1 Introduction

Gas-phase synthesis of nanoparticles is increasingly being exploited for a large variety of materials [1–4]. Fumed silica is produced in industry on a large scale [5] and ultrapure optical-grade silica is produced via flame-based methods [6]. Flame synthesis also allows for the production of high-purity and phase-specific nanomaterials that are not accessible via wet-chemistry methods [1]. A large variety of metal-oxide nanoparticles, as well as next-generation smart nanostructured materials [7] incorporating SiO2, can be formed by doping a flame with either a metal-organic or metal-halide precursor. The properties of the synthesized nanoparticles strongly depend on the reaction conditions, where the spatial variation of concentrations and gas-phase temperature during particle formation within and behind the flame is important for understanding and optimizing the process [8]. These data also provide valuable input for improving and validating detailed flame chemical-kinetics and particle-formation mechanisms [9].

Measurement of temperature is of particular interest, because the precursor decomposition rates, the particle growth rates, and the particle–particle interaction, and thus the properties of the nanoparticles strongly depend on the temperature history along the path through the reactor [10]. Use of thermocouples fails to accurately capture gas-phase temperature within flames due to perturbation of the process. Laser-based diagnostics overcome this limitation with techniques ranging from line-of-sight laser absorption spectroscopy [11, 12], pointwise CARS [13–15], and spontaneous Raman scattering (SRS) [16]. Although SRS can generate planar images, it suffers from weak signal strengths that are problematic especially in the presence of intense elastically scattered light. Filtered Rayleigh scattering has also been used for gas-phase temperature imaging close to surfaces and in the presence of particles [17, 18], but the discrimination of signal generated from gas-phase species and small nanoparticles is difficult because of similar Doppler broadening and the unknown local scattering cross-sections in the reactive media. Alternatively, laser-induced fluorescence (LIF) methods offer strong signals and thus imaging capability [19]. LIF of the NO (nitric oxide) molecule is one example whereby quantitative temperature imaging can be achieved [20], as demonstrated in a wide range of combustion applications including flame synthesis of iron oxide and silica nanoparticles [21] and in plasma flows [22], spray flames [23], and high-pressure flames [24]. This technique involves seeding the flame with typically ~500 ppm NO and exciting an electronic transition of the molecule. With added NO, the entire flow field before and after the flame can be visualized. However, introducing NO to O2-deficient flames or plasmas, even in small amounts, can perturb the system of reactions due to its strong oxidizing potential leading to erroneous temperature measurements.

Using native species present in flames or plasmas is an alternative approach, obviating the need to add LIF-active temperature markers. In high-temperature processes in the presence of nitrogen and oxygen, naturally formed NO can be used for thermometry [20]. The OH radical naturally present in hydrocarbon flames has been extensively used for thermometry, e.g., Refs [25, 26]. However, native OH is only present in combustion systems and spatially limited to the flame front and the high-temperature exhaust gas.

In this study, we focus on measurements in a laminar lean premixed low-pressure hydrogen/oxygen flat flame for synthesizing SiO2 nanoparticles. The fuel/air mixture is doped with the precursor HMDSO (hexamethyldisiloxane: O[Si(CH3)3]2) that decomposes at high temperatures within the flame. Silicon monoxide (SiO) is present at high concentrations, being one of the intermediates in the flame’s gases that is thermodynamically stable at high temperature [27], leading to the formation of SiO2 nanoparticles at lower temperature. SiO can be excited in the UV and observed via LIF, and can thus be used as a native temperature marker.

The spectroscopy of SiO has hitherto been studied and applied to various nanoparticle synthesis processes. SiO has been used before as a LIF-based native temperature marker for point measurements in the context of surface coating [28–32]. All such studies involved excitation of the A 1Π←X 1Σ electronic system using various vibrational bands. Le et al. [30] excited SiO transitions within the (3,0) band and found that it was feasible to measure relative peak intensities of two intra-band lines R(39) and P(29) without encountering problems of line-overlap to derive rotational temperature. This was achievable owing to the very low-pressure conditions (40 Pa) of the laser ablation process used to understand formation of molecules and clusters. Hynes [29] on the other hand compared experimental and simulated SiO spectra for a glow discharge and an atmospheric pressure flame at predetermined temperatures; however, no fitting was attempted to infer temperature from their spectra. In view of difficulties trying to determine rotational temperature via the simple Boltzmann plot technique due to line overlap, van de Weijer and Zwerver [31] attempted to infer vibrational temperatures instead yielding values 400 K higher than those inferred from well-characterized rotational OH spectroscopy. They suspected the discrepancy to be due to the vibrational states of SiO being insufficiently thermalized at a pressure of 133 Pa.

