Hindawi Publishing Corporation Advances in Optical Technologies Volume 2010, Article ID 656421, 7 pages doi:10.1155/2010/656421 Research Article Thermal Temperature Measurements of Plasma Torch by Alexandrite Effect Spectropyrometer 1 1 2 Peir-Jyh Wang, Chin-Ching Tzeng, and Yan Liu Institute of Nuclear Energy Research, Atomic Energy Council, 1000 Wenhua Road, Taoyuan 32546, Taiwan Liu Research Laboratories, 2202 Seaman Avenue, South El Monte, CA 91733, USA Correspondence should be addressed to Yan Liu, yanliu@liulabs.com Received 18 February 2010; Revised 15 June 2010; Accepted 5 July 2010 Academic Editor: Jagdish P. Singh Copyright © 2010 Peir-Jyh Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. An alexandrite eﬀect spectropyrometer is used to directly measure the thermal temperature of an argon gas plasma jet from a 100 kW DC plasma torch, and the directly measured thermal temperature of the plasma is 11178 ± 382 K. By using the spectral correction function to delete the spectral lines and to correct its underlying spectrum of the relative spectral power distribution of the plasma jet, the remaining continuum spectral power distribution represents the thermal spectral emission of the plasma jet. The calculated thermal temperature of the corrected relative continuum spectral power distribution by the spectropyrometer is 10106 K ±345 K, which is the true thermal temperature of the plasma jet. The blackbody level (BL) of the thermal plasma jet is deﬁned as the ratio of the true thermal temperature to the directly measured temperature, and the blackbody level is a measure of how well the thermal plasma jet approaches a blackbody. The accuracy of directly measured thermal temperature depends on the blackbody level, the higher the blackbody level, and the higher the thermal temperature measurement accuracy. 1. Introduction concentration gradients are low, which are not true in jet fringes or close to electrodes or substrates. The diﬀusion of Plasma jets generated in DC arc torches are used for particles and electrons plays an important role in the regions spraying, cutting, synthesis, carbon material vaporization, of the plasma. The temperatures calculated from the spectral and decomposition of persistent chemical substances. The lines are generally overestimated [4]. temperature ﬂuctuation of a plasma torch signiﬁcantly Planck’s radiation law gives the spectral power distri- reduces its reliability for industrial applications. The char- bution of a thermal radiator (blackbody), and the wave- acteristics of emission spectra from the ﬂame jet of a plasma length with the maximum spectral density obeys Wein’s torch directly indicate the plasma properties and operation displacement law [5]. The Planck distribution forms a conditions. It’s a well-established technique [1–3]tomeasure locus in the CIE color space, and the color of a thermal the kinetic temperature using optical emission spectroscopy radiator changes from red, orange, yellow, and white to (OES) methods; however, none of the methods were accurate blue as temperature increases [6]. Temperature is commonly under temporal and spatial changing conditions. measured by radiation thermometers, such as total radiation Local Thermodynamic Equilibrium (LTE) is assumed thermometer, spectral-band radiation thermometer, wide- for calculating the temperature from the populations of band pyrometer, two-color pyrometer, and disappearing excited levels. The calculated temperature is based on the ﬁlament optical pyrometer. absolute and relative intensities of various atomic lines. The The alexandrite eﬀect refers to the color change phe- temperature is often calculated from the ratios of gas atomic nomenon in alexandrite crystals between diﬀerent light to ionic line emission coeﬃcients by the Saha equation using sources [7]. For example, an alexandrite gemstone can the measured electron number density or is calculated by the appear bluish green under daylight (6500 K) and purplish ratio of spectral lines by the Ornstein method. It assumes red under incandescent light (2856 K). The two colors in this that collisions are predominant and the temperature and example are opponent colors, with a hue-angle diﬀerence 2 Advances in Optical Technologies of about 180 degrees in the CIELAB color space. This is the largest possible color change for human color vision perception. Liu [8] also