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Abstract
In this study, emission and extinction spectroscopy were combined to in situ measure temperature and volume fraction distributions of liquid germanium nanoparticle gas-phase synthesized in an argon/hydrogen/germane flow through a microwave plasma. Emission of the hot particles and extinction against a continuous background were recorded by a spectrometer in the 380–703 nm and 230–556 nm ranges, respectively, selected based on the specific optical properties of the material. Absorption coefficients were deconvoluted from line-of-sight attenuation (LOSA) measurements by a least-square algorithm and then used to determine the local volume fraction distribution. The temperature field was derived from the line-of-sight emission (LOSE) spectra with the prior knowledge of absorption coefficients. A multi-wavelength reconstruction model was developed for the determination of the spatially-resolved distribution of the measured quantities assuming a stationary axisymmetric flow. Advantages of the method include experimental simplicity, low cost, and adaptability to up-scaled reactor sizes.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Nanotechnology shows promising applications in many fields, such as agriculture [1], medicine [2], biosciences [3], and engineering [4]. Nano-sized germanium (Ge) is an attractive semiconductor material that exhibits size-dependent optical properties, and it is potentially applied in optoelectronics, lithium-ion batteries, thermoelectrics [4] and biological imaging [5]. One-step production of Ge-nanoparticles can be accomplished by gas-phase synthesis, which also shows potential for scale-up towards industrial production rates [6].
Spatially-resolved in situ and perturbation-free optical diagnostics during particle synthesis is indispensable for deepening physical insight into particle formation and to better monitor and potentially control the generation process [7]. Particular interests are in temperature and volume fraction fields of nanoparticles, since these parameters reflect their optical properties, and, e.g., the local growth rate, and are crucial parameters to understand the particle-formation mechanisms. In comparison to, e.g., probe sampling techniques, non-contact optical diagnostics do not disturb the reactive flow field. Generally, optical diagnostics can be divided into laser methods and non-laser methods. Laser diagnostics methods, such as laser-induced incandescence (LII) [8–10] and low-intensity laser-induced break-down spectroscopy (LIBS) [11,12], are currently being developed to provide spatially- and temporally-resolved information for the particle-phase in gas-phase synthesis. By the interaction between a particle-laden flow and a laser light-sheet, two-dimensional (2D) volume fraction and size distribution of the particle phase can be determined. It is, however, still a challenge to develop these methods towards quantitative measurements [6].
Line-of-sight attenuation (LOSA) [13–16] and line-of-sight emission (LOSE) [17–20] have been successfully applied for quantitative combustion diagnostics and measurement of optical properties of the solid phase in particle-laden media, e.g., for carbon particles exploiting their high emissivity and absorptivity. LOSA enables the determination of particle volume within the Rayleigh limit with the prior knowledge of the refractive index [14,15]. Combined with two-dimensional (2D) tomographic reconstruction algorithms [21,22], 2D volume fraction distributions can be obtained for axisymmetric flows. Additionally, with the help of three-dimensional (3D) tomographic reconstruction algorithms [23,24], 3D non-symmetric volume-fraction distributions can be obtained. LOSA provides information about the particle-based wavelength-depended extinction coefficient, while LOSE delivers complementary information about particle emissivity (and thus temperature). LOSE has been demonstrated in various flames to retrieve temperature [17–20], soot volume fraction [17,19,20], and particle size [20] based on an inverse radiation heat transfer analysis. The LOSE technique has been developed recently with respect to refined measurement complexity, data dimensionality and deconvolution algorithms. Not only for soot diagnostics, but also as a potential simple diagnostics method in the field of gas-phase nanoparticle synthesis where freshly produced nanoparticles emit significant radiation in the outflow of the process reaction zone.
Until now, very few studies applied the LOSE method to the in situ analysis to aerosols containing non-soot inorganic nanoparticles. Goroshin et al. [25] used a low-resolution spectrometer to acquire spatially resolved broadband emission spectra of Bunsen-type flames with aluminum suspensions retrieving radial temperatures profiles of the particle-phase using Abel inversion. Liu et al. [26] developed models for simultaneously reconstructing temperature and volume fraction distributions of nanoparticles in nanofluid flames based on simulation studies. One important challenge when transferring the method to inorganic nanoparticles is the dependence on their (temperature-dependent) optical properties. Therefore, a direct transfer of the soot (i.e., black-body)-based approaches is not possible and the measurement strategy must be adjusted accordingly.
