Temperature profile measurements in stagnation-flow, diamond-forming flames using hydrogen cars spectroscopy

Twenty-Sixth Symposium (International) on Combustion/The Combustion Institute, 1996/pp. 1825–1833

TEMPERATURE PROFILE MEASUREMENTS IN STAGNATION-FLOW, DIAMOND-FORMING FLAMES USING HYDROGEN CARS SPECTROSCOPY KEN E. BERTAGNOLLI and ROBERT P. LUCHT University of Illinois at Urbana-Champaign Urbana, IL, USA

Gas-phase temperature profiles were measured near the deposition substrate in atmospheric-pressure, stagnation-flow, diamond-forming flames. In these flames, an acetylene–oxygen–hydrogen mixture accelerates through a nozzle and impinges on a water-cooled molybdenum substrate, stabilizing a flat flame approximately 1 mm below the substrate. A thin, polycrystalline diamond film is deposited on the substrate under appropriate conditions of flame stoichiometry and substrate temperature. Coherent anti-Stokes Raman scattering (CARS) spectroscopy of H2 was used to determine the temperature at various points between the substrate and the incoming premixed jet. The CARS measurements show that the boundary layer (the region between the premixed flame reaction zone and the substrate) is approximately 0.6–0.8 mm thick along the stagnation streamline, depending on the velocity of the incoming jet. The CARS measurements also show peak flame temperatures ;200–300 K above the adiabatic equilibrium temperature—an effect of the short residence times in the flame. Measured temperature profiles are in good agreement with a theoretical calculation of the profile performed by Meeks and coworkers at Sandia National Laboratories, except that the measured distance between the substrate and the reaction zone is much less than predicted. H2 CARS was also compared to N2 CARS in a calibration burner and found to be in good agreement, with the H2 CARS temperatures an average of 3.6% higher than the N2 CARS results. The estimated H2 CARS temperature accuracy is 54% in the diamond-forming flames, and the estimated spatial resolution is 550 lm perpendicular to the deposition surface.

Introduction The deposition of polycrystalline diamond film has been demonstrated using a wide variety of flames and plasmas. Uniform diamond deposition was recently demonstrated in a rich acetylene–oxygen–hydrogen (C2H2–O2–H2) flat flame stabilized in the stagnation region of a molybdenum substrate [1,2]. Stagnation-flow, diamond-forming flames are of great interest because of the high growth rates that can be achieved, the uniformity and high quality of the deposited polycrystalline films, and the potential for scaling the flame systems for the deposition of large-area films [3]. Current attention is focused on how to increase the area of diamond deposition, reduce the required substrate temperatures without sacrificing growth rate, and deposit diamond film on surfaces with complex geometry. Progress in these areas depends on increased understanding of the diamond growth process through both experimental and theoretical studies [4]. In addition to issues associated with diamond deposition, these stagnation-flow flames are of fundamental interest in combustion science because of their high strain rates. They also pose a challenging test of current flame models. The stagnation-flow, diamond-deposition flames of Murayama and Uchida have been modeled recently by Meeks et al. at

Sandia National Laboratories [3]. The numerical results show a steep temperature gradient near the substrate and, strikingly, peak flame temperatures that exceed calculated adiabatic equilibrium flame temperatures by 200 K. Meeks et al. speculated that the primary reason for the occurrence of the superadiabatic flame temperatures was that unreacted acetylene did not have time to fully dissociate to its equilibrium concentration. Acetylene oxidation occurs quickly, but in the model, a significant amount of acetylene remains unreacted in the fuel-rich environment. Endothermic dissociation of acetylene is required to reach equilibrium concentrations, and the superequilibrium acetylene concentration results in superadiabatic flame temperatures [3]. We have constructed a combustion apparatus similar to the Murayama and Uchida burner [2] and have begun a series of laser diagnostic measurements to improve fundamental understanding of these flames and to provide experimental data for comparison with numerical models. We have demonstrated diamond film formation in our apparatus under various run conditions. The measurement of accurate temperature and species-concentration profiles in these flames is challenging because of the high temperatures and spatial gradients. In this paper, we discuss coherent anti Stokes Raman scattering (CARS) temperature measurements near the

