The spectral reflectivity of a commercial silicon carbide (SiC) ceramic surface was measured at wavelengths from 2.5 to 14.5 microns and at temperatures ranging from 358 to 520 K using a NASA-developed multiwavelength pyrometer. The SiC surface reflectivity was low at the short wavelengths, decreasing to almost zero at 10 microns, then increasing rapidly to a maximum at approximately 12.5 microns, and decreasing gradually thereafter. The reflectivity maximum increased in magnitude with increasing surface temperature. The wavelength and temperature dependence can be explained in terms of the classical dispersion theory of crystals and the Lorentz electron theory. Electronic transitions between the donor state and the conduction band states were responsible for the dispersion. The concentration of the donor state in SiC was determined to be approximately 4 x 10 exp 18 and its ionization energy was determined to be approximately 71 meV

Ng, Daniel

English

NASA Technical Reports Server

/A/
NASA Technical Memorandum 105287
- / /
Temperature-Dependent Reflectivity
of Silicon Carbide
Daniel Ng
Lewis Research Center
Cleveland, Ohio
;NASA-TM-105287) TEMPtRATUR N<?,'
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1 p CSCL
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30
February 1992
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https://ntrs.nasa.gov/search.jsp?R=19920010021 2020-03-17T12:45:32+00:00Z
TEMPERATURE-DEPENDENT REFLECTIVITY OF SILICON CARBIDE
Daniel Ng
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135
SUMMARY
The spectral reflectivity of a commercial silicon carbide (SiC) ceramic surface was measured at
wavelengths from 2.5 to 14.5 |um and at temperatures ranging from 358 to 520 K using a NASA-
developed multiwavelength pyrometer. The SiC surface reflectivity was low at the short wavelengths,
decreasing to almost zero at 10 urn, then increasing rapidly to a maximum at approximately 12.5 jam,
and decreasing gradually thereafter. The reflectivity maximum increased in magnitude with increasing
oo surface temperature. The wavelength and temperature dependence can be explained in terms of the
^g classical dispersion theory of crystals and the Lorentz electron theory. Electronic transitions between
rt the donor state and the conduction band states were responsible for the dispersion. The concentration
of the donor state in SiC was determined to be approximately 4xl018 and its ionization energy was
determined to be approximately 71 meV.
INTRODUCTION
s
Ceramics are expected to be used in the design of the next generation of advanced propulsion
systems. Accurate surface temperature measurements of these materials in engine environments is
urgently needed for their research and development.
Pyrometry is a remote temperature measurement method. It measures temperature by measuring
the thermal radiation emitted by a surface using Planck's law of radiation. Traditional pyrometers are
either the one- or the two-color variety. The one-color pyrometer measures the radiation at one
narrow wavelength band. The surface emissivity must be known for accurate temperature results. The
two-color pyrometer measures the radiation at two narrow wavelength bands and does not require
knowing the surface emissivity; instead, the surface emissivities at the two bands are assumed to be
equal.
Both types of pyrometers are susceptible to interference from extraneous radiation, which is of
great concern when highly reflective surfaces are involved (ref. 1). NASA Lewis Research Center has
developed a multiwavelength pyrometer to measure the surface temperatures of ceramic materials such
as silicon carbide (SiC). This pyrometer has been shown to be applicable even in the presence of
interfering radiation (refs. 2 and 4).
After developing this pyrometer, we have used it to measure the surface temperature of a silicon
carbide ceramic sample and to obtain simultaneously its reflectivity and emissivity. The measured
reflectivity can be compared to a theoretical value using the classical dispersion theory for crystals.
EXPERIMENTAL METHOD
The NASA-developed multiwavelength pyrometer (ref. 3) has been applied to measure the
temperature of silicon carbide and to investigate the temperature dependence of its reflectivity and
emissivity. The experimental arrangement was the same that was used previously and is shown in
figure 1. In general, the location of the spectrometer and the auxiliary radiation source is specified by
angular coordinates (B,0) where B is the angle measured from the surface normal to the surface, and
0 is the angle above the plane of the figure. In these experiments, the spectral radiometer was
positioned to view the surface at an angle of about 30° measured from the surface normal. The
auxiliary radiation source was located at approximately the same angle on the opposite side of the
surface normal. Thus, the directional reflectivity and emissivity measured correspond to B=30°
and 0=0°. .
The SiC sample used in the study is described in reference 3. Its dimensions were 25 by 50
by 3 mm (1 by 2 by 1/8 in.) and it was gray to black in appearance with a nominal surface finish of
10 urn. The sample was positioned at the opening of a blackbody furnace cavity so that is was
completely covered. The temperature of the sample is the equilibrium temperature resulting from the
blackbody furnace heat flux incident on the back surface of the sample and heat loss from the front
surface. For each temperature measurement, two radiation spectra were collected and analyzed (ref. 4)
to determine the sample temperature.