To overcome the limitations of simple Boltzmann fitting, a complete spectral simulation is required. In general, the combination of line-spacing, laser-linewidth, and pressure-broadening often result in individual rotational lines unable to be fully spectrally resolved, and therefore calls upon full spectral multi-line fitting to derive rotational temperature. The multi-line fit approach had been used previously by Yamashiro et al. [32], attempting to measure rotational temperature of SiO formed in crossing atomic beams of Si and O. The authors found rotational temperatures to range from 1500 to 2000 K depending on the vibrational band employed, and suspect this to insufficient thermalization at extremely low-pressure conditions (1.3 mPa). A plasma-enhanced CVD study by Buss et al. [28] also used multi-line fitting, whereupon the resulting rotational temperature of the plasma was compared to translational temperature measurements using a thermocouple. In their study, they believe the 200 K difference between the two methods is attributable to inaccuracies in spectroscopic knowledge of SiO as opposed to any thermal disequilibrium between the translational and rotational states [28].

In all of the abovementioned studies [28–32], either simple Boltzmann ratios were calculated, or due to line overlap, more rigorous multi-line spectral fitting was attempted. In the latter case, attempts proved always to be problematic in earlier work; this appears either to be due to non-equilibration of molecular states at very low-pressure [32], or possible inaccuracies in spectroscopic data [28]. In this study, we use the multi-line fitting approach of LIF excitation spectra yielding rotational temperatures in a low-pressure flame environment, which advantageously closely matches to translational temperature, being less prone to non-thermalization. For enhanced accuracy, we also apply up-to-date spectroscopic parameters, perform resolved emission measurements to check for spectral interference from other species, and assess quenching rates of individual lines through lifetime measurements. Furthermore, precision is also improved by seeking a spectral region to deliver good temperature sensitivity from fitting.

The specific objective of the current study is to apply spectral fitting to a temperature imaging method as demonstrated before for NO [20]. We achieve this by imaging LIF of native SiO in a precursor-doped hydrogen/oxygen flame with a camera and by multi-line spectral fitting after scanning the laser over a limited range of the SiO absorption spectrum. We also compare our results of SiO-LIF temperature measurements with well-characterized NO-LIF multi-line thermometry, all with the aim to ultimately understand and optimize gas-phase nanoparticle synthesis.

2 Methodology

2.1 Experimental setup

Figure 1 illustrates the setup, comprising the reactor chamber, laser excitation source and detection modules. A vertically translatable burner with a sintered-bronze matrix of 36 mm diameter is housed inside a cylindrical chamber with a diameter of 10 cm and height of 50 cm; more details are given in Ref [33]. Above the matrix, a premixed flat flame can be stabilized at a chamber pressure of 30–1000 mbar, with typical flow rates of 700 sccm H2, 900 sccm O2, and 300 sccm Ar yielding an equivalence ratio of φ = 0.39. The vapor-phase precursor HMDSO was introduced to the premixed gases via the use of a bubbler; the vapor pressure of HMDSO and the temperature of the bubbler was used to infer the concentration of HMDSO in the flame for SiO-LIF measurements, whilst NO could be added to the flame gases for corresponding NO LIF. Optical access to the flame is possible by four 85-mm-diameter quartz windows that were flushed with argon to reduce undesired particle deposition.

Fig. 1
figure 1

Schematic of the experimental arrangements for: (i) NO and SiO-LIF imaging with an ICCD camera, (ii) SiO-LIF lifetime measurements using a PMT, and (iii) spectral measurements of SiO LIF using a spectrometer. FCU frequency conversion unit, DG delay generator, ICCD intensified charged-coupled device, PMT photomultiplier tube

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SiO and NO were excited with the light generated by a narrowband tunable dye laser system in conjunction with frequency conversion. A dye laser (Sirah, Cobra Stretch, 0.15 cm−1 HWHM linewidth) was operated with Coumarin 47 and pumped by the tripled output (355 nm) of a flashlamp-pumped Nd:YAG laser (Spectra Physics, Lab Series, 10 Hz repetition rate), producing tunable radiation between 435 and 485 nm. UV radiation for exciting SiO and NO between 218 and 243 nm was generated by frequency doubling in the thermally stabilized BBO crystal of the frequency conversion unit (FCU).

