Investigation of local thermodynamic equilibrium in ...

Spectrochimica Acta Part B 101 (2014) 86–92

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Investigation of local thermodynamic equilibrium in laser-induced plasmas: Measurements of rotational and excitation temperatures at long time scales☆ Julien Lam ⁎, Vincent Motto-Ros, Dimitri Misiak, Christophe Dujardin, Gilles Ledoux, David Amans ⁎ Université Lyon 1, F-69622 Villeurbanne, France UMR5306 CNRS, Institut Lumière Matière, Lyon, France PRES-Université de Lyon, F-69361 Lyon, France

a r t i c l e

i n f o

Article history: Received 26 November 2013 Accepted 17 July 2014 Available online 26 July 2014 Keywords: Laser ablation Plasma diagnosis LIBS Molecular temperature Local thermodynamic equilibrium

a b s t r a c t We studied the rotational temperature of diatomic molecules in the context of laser induced plasma from a solid target. In particular, its temporal evolution is investigated at long time scales (≥30 μs). The measured values are compared to ionic and atomic excitation temperatures and the issue of local thermodynamic equilibrium is discussed. The investigation was carried out using an aluminium oxide (Al2O3) target doped with titanium (Ti) and iron (Fe). The ionic and the atomic excitation temperatures are deduced from the Ti II lines and the Fe I lines respectively. For the molecular temperature, a temporally resolved study of the aluminium monoxide (AlO) blue-green spectrum was carried out. We show that underthese experimental conditions, a complete thermodynamic equilibrium is not reached for up to 50 μs after the laser pulse. The plasma is identified as cold plasma, with two different temperatures: the electron kinetic temperature and the heavy species kinetic temperature. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Laser ablation from a solid target is widely used either for the elaboration of specific materials (pulse laser ablation in liquid, pulse laser deposition, low-energy cluster beam deposition) or as an analytical tool, as in laser induced breakdown spectroscopy (LIBS). In both cases, the transformation of the matter is a non-equilibrium process. In order to control the results of material synthesis experiments or to understand the implications of LIBS measurements, it is crucial to investigate the thermodynamic evolution and to examine the local equilibrium conditions in the induced plasma. Currently, the research community tends to focus on the use of molecular species for the plasma diagnosis [1]. One possible application concerns the chemical processes involved during the laser ablation of a solid target. During the early stages (≤ 1 μs after the laser pulse), the plasma is mainly composed of ions and atoms evaporated from the target. Later, they may react either with each other or also with species from the environment. In both cases, diatomic molecules and small clusters are formed. Probing the relative intensities of the molecular and atomic

☆ Selected paper from the 7th Euro-Mediterranean Symposium on Laser Induced Breakdown Spectroscopy (EMSLIBS 2013), Bari, Italy, 16–20 September 2013. ⁎ Corresponding authors. E-mail addresses: [email protected] (J. Lam), [email protected] (D. Amans).

http://dx.doi.org/10.1016/j.sab.2014.07.013 0584-8547/© 2014 Elsevier B.V. All rights reserved.

emissions is an efficient method to analyse and describesuch chemical reactions [2]. One can even discriminate between atomic isotopes using their molecular spectral specific signatures, as performed by Dong et al. [3]. Also, since molecules usually have a longer lifetime in the plasma than atoms or ions, they can be useful for plasma investigations [4]. The ionic and atomic emissions are rapidly quenched. The spectroscopy of diatomic molecules enables LIBS measurements at longer time scales. It is generally thought that after a few μs, the system is in local thermodynamic equilibrium (LTE). This would guarantee that all the classical thermodynamic relations could be used. This assumption has already been widely discussed [5–9] and traditionally, the McWhirter criterion is used. Nevertheless, it is only a necessary condition since spatial and temporal variations should be discussed as well. However, to our knowledge, very few attempts to question its validity in the context of molecular species have been made [10]. In the research described in the present paper, an aluminium oxide Al2O3 target doped with titanium (Ti) and iron (Fe) was used as a model material. To examine the McWhirter criterion, the electron density was deduced from the H-αline. The excitation temperatures (of the electronic states) of the atoms and ions were obtained using the Fe I lines (~375 nm) and the Ti II lines (~ 350 nm) respectively. The AlO rovibrational spectra (~ 487 nm) were also measured and the rotational temperature was derived from a home-made fitting programme. Based on these results, we present the complete time evolution of these different temperatures