Successful temperature measurements were made up to 517 K. Above this temperature, the
surface-emitted radiation overwhelmed that from the 22-W auxiliary radiation source. As a result, the
fractional increase in radiation was less than the resolution of the spectral radiometer. When this
happens, the procedure of obtaining the reflected spectrum by subtraction of two spectra (ref. 3) is no
longer feasible. This difficulty will be overcome in a future system design in which the reflected
spectrum can be obtained from a single measuring operation by mechanically chopping the auxiliary
radiation and using phase-sensitive detection.
Shown in figure 2 are the SiC surface emission spectra of each of the measurements, the Planck
curve corresponding to the temperature as measured by the multiwavelength pyrometer, and the fitted
curve obtained by modifying this Planck curve using the emissivity values determined during curve
fitting. The fitted curve (modified Planck curve) at each temperature agrees well with the measured
spectrum. We previously attached a thermocouple to the sample surface and demonstrated that a good
fit to the spectrum is an indication of accurate temperature measurement (refs. 3 and 4).
As a result of measuring the SiC surface temperature by curve fitting, the reflectivity and
emissivity of the SiC surface (8 = 30°, 0 = 0°) at these temperatures were automatically obtained.
Their spectral and temperature dependence are shown in figures 3 and 4, respectively.
THEORY AND DISCUSSIONS
The SiC surface was not very reflective in the wavelength region between 2.5 and 10 urn as
shown in figure 3. The temperature dependence was also very weak in this region. Above 10 urn,
both wavelength and temperature dependence were more pronounced. The reflectivity peak occurred
at a wavelength of approximately 12.13 |jm and its magnitude increased from 40 percent at the lowest
temperature to 70 percent at the higher temperature. An emissivity minimum occurred at about
12.5 urn and decreased with increasing temperature. This minimum was also reported in reference 5.
The surface finish of those samples were reported to be rough, resembling that of a diamond wheel
cut. The emissivity was measured by comparing the radiation from the specimen surface with that
from a cavity at the same temperature.
A broad, unresolved peak at approximately 10 um was also observed by Atkinson et al. who
measured the emissivity of silicon carbide using an emissometer at discrete wavelengths (ref. 6).
Because of the difficulties inherent in this measurement procedure, previous emissivity measurements
on SiC and other nongray ceramic surfaces were done only at discrete wavelength regions and at
wavelengths below 10 |jm (unpublished research by W. Atkinson of Pratt and Whitney).
Spitzer et al. (ref. 7) have published reflectivity data on green, alpha (hexagonal) SiC. The
results were obtained for optic axis-oriented crystalline samples using polarized radiation. The data
were satisfactorily analyzed using the classical dispersion theory of crystals (ref. 8) and the Lorentz
electron theory. The classical dispersion theory gives a theoretical reflectivity r, for normal incidence
as
r =
(n + I)2 + k 2
(1)
where
n2 = (1/2) {[e2 + 4(a/v)2]1/2 + e }
k2 = (1/2) {[e2 + 4(a/v)2]"2 - e}
e = e. + 47tX (4)
X = P (5)(1 - v2)2 +
 Y
2v2
1 = 27TP !V
 (6)
v (1 - v2)2 + vV
characterized by only four quantities, e^ V0, y, and p, (the high frequency dielectric constant, the
resonance frequency, the resonance width, and the resonance strength, respectively) through their
relation to the susceptibility x> the conductivity a, the index of refraction n, and extinction
coefficient k. The quantity v .is the measured frequency divided by v0.
Results of applying the classical dispersion theory to analyze the reflectivity data obtained at
517 K are shown in figure 5. By trial and error, the values for the four quantities were determined to
be 60 = 1.6, V0 = 2.35xl013 Hz, p = 0.045 and y = 0.08 and were used to calculate the reflectivity.
By applying the result for normal incidence, we have. ignored the angular dependence in the
reflectivity. Siegel et al. (ref. 9) calculated the directional emissivity e(6)=l-r(6) of an optically
smooth, opaque dielectric and found that the emissivity does not exhibit strong angular dependence for
values of B less than 50°. In view of this, the agreement is satisfactory.
The Lorentz theory describes the motion of an electron as an oscillator bound to the equilibrium
position in a crystal by Hooke's law forces for which the force constant is K. The oscillating electron
is subject to a periodic electric field of frequency v as well as to a velocity-dependent damping force
with damping constant 27rmY. The theory gives an expression for p as
P •= (7)
where N is the concentration of ion pairs in the solid, e is the electronic charge, m is the electronic
mass, and v0, the natural frequency of the oscillator, is given by
Denoting R,^ as the maximum reflectivity, Spitzer showed that
R ~ 1 - J_ (9)
or
e2
 N (10)
47T2mVn
The ion pairs in this theory are assumed to originate from thermal excitation of donor (or
acceptor) states in silicon carbide. From solid-state physics, the equilibrium concentration' of
conduction electrons at temperature T, as a result of ionized donors (or acceptors), is given by
(ref. 10)
'' • N = (n0Nd)1/2 exp(-Ed/2kT) ,. . .(11)
with no = 2(27rkmT/h2)3'2. Here, Nd is the concentration of donors, Ed is the donor ionization
(activation) energy, k is the Boltzmann constant, and h is Planck's constant. Equation (11) holds for
kT « Ed.
