson coefficient for all the samples is more than 0.9 which corresponds to good linearity of the results. Although the Boltzmann process is nonlinear in the whole studied temperature range, it seems that other sophisticated temperature-dependent quenching processes compensate nonlinearity of the Boltzmann process. It can be suggested that synergetic action of all abovementioned processes leads to simple linearity of τeff temperature dependence. Both core nanoplates and nanospheres demonstrate almost the same values of temperature sensitivity (∼40 · 10−4) which can be defined as the slope. In turn, both core-shell nanoplates and nanospheres demonstrate the same values of temperature sensitivity (∼70 · 10−4) which are bigger than these values for core NPs. These differences in values of temperature sensitivities Sa are the subjects of further research. However, it can be suggested that the shell turns off some temperature-independent quenching process which leads to increasing of temperature sensitivity based on luminescence lifetime.
Nevertheless, Sa based on FIR technique is notably higher ∼100 · 10−4 K−1 in comparison with Sa based on luminescence lifetime. It seems that FIR thermometry is easier and more effective than lifetime thermometry.
3.6. Temperature Uncertainty and Repeatability
The thermometer performance is characterized not only by the relative sensitivity but also the maximum temperature uncertainty. The minimum temperature uncertainty can be estimated usingwhere δD/D is the relative uncertainty in the determination of the thermometric parameter (we use the typical δD/D value of a portable detector, 0.5%) . The temperature uncertainty at 300 K for all the Pr3+ : LaF3 samples in FIR thermometry was 0.5°C. The repeatability of the thermometers readout upon temperature cycling is quantified using the following expression :where Δc is the mean thermometric parameter (extracted from the calibration curve) and Δi is the value of each measurement of the thermometric parameter. Usually, 10 consecutive measurements are enough to have a minimal statistical significance of the computed results. The thermometric parameter recorded in 10 heating-cooling temperature cycles showing reproducibility was around 99.1% for all the samples.
The core Pr3+ : LaF3 (CPr = 1%) plate-like nanoparticles (nanoplates), core/shell Pr3+ : LaF3 (CPr = 1%)/LaF3 nanoplates, core Pr3+ : LaF3 (CPr = 1%) sphere-like nanoparticles (nanospheres), and core/shell Pr3+ : LaF3 (CPr = 1%)/LaF3 nanospheres were synthesized via the coprecipitation method of synthesis. The nanoparticles (NPs) were characterized by means of TEM, XRD, and optical spectroscopy. The formation of the shell was proved by detecting the increase in physical sizes, sizes of coherent scattering region, and luminescence lifetimes of core/shell NPs comparing with single core NPs. The average diameters of core nanoplates, core/shell nanoplates, core nanospheres, and core/shell nanospheres were 62.2 ± 0.9, 74.7 ± 1.2, 13.8 ± 0.9, and 22.0 ± 1.2 nm, respectively. The formation of the NP shell led to increasing of effective luminescence lifetime τeff of the 3P0 state of Pr3+ ions. For the core nanoplates, core/shell nanoplates, core nanospheres, and core/shell nanospheres, the values of τeff were 2.3, 3.6, 3.2, and 4.7 μsec, respectively (at 300 K). The values of absolute sensitivity Sa for fluorescence intensity ratio (FIR) thermometry was 0.01 K−1 at 300 K for all the samples. The FIR sensitivity can be attributed to the fact that 3P1 and 3P0 states share their electronic populations according to the Boltzmann process. The values of Sa for lifetime thermometry for core nanoplates, core/shell nanoplates, core nanospheres, and core/shell nanospheres were (36.4 ± 3.1) · 10−4, (70.7 ± 5.9) · 10−4, (40.7 ± 2.6) · 10−4, and (68.8 ± 2.4) · 10−4 K−1, respectively. The difference in values of Sa for lifetime thermometry is attributed to the presence of several temperature-dependent luminescence quenching processes [44, 53, 54]. Since the samples differ between each other by morphology and structure, the contribution of these quenching processes (by different defects probably) is different. This phenomenon is the subject of further research. Finally, Pr3+ : LaF3 is well proven as an excellent material in different areas [53–55].
The TEM microscopy, XRD, spectra, and lifetime data used to support the findings of this study have been deposited in the Google disk repository (https://drive.google.com/drive/folders/1V-2yCykIjqfpech3ysKHcXthajYvkWg1?usp=sharing). The size distribution, Debye–Scherrer, Williamson–Hall, and elemental analysis data used to support the findings of this study are included within the article. These data are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
The chemical synthesis and material characterization works were supported by the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities (3.1156.2017/4.6 and 3.5835.2017/6.7). The optical spectroscopy works were supported by the research grant of Kazan Federal University. Microscopy studies were carried out at the Interdisciplinary Center of Analytical Microscopy of Kazan Federal University.
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