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Fig. 1. Schematic diagram of the stagnation-flow, diamond-forming flame with the high-growth-rate (15-mm– diameter, 30-mm–long) substrate. The low-growth-rate substrate has a diameter of 15 mm and a length of 15 mm. Also shown is the position of the hydrogen CARS laser beams relative to the deposition substrate.

deposition substrate. CARS is well suited for probing these stagnation-flow flames because of its excellent spatial resolution and the coherent nature of the signal beam. We chose to use CARS spectroscopy of diatomic hydrogen for the temperature measurements because hydrogen is present in major concentrations throughout the flame, its Raman cross section is large, and the widely spaced vibrational Q-branch transitions (Dv 4 51, DJ 4 0) are within the spectral working range of a broadband dye laser. Experimental Methods Burner Apparatus Figure 1 is a schematic of the atmospheric-pressure, diamond-forming flame apparatus. A rich, premixed mixture of acetylene, oxygen, and hydrogen is accelerated through a converging nozzle with an exit diameter of 3 mm. An annular flow of hydrogen gas shields the premixed gases. This flow impinges on the bottom of 15-mm-diameter molybdenum substrate, and a rich, premixed flat flame is stabilized approximately 1 mm below the substrate surface. Polycrystalline diamond film is deposited on the bottom of the substrate under appropriate conditions of flame stoichiometry and substrate temperature. The top surface of the substrate is cooled by a water flow of 3.4–3.8 L/min. The substrate surface

temperature was estimated (510% uncertainty) by assuming one-dimensional conduction between two embedded thermocouple probes. Constant coolingwater flow rates kept the substrate temperature nearly constant over the course of an experiment. Two substrates with different lengths were used in the study. A 30-mm-long substrate produced surface temperatures ranging from 1000 to 1200 K, leading to the deposition of a high-quality diamond film at growth rates up to ;70 lm/h. Surface Raman scattering analysis and scanning electron microscopy (SEM) images of the freestanding diamond films have confirmed their quality. We also constructed a 15-mm–long substrate to study the case where the substrate temperature was too low for high–growthrate deposition of polycrystalline diamond. The 15mm–long substrate maintains the surface temperature between 800 and 900 K, which reduces the growth rate to ;1.5 lm/h. Both substrates were designed with a slight end curvature to allow the diagnostic laser beams to approach closer to the surface. The burner apparatus is mounted on a three-axis positioner, which allows movement of the flame relative to the CARS laser probe with resolution of 52.54 lm. Tylan FC-280 mass flow controllers control the flow rates for each gas with an accuracy of 50.3 standard liters per minute (SLM). Oxygen and hydrogen are supplied from pressurized gas bottles at 99.95% purity. Absorption-grade acetylene (99.6% pure) is supplied in a commercial gas cylinder and passed through an activated charcoal filter to reduce the amount of acetone in the gas stream. Hydrogen CARS Instrument The 532-nm pump beams for the hydrogen CARS process were provided by a 10-Hz Continuum NY81C injection-seeded Nd:YAG laser with a pulse length of 5–7 ns. This laser is nearly monochromatic, with a line width of 0.0045 cm11. A portion of the Nd:YAG output was used to pump a Mode-X System-2 modeless, broadband dye laser [5]. This laser generates a broadband Stokes beam with a frequency spectrum centered around 680 nm using a mixture of LDS-698 and DCM dye in ethanol. The concentrations of LDS-698 in the oscillator and amplifier were 4 2 1014 and 5 2 1015 M, respectively. The concentrations of DCM in the oscillator and amplifier were 2 2 1014 and 3 2 1015 M, respectively. The pump and Stokes beams were arranged in a folded BOXCARS fashion and focused into the combustion medium, generating a fourth coherent CARS beam. The CARS signal was directed into a SPEX-1000M single-grating, 1-m focal length spectrometer. A Photometrics blue-sensitive, unintensified charged couple device (CCD) camera with a 512-by-512 pixel array was used to detect the dispersed CARS signal. An unintensified CCD camera