To perform imaging measurements, the laser beam was formed into a vertical light sheet (50 mm high, 0.5 mm thick) by a cylindrical telescope. Pulse-to-pulse intensity fluctuations were recorded by an energy monitor (LaVision) and stored with each image for subsequent intensity correction. LIF images were collected perpendicular to the light-sheet plane and focused using a UV-lens (B. Halle, f = 100 mm, f # = 2) onto an intensified CCD camera (LaVision, Imager Intense, 1375 × 1039 pixel sensor with a high-speed intensifier LaVision, HS-IRO) yielding a projected pixel size of 40 µm/pixel and a gate width set to 500 ns. Elastically scattered light was suppressed by custom-made longpass filters to transmit beyond 225 and 235 nm for NO A←X(0,0) and SiO A←X(0,0) LIF measurements, respectively. The linearity of the LIF signal with respect to the laser-pulse energy was verified in the investigated range up to 0.5 mJ/cm2. Typical laser fluences of up to 0.4 mJ/cm2 were used, corresponding to laser-pulse energies of ~0.1 mJ at the measurement volume.

The thermometry approach used herein is based on multi-line spectral fitting. Images of LIF were captured and averaged over 50 laser pulses, then repeated again for an incremental change in the laser wavelength over a defined spectral range. Excitation spectra were then extracted for each pixel from the stack of LIF images. Simulated spectra were then fitted to the experimental data with temperature, total intensity, and broadband offset as free parameters using LIFSim [20].

2.2 Choice of wavelength region

The exact choice of which SiO transition to excite was determined by both practical and theoretical considerations. Herein, we chose to excite A←X(0,0) of SiO, whose bandhead lies at 42650 cm−1 (234.5 nm). This wavelength region was easily accessible with the use of our dye laser, and also delivers strong fluorescence since excitation originates from the lowest vibrational level (i.e., v” = 0), leading to strong absorption of laser radiation. Although strong absorption is advantageous for improving LIF signal-to-noise ratios, it can result in distortion of the recorded LIF-excitation spectra, because the local laser intensity is influenced through the (temperature dependent) attenuation of the laser beam. This effect can lead to errors in the inferred local temperature. For our axisymmetric low-pressure flame with a small path length, it was confirmed that the laser attenuation was negligible which was evident from the symmetry of the SiO-LIF images generated in our experiments. However, in general, absorption effects need to be assessed based on measurement conditions thus guiding the appropriate choice of wavelength region. In the following sections, we also examine the possibility of spectral interference from other species in the flame relevant to the (0,0) band, as well as determining a more specific spectral region that yields best precision in temperature measurement.

2.2.1 Spectral interference

For selective measurements of SiO, interference that may originate from LIF of OH, hot O2, NO, or other intermediate species in the flame must be ruled out. Excitation wavelength dependent detection of spectrally resolved fluorescence allows one to distinguish between signal contributions from various species on the basis of their spectral signature [34]. Figure 2 shows an excitation–emission chart for the A←X(0,0) region of SiO (near 235 nm) measured from the spectrometer setup shown in (iii) of Fig. 1, corresponding to an HMDSO concentration in the burner gases of 250 ppm and measurements were imaged at a height above burner HAB = 12 mm. Profiles along the vertical axis in Fig. 2 yield excitation spectra, where the ‘bandpass’ of the detection can be arbitrarily selected over the entire fluorescence range. Similarly, fluorescence spectra can be extracted with the excitation frequency being fixed at a given value.