established the relationship between temperature of a thermal radiator (blackbody) and hue-angle in the CIELAB color space, introduced a novel alexandrite eﬀect method, and developed an alexandrite eﬀect spec- tropyrometer for the thermal temperature measurement. In this paper, we use the alexandrite eﬀect spectropy- rometer to directly measure the thermal temperature of a plasma jet, and the results are compared with the kinetic temperature calculated by the optical emission spectroscopy 400 500 600 700 (OES) method. We also use the spectral correction function Wavelength (nm) of the spectropyrometer to delete all spectral lines and correct the underlying spectrum, and we calculate the true Figure 1: The typical spectral transmittance of alexandrite crystal in the visible wavelength range. thermal temperature using the remaining relative continuum spectral power distribution that represents the thermal spectral emission of the plasma jet. In addition, we deﬁne the blackbody level (BL) of the thermal plasma jet to estimate transmittance of the alexandrite; and λ is the wavelength in how well the thermal plasma jet approaches a blackbody. the visible range. Then, the three coordinates of the CIELAB color space can be calculated as follows: 2. Alexandrite Effect Method 1/3 The “alexandrite eﬀect” is used in gemology to describe L = 116 − 16, a distinct change of color appearance when alexandrite 1/3 1/3 is switched from being illuminated by daylight (6500 K) X Y a = 500 − , (2) to incandescent light (2856 K) [7]. The alexandrite shows X Y n n the same color if a blackbody and a gray body have 1/3 1/3 the same temperature, because the relative spectral power Y Z b = 200 − , distributions of a blackbody and a gray body are the same Y Z n n at the same temperature. The typical spectral transmittance of an alexandrite where X , Y ,and Z are the tristimulus values of the n n n crystal has two bands in the visible spectrum [7]. Figure 1 measured radiating body. Finally, the hue-angle h in CIELAB illustrates the typical two-band spectrum of an alexandrite space is given by crystal. When the radiation of a radiating body passes through the crystal, the crystal appears diﬀerent colors at −1 diﬀerent temperatures of the radiating body. h = tan . (3) ab The continuous color sequence of a thermal radiator is displayed as the Planck locus in the CIE color diagram, Figure 2 illustrates the relationship between temperature from red, orange, yellow, and white to blue as temperature of the thermal radiator and the hue-angle of the alexandrite increases. In fact, the temperature of the thermal radiator crystal in the CIELAB color space. Temperature is a function only relates to the hue red to blue, regardless of it lightness of the hue-angle that can be determined by mathematical and saturation, because the thermal radiator always has a methods [8]. A polynomial function to the sixth power lightness of 100 and a saturation of 0 as a light source of hue-angleisusually adequate formosttemperature regardless of its temperature. measurement applications The color of alexandrite at diﬀerent temperature is represented by the hue-angle in the CIELAB color space, and 2 3 4 5 6 T = a + a h + a h + a h + a h + a h + a h . (4) 0 1 2 3 4 5 6 can be calculated by In a small temperature range, a polynomial function to the ( ) ( ) ( ) X = x λ s λ P λ dλ, third power of hue-angle is suﬃcient. The alexandrite eﬀect spectropyrometer [8] consists of an optical probe, a spectrometer and a computer with a digital Y = y(λ)s(λ)P(λ)dλ, (1) alexandrite eﬀect ﬁlter, which tabulates the spectral trans- mittance along the a-crystallographic axis of the alexandrite Z = z(λ)s(λ)P(λ)dλ, with a maximum hue change of about 180 degrees in CIELAB color space between 6500 K and 2856 K. The spectropyrom- where X, Y,and Z are the tristimulus values, x(λ), y(λ), and eter measures the spectral power distribution of a thermal z(λ) are CIE color-matching functions; s(λ) is the spectral plasma torch through the alexandrite ﬁlter and calculates the power distribution of a radiating body; P(λ) is the spectral hue-angle to determine its thermal temperature. Transmittance Advances in Optical Technologies 3 b can simultaneously provide a temperature and an emission spectrum of the plasma jet measured. The OES system includes a collimator (74-UV, Ocean Opt.), a monochromator (Inspectrum 