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however, the theory and data appear to agree well at a temperature of 3290 K. Because the Q-branch transitions of hydrogen are isolated spectrally, temperature can also be determined by comparing the relative integrated line intensities using a Boltzmann analysis [8]. Assuming that the nonresonant susceptibility of the gas is negligible (valid for fuel-rich conditions) and that the pump beams are monochromatic, the integrated intensity for each isolated Q-branch transition j is given by Ij }

Fig. 2. Comparison of a theoretical CARS spectrum at 3290 K to an experimental H2 CARS spectrum obtained 0.56 5 0.05 mm below the substrate. The experimental spectrum was accumulated for 20 s on the CCD and has been divided by the nonresonant CARS spectrum, thus accounting for variations in the dye laser spectral profile.

was used for signal collection because of its excellent linearity, dynamic range, and spectral resolution [6]. The spectral resolution of the CARS instrument is 1.0 cm11, as determined by the spectrometer grating, the exit-slit relay lenses, and the CCD pixel size. A high-speed mechanical shutter (Vincent Associates Uniblitz LS6T2) was placed in front of the spectrometer entrance slit to reduce the amount of unwanted flame emission recorded by the CCD array. Results and Discussion Hydrogen CARS Thermometry The CARS spectrum reflects the internal energy partitioning among the various vibrational-rotational states of the molecule being excited. Normally—as in nitrogen CARS—temperature is determined from a least-squares fit of a theoretical CARS spectrum to an experimental spectrum. We initially attempted to use the Sandia CARSFT code [7] to analyze our data but encountered problems due to slight variations in spectral dispersion across the CCD array. Figure 2 shows a comparison of an experimental spectrum obtained 0.56 5 0.05 mm below the substrate and a theoretical spectrum generated by CARSFT at 3290 K. There is a slight difference between the location of the experimental and theoretical Q-branch line centers, preventing the CARSFT program from automatically fitting the theory to the data. Visually,

(na 1 nb)2j x23 ]r Cjx28 ]X

2

1 2

j

I2x

(1)

where Cj is the Raman line width (full width at halfmaximum, FWHM) (s11), na and nb are the number densities (m13) of the lower (v 4 0, J) and upper (v 4 1, J) transition levels, I2x is the spectral intensity [W/(s11•m2))] of the broadband Stokes beam, and x2 and x3 are the Stokes laser frequency and the CARS signal frequency (cm11), respectively [9]. Mean spectral intensity variations in the broadband Stokes beam are accounted for by dividing the hydrogen CARS spectrum by a nonresonant background spectrum generated in room air. The (]r/ ]X)j term is the differential Raman cross section (cm2) for each Q -branch transition, (]r/]X)j } (x42/xj) [1 ` (4/45) bJ, J (c8/a8)2] [1 1 6J(J ` 1) (Be/xe)2]

(2) 11

where xj is the vibrational frequency (cm ), bj, j is the Placzek–Teller coefficient, Be and xe are Herzberg molecular parameters (cm11), and c8/a8 is the ratio of the anisotropy of the polarizability derivative to the mean polarizability derivative. The ratio c8/a8 is equal to 0.855 for diatomic hydrogen. The rightmost bracketed term in Eq. (2) is a centrifugal force correction [7]. The population of a particular rotational level J is proportional to the rotational degeneracy 2J ` 1 and the nuclear spin statistical weight gnuc (1 for even J, 3 for odd J). To determine temperature, the rotational energy F(J) (cm11) is plotted versus the product of 1k/hc and the natural log of b, where b4

x42 !IjCj gnuc(2J ` 1)x3(]r/]X)j

(3)

The slope of a linear least-squares fit through the data points is equal to the temperature. Figure 3 shows the corresponding Boltzmann plot for the Q(1)-to-Q(7) transitions of the experimental spectrum shown in Fig. 2. The line-integrated Boltzmann temperature is 3290 5 60 K, the same temperature used to generate the theoretical CARS spectrum in Fig. 2. For the data in Fig. 3, the average uncertainty in the measurement of the integrated line intensities is 50.8% (corresponding to

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Fig. 3. Line-integrated Boltzmann plot for the experimental CARS spectrum shown in Fig. 2. The slope of the line fit to the Q(1)-to-Q (7) transitions gives a temperature of 3290 K with an uncertainty in the slope of 560 K. The error bars correspond to a 50.8% uncertainty in the measurement of the integrated line intensities.