Fig. 2
figure 2

Excitation–emission chart for the A←X(0,0) band for a flame at 30 mbar with 250 ppm HMDSO and an equivalence ratio of 0.39. Each vertical band in the chart represents the spectrally resolved emission. The arrow in the excitation spectrum indicates the position where the emission spectrum was extracted. The arrow in the emission spectrum indicates the emission where the excitation spectrum was extracted

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The excitation–emission chart of A←X(0,0) in Fig. 2 shows that after excitation in this band the emission originates from A→X(0,0) in addition to the red-shifted A→X(0,1), (0,2), (0,3), (0,4), and (0,5) bands (λ = 235–275 nm). Furthermore, a weak blue-shifted fluorescence signal at 221.6 nm is visible originating from electronically excited higher A-state vibrational levels. Figure 2 also indicates, at least for the measurement corresponding to HAB = 12 mm and a HMDSO concentration of 250 ppm, that no spectral interference is evident owing to the lack of irregular features in the excitation–emission chart for these flame conditions. If interference were present, features other than from SiO would appear in the fluorescence spectrum shown on the horizontal-axis in Fig. 2.

Despite the utility of excitation–emission charts for demonstrating absence of interference in the presence of SiO, another approach was also used to double-check for potential interference near 235 nm. A standard excitation scan was made without spectrally resolved detection, as per setup (i) in Fig. 1, without HMDSO seeded to the flame. Although interference is not evident in Fig. 2 for 250 ppm HMDSO, weak interference may still be strong enough to present problems for detection at smaller HMDSO concentrations. An excitation scan is a spectrally integrated signal, and therefore is more likely to show the occurrence of weaker signals from other species in the absence of relatively strong SiO LIF. Furthermore, such a standard scan, as described in Sect. 2.1, has the advantage of yielding 2D profiles of LIF, thus allowing the occurrence of spectral interference to be assessed throughout the flame with a single measurement. It was found from an excitation scan for a single point in the flame clearly demonstrating without HMDSO that there is no evidence of spectral features from OH, O2, or flame intermediates within an example spectral 10 cm−1 range centered on 235.1 nm. We also found that the lack of discernible features is evident in all other regions of the measured flame—therefore, no interference occurred across the measured flame area.

For the corresponding NO-LIF measurements, excitation was performed in the A←X(0,0) band of NO near 225 nm, where all the scanned transitions in our experiments are shown in Table 1. Such a spectral region has previously been found to deliver reliable evaluated temperatures, and is discussed in detail elsewhere [20]. However, in the presence of SiO in the flame, there exists interference in this spectral region, which originates from SiO A←X(3,0). Figure 3 shows the NO transitions that are used for thermometry in this study, in addition to the coexistence of lines from SiO when the flame is seeded with ~500 ppm NO and ~200 ppm HMDSO, respectively. In order to circumvent the problem of interference, we chose not to seed the flame with HMDSO during our NO-LIF measurements. It should be noted that removal of the precursor will influence the flame, and this is discussed in more detail later in Sect. 3.3.

Table 1 Spectroscopic properties of the SiO LIF transitions located in the 42528–42542 cm−1 wavenumber range used for the optimized multi-line thermometry strategy. Properties for corresponding NO LIF measurements are also included. Ground-state energies are relative to \(v^{\prime\prime} = J^{\prime\prime} = 0\)
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Fig. 3
figure 3

Simulated NO-LIF excitation spectra corresponding to the chosen scan range in Table 1. Strong contributions from SiO A←X(3,0) LIF are also shown

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2.2.2 Sensitivity analysis

In multi-line thermometry, a compromise needs to be found between the spectral range (i.e., the spectral position and number of transitions probed) and the signal-to-noise ratio for the measurement at each excitation wavelength. To limit the measurement duration, the spectral regions and ranges that provide the overall largest sensitivity for temperature measurement must be found. We analyzed the temperature sensitivity of the spectral scan ranges within the A←X(0,0) band by numerical experiments following the strategy of Bessler et al. [20] that considers the combined effect of line strength and temperature dependence of each single transition. Simulated SiO-LIF excitation spectra were added with normally distributed random noise to create realistic experimental spectra for some target temperature, pressure, scan origin and range, and a spectral resolution (laser linewidth) according to the experiment. The temperature fitting algorithm was then applied to the synthetic spectra, resulting in an evaluated temperature close to the target temperature. The procedure was repeated 200 times and the average and standard deviation of the fitted temperatures were calculated. The deviation of the average from the pre-set temperature is a measure for the accuracy, and the standard deviation is an indication of the measurement precision at the given conditions.