In LOSE experiments, an ill-posed inverse problem needs to be solved to retrieve desired physical quantities from emissions in particle-laden media. This problem gets more difficult with an increase in the number of unknown parameters. Therefore, combining complementary experimental techniques, e.g., extinction and emission measurements leads to reduced uncertainties and increased accuracy in determining the desired particle-phase properties. The combination of modulated absorption/emission spectroscopy has successfully been applied in sooting flames [27,28]. Jenkins and Hanson [27] applied the two-color pyrometry technique combining measurements of modulated laser absorption with flame emission to one-dimensional temperature measurement of soot, and they found the combined technique reduced the uncertainty of the measured temperature to around 20 K. Furthermore, the combined technique was further extended to determine the 2D radial temperature and volume fraction of soot [28]. To the best of our knowledge, we are the first to explore the combined extinction/emission technique to a non-soot nanoparticle system, where the extinction/emission strength is commonly much lower than in the case of “black” soot. We used the full emission/ extinction spectra instead of the commonly employed two-color pyrometry to ensure the absence of unknown interferences from atomic or molecular species that could otherwise bias the results of the two-color approach.
The present study first explains the theoretical model for the combined application of tomographic extinction and emission measurements for the in-situ probing of hot nanoparticles in gaseous reactive flows from the derivation of the radiation transfer equation (RTE), and discusses potential uncertainties caused by the assumption of the particles residing in the Rayleigh limit. The technique is then applied for the determination of temperature and volume fraction fields of germanium nanoparticles produced by gas-phase synthesis from germane in an argon/hydrogen flow reactor that is heated locally by a microwave plasma. The optical measurements are carried out at a location where the germanium is in the liquid phase. This reactor has been used previously for synthesis of Si, Si/Ge, and graphene particles [4,29,30] and has been also upscaled to larger production capabilities [31]. In situ emission and extinction spectra from the hot Ge nanoparticles in the plasma off-gas flow were captured by a spectrometer fitted with an electron-multiplying charge-coupled device (EMCCD) camera. The reconstructed spatial profiles of temperature and volume fraction were compared to results obtained earlier in the same reactor [32] using laser-induced fluorescence (LIF) and laser-induced incandescence (LII), respectively, which demonstrates the feasibility of the proposed method for spatially resolved measurement of particle properties.
2. Theoretical background
LOSA is a well-established optical method for the measurement of particle volume fraction, while the emission spectra captured from LOSE measurement offer a close relationship with volume fraction and temperature distributions of the particle-phase. In this section, the principles of LOSA and LOSE are outlined based on the radiative transfer equation (RTE) [33] with the objective to describe the relationship between the signal received by the detector and the temperature and volume fraction fields, respectively. This derivation is followed by the measurement strategy for combining emission and extinction spectroscopy for retrieval of these physical quantities.
The schematics of the reconstructed distribution of the respective quantity in a cross-section in an axisymmetric arrangement is shown in Fig. 1. The cross-section is subdivided into several ring-shaped segments, where the volume fraction and temperature of particles in each ring is assumed constant. Position-resolved line-of-sight emission and attenuation spectra of the particle-phase are captured by a spectrometer with an attached EMCCD camera detector. In the experiments described below the reactor with the particulate flow, i.e., the measurement object, is moved step-wise perpendicular to the flow axis to record the emission and attenuation spectra for consecutive positions along the cross-section.
Fig. 1. Line-of-sight 2D reconstruction scheme of a horizontal cross-section of a symmetric object. The cross-section is equally divided into M rings that are crossed by N detection lines. ymin and ymax are the entrance and exit intersections of the line j through the cross-section.