Fig. 4. Comparison of measured H2 CARS (●) and N2 CARS (C) temperatures in a Hencken burner. The solid line (—) represents the calculated adiabatic equilibrium temperature.

the error bars), and the resulting uncertainty in the linear least-squares-fit slope (i.e., temperature) is 51.8%. The average uncertainty in the slope for all of the data presented in this paper is 2.0%, providing a measure of the random error or precision of the hydrogen CARS measurements.

As a check of the Boltzmann method accuracy, the Sandia CARSFT code was used to generate theoretical H2 CARS spectra at specified temperatures, and then these spectra were analyzed as if they were experimental data. The temperatures calculated using the Boltzmann analysis varied by only 51% relative to the theoretical temperatures. It is assumed in writing Eq. (1) that the CARS lines are collisionally broadened. In fact, the CARS lines are primarily Doppler broadened in atmospheric pressure flames. Using the measured collisional parameters of Bergmann and Stricker [10], we calculate that the collisional width is less than 10% of the Doppler width in the diamond-forming flame. This is indeed fortunate because their line-width measurements show a pronounced decrease of the collisional line width with increasing rotational quantum number J. Dicke narrowing of the Doppler profile due to velocity-changing collisions is probably significant, but the rate of velocity-changing collisions is likely to be independent of J. Since the H2 CARS lines are neither purely Doppler broadened nor purely collisonally broadened, a Voigt line shape model is used to compute the Raman line-width Cj. To assess hydrogen CARS thermometry accuracy, we used both hydrogen and nitrogen CARS to measure temperature in a surface-mixing, flat-flame calibration burner—a so-called Hencken burner. Temperatures were measured at a central position approximately 3.8 cm above the burner in a hydrogen-air flame at various equivalence ratios. Temperatures measured using hydrogen and nitrogen CARS and calculated adiabatic equilibrium flame temperatures are plotted versus the flame equivalence ratio in Fig. 4. Comparison of nitrogen CARS data and the equilibrium code calculations confirm that for sufficiently high flow rates, the Hencken burner produces nearly adiabatic flames [11]. Hydrogen CARS data could only be obtained under fuel-rich conditions because of the CARS signal diminishing as the hydrogen concentration decreased. The scatter in the data is due primarily to variations in the Stokes beam spectral profile. On a percentage basis, the difference between the measured hydrogen CARS temperatures and the equilibrium calculations is 53.6%, with a standard deviation of 52%. The 53.6% difference is a measure of the systematic error of the measurements. The difference between the H2 CARS results and the equilibrium calculations is probably due to the assumption of purely Doppler-broadened lines. The fact that the temperatures calculated from the H2 CARS spectra are high compared to the N2 CARS temperatures may indicate that low-J Q-branch lines are actually broader than high-J Q-branch lines, a result that would be consistent with the reported J dependence of the high-pressure, collision-broadened line widths [10]. High-resolution measurements of H2 CARS line shapes in atmospheric

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TABLE 1 Experimental conditions for the stagnation-flow, diamond-forming flame hydrogen CARS temperature measurements Flame Parameter Mean exit velocity (m/s) Substrate temperature (K) Premixed C–O ratio Premixed H–O ratio Premixed equivalence ratio Adiabatic flame temperature (K)