300, Princeton Instru- ments, wavelength resolution is 0.1 nm), and a computer for acquiring the spectra of the plasma jet. 4. Experimental Results Argon was used for the plasma torch, and the power is kept at 20 kW and current at 100 A. The location of collimator, along the axis direction of the plasma, is 1.5 m away from 2000 the torch head. Figure 4 shows a measurement window of the spectropyrometer of the argon plasma. The temperature (11,329 K) and the emission spectrum are simultaneously displayed. The average measured thermal temperature is 11178 ± 382 K for 12 measurements. The spectral power Figure 2: Relationship between the temperature and hue-angle in distribution consists of continuum underlying distribution CIELAB color space. and spectral lines. In general, the state of high-pressure thermal plasma can be usually described as local thermodynamic equilibrium Argon supply (LTE) or partial local thermodynamic equilibrium (PLTE). Detecting system Steam generator At the known transition probabilities, initial composition of Gas swirler thermal plasma, the temperature depends on the intensities of the spectral lines. The Ornstein method of measuring kinetic temperature on the basis of the ratio of the intensities DC power supply of two spectral lines can be extended to a group of spectral Cooling supply lines belonging to the same type of atoms [10]. The Ornstein method can be expressed by the ratio of the intensities of the Figure 3: The layout of the nontransferred 100 kW dc plasma torch spectral lines and temperature measurement setup. Agv Agv ε E E − E i i i i i i = exp − = exp − ,(5) ε Agv E Agv kT i i i i 3. Experimental Setup The thermal temperature of a 100 kW DC plasma torch ε E ln = y = C − ,(6) is measured (Figure 3). The plasma torch is operated with Agv kT hollow electrodes. The gap between the two electrodes is 2 mm for easily initiating the electrical breakdown for where T is the kinetic temperature; ν is the emission working gas. The steel gas-swirler has four small annular frequency; A is the transition probability; and g is the holes of 2 mm diameter, which are bored with a near- statistical weight factor; ε is the intensity of ith spectral line; tangential slope towards the inside ring to make the injected and E is the energy associated with the ith spectral line. To gas form a swirl ﬂow. The working gas is supplied through simplify the temperature calculation, we do not consider the these holes from an argon or steam supply system into the absorption eﬀect of the plasma. The temperature of plasma electrodes gap in a vortex motion, which is necessary for arc jet is estimated to be 13, 410± 500 K by the Ornstein method stabilization. The rear electrode of torch is linked to negative using the measured spectra of Ar I, as shown in Figure 5 with polarity, and the working current I is adjusted from 100 to the parameters in Table 1. 200 A, depending on the mass ﬂow rate of argon or steam The spectral power distribution of the plasma torch for a typical operating condition. In order to avoid inﬂuence includes underlying continuum spectral power distribution by the cold particle scattering, the collimator was directed and spectral lines. In fact, the underlying continuum spectral toward the nozzle of the plasma torch to measure the kinetic power distribution is attributed to the thermal emission of temperature of the plasma jet. the plasma, and the spectral lines are caused by the electron For comparison purposes, two temperature measure- transitions between speciﬁc energy levels of the atoms argon ment methods are used: an alexandrite eﬀect spectropyrom- and copper, which is the nozzle material. If a plasma object eter with an extended temperature range of 1,800–50,000 K is in the complete thermodynamic equilibrium, such as the (LASP 4260, Liu Research Laboratories) and a conventional Sun, its spectral power distribution is almost the same as that optical emission spectroscopy (OES) system. The wavelength of blackbody at the same temperature. The directly measured range of the spectropyrometer is from 380 to 760 nm with thermal temperature in Figure 4 has an error caused by the a wavelength resolution of 1.0 nm. The spectropyrometer present of spectral lines. 