2.1 Radiative transfer equation
For a quasi-steady system, the radiative transfer equation [33] can be expressed as
Integrating Eq. (1) gives
2.2 Line-of-sight attenuation (LOSA) measurement
An LOSA measurement consists of four individual cases [28] and the integrated extinction coefficient Kλ along one detection line j reads,
Case 2) the nanoparticle stream is switched on and the light source is off. The signal output V2 of the detector is defined by,
Case 3) the light source is switched on with the nanoparticle stream off. The signal output V3 of the detector as,
Case 4) the background with light source and nanoparticle stream off. The signal output V4 of the detector then is,
where $\varepsilon _\lambda ^{({\textrm{off},0} )}\; $ is the radiation energy from the background only. Note, the background signal is a combination of any non-specific constant signal contribution as well as the constant offset of data digitization.The measured quantities given above are introduced into the RTE model. Based on Eq. (2), the radiation energy from nanoparticles $\varepsilon _\lambda ^{\textrm{emi}}$ and the light source $\varepsilon _\lambda ^{\textrm{ls}}\; $ accumulated within a time period Δt, over the detected wavelength bandwidth Δλ and the solid angle ΔΩ, impinging on the area ΔA of the spectrometer entrance slit can, respectively, be described as,
The radiation energy from the light source $\varepsilon _\lambda ^{({\textrm{ls},0} )}$ is different from $\varepsilon _\lambda ^{\textrm{ls}}$ in case 1) due to lack of participating nanoparticles, and is expressed as,
After discretization, N detection lines form Eqs. (13)
Rewriting this in matrix form gives
where the elements of the cross-length matrix L are formed by the cords between the rings. Equation (14) can be treated as a linear optimization problem, in which the extinction coefficient matrix βλ is retrieved by least-squares QR-factorization decomposition (LSQR) [34,35] with the prior knowledge of L and Kλ. The least square problem in the LSQR method is to solve min ||Ax - b||2. In comparison to the standard methods of conjugate gradients, LSQR method has more favorable numerical properties [34]. The LSQR method has been successfully applied when reconstructing temperature and volume fraction fields of sooting flames [18,36].2.3 Line-of-sight emission (LOSE) measurement
The temperature will be derived from the combination of spectrally resolved LOSA and LOSE measurements. In the LOSE measurement the two cases with the radiation energy detected with (V5) and without (V6) the presence of luminous nanoparticles needs to be considered:
Therefore,
Since $\Delta \lambda \Delta t\Delta {A_{\textrm{emi}}}\Delta {\mathrm{\Omega }_{\textrm{emi}}}$ is constant in the experiments, Eq. (17) can be further simplified to
Introducing γ as the ratio of the signal counts by the CCD sensor and the energy received by the illuminated pixel, Eq. (18) transforms to,
Discretizing the integral across the detection cords of the right-hand side in Eq. (19) generates Eq. (20) with the assumption βλ = κλ.
The attenuation coefficient βλ in each ring in Eq. (20) can be determined from the LOSA measurements. The combination of N detection lines then leads to Eq. (21)
Conversion into matrix form then results in
The blackbody radiation intensity Ibλ based on the Wien law is expressed as
This leads to Eq. (24)
2.4 Combination of LOSA and LOSE methods
Radiation interacting with a spherical particle will be absorbed and scattered from the original direction. Mie theory as an equivalent solution to Maxwell equations describes these processes correctly for various particle sizes. Two assumptions are provided in the model: Rayleigh approximation theory instead of Mie theory, and the scattering is neglected compared to the absorption effect. As for the liquid Ge particles, the refractive index is quite different from that of soot, which may render the second assumption invalid [13]. In this section, the rationality of the two assumptions for particles with various particle sizes were analyzed first.
In the case of spherical nanoparticles, the scattering Qsca and extinction Qext efficiencies are expressed, respectively, within the Mie regime as [37]
For small particles, the Rayleigh limit $2\mathrm{\pi }a/\lambda \ll $ 1 holds, bn is equal to 0 irrespective of n, and an is also equal to 0, except for when n = 1 [37]. This further simplifies Eqs. (25) and (26) to
Fig. 2. Absorption and scattering efficiency of Ge nanoparticles with sizes of 10, 20, 30, and 40 nm in the wavelength range from 250 to 800 nm based on Rayleigh and Mie theory.
Fig. 3. Absorption to scattering efficiency ratios for Ge nanoparticles of various size in the wavelength range from 250 to 800 nm based on Rayleigh and Mie theory.
Considering the extinction coefficient βλ of a nanoparticle cloud with nonuniform sizes,
As explained in the ‘Experimental details’ section, the particle stream forms an upward flowing hollow cylindrical structure with an approximately 1-mm thick particle-laden “wall” [32] and the liquid germanium nanoparticles behave like a weakly absorbing/emitting body—contrary to soot, which results in difficulties detecting absorption/emission signals with sufficient signal-to-noise ratios. As for particles with a size below 30 nm, the absorption efficiency of soot is more than 2.5 times higher than of germanium as averaged over the visible wavelength range and as determined from Mie theory (wavelength-dependent refractive index for soot taken from Ref. [40]). As shown in Fig. 2, the absorption and scattering efficiency increases with shorter wavelengths. Therefore, LOSA measurements are preferred in the ultraviolet. According to the Planck law, however, the thermal emission intensity increases with the wavelength, which is why the LOSE measurements are evaluated from the visible range of the spectrum.