1A

2A

1B

2B

40 1050 5 110 1.05 0.5 2.9 3082

55 1150 5 120 1.02 0.5 2.8 3109

40 800 5 50 1.05 0.5 2.9 3082

55 900 5 55 1.02 0.5 2.8 3109

Fig. 5. Measured H2 CARS temperatures (●) in the diamond-forming flame for flame 1A (40-m/s mean flow, 1050 K substrate). The solid line (—) represents the computational results of Meeks et al. [3]. The dashed line (---) represents the adiabatic equilibrium temperature for this gas mixture, and the solid diamond (l) is the estimated substrate surface temperature. Temperatures in the shaded region are a spatial average across the steep temperature gradient due to the finite size of the CARS probe volume. The accuracy of the temperature measurements between the substrate and 0.8 mm is 54%.

pressure combustion environments are needed to resolve this issue. However, temperature measurement errors associated with this assumption should be reduced in the diamond-forming flames, since the ratio of Doppler to collisional width scales linearly with temperature. Temperature Profiles CARS temperature profiles were obtained in the diamond-forming flame under four different condi-

tions, summarized in Table 1. The substrate was located 4.5 mm away from the nozzle for each run. An annular flow of hydrogen gas surrounded the core gas flow at 3.5 SLM for all cases. CARS spectra were obtained along the central stagnation streamline between the nozzle exit and the substrate surface. The spatial resolution of the CARS probe volume was measured to be ;50 lm normal to the substrate and 1.5 mm long (FWHM). Radial temperature profile measurements showed the diamond-forming flame temperature was uniform over the center 4 mm of the flame, thus minimizing the effect of the probe volume length. Temperature probability density functions obtained from single-shot CARS spectra confirmed that the flame was steady. Therefore, each CARS spectrum was accumulated for 20 s (200 laser shots) on the CCD array. Two spectra were obtained at each location, and their temperatures were averaged. A measured hydrogen CARS temperature profile obtained along the stagnation-point streamline for the base-case flame 1A (40 m/s mean flow, 1050 K substrate) is shown in Fig. 5. The computational results of Meeks et al. [3] are included in the plot for comparison. The model calculations were performed using a mean exit velocity of 37.6 m/s, a C–O ratio of 1.16, an H–O ratio of 0.5, and a substrate temperature of 1073 K. These exact conditions could not be matched in our experiments due to slight instabilities in the flame at the model conditions, but they are close to the flame 1A conditions. The plot also shows the calculated adiabatic flame temperature and the substrate surface temperature as measured by the embedded thermocouples (510%). For flame 1A, the hydrogen CARS temperature data points measured within 0.75 mm from the substrate are accurate to within 54%, based on a rootmean-squared sum of the random and systematic errors. The relative positions of each data point are accurate to within 52.5 lm, with a 550-lm uncertainty in the position of the first data point. In the region approximately 0.8 mm below the substrate,

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Fig. 6. Measured H2 CARS temperatures (●) in the diamond-forming flame for flame 2A (55-m/s mean flow, 1150 K substrate). The results from the base-case flame 1A (—), the adiabatic flame temperature (---), and the estimated substrate surface temperature (l) are plotted for comparison. The temperatures in the shaded region are a spatial average across the steep temperature gradient. The accuracy of the temperature measurements below 0.6 mm is 55.2%.

the temperatures are a mixture of both cold and hot gases, since the CARS probe volume spans a portion of the steep temperature gradient. The relatively high-energy spacing of the rotational states in the ground vibrational state of hydrogen leads to a very rapid decrease in population density with increasing rotational quantum number at room temperature. Thus, cool gas produces a CARS signal only for the first four resonances of the hydrogen Q-branch [Q(0) to Q(3)]. The higher-energy levels [Q(4) to Q(7)] are populated only at high temperature. The error bars associated with the temperature measurements in this region correspond to a separate Boltzmann analysis of lines Q(0) to Q(3) and lines Q(4) to Q(7). The actual temperature is assumed to lie somewhere between these extremes. For data obtained at distances greater than 0.95 mm from the substrate, the uncertainty associated with the temperature is 57%. The error is larger in this region because only four lines are available for the leastsquares fit. The hydrogen CARS measurements in this region are on average 315 5 20 K, close to the actual measured, premixed gas temperature of 300 K. The hydrogen CARS temperature profile agrees well with the general model profile in the region less than 0.75 mm below the substrate. Peak measured temperatures in this region are on the order of 200