4 Advances in Optical Technologies 400 500 600 700 760 Wavelength (nm) Figure 4: A temperature measurement of the plasma torch by the alexandrite eﬀect spectropyrometer. Table 1: The kinetic temperature of the argon plasma torch calculated by the Ornstein method. Wave-length A(1/s) g N(counts) E (ev) Ek (ev) ln(N/g) 810.37 2.50E + 07 3 50989.5 11.6236 13.1531 9.7408 794.82 1.86E + 07 1 32775.5 11.7232 13.2826 10.097 852.14 1.39E + 07 3 35793 11.8281 13.2826 9.3869 738.4 8.47E + 06 3 41350 11.6236 13.3022 9.5312 826.45 1.53E + 07 3 48011 11.8281 13.3279 9.6806 750.39 4.45E + 07 3 42051 11.8281 13.4799 9.548 426.63 3.12E + 05 3 19407 11.6236 14.5289 8.7748 521.05 1.10E + 05 7 15780 13.0757 15.4546 7.7206 Note A is transition probability, g statistical weight factor, and N counts of the spectral line. The spectropyrometer has a spectral correction function, and the calculated kinetic temperature by the conventional which can be used to correct the spectral power distribution Ornstein method is 13, 410 ± 500 K. The temperature mea- by deleting the spectral lines in Figure 4. The corrected sured by the alexandrite spectropyrometer is lower (about spectral power distribution of the plasma is shown in 15%) than that calculated by the Ornstein method. The Figure 6, and the thermal temperature is 9949 K. heat exchange eﬃciency between the plasma and gas particle (or ion) is overestimated for the plasma torch. Additionally, the process of photoionization, reabsorption and photo- excitation by excited particles of plasma cannot be ignored 5. Discussion completely. Thus, the state of thermal plasma cannot reach The alexandrite eﬀect spectropyrometer measures the spec- the thermodynamic equilibrium. As stated by Fauchais et tral power distribution of a thermal radiator through the al. [4], the kinetic temperatures calculated from the spectra alexandrite ﬁlter, and calculates the hue-angle to determine lines are generally overestimated due to the fact that the thermal plasma jet cannot be in true local thermodynamic the thermal temperature. The spectropyrometer can directly measure the thermal temperature of electric arcs and equilibrium. These considerations exactly correspond with discharges, plasma jets, and high temperature combustion our measurement results. Considering the plasma jet is not in ﬂames. The argon gas plasma temperature directly measured true thermal equilibrium and the directly measured thermal by the alexandrite eﬀect spectropyrometer is 11178 ± 382 K, temperature by the alexandrite eﬀect spectropyrometer is Relative spectral power distribution Advances in Optical Technologies 5 10.5 higher than the calculated thermal temperature of 9949 K ± 340 K in Figure 6. The thermal temperature calculated from the further corrected spectral power distribution in Figure 7 is the true thermal temperature of the measured plasma jet, and it is more accurate than that calculated from the corrected spectral power distribution in Figure 6. 9.5 However, the diﬀerence between the two corrected thermal Y =−0.864158217∗ temperatures is about 1.5%, which is not signiﬁcant for the X + 21.20419142 thermal temperature measurement of the plasma jet. Although the corrected spectral distributions are still in a zigzag shape, the zigzag-shaped spectral power distribution has little eﬀect on the accuracy of calculating the thermal 8.5 temperature due to the calculation of the tristimulus values of the spectropyrometer is an integration calculation in the T =−(1.6E − 19/1.38E − 23) / wholemeasuredwavelengthrange. slope = 13410 + 500K The true thermal temperature is lower than the directly measured thermal temperature, and the temperature diﬀer- ent is about 12%. Generally, the 12% diﬀerence is acceptable 7.5 for on-line temperature measurement of a plasma jet in 13 13.5 14 14.5 15 15.5 practical applications. However, to accurately measure the E (eV) thermal temperature of a thermal plasma jet, it is very Figure 5: Temperature calculation of the plasma torch by the important to optimize the design and operation conditions Ornstein method using the measured spectra of Ar I. of the thermal plasma torch. As shown in this paper, the alexandrite eﬀect spectropyrometer is accurate and capable of monitoring the temperature variation of a plasma jet, which is a signiﬁcant beneﬁt to increase the reliability of a lower than that calculated by the OES method, the direct thermal plasma torch. In fact, the stronger the spectral lines, the less accurate thermal temperature measurement by the alexandrite