The measurement and data evaluation strategy for the combined application of the LOSA and LOSE diagnostics to measure particle temperature and volume fraction distributions of germanium nanoparticles in this work is illustrated in Fig. 4. It should be noted that this combined model is different from the one used in sooting flames [28]. In sooting flames, βλ is determined from LOSA in the same wavelength range used for LOSE. For the germanium nanoparticle aerosol, in contrast, due to weak attenuation and emission and thus low S/N ratios in the visible, optimized wavelength regions for each technique are selected. Thus, the wavelength ranges of βλ for LOSA and LOSE are not identical. Therefore, one additional step is required for data evaluation. We use the particle volume fraction distribution to transfer βλ at the wavelength range identical to the LOSA to the LOSE measurement. Subsequently βλ is introduced into the LOSE measurement to finally determine the temperature distribution.
Fig. 4. Flowchart illustrating the strategy for reconstruction of volume fraction and temperature distributions by combined LOSA and LOSE measurements.
3. Experimental details
3.1 Reactor configuration
Germanium nanoparticles were synthesized in a microwave plasma reactor ([4,32], Fig. 5) with 800 W microwave power at a total pressure of 100 mbar. The microwave radiation was generated by a magnetron (Fricke und Mallah, FMG 1×2.0 kW SNT), and adapted to a circulator before being directed towards the reactor. The gaseous precursor germane (GeH4) with a volumetric flow rate of 0.03 slm (standard liter per minute) was mixed with argon and hydrogen (2/0.2 slm) and injected through a nozzle at the bottom on the center of the reactor coaxially into a fused-silica tube placed in the center of the microwave plasma zone. To reduce materials deposition on the inside of the quartz tube and to stabilize the nanoparticle-laden flow, a swirling flow of Ar/H2 (6.6/0.5 slm) coaxially surrounded the nozzle flow. The total pressure was adjusted to 30 mbar via an adjustable valve before the particle-laden flow passed through a filter to keep particles from entering the vacuum pump. From previous Rayleigh imaging performed in the same reactor synthesizing silicon nanoparticles from SiH4 precursor, it is known that the particle stream forms a hollow cylinder with a wall thickness of approx. 1 mm when flowing downstream through the optically accessible section of the flow reactor ([32], Fig. 5). LOSE and LOSA measurements were carried out through optical ports fitted with polished quartz windows. The spectrometer fitted with an EMCCD camera was pas positioned to record signal approx. 300 mm downstream of the plasma zone. The reactor was mounted on two cross-mounted translation stages (Aerotech) to enable xy translation of the particle stream through the analysis beam.
3.2 Optical setup
The optical layouts of the LOSA and LOSE measurements are shown in Fig. 6 and are similar to what was presented in previous work [13]. Broadband radiation from a laser-driven light source (LDLS, Energetiq EQ-99) is collimated by an off-axis parabolic mirror before it passes an aperture limiting the light beam diameter. A plano-convex quartz lens (300 mm focal length) focuses the light to the centerline of the reactor with the particles stream. After leaving the reactor, a plano-convex lens (300 mm focus length) re-collimates the light beam after which another quartz lens (150 mm focal length) focuses the beam through the slit of the spectrometer (Acton, SP-150, 150 mm focal length, fitted with a grating with 150 l/mm). The aperture #3 (diameter ≈ 1.4 mm) placed between the reactor and collimating lens 4 reduces the field of view and the radiance from the light source to not saturate the detector. In the case of LOSE measurements, the set-up is the same except the light source is blocked. The light is then dispersed into the spectrometer (objects 7–12 in Fig. 6) and imaged onto the EMCCD detector (Andor, iXon DV887, 512×512 pixels).
Fig. 6. Experimental setup for line-of-sight attenuation/emission measurements. The dashed rectangle (left) includes the light source for the extinction measurement that is switched off during emission measurements.