The temperature sensitivity was analyzed for scan origins within range 42280–42650 cm−1 and with 5, 10, 15, and 20 cm−1 scan ranges with a spectral resolution of 0.05 cm−1. The procedure was applied to conditions at low pressure (30 mbar) and atmospheric pressure and for temperatures of 500 and 2000 K, respectively. Figure 4 shows the results for the A←X(0,0) bandhead region around 235 nm. Figure 4a shows simulated SiO-LIF excitation spectra (normalized to their most intense peaks in the respective scan range) for 500 and 2000 K. Figure 4b depicts the temperature sensitivity for 500 and 2000 K at atmospheric pressure. In this plot, minimum standard deviation equates to best precision and therefore highest temperature sensitivity of the multi-line technique. For our purpose, only the global minima in the plotted curves are of interest. The overall sensitivity is better for 500 K compared to 2000 K. We also find that the sensitivity at 30 mbar is better than at atmospheric pressure (not shown here). Therefore, only the results for 1 bar are presented to demonstrate a limiting case. The sensitivity strongly depends on the scan range and scan origin. The 42490–42570 cm−1 scan range (red-shaded region of interest in Fig. 4a, b) was found suitable, and zoomed-in LIF spectra are presented in Fig. 4c, d. Within a typical range of temperatures encountered in a flame, such a region of interest indicates an optimal compromise of lowest standard deviation in temperature and being sufficiently far away from the bandhead where the rotational lines tightly cluster together being more difficult to experimentally spectrally resolve.

Fig. 4
figure 4

Results of the sensitivity analysis for multi-line thermometry at 1 bar for 500 K (left column) and 2000 K (right column). The SiO excitation spectra correspond to the A–X(0,0) wavelength range and are presented in rows (a) and (c). The standard deviation, a measure of precision, is plotted in rows (b) and (d) for spectral scan ranges of 5, 10, 20, and 40 cm− 1 with the center of optimum ranges being marked as (*) in rows (c) and (d)

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In the experiment, short scan ranges that lead to maximum measurement precision are desired to limit the data acquisition time (which can typically take the order of 10 min for a ~10 cm− 1 scan with a 50 laser-shot average per spectral position). For our application, we further consider the choice of an appropriate scan range for the 2000 K case (right column in Fig. 4). We identify a scan origin around 42530 cm−1 that yields good sensitivity (standard deviation ≤4%, see asterisks in Fig. 4d) not only for 40 cm−1 ranges but also for shorter ranges. From this analysis an excitation scan range of 42528–42542 cm− 1 is proposed for multi-line SiO-LIF thermometry in the 500–2000 K range. This scan range covers six transitions (Fig. 5) originating from rotational ground states with different ground-state energies (Table 1) that blend into four distinct features. Excitation spectra in Fig. 5 were simulated within this scan range for 500, 1000, and 2000 K, and at a pressure of 30 mbar. It is observed that the peak intensities of the individual features vary strongly with temperature, indicating high temperature sensitivity in this scan range.

Fig. 5
figure 5

Simulated SiO-LIF excitation spectra corresponding to the chosen scan range in Fig. 4 for three representative temperatures at 30 mbar. The spectra are normalized with respect to the peak at Q(33) at 1000 K

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2.3 SiO-LIF lifetime measurements

Strong variations in state-specific quenching rates in the spectral range of interest could be detrimental for temperature measurements because the LIF spectra would be distorted depending on the collisional environment. We therefore investigated the quenching rates, Q, associated with each line probed within the excitation spectrum of Fig. 5. This can be done by measuring the effective lifetime of a transition, given by relation (1) where the Einstein A jk coefficients are summed over all de-excitation pathways.

$$\tau _{{{\text{eff}}}} = \frac{1}{{\mathop \sum \nolimits_{k} A_{{{\text{jk}}}} + Q}}.$$
(1)

We measured effective fluorescence lifetimes with setup (ii) in Fig. 1. Firstly, an instrument function was measured by recording the temporal profile of the signal obtained from elastically scattered light originating from the laser pulse, as illustrated by the black dashed trace in Fig. 6. This represents the temporal duration of the pulse (i.e., FWHM = 7 ns) and the time response of the detection system (rise-time of the PMT: 0.78 ns).