K above the adiabatic flame temperature, a feature predicted by the model. The hydrogen CARS technique also provided the spatial resolution necessary to measure temperatures near the substrate. The temperatures very near the substrate (,100 lm) are a spatial average of the temperatures contained in the CARS probe volume. However, there is a significant difference between the measured and computed flame standoff distance (the distance between the substrate surface and the steep temperature gradient indicating the location of the reaction zone). The model predicts a standoff distance of nearly 1.2 mm, while the measurements show a distance of about 0.8 mm. The difference between computed and measured flame standoff distance is a matter for conjecture at this point. Hotfilm anemometer measurements showed that the velocity profile at the nozzle exit was uniform for the conditions found in the diamond-forming flame, eliminating this as a possible source of discrepancy. The difference between predicted and measured flame standoff distances is probably due to differences between the actual and calculated velocity fields [12], although in these high-temperature flames, the accuracy of the chemistry and transport models must be examined also. A hydrogen CARS temperature profile obtained in flame 2A (55 m/s mean flow, 1150 K substrate) is shown in Fig. 6. The base-case (flame 1A) temperature profile is shown for comparison. The accuracy of each data point is 55.2%, slightly higher than for the flame 1A measurements because the dye laser spectral profile was not as well behaved. For this 55m/s mean flow condition, the boundary layer is thinner than for the 40-m/s case, scaling approximately as 1/!Re. The peak temperatures are also higher for this case. The temperature overshoot is consistent with the results in the well-stirred reactor model of Meeks et al. [3]. The residence time for the premixed gases is on the order of 100 ls for the 40-m/ s mean flow and 80 ls for the 55-m/s mean flow. Reducing the residence time increases the peak temperature because now there is even less time for equilibrium acetylene dissociation. The temperature gradient near the substrate is also greater for this case than for the base case, a result expected with a thinner boundary layer. A hydrogen CARS temperature profile measured in flame 1B (40-m/s mean flow, 800 K substrate) is shown in Fig. 7. The 30-mm–long substrate was replaced with the 15-mm–long substrate to produce much lower substrate surface temperatures. For this case, the CARS temperature accuracy is 53.8%. Overall, the temperature profile is very similar to the base case (flame 1A). The boundary-layer thickness and peak flame temperature are approximately the same for both flames. The temperature gradient near the substrate surface is also nearly the same, even though the substrate surface temperature is

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Fig. 7. Measured H2 CARS temperatures (●) in the diamond-forming flame for flame 1B (40-m/s mean flow, 800 K substrate). The results from the base-case flame 1A (—), the adiabatic flame temperature (---), and the estimated substrate surface temperature (l) are plotted for comparison. The temperatures in the shaded region are a spatial average across the steep temperature gradient. The accuracy of the temperature measurements below 0.8 mm is 53.8%.

Fig. 8. Measured H2 CARS temperatures (●) in the diamond-forming flame for flame 2B (55-m/s mean flow, 900 K substrate). The results from the base-case flame 1A (—), the adiabatic flame temperature (---), and the estimated substrate surface temperature (l) are plotted for comparison. The temperatures in the shaded region are a spatial average across the steep temperature gradient. The accuracy of the temperature measurements below 0.6 mm is 53.8%.

roughly 300 K less. This is probably a result of the spatial averaging near the substrate by the 50 lm– diameter CARS probe volume. Upon increasing the mean premixed gas flow velocity to 55 m/s with the 15-mm–long substrate (flame 2B), a temperature profile as seen in Fig. 8 results. As in the results for flame 2A, the boundarylayer thickness for this higher-velocity case is less than that for the base case. However, the peak temperatures are only slightly higher than for the base case where we saw a significant increase in peak temperature for flame 2A. The peak temperatures appear to rise faster than in the base case in the region between 0.2 and 0.4 mm below the substrate, indicating a higher-temperature gradient into the substrate.

showed good agreement. The temperatures measured in the diamond-forming flame are estimated to be accurate within 54% based on the results of this calibration and linear-regression analysis of the Boltzmann plots. The measured diamond-forming flame temperature profile results are in good agreement in many respects with the numerical computations of Meeks et al. [3]. Peak measured temperatures are up to 300 K above the adiabatic flame temperature, as predicted by the model. However, the measured flame standoff distances are much less than the calculated distances. This difference may result from differences between the actual and calculated velocity fields.