As for the extinction measurement, the smallest diameter of the light beam focused by the lens (item 4 in Fig. 6) can be estimated from the diffraction limit equation,
where λ is the incident light wavelength, D is the diameter of the limiting aperture, and f is the focal length of the lens. The largest wavelength in the extinction measurement is 556 nm; therefore, the diameter at the focal spot is approx. 0.13 mm. This would indicate the attainable spatial resolution in the extinction measurements if the reactor was translated through the beam by an infinitely small step size. However, the translation step size in the present experiments was 1 mm.The commercial software ZEMAX [41] was used to estimate the spatial resolution attainable in the emission measurements. ZEMAX was operated in ‘non-sequential mode’, which takes reflection and refraction into account. We built the non-sequential component editor based on the geometric distances between each object in the experiment and took advantage of the accessible ZEMAX optics toolbox downloaded from Thorlabs [42] for the lenses utilized in the experiments. A “virtual” flat rectangle surface modeling a light source that emits rays was placed at the spectrometer slit position, and its size is equal to the entrance slit (8.2 mm high, 1 mm wide). A “virtual” rectangular detector sensor element was positioned at the centerline of the reactor. Four billion rays were backward traced from the light source to the detector, and the irradiance distribution impinging on the detector was recorded. The normalized irradiance distributions along the slit height and the slit width were fitted by Gaussian functions. The full width at half maximum (FWHM) is about 1.21 and 1.20 mm along the slit height and width, respectively. Since the slit is assumed to be filled in the model, but is not filled in the experiment, a smaller FWHM in the slit width direction is expected in the practical emission experiments.
3.3 Experimental procedure
The wavelength and relative detection efficiency of the spectrometer/detector system was calibrated with light from a mercury penray lamp and a calibrated Ulbricht sphere illuminated by a tungsten lamp, respectively. Even through the optical windows are purged during the particle synthesis process, they may suffer from particle deposition over time, modifying their transmission characteristics. In the case of LOSA measurements, the transmission efficiency of the optical path ηx,emi is assumed to be the same as ηx,ext at the same position. Therefore, the transmission efficiency term is not included in Eq. (5). However, in the LOSE measurement, possible window fouling on the detector side changes the transmission efficiency ηx,emi over time and position, and this was compensated by comparing the LDLS spectrum on the detector with and without the window in the beam path.
Extinction and emission spectra of the particle stream were recorded with one-dimensional spatial resolution by sequentially translating the reactor in 1 mm steps perpendicular to the analysis beam. With the grating positioned at two selected center wavelength positions and the current sensor size, the wavelength span from 230 to 556 nm and 380 to 703 nm can be recorded on a single camera image in the LOSA and LOSE measurements, respectively.
The reliability of the reconstruction model is related to the particle size depending on the validity of the Rayleigh approximation. To independently measure the particle size, we extracted particles with a pneumatically driven thermophoretic sampling device with a sampling time of about 500 ms, which were further analyzed by transmission electron microscopy (TEM) for determining the particle size distribution (PSD). The Ge particle diameters follow approximately a normal distribution with a count mean diameter of 38.3 nm and a standard deviation of 5.7 nm [13]. As discussed in the Theory section, the employed reconstruction model is applicable in the current system with particle sizes smaller than 30 nm. Larger particles will introduce errors to the reconstructed results. To further develop the current algorithm, Rayleigh theory needs to be replaced with Mie theory to improve the reconstruction model in the future.
4. Phantom study
In this section, we attempt to recover temperature and volume fraction profiles based on measurement data obtained from a ground truth data set (phantom) to demonstrate the feasibility of the reconstruction method. For this purpose, the ground truth input data used volume fraction (fV) and temperature (T) profiles that were taken from previous LII (fV) and SiO-LIF (T) in situ measurements during experiments of the gas phase synthesis of silicon nanoparticles in the same reactor [32], as shown in Fig. 7. Firstly, the input profiles were used to generate synthetic measurement data, these being the Kλ in Eq. (5) of the LOSA measurement and $\textbf{C} \times {\textbf{I}_{\textbf{b}\lambda }}$ in Eq. (22) of the LOSE measurement. Secondly, and the synthetic measurement data was contaminated with artificial noise sampled from normal distributions with a standard deviation σ as a percentage of the signal. Two values of σ, 0.005 and 0.025, were tested and the noise level for the σ = 0.025 case was considered to be higher than that in the experiments.