Fig. 6
figure 6

PMT capture of the instrument function (IF) illustrating an FWHM of 7 ns for the pulsed UV laser output. The corresponding transient fluorescence signal is displayed as blue circles, fitted with a mono-exponential as shown by the pink curve. The difference between the raw signal and fit is given by the residual (red curve)

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The signal trace, shown as blue circles in Fig. 6, represents an example fluorescence trace for one of the lines in Fig. 5. This represents the fluorescence focused from a point in the center plane of the flame, which is captured by the PMT. By employing a mono-exponential decay curve and convolving with the instrument function (as represented by the laser stray light pulse from the PMT depicted as the black dashed line in Fig. 6), a synthetic fluorescence transient can be fitted as displayed by the pink trace in Fig. 6, thus allowing lifetimes to be evaluated.

Fluorescence lifetimes were evaluated in this way for four distinct features of the spectrum in Fig. 5. We probed the P(26) and P(27) lines, which are completely isolated at 30 mbar; however, the Q(32) and Q(33) lines overlap with the neighboring R-branch, and therefore we probed the peaks as close as possible to the Q-branch lines. For all four features, there was very little variation in the values (for a given HAB) with a maximum standard deviation of about 2% between them. At HAB = 30 and 6 mm, effective lifetimes were 10.3 and 8.2 ns, respectively. Furthermore, by evaluating the sum of Einstein A jk coefficients from spectroscopic tables [35], it is possible to derive quenching Q for each line probed. Over the range HAB = 6–30 mm, we calculated that Q ranged 3.7–6.2 × 107 s−1. We also found that the Einstein sum associated with each line in the excitation spectrum varies from line to line by a maximum of 0.8%, according to the data from [35]. As seen from Eq. (1), given the Einstein sum and lifetimes are essentially the same for each probed line, the quenching rates therefore also appear to be invariant—and hence Q is independent of the upper rotational state within A–X(0,0) showing similar behavior to the NO molecule [36]. Fortuitously, for the current conditions this obviates the need to measure and calculate quenching rates for each probed line for various quenching environments during the simulation and fitting of excitation spectra within LIFSim [20]. Under these circumstances, for thermometry, Q can be arbitrarily fixed to zero for all of the lines, since relative measures of LIF intensity are all that is important in evaluating temperature from experimental spectra.

3 Results and discussion

3.1 Spectral fitting

Excitation spectra were measured and fitted using LIFSim, as exemplified by the plots in Fig. 7, in order to extract temperature information, i.e., T fit, at each point in the imaged area. As a result of scanning the dye laser with a spectral width HWHM of 0.15 cm−1 and a step width of 0.1 cm−1 near 235 nm, each spectrum represents four features composed of six underlying rotational lines from the A←X(0,0) band of SiO as displayed in Table 1. Figure 7 demonstrates good fits of the experimental data for a range of temperatures and HMDSO concentrations, and furthermore indicates the necessity of full spectral modeling over simple Boltzmann plots to extract reliable temperature information due to considerable line overlap. The spectra are smooth, characterized by a typical SNR in excess of ~100 based on the signal at the Q(33) peak. Such effective SNRs were possible due to averaging over 50 laser pulses for each laser wavelength and binning 8 × 8 pixels to yield a nominal spatial resolution of 320 µm/pixel.

Fig. 7
figure 7

Results of the fitting to experimental SiO-LIF excitation spectra using LIFSim. The spectra correspond to different temperatures above the burner and HMDSO seeding concentrations. For clarity, each spectrum is offset from each other on the vertical axis

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Across various compositions and temperatures, it can also be seen in Fig. 7 that there is consistent matching of spectral widths for each feature between the fitted and experimental data. The low-pressure condition of 30 mbar inside the reactor chamber minimizes collisional broadening, which depends on the local composition and temperature within the flame, and as such is not easily known a priori. Aside from the laser linewidth, the spectra are predominantly Doppler-broadened with a typical FWHM width of the order of Δν D = 0.23 cm−1 (at 1300 K) for all lines within the investigated spectral region of interest. Similarly, pressure affects collisional quenching, which affects the signal intensity. The pressure of the reactor chamber was held at a low value of 30 mbar, resulting in low rates of collisional quenching of the excited SiO molecules with corresponding fluorescence quantum yields of 50–70% independent of excited-state rotational states as determined from measuring lifetimes described in Sect. 2.3.