eﬀect spectropyrometer is more precise than that measured by the the directly measured thermal temperature by the spectropy- OES method. rometer. The ratio between the directly measured thermal The very strong spectral lines of the plasma jet can temperature and the corrected true thermal temperature can cause an error for directly measuring thermal temperature be used to indirectly estimate the thermal equilibrium state by the spectropyrometer. However, the measurement error of the thermal plasma jet. The ratio of the true thermal caused by the spectral lines can be corrected using the temperature to the directly measured temperatures is a spectral correction function of the spectropyrometer. The measure of how well the plasma approximates a blackbody, and the ratio is deﬁned as the blackbody level (BL) of a thermal temperature calculated from the corrected contin- uum underlying spectral power distribution of the plasma thermal plasma jet is 9949 K with an estimated standard deviation of about ±340 K (see Figure 6). TT BL =,(7) From Figure 6, we can know that the corrected spectral MT power distribution is approximately similar to that of black- body in the visible wavelength range from 380 to 680 nm. where TT is the calculated true thermal temperature (in However, the spectral distribution slightly increases from Kelvin) and MT is the directly measured thermal temper- 680 to 760 nm, which is not normal for a thermal radiator. ature (in Kelvin). When the BL of a thermal plasma is 1, The increase of the spectral power distribution is caused by such as that of the Sun, the thermal plasma is a blackbody very strong electronic transitions of argon in this wavelength in the state of complete thermodynamic equilibrium. When range, particularly at 696.5, 706.7, 738.4, and 751.5 nm. The the BL of a thermal radiator is less than 1, it does not reach very strong electronic transitions also contribute a small the complete thermal equilibrium. The smaller the BL is, amount of continuum spectral power distribution in the the less the thermal plasma reaches the complete thermal wavelength range from 680 to 760 nm. equilibrium. The BL of the thermal plasma jet is An optically thick thermal plasma at high temperature can be approximately considered as a gray body, even as 10106 K a blackbody, in the visible wavelength range [11, 12]. The BL = = 0.892. (8) 11329 K relative spectral power distribution of a gray body is the same as that of a blackbody at the same temperature. Figure 7 shows the further corrected spectral power distribution of In general, the directly measured thermal temperature is the plasma jet according to that of the relative spectral always higher than the true thermal temperature calculated power distribution of a blackbody. The calculated thermal by the corrected spectral power distribution of a thermal temperature changes to 10106 K ± 345 K, which is slightly plasma, thus the BL is always less than 1. ln(n /g ) n n 6 Advances in Optical Technologies 400 500 600 700 760 Wavelength (nm) Figure 6: The corrected spectral power distribution of the plasma jet. 400 500 600 700 760 Wavelength (nm) Figure 7: Corrected spectral power distribution according to that of thermal radiator. Relative spectral power distribution Relative spectral power distribution Advances in Optical Technologies 7 6. Summary [3] J.F.Key,J.W.Chan, andM.E.McIlwain, “Process variable inﬂuence on arc temperature distribution,” Welding Journal, The alexandrite eﬀect spectropyrometer is used to directly vol. 62, no. 7, pp. 179–184, 1983. measure the thermal temperature of a 100 kW DC plasma [4] P. Fauchais, J. F. Coudert, M. Vardelle, A. Vardelle, and A. Denoirjean, “Diagnostics of thermal spraying plasma jets,” torch, and the average measured thermal temperature is Journal of Thermal Spray Technology, vol. 1, no. 2, pp. 117–128, 11178 ± 382 K for 12 measurements. The true thermal temperature is also calculated by deleting the spectral lines [5] M. Ballico, Temperature and Humidity Measurement, edited by and correcting the underlying continuum spectrum of the R. Bentley, Springer, Singapore, 1998. measured spectral power distribution using the spectral cor- [6] K. Nassau, The Physics and Chemistry of Color, John Wiley & rection function, and its true thermal temperature is 10106± Sons, New York, NY, USA, 2nd edition, 2001. 