Fig. 7. The input temperature and volume fraction profiles from previous LII and LIF measurements (Ref. [32]), considered as ground truth phantom data.
The relative errors RT and RfV between the ground truth and reconstructed data were evaluated and are defined as
Figure 8 shows the retrieved temperature and volume fraction relative errors without added artificial noise. The small relative errors indicate that the measurement model is reasonable and the values on the graph indicate the lowest theoretical error that would be expected from a reconstruction using noise-free measurement data.
Fig. 8. Relative errors of the temperature and volume fraction reconstructions using synthetic measurement data without noise addition.
Various levels of noise were added to the LOSA and emission measurements, and the resulting relative errors of the reconstructed volume fraction and temperature profiles are presented in Fig. 9. Five samples were considered because of the artificial noise characteristic of random (i.e., Gaussian) distribution, on the basis of which the error bars have been added. Overall, the relative errors of the recovered temperature and volume fraction distributions are quite acceptable with σ of 0.005, while for the larger σ of 0.025 the retrieved temperature and volume fraction profiles in the center region feature larger deviations from the ground truth. The poorest reconstruction is obtained for the innermost ring, where the nanoparticle stream is hollow as mentioned previously and the signal is weak. The same problem occurred on reconstruction of soot volume fraction in a methane/air coflowing flame using Abel inversion, and it also showed a higher uncertainty in the inner region of the flame [43]. The results also indicate that generally larger relative errors result from the reconstruction of temperature than that of volume fraction. The noise in the LOSA measurement affects the reconstruction of temperature and volume fraction, whilst the LOSE measurement contributes noise to the temperature reconstruction only.
Fig. 9. Relative errors of the temperature and volume fraction reconstructions using synthetic measurement data that contained two different noise levels, σ = 0.025 and 0.005.
5. Reconstruction of experimental data
5.1 Line-of-sight attenuation measurement
Horizontal scans of the Ge nanoparticle stream were performed from −7 to +7 mm from the centerline with a step size of 1 mm. Figure 10 displays the projected spectrally resolved (y axis) attenuation coefficient (color scale) calculated based on Eq. (5). The axisymmetric distribution of the particle stream (i.e., the projected absorption coefficient) can be clearly observed, from which the Ge stream was equally divided into eight rings for the reconstruction model. The line-of-sight integrated attenuation coefficient Kλ in the wavelength range from 230 to 556 nm is extremely small in the visible wavelength range, which entails a low S/N-ratio in LOSA measurements (Fig. 10).
Fig. 10. Spectrally-resolved integrated values of attenuation coefficients Kλ obtained from the LOSA measurement.
As expected from previous measurements [13], the attenuation signal increases monotonously from the visible to the ultraviolet in the recorded wavelength interval. The wavelength range from 250 to 300 nm was chosen for further processing by the LSQR algorithm. The deconvoluted attenuation spectra for each ring structure are shown in Fig. 11. For brevity, we show the spectra from half of the Ge stream, which corresponds to the region 0 to 7 mm from the centerline in Fig. 10. The attenuation coefficients in all the rings show the decreasing trend with wavelength. The attenuation coefficients are larger in Ring 2 and Ring 3 than the other rings, which indicates the locally higher nanoparticle concentration in the rim of the cylindrical particle stream.
Fig. 11. Wavelength dependence of the attenuation coefficient βλ for each reconstruction ring between 250 and 300 nm.
The volume fraction profile was reconstructed by substituting the absorption coefficient from Fig. 11 into Eq. (31). In our analysis, the volume fraction profiles varied somewhat with wavelength, which is attributed to measurement errors. The results presented in Fig. 12 were averaged from the data at different wavelengths and compared with the LII intensity profiles obtained previously in the same reactor under the same operating conditions [32]. In the previous experiments, the LII signals were recorded while the reactor was shifted horizontally perpendicular to the detector. It should be noted that the LII signal intensities are proportional to the volume fraction but with arbitrary units, while the LOSA results represent absolute concentration values. To guide the eye, the plots individual data points are connected by Akima spline functions. The relative errors of the reconstructed volume fraction profile, calculated for the case with the higher noise addition in the synthetic measurements, σ = 0.025, as detailed in the section “Phantom study”, are displayed as error bars in Fig. 12. The profiles with the two volume fraction maxima closely peak at the same position from both methods and represent the structure of the nanoparticle stream as a hollow cylinder with the same diameter in both measurements, demonstrating the reproducibility of the synthesis conditions. However, the determined “thickness” of the particle stream is smaller in the LOSA measurements and higher values are revealed in the region closer to the centerline. Considering the low particle concentration in the interior of the hollow cylinder particle stream, the LOSA signals extracted from the inner region are quite low, which may have caused systematic errors in the reconstruction.