Conclusions In conclusion, we have successfully measured temperature profiles in the region near the deposition surface in a diamond-forming flame using H2 CARS. We were able to measure temperatures to within approximately 50 lm of the deposition surface with a spatial resolution of 50 lm. A comparison of measured hydrogen and nitrogen CARS temperatures and calculated adiabatic equilibrium flame temperatures in a calibration flat-flame burner

Acknowledgments This research is supported by the National Science Foundation, Combustion and Thermal Plasma Program, Chemical and Transport Systems Division Grant #CTS9313829 under the supervision of Dr. Milton J. Linevsky. The authors also gratefully acknowledge Dr. Roger Farrow and Dr. Robert Kee at Sandia National Laboratories, Livermore, CA, for helpful suggestions and stimulating discussions. REFERENCES 1. Murayama, M., Kojima, S., and Uchida, K., J. Appl. Phys. 69:7924–7926 (1991).

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2. Murayama, M. and Uchida, K., Combust. Flame 91:239–245 (1992). 3. Meeks, E., Kee, R. J., Dandy, D. S., and Coltrin, M. E., Combust. Flame 92:144–160 (1993). 4. Goodwin, D. G., J. Appl. Phys. 74:6888–6894 (1993). 5. Ewart, P., Optics Comm. 55:124–126 (1985). 6. Rakestraw, D. J., Lucht, R. P., and Dreier, T., Appl. Optics 28:4116–4120 (1989). 7. Palmer, R. E., The CARSFT computer code for calculating coherent anti-Stokes Raman spectra: User and programmer information, Sandia National Laboratories Report No. SAND89-8206, 1989. 8. Chen, K.-H., Chuang, M.-C., Penney, C. M., and

9.

10. 11. 12.

Banholzer, W. F., J. Appl. Phys. 71:1485–1493 (1992). Eckbreth, A. C., Laser diagnostics for combustion temperature and species, Abacus Press, Cambridge, MA, 1988, pp. 220–300. Bergmann, V. and Stricker, W., Appl. Phys. B 61:49– 57 (1995). Hancock, R. D., Bertagnolli, K. E., and Lucht, R. P., Combust. Flame, submitted. Sick, V., Arnold, A., Diebel, E., Dreier, T., Ketterle, W., Lange, B., Wolfrum, J., Thiele, K. U., Behrendt, F., and Warnatz, J., Twenty-Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1990, pp. 495–501.

COMMENTS D. E. Rosner, Yale University, USA. In view of your evident concern with accurate local temperature measurements and their importance for future modeling efforts, it may be relevant to point out that the conditions for diamond film growth from atmospheric (or subatmospheric) pressure flames seem to be those that will inevitably be associated with non-negligible temperature “jumps” at gas/ solid interfaces [1]. The high energy fluxes, small dimension gas gaps, large disparities between the molecular weights of the participating gases (e.g., mixtures “rich” in H atoms and CH3-radicals) and the solid substrates (Mo(s)), and/or the vibrational frequency mismatch (between adatoms and C-atoms within the diamond film itself), all seem to “conspire” to produce an expected systematic difference between the gas temperature evaluated at the growth surface and the (colder) solid surface itself. Does the spatial resolution of your present near-deposition-surface measurements permit you to comment on this?