Given both collisional broadening and quenching can be accounted for in our modeling, the Einstein B coefficient is the remaining parameter that determines relative values of line intensities. It should be noted that in general the Einstein B coefficients are often known to be within ±30% of their true value [37]. It was found in this study that the coefficients needed to be adjusted; the old and updated values are shown in Table 2.

Table 2 Absorption coefficients calculated from PGOPHER [38] for each line considered in this study. Each coefficient is normalized with respect to that of line Q(33) for comparison to the values found in this study
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Einstein B coefficients have been tabulated relative to that of the Q(33) line, since only relative values are relevant to the goodness of fit in multi-line thermometry. Relative B values were determined by taking an SiO-LIF excitation spectrum at a specific position in the flame, and together with knowledge of the temperature—as measured via NO LIF—fixing the temperature during the fitting process then adjusting the B values to ensure a best spectral fit. The results of which can be seen later in Sect. 3.3.

3.2 LIF and temperature imaging

Figure 8 displays 2D distributions of LIF intensity and temperature resulting from spectral fitting for both NO and SiO excitation. Despite similar levels of NO and HMDSO seeding to the flame (500 and 210 ppm respectively) and similar incident laser intensities, the SNR is generally lower for NO LIF in Fig. 8a compared to SiO LIF in Fig. 8b. This is manifested by the distinct contrast in pixel noise between the images of fitted temperature in Fig. 8c, d. A comparison between the two spectral regions scanned for both NO and SiO in this study reveal that SiO LIF possesses linestrengths that are an order of magnitude larger, as revealed earlier in Fig. 3. Such a difference stems from the fact that the Einstein B coefficients for SiO are roughly ten times larger, whereas the Boltzmann fractions are comparable.

Fig. 8
figure 8

(a) Images of NO-LIF signal intensity corresponding to 500 ppm NO and 0 ppm HMDSO seeding at a wavelength near 225 nm, resulting in a derived temperature field above the burner surface (c) as a result of a spectral scan. (b) shows a similar image for SiO LIF near 235 nm with 210 ppm HMDSO seeding, resulting in a temperature field (d) without NO seeding. The masked areas near the burner surface in (b) and (d) denote regions of insufficient signal intensity for reliable temperature evaluation

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Figure 8a, b also show how the spatial variation of the LIF intensity differs between the two species. It should be noted that these images resulting from the fitting process offer a qualitative measure of the SiO number density throughout the flame. For quantification, it would be necessary to calibrate signal intensities and correct for potential spatial variation in collisional quenching, which is not attempted here. Nevertheless, it is apparent from Fig. 8a that the NO number density tends to generally decrease with larger HAB, whereas in Fig. 8b SiO number density tends to peak higher up from the burner surface before diminishing with larger HAB. One undesired side effect of employing SiO as a molecular marker for temperature is that it only forms at higher temperatures. This results in a region close to the burner surface which is devoid of SiO, as highlighted by the masked area in Fig. 8b where no temperature information can be gained. In the case of 210 ppm HMDSO shown in Fig. 8d, where substantial LIF intensity was present, temperature rose from ca. 900 K (at HAB 5 mm) to a peak of 1350 K (at HAB 20 mm) before slowly diminishing with further height. It is evident that there is agreement in this sense between the case measured with NO LIF (and no HMDSO seeding) and small HMDSO seeding of 210 ppm using SiO LIF (with no NO seeding). Greater level of detail between various temperature profiles for different conditions are shown in the next section.

3.3 Detailed temperature profiles

Figure 9 shows temperature profiles as a function of HAB along the centerline corresponding to x = 0 in Fig. 8. The NO LIF-based temperature profile corresponds to the case of 0 ppm HMDSO seeding, and so the effective equivalence ratio of the flame (base case) is φ = 0.39. The annotation in Fig. 9 denotes the adiabatic flame temperature for φ = 0.39 to be T ad = 1381 K, which is slightly higher by 50 K than the peak temperature measured with NO LIF. This is consistent with some expected heat loss to the surroundings via heat conduction and radiation. At the lowest height, the temperature from NO LIF is ~620 K, which is also consistent with thermocouple measurements at the burner surface.