5.2 Line-of-sight emission measurement
The position-dependences of the line-of-sight-projected emission spectra of the particle stream are displayed in Fig. 13(a) between 550 and 650 nm, and the retrieved radiation intensities γαIbλ in each ring from Eq. (22) are given in Fig. 13(b). The fits based on Eq. (24) in all the rings are presented in Fig. 14, from which the values of ln(γαIbλ/λ5) show strong a linear dependence on the values of c2/λ, indicating the reasonability of the multi-wavelength fitting method. Temperature is then given as the inverse of the least-squares fitted slopes of the plots.
Fig. 13. (a) Measured LOSE spectra along the selected detection lines of sight (cf., Fig. 1), (b) γαIbλ deconvoluted from the integrated values in (a) over the depicted wavelength range.
Fig. 14. Retrieved functional evaluations from Eq. (24) from which local temperatures were determined: symbols: experimental data; lines: linear fit.
In Fig. 15, the reconstructed particle temperature profile obtained by the combined LOSA/LOSE method (red symbols) is compared to a gas phase temperature profile from Ref. [32], which was obtained from least-squares fitting of the SiO-LIF excitation spectra to the measured ones in a similar experiment using SiH4 instead of GeH4 for the formation of Si nanoparticles. The assumption for this comparison is that firstly, a similar temperature environment should exist in both synthesis conditions, and secondly, further downstream of the discharge region the gas phase temperature should be close to the particle temperature. Error bars are introduced to the combination method data from the simulated relative error profile, of the case with noise-contaminated synthetic measurements with σ = 0.025 as detailed in the section “Phantom study”. The reconstructed results are generally lower than the results from LIF measurement at the same location, and the largest difference is about 100 K at a radial distance of 5 mm.
Fig. 15. Comparison of the reconstructed temperature profile with the LIF measurement result (Ref. [32]).
6. Conclusions
In this work, we propose and describe the combined application of in situ spectrally-resolved line-of-sight emission (LOSE) and attenuation (LOSA) spectroscopy for the spatially-resolved reconstruction of volume fraction and temperature profiles of the particle-phase in the gas-phase synthesis of germanium nanoparticles in a gaseous mixture flow of GeH4/Ar/H2 through a microwave plasma as a heat source. Due to the swirl-stabilized gas flow in this particular flow reactor the generated particle stream is shaped into a hollow thin-walled cylindrical flow downstream of the plasma region. The multi-wavelength tomographic reconstruction model was applied here for lower emissivity germanium nanoparticles and is expected to be applicable for other kinds of nanoparticles. Therefore, depending on the spectral signatures appropriate wavelength ranges need to be selected for the LOSA and LOSE measurements to guarantee acceptable signal to noise values for the reconstruction algorithm to work properly. A comparison with earlier measurements of the particle volume fraction via LII using pointwise detection showed satisfactory agreement with the reconstructed volume fraction distribution. Similarly, the maximum difference between the reconstructed particle temperature profile and the local gas temperature profile evaluated from SiO-LIF thermometry is about 100 K. To overcome the low signal-to-noise issues due to the small probe volume in the hollow-cylinder particle stream, a modified swirl-stabilized flow field through the discharge region might thicken the particle layer in the downstream probe region.
In the UV wavelength range applied here, particles smaller than ∼30 nm can be considered to be in the Rayleigh limit and thus, scattering is considered negligible. Nevertheless, in future work, directly measured particle size distributions will be tested for improving the measurement accuracy based on Mie theory. Additionally, the critical and useful wavelengths can be chosen from the extinction and emission spectra so that the spectral resolved reconstruction model can be simplified to apply in bandpass-filtered imaging systems. Overall, this study showed the feasibility of the combined absorption/emission technique for particle temperature and volume fraction measurements, which, due to its experimental simplicity, might be particularly promising for applications in large-scale industrial pilot plant environments.
Funding
Alexander von Humboldt-Stiftung; Deutsche Forschungsgemeinschaft (222540104, 262219004).
Disclosures
The authors declare no conflicts of interest.
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