J. Lam et al. / Spectrochimica Acta Part B 101 (2014) 86–92

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Table 1 Spectroscopic data of the lines used for temperature calculation extracted from NIST [14]. Element

λ (nm)

Aki (10+6 ⋅ s−1)

Eup (eV)

gup

Ti II Ti II Ti II Ti II Ti II Fe I Fe I Fe I Fe I Fe I Fe I Fe I Fe I

347.718 350.489 351.084 352.025 353.540 370.557 370.925 371.993 372.762 373.332 375.823 376.379 376.719

7.59 135 133 93.1 96.1 3.21 15.6 16.2 22.4 6.48 6.34 5.44 6.39

3.69 5.43 5.42 5.57 5.57 3.40 4.26 3.33 4.28 3.43 4.26 4.28 4.30

8 10 8 4 6 7 7 11 5 3 7 5 3

over a long time scale [0.1–90 μs] and discuss the issue of their convergence. 2. Experimental details The target was synthesized by solid state reaction at 1400 °C for 6 h under ambient atmosphere, after grinding and mixing powders of Al2O3, TiO2 and Fe2O3. Thus, we obtained a 1.25% atomic percentage (with respect to aluminium) iron and titanium doped Al2O3 target. The plasma plume was generated by the third harmonic of an Nd: YAG laser (λ = 355 nm, Δt = 5 ns, f = 10 Hz). The energy per pulse was set at 40 mJ and the measured crater diameter was d = 191 ± 42 μm after 50 pulses. The plasma emission was collected through a 2f/2f light collection set-up (f = 75 mm) and imaged on the entrance of a circular to rectangular fibre bundle from LOT Oriel (LLB552-UV-0,22) with a N.A. of 0.22. The observed volume size was equal to the whole optical fibre diameter which is 800 μm. The monochromator was then coupled to an iStar intensified CCD (iCCD) from Andor Technology. The laser and the iCCD were both controlled by a pulse generator DG645 from Stanford Research Systems. Two different monochromators were used. The first one was a Ramanor U1000, from Jobin Yvon, with a 1 m focal and a 1800 line/ mm grating. This monochromator provided a spectral resolution of 0.032 nm over all the investigated spectral range. It enables an accurate measurement of the AlO rotational lines and a proper spectral separation of the atomic lines, especially the Fe I lines. With that apparatus, we collected the light in windows 7 nm wide. The spectra could be measured from 325 nm to 870 nm.The Fe II lines, being located at 250 nm, are outside the reach of our system. Consequently, the Ti II lines were used to determine the ionic excitation temperature. The second monochromator is a Shamrock 303, from Andor Technology, with two different gratings (1200 lines/mm and 300 lines/mm). The Stark effect of the H-α line was measured with the 1200 lines/mm grating [see Inset Fig. 1] and the atomic aluminium and aluminium monoxide lines were measured simultaneously with the 300 lines/mm grating [see inset Fig. 9]. In both cases, the wavelength calibration was performed with a mercury argon lamp (HG-1 from Ocean Optics) and the measured line widths enabled an accurate measurement of the resolution (RES). The optical response of the entire collection system was measured through a calibrated blackbody source and the spectra were thus corrected by the apparatus spectral sensitivity. For the plasma imaging, we used an iStar 334 T intensified CCD. The plasma light was collected through a refractive telescope composed of two lenses, with four times magnification. Narrow band filters were placed in front of the optical system to select the light from the aluminium lines or the aluminium oxide lines. We used bandpass filters at 390 ± 5 nm and 488 ± 5 nm for the aluminium lines and the aluminium oxide lines, respectively. Each image is the accumulation of 50 acquisitions.