REFERENCE 1. See, e.g., the recent invited paper: Rosner, D. E. and Papadopoulos, D. E., “Jump, Slip and Creep Boundary Conditions at Non-Equilibrium Gas/Solid Interfaces,” Industrial Eng. Chem. Res. (Am. Chem. Soc.), September 1996. Author’s Reply. At this point it is not possible to comment definitively on this question. Our estimate of a spatial resolution of 50 micrometers in a direction perpendicular to the surface is based on burn patterns observed when the 532-nm beam from our Nd:YAG laser is brought to a line focus. The actual spatial resolution of the CARS measurements should be somewhat better than this because the signal is proportional to the square of the 532-nm intensity. However, the temperature gradients near the surface are very large, on the order of 10 K per micrometer, and we cannot resolve the near-surface gradient accurately. It is

interesting to note, though, that if significant spatial averaging in the CARS probe volume is occurring for measurements near the wall, the measured temperatures would tend to be weighted towards lower temperatures because cold gases generate more CARS signal than hot gases. In addition, we might expect to see a significant deterioration in the quality of our Boltzmann fits, but we do not. The lowest temperatures that we observe are approximately 2000 K, and the Boltzmann fits even for the measurement points closest to the wall are still quite good. Based on these results, it is certainly possible that there is a significant temperature jump at the gas/solid interface. We may be able to address this question more definitively in future experiments in low-pressure diamond-forming flames in a facility that has just become operational in our laboratory. ● Katharina Kohse-Ho¨inghaus, Universitat Bielefeld, Germany. Based on you current understanding of the deposition process and with semiconductor quality diamond in mind, how well does the flame CVD process compete with other CVD methods? And will the answer differ for high (atmospheric) pressure or low-pressure flames? Author’s Reply. Our paper did not focus on the economics of diamond-forming flames. We asked Prof. David G. Goodwin of Caltech and Dr. Jay B. Jeffries of SRI International for their answers to these questions and they were kind enough to reply. Prof. Goodwin: A cost analysis carried out recently by IBIS Associates, Inc. (Wellesley, MA) concluded that the microwave plasma and DC arcjet methods are currently the most economical techniques for production of 1-mm thick diamond thermal management substrates for electronic cooling applications. The combustion technique suffers currently from high gas cost and low carbon conversion efficiency (, 1015). A combustion method using a fuel cheaper than acetylene could

TEMPERATURE MEASUREMENTS IN DIAMOND-FORMING FLAMES become competitive, but only if the conversion efficiency, which is directly related to how much atomic hydrogen the flame can deliver to the substrate, were also increased. So far, using alternative fuels has been found to lower the conversion efficiency. Nevertheless, there may well be other applications for which combustion-grown diamond has a cost advantage. Depending on the application, the high growth rate of an atmospheric-pressure process or the large area coverage of a low-pressure process may be desirable. For active electronic applications, the economics are much less certain, since state-of-the-art CVD diamond is not yet close to semiconductor grade, and significant problems with single-crystal growth, twinning, and n-type doping remain to be solved. Dr. Jeffries: It is not at all clear that flame grown diamond will have sufficiently low defect densities to be useful for semiconductor devices; in fact control of defects is currently the biggest challenge to semiconductor device quality CVD diamond. Both atmospheric and low-pressure flames produce good thermal management diamond material; however, the fuel costs are significantly higher than arcjet and microwave CVD methods.

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● Jerry Finlinson, NAWL, USA. In these experiments you quote a substrate surface temperature near 1100 K. How is it measured and what is the accuracy? Does it change significantly when diamond is coating the surface? Is it possible to measure temperature on the surface of diamond film after formation begins? Author’s Reply. The surface temperature was estimated from the measured temperature difference between thermocouples imbedded in the molybdenum substrate at distances of 5 mm and 8 mm from the surface. We assume one-dimensional heat conduction and estimate the uncertainty of the measurement as 510%. The substrate surface temperature typically varied by only about 10 K during an experimental run as the diamond film was depositing, indicating that there was little temperature drop across the diamond film. It would be possible to measure the diamond film surface temperature by optical pyrometry as the film is growing, and a number of groups have measured the film temperature in this fashion.