345 K. The diﬀerence between the directly measured thermal [7] Y. Liu, J. Shigley, E. Fritsch, and S. Hemphill, “’Alexandrite temperature and the true thermal temperature is about eﬀect’ in gemstones,” Color Research & Application, vol. 19, no. 1223 K. In practical applications, the accuracy of directly 3, pp. 186–191, 1994. measured thermal temperature by the spectropyrometer [8] Y. Liu, “Alexandrite eﬀect spectropyrometer,” in Photonic is accurate enough for scientiﬁc research and industrial Devices and Algorithms for Computing VIII, vol. 6310 of applications. By using the spectral correction, the true Proceedings of SPIE, pp. 1–8, San Diego, Calif, USA, 2006. [9] CIE, Publication No. 15.2, Colorimetry, (CIE Central Bureau, thermal temperature can be obtained. Vienna), 1996. The directly measured thermal temperature of 11178 ± [10] A. Ovsyannikov and M. Zhukov, Plasma Diagnostics,Cam- 382 K is approximately consistent with the measured kinetic bridge International Science Publishing, London, UK, 2000. thermal temperature of 13, 410 ± 500 K by the OES method. [11] M. Boulos, P. Fauchais, and E. Pfender, Thermal Plasmas, In fact, the directly measured thermal temperature by Plenum Press, New York, NY, USA, 1990. the spectropyrometer is more precise than the kinetic [12] R. Siegel andJ.Howell, Thermal Radiation Heat Transfer, temperature measured by the OES method to characterize McGraw-Hill, New York, NY, USA, 1981. the thermal property of the plasma torch. Furthermore, the true thermal temperature can be obtained by the spectropyrometer, but not by the OES method if the thermal equilibrium is not reached. The accuracy of directly measured thermal temperature by the spectropyrometer depends on the state of ther- mal equilibrium. The weaker the spectral lines caused by electronic transitions are, the higher the accuracy of the thermal temperature measurement directly measured by the spectropyrometer. In other words, the closer to a blackbody radiator a measured plasma jet is, the higher the accuracy of the directly measured thermal temperature by the alexandrite eﬀect spectropyrometer. The blackbody level of the thermal plasma jet is deﬁned as the ratio of the true thermal temperature to the directly measured thermal temperature by the spectropyrometer. The higher the blackbody level, the more the thermal plasma jet approaches a blackbody. The BL can be used to indirectly estimate the thermal equilibrium level of the thermal plasma jet or any other types of thermal plasma, since when a plasma reaches a complete thermal equilibrium, it will approach a blackbody. Acknowledgment The authors are indebted to the anonymous reviewer for providing helpful comments. References [1] C. Corliss, “Temperature of a copper arc,” Journal of Reserch of the National Bureau of Standatds-A. Physics and Chemistry, vol. 66A, pp. 5–12, 1962. [2] P. G. Slade and E. Schulz-Gulde, “Spectroscopic analysis of high-current free-burning ac arcs between copper contacts in argon and air,” Journal of Applied Physics,vol. 44, no.1,pp. 157–162, 1973. International Journal of Rotating Machinery International Journal of Journal of The Scientific Journal of Distributed Engineering World Journal Sensors Sensor Networks Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 Volume 2014 Journal of Control Science and Engineering Advances in Civil Engineering Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 Submit your manuscripts at http://www.hindawi.com Journal of Journal of Electrical and Computer Robotics Engineering Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 VLSI Design Advances in OptoElectronics International Journal of Modelling & Aerospace International Journal of Simulation Navigation and in Engineering Engineering Observation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2010 Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com http://www.hindawi.com Volume 2014 International Journal of Active and Passive International Journal of Antennas and Advances in Chemical Engineering Propagation Electronic Components Shock and Vibration Acoustics and Vibration Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014
Advances in Optical Technologies – Hindawi Publishing Corporation
Published: Aug 18, 2010
You can share this free article with as many people as you like with the url below! We hope you enjoy this feature!
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.