Fig. 1. Temporal evolution of the electron density in log/log scale. The inset graph is the time evolution of the H-alpha line measured with 0.19 nm resolution. The red curve is the measured curve at 1.5 μs with a typical Voigt fit. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

3. Experimental results and data processing Four different thermodynamic parameters were measured and all the data processing methods are presented below. 3.1. Electron density The hydrogen residues composing the ambient atmosphere were used to measure the electron density. The H-α line around 656.6 nm was collected from 0.10 μs to 3.0 μs (see inset Fig. 1). For longer times, it was no longer resolved because the hydrogen electronic levels were not excited anymore and the titanium and iron lines emerged. The Stark effect was observed. The electron density (Ne) was deduced from the measured full width at half maximum (FWHM). We used the expression reported by Sherbini et al. [11]. We took into account the temperature through the weak dependence of the reduced Stark profiles for the Balmer series reported in [12] (Table AIII.a). The background is subtracted from each spectrum using the continuum emission. Each spectrum was fitted by a Voigt profile with the Gaussian width taken as the experimental width. The self-absorption effect was not taken into account. The error bars were calculatedconsidering the fit error and the uncertainty in the numerical constants used. In Fig. 1, we observe a decrease of the electron density from 1 × 1018 cm−3 to 5 × 1016 cm−3 during the first 3 μs. 3.2. Excitation temperatures The Boltzmann plot method was used to derive the excitation temperatures (TXexc, where X is the considered element). With this method, one assumes that the intensity Iij of each electronic transition between an excited level j and a level i is given by the Boltzmann distribution [13]: Iij λ ln Aij g j

!

! N 1 ¼ ln exc − Ej kB T exc Z TX X

ð1Þ

where λ is the wavelength transition, Aij is the spontaneous emission probability, gj is the statistical weight, N is total density number, Z(TXexc) is the partition function of the considered element, kB is the Boltzmann's constant, and Ej is the excited electronic level energy. Therefore, plotting ln AI gλ with respect to Ej should allow the determination of −k T1 . ij

ij

j

exc B X

The excitation temperature of the ions was measured through the Ti II lines around 350 nm with a resolution equal to 0.032 nm. Fig. 2 shows

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typical spectra measured from 347 nm to 354 nm at different detection delays after the laser pulse. Five lines were selected in order to avoid any self-absorption effect or any overlapping with undesired lines. The excited electronic level energies go from 3.69 eV to 5.57 eV. In Fig. 3, we show two typical Boltzmann plots and the corresponding temperatures obtained at 5 μs and 10 μs. For the atomic excitation temperature, the Fe I spectra were measured around 375 nm with a resolution equal to 0.032 nm. Fig. 4 shows typical spectra measured from 370.5 nm to 377 nm at different detection delays after the laser pulse. We chose eight lines which showed no overlapping with others nor exhibited a self-absorption effect. In this case, the excited electronic level energies range is from 3.33 eV to 4.30 eV. Two typical Boltzmann plots are shown in Fig. 5 where the obtained temperatures are equal to 6670 ± 1034 K at 30 μs and 5525 ± 922 K at 50 μs. 3.3. Rotational temperature In diatomic molecules, considering electronic, vibrational and rotational quantum states, the energy of the observed transitions is given by ΔE = E(e″, v″, J″) − E(e′, v′, J′) with:

Fig. 3. Typical Boltzmann plots using the five Ti II lines referenced in Table 1 for delays equal to 5.0 μs and 10.0 μs.

Thus, the position of each observed transition can be calculated using [15,16].

The intensity is proportional to the transition probability listed in [17] and to the population of the excited state N(e″, v″, J″). Assuming a canonical ensemble, it is given by a statistical distribution in which exc , Tvib, and Trot are reported [2]. In three different temperatures, TAlO addition, to take into account the experimental broadening (the transfer

Fig. 2. Typical Ti II normalized spectra measured at different time delays around 350 nm with a 0.032 nm resolution. The red markers represent the lines used for the temperature calculation. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 4. Typical Fe I normalized spectra measured at different time delays around 375 nm with a 0.032 nm resolution. The red markers represent the lines used for the temperature calculation. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Eðe; v; J Þ ¼ Eel ðeÞ þ Evib ðe; vÞ þ Erot ðe; v; J Þ:

ð2Þ


89

detection delays with a resolution equal to 0.032 nm and the corresponding simulated curve. The temperature value was obtained using a chi-square minimization algorithm. The (ν″, ν′) = (0, 0) lines [484.26–486.60 nm] were chosen because they do not depend on the vibrational temperature. Before any chi-square calculation, the experimental and the tested curve were normalized at 484.56 nm to avoid self-absorption effects in the band heads (ν″, ν′) = (0, 0) and (ν″, ν′) = (1, 1) located at 484.26 nm and 486.67 nm, respectively. We assumed an error of 10% due to the experimental reproducibility and the fitting uncertainties. These results are consistent with measurements published by Parigger et al. [18]and Chaudhari et al. [19]. The vibrational temperature could have been determined using the rest of the spectrum. However, such a method did not seem adequate because the variation of the Δν = 0 band with respect to Tvib was not sufficient to obtain a reliable numerical value. 3.4. Temporal evolution of the temperatures Fig. 5. Typical Boltzmann plots using the eight Fe I lines referenced in Table 1 for delays equal to 30 μs and 50 μs.

function of the monochromator), the peaks are convolved with Gaussian profiles. We developed a simulation programme which can reproduce the spectrum as a function of each temperature and derive the best fitting parameters. For the rotational temperature calculations, the AlO spectra were measured around 487 nm, which corresponds to the Δν = 0 lines. In Fig. 6, we plot three typical curves measured at three different

Using the methods introduced previously, the temporal evolution of the different temperatures is presented from 0.1 μs to 90 μs (see Fig. 7). For each parameter, the calculation was stopped when one of the considered peaks was no longer resolved. The excitation temperatures of the Ti II ions and the Fe I atoms decrease and meet after approximately 10 μs. In the meantime, the rotational temperature measured via the AlO molecules does not tend towards the same value. This point is discussed below. 3.5. Spatio-temporal evolution of the chemical composition In Fig. 8, the spatial distributions of the aluminium and the aluminium monoxide species are represented for different time delays. From 4 μs to 28.8 μs, the species are not disposed in the same region. Aluminium monoxide molecules are created at the plasma periphery and close to the target surface. For longer delays, roughly 40 μs, the two species seem to merge into a homogeneous phase. From 40 μs, the difference between the rotational temperature and the excitation temperature observed in Fig. 7 cannot really be interpreted as a temperature gradient. The AlO lines and the Al lines were measured simultaneously using the Shamrock 303 monochromator (see inset Fig. 9) and integrated in the wavelength ranges of, respectively, [464.0–524.3 nm] and [381.78–399.9 nm]. These two areas are each proportional to the content of the species, as described in [2]. The temporal evolution of the ratio between the intensities of AlO and Al is presented in Fig. 9. The ratio increases during the early stages. Aluminium monoxide

Fig. 6. AlO spectra for different time delays with corresponding fitting curve. The black curve is the experimental one and the red curve is the simulated one. Two Ti I lines are also observed at 40 μs. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 7. Temporal evolution of the excitation temperatures of the atoms (Fe I) and the ions (Ti II) and the rotational temperature (AlO). The dotted lines stand for the mean values calculated from 10 μs.

90


Aluminium monoxide Aluminium 488 +- 5 nm filter 390 +- 5 nm filter Target Δt= 4μs

Aluminium 390 +- 5 nm filter

Aluminium monoxide 488 +- 5 nm filter Δt= 28.8μs

1 mm Δt= 8.8μs

Δt= 48.8μs

Δt= 13.8μs

Δt= 78.8μs

Δt= 23.8μs

Δt= 98.8μs

Fig. 8. Spatio-temporal distribution of the light emission from aluminium atoms (columns 1 and 3) and aluminium monoxide molecules (columns 2 and 4). The light emission from aluminium atoms and aluminium monoxide molecules was collected through bandpass filters at respectively 390 ± 5 nm and 488 ± 5 nm The dotted lines stand for target surface. These results are coherent with those published by Dutouquet et al. [20].