Fig. 9
figure 9

Fitted temperature profiles along the burner axis corresponding to the data at x = 0 in Fig. 8c, d for NO-LIF and SiO-LIF thermometry respectively. Temperature profiles derived from SiO LIF are shown for three HMDSO seeding concentrations. The NO-LIF temperature profile is obtained for zero HMDSO seeding. The dashed line represents temperatures using the untuned B coefficients directly from PGOPHER (see Table 2). Error bars depict standard deviation of fitted temperature (only for NO-LIF thermometry). Adiabatic flame temperatures corresponding to 210 (φ = 0.39) and 1030 ppm (φ = 0.42) HMDSO are also shown for comparison to maximum fitted temperatures

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The temperature profile corresponding to an HMDSO seeding of 210 ppm in Fig. 9 agrees well with the NO-LIF thermometry result. This was made possible by tuning the B coefficients, as outlined in Sect. 3.1, in such a way that the temperature from the SiO-LIF method was forced to match that of the NO-LIF method for HAB = 15 mm. It is noteworthy that B coefficient tuning translates the temperature profiles up and down as demonstrated by the offset between the profiles for the tuned and untuned cases within Fig. 9. For the tuned case, we aimed to overlap the SiO-LIF profile (210 ppm HMDSO) with that from NO LIF, as it was expected that 210 ppm HMDSO seeding would result in very similar temperatures owing to a mere 1.71% increase in effective equivalence ratio due to the hydrocarbon content within the HMDSO precursor.

However, it is evident from Fig. 9 that raising HMDSO seeding to 510 and 1030 ppm results in noticeable and consistent increases in temperature. Such a monotonic increase is attributed to greater amount of hydrocarbon input from HMDSO, which itself is a fuel as well as a source of SiO in the flame. A seeding of 510 ppm results in an effective equivalence ratio of 4.23% higher (φ = 0.406) than the base case of φ = 0.39, while 1030 ppm is 8.26% higher (φ = 0.422). The temperature rise also correlates with calculations of the adiabatic flame temperature for φ = 0.422 being T ad = 1453 K.

Despite clear trends in the data as seen in Fig. 9, there is an element of uncertainty which is characterized by both precision and accuracy. Precision wise, we can see that the NO-LIF temperature profile exhibits the largest errors with standard deviations ranging from 3 to 18%, while also noting the spatial variation of the errors correlates with that of the LIF intensity seen in Fig. 8a. For SiO LIF, the signal strengths are generally ten times larger, and so the corresponding errors are smaller and therefore not apparent. It is, however, interesting to note that the first two points in the plot for the 210 ppm case systematically deviate from the NO-LIF temperature profile (i.e., HAB = 5 and 7.5 mm) in spite of very small error bars at these locations. The source of the systematic difference remains unclear; however, it may result from some precursor-induced chemistry leading to a small temperature increase in this region close to the burner surface. Alternatively, the deviation may result from uncertainty in the spectroscopic database and therefore would necessitate accurate measurement of spectra under well-controlled known conditions to derive less error-prone spectroscopic data for SiO.

4 Conclusions

A multi-line laser-induced fluorescence method was developed to quantitatively image temperature during flame-synthesis of nanoparticles without tracer seeding. This was achieved by exciting SiO natively present during the synthesis of SiO2 nanoparticles. It was demonstrated that temperature imaging based only on native SiO is possible. We found a good semi-quantitative agreement with temperature distributions measured by NO-LIF multi-line thermometry after seeding NO to the fresh gases. Owing to some uncertainty in one of the trends in temperature using the SiO-LIF approach, it is not possible to conclude on the accuracy at this stage. We also found, similar to NO, that the quenching rate of excited SiO does not depend on the upper-state rotational level under our conditions. This simplifies modeling of the excitation LIF spectra for fitting purposes to infer measured temperature. The drawback to using SiO as a native temperature marker is its inhomogeneous spatial distribution within the flame, where it does not exist in sufficiently high concentrations in the cooler regions and further downstream where this intermediate is consumed. It was found that the LIF-intensities were considerably stronger compared to NO with the same concentration, resulting in signal-to-noise ratios in excess of 100 for HMDSO precursor seeding of 210 ppm. SiO LIF possessing linestrengths of the order of ten times that of NO means that even in the presence of low SiO concentrations temperature can be determined with good precision.