seems to emerge while the aluminium is quenching. Meanwhile, from 20 μs, Fig. 7 shows that the temperatures do not change significantly. The early stage of increase has two sources. It may be regarded as the chemical oxidation occurring in the plasma centre. But the observed volume is 800 μm in size and centred on the plasma plume. The AlO/ Al ratio is mainly driven by the time evolution of the spatial density of each species observed in Fig. 8. 4. Discussion The first condition to assess the LTE is the McWhirter criterion: 12 1=2

3

Ne ≥1:6 10 T elec ðΔEÞ

ð3Þ

where Telec is the electron temperature (K) and ΔE (eV) is the largest energy gap in our system (0.9 eV in our case for Fe I). The highest measured temperature is 16640 ± 434 K which corresponds to the excitation temperature measured at t = 0.6 μs for Ti II. This leads to

Ne ≥ 1.5 × 1014 cm−3. According to the values obtained in Fig. 1, the condition is satisfied up to a few μs. At longer time scales, from 10 μs until the Ti II lines are quenched, exc exc and Tatom converge and the asymptotic values are, respectively, Tion 6743 ± 310 K and 6965 ± 543 K. The overlap of the numerical figures suggests that a steady state is reached. In other words, LTE for the electronic excitation populations of the ions and atoms seems to be achieved during the entire experimental time scale. In the McWhirter criterion, this means that the plasma is so dense in electrons that the thermalization of the various electronic levels by collision with the components of the system has been achieved. Consequently, all the species must share the same excitation temperature, which corresponds to the kinetic temperature of the electrons Telec. However, the rotational temperature exhibits a different asymptotic value, T rot → 3515 ± 470 K, suggesting a deviation from a local thermodynamic equilibrium including the excitation temperatures and rotational temperatures. In order to justify this peculiar result, we will establish that the rotational temperature is predominantly driven by


Fig. 9. Temporal evolution of the ratio of the AlO/Al intensities. The inset graph is the typical spectrum of AlO/Al lines, measured at 50 μs with 0.72 nm resolution, in which the red markers stand for the wavelength ranges used to calculate the intensities. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

the collisions between the heavy species. For numerical applications, we assume that the kinetic temperature TKin of the electrons and heavy species have similar orders of magnitude. We set it to 5000 K. The collisional cross-section, σ, for electron/heavy and heavy/ heavy [21] collisions are similar in terms of their orders of magnitude (10−15 cm2) for neutral heavy species. Finally, we assume that the heavy species density NH is greater than or equal to the electron density Ne. First, we consider the rotational energy transfer due to a collision. This process is a momentum transfer. The transferred mechanical energy between an electron and a heavy species is similar to Ee=H ¼ mm kB T Kin, while between two heavy species, it is EH/H = kBTKin. But, the mass of the heavy species, mH, is approximately 10,000 times bigger than the mass of an electron, me (43,000 for AlO, 16,000 for O and 27,000 for Al). As a consequence, the energy transfer due to an electron/AlO collision contributes 43,000 times less than a heavy/AlO collision. Moreover, in a given vibrational state ν, the rotational energy is distributed as BνK(K + 1) where K is the rotational quantum number. Evolution from the K to the K + 1 level requires a collision energy transfer of 2(K + 1)Bν. In terms of orders of magnitude, the energy available after an electron/heavy collision (Ee/H ∼ 1 × 10−5 eV) is smaller than the rotational constants Bν ∼ 7 × 10−5 eV for AlO while the energy available after a heavy/heavy collision (EH/H ∼ 4 × 10− 1 eV) is four orders of magnitude higher. When K is too high, electrons can no longer provide enough energy, and only heavy/heavy collisions excite the rotational level. Now we estimate the collision rates and the characteristic times of the process. The rates are generally given by f ¼ N σ u where u is qffiffiffiffiffiffiffiffiffi the average velocity, u ¼ 8kπuT with μ the reduced mass of the two e

H

B

Kin

considered species. Therefore, the ratio between the collision rates for electron/heavy and for heavy/heavy is bounded above by f e=H ≤ f H=H

rffiffiffiffiffiffiffi mH : me

ð4Þ

There are approximately hundreds of times more collisions between electrons and the heavy species than between the heavy species. Assuming densities of at least 1016 cm−3, the mean time between two collisions between heavy species, at most 500 ns, is a couple of orders of magnitude smaller than the time scale of the experiment and the time evolution of Trot. Therefore, we can assume that the rotational levels

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of the AlO ground state are thermalized, so there is a translational– rotational equilibrium. Then, τe/H ∼ 3 ns is short enough to excite the B2Σ+ level of AlO in comparison to its emission lifetime of 116 ns. According to Bruggeman et al. [22], “the electron excitation will basically map the ground state rotational distribution onto the excited state rotational distribution.” As a consequence, having more collisions between electrons and heavy species is not critical since only the rotational levels of the ground state require a rotational thermalization. Also, it is less favourable for the electron gas to drag a diatomic molecule into rotation, especially for the highest rotational levels, since these quantum levels need to be excited via collisions with the heavy species such as ions, atoms or molecules. The low K levels only contribute to the headbands, which are not considered in our fit procedure. Therefore, since we only used the high value of K for our calculation, the obtained rotational temperature can be seen as a signature of the kinetic temperature of the heavy species Kin . Furthermore, in cold plasma such as in laser plasmas, the kinetic Theavy temperature of the electrons is assumed to be higher than the kinetic temperature of the heavy species. Two different physical processes drive the establishment of the equilibrium forthe excitation temperature and the rotational temperature. As a result, the temperatures do not converge to each other. 5. Conclusion The question of local thermodynamic equilibrium at long time scales has been raised in this paper. An Al2O3 target doped with Ti and Fe was used. Different methods to extract the thermodynamic parameters were presented. These allowed usto measure precisely the temporal evolution of the excitation temperatures and the rotational temperature. Even though the McWhirter criterion was fulfilled and the convergence of the two excitation temperatures was achieved, we demonstrated a peculiar long-time behaviour of the plasma. The rotational temperature does not necessarily match the excitation temperatures. This can be explained by the difference between the physical processes that ensure the thermalization of the species. As a matter of fact, collisions between bound electrons and free electrons are responsible for the excitation of the electronic levels, while collisions between the heavy species and diatomic molecules are responsible for the excitation of the rotational levels. The two different mechanisms provide two different sources of excitation and consequently two different temperatures. This is characteristic of the properties inside a cold plasma in Kin Kin b TElectrons . But, it still raises one critical point. We do not which THeavy know if the rotational temperatures of different diatomic molecules are necessarily equal to each other. An accurate measurement of the TiO and FeO rotational temperatures will be carried out in upcoming research. Finally, the question of the coincidence between the excitation temperature of the molecules and atoms and that of the ions remains open. References [1] C.G. Parigger, Atomic and molecular emissions in laser-induced breakdown spectroscopy, Spectrochim. Acta Part B 79–80 (2013) 4–16. [2] J. Lam, D. Amans, F. Chaput, M. Diouf, G. Ledoux, N. Mary, K. Masenelli-Varlot, V. Motto-Ros, C. Dujardin, γ-Al-2O3 nanoparticles synthesised by pulsed laser ablation in liquids: a plasma analysis, Phys. Chem. Chem. Phys. 16 (2013) 963–973 (http:// dx.doi.org/10.1039/C3CP53748J). [3] M. Dong, X. Mao, J.J. Gonzalez, J. Lu, R.E. Russo, Carbon isotope separation and molecular formation in laser-induced plasmas by laser ablation molecular isotopic spectrometry, Anal. Chem. 85 (2013) 2899–2906. [4] A.C. Woods, C.G. Parigger, J.O. Hornkohl, Measurement and analysis of titanium monoxide spectra in laser-induced plasma, Opt. Lett. 37 (2012) 5139–5141. [5] H.R. Griem, Validity of local thermal equilibrium in plasma spectroscopy, Phys. Rev. 131 (1963) 1170–1176. [6] H.W. Drawin, Validity conditions for local thermodynamic equilibrium, Z. Phys. 228 (1969) 99–119. [7] R. McWhirter, Plasma Diagnostic Techniques, Academic Press, New York, 1965. [8] G. Cristoforetti, A. De Giacomo, M. Dell'Aglio, S. Legnaioli, E. Tognoni, V. Palleschi, N. Omenetto, Local thermodynamic equilibrium in laser-induced

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