By substituting equation (11) into equation (10) we obtain
e 2(1 - R^J'1 = (TT/Y)— (2Nd(27rkm/h 2)3/2)1/2 T3'4 exp(-E/2kT)
47T2mVo
= A T3/4 exp(-Ed/2kT)
At each temperature for which the reflectivity of SiC was measured, the maximum reflectivity
was measured (all at wavelength 12.13 jam), the quantity (l-R^)"1 at the different temperatures was
calculated, and then least-squares fitted to equation (12). From curve fitting, A and E^k were
determined to be 0.0585 (±0.0014) and 415.77 (±11), respectively. The experimental data and
the fitted relation are shown in figure 6. From these results, values of Nd = (3.7 + 0.08)xl018 cm"3
and Ed = 71 (±1.8) meV were obtained. A value of the order 1019 cm"3 is reasonable for shallow
donors (assumed to be nitrogen) in the noncrystalline SiC that we used. The activation energy of such
donors in crystalline SiC is about 90 meV. The value of Ed = 71 meV is reasonable because in
situations where the concentration is of this magnitude and the nature of the material is noncrystalline,
the activation energy is effectively decreased. For the temperatures involved here, the condition
kT « Ed is satisfied. For kT » Ed, the result becomes (ref. 5)
N s: Nd (13)
which means that as the temperature increases, the concentration of ion pairs will not increase further,
and the reflectivity will not increase beyond 100 percent.
CONCLUSION
The multiwavelength pyrometer developed at NASA Lewis Research Center for measuring
nongray surface temperatures was applied to measure the temperature of a silicon carbide surface from
358 to 517 K. The spectral reflectivity and emissivity of silicon carbide at those temperatures and at
angles B = 30° and 0 = 0° were also obtained. The emissivity varies rapidly with temperature and
wavelength at wavelengths longer than 10 jam.
The reflectivity of SiC obtained during surface temperature measurement using a
multiwavelength pyrometer was analyzed using the classical dispersion theory of crystals. The
reflectivity maximum at each temperature was fitted to a T3'4 exp(-Ed/2kT) temperature dependence.
The curve-fitting-determined constants yielded a donor concentration of 4xl018 cm"3 and a donor
ionization (activation) energy of 71 meV.
REFERENCES
1. Bennethum, W.H.; and Sherwood, L.T.: Sensors for Ceramic Components in Advanced
Propulsion Systems. NASA CR-180900, 1988.
2. Ng, D.: Multiwavelength Pyrometry to Correct for Reflected Radiation. NASA TM-102578,
1990.
3. Ng, D.: Multiwavelength Pyrometry for Non-Gray .Surfaces. NASA TM-105285, 1991.
4. Ng, D.: Multiwavelength Pyrometry for Non-Gray Surfaces in the Presence of Interfering
Radiation. NASA TM-105286, 1991.
5. Durand, J.L.; and Houston, C.K.: Infrared Signature Characteristics. The Martin Company, OR-
6820, ATL-TR-66-8, Jan. 1966 (Avail. NTIS, AD-478597).
6. Spitzer, W.G.; Kleinman, D.; and Walsh, D.: Infrared Properties of Hexagonal Silicon Carbide.
Phys. Rev., vol. 113, no. 1, Jan. 1959, pp. 127-132.
7 Atkinson, W.; Cyr, M.A.; and Strange} R.R.: Development of Sensors for Ceramic Components
in Advanced Propulsion Systems: Survey and Evaluation of Measurement Techniques for
Temperature, Strain and Heat Flux for Ceramic Components in Advanced Propulsion Systems.
NASA CR-182111, 1988, pp. 33-34.
8. Seitz, F.: Modern Theory of Solids. McGraw-Hill, 1940, Chapt. 17.
9. Siegel, R.; and Howell, J.R.: Thermal Radiation Heat Transfer. Vol. 1, NASA SP-164, 1968,
p. 113.
10. Kittel, C.: Introduction to Solid State Physics. 5th ed., John Wiley & Sons, 1976, Chapt. 8.
Temperature of reflecting
surface,Te L Surface
Pyrometer Auxiliary radiation source
Figure 1.—Experimental arrangement of the pyrometer
components, p is an angular direction referred to the surface
normal; 0 (not shown) is an angle measured from the plane
of the figure.
12XKT3
Surface-emitted radiation spectrum
Calculated spectrum
Planck curve
(a) 358 K. (b) 385 K.
25X10-3
20
to
§ 15
18 10
I I
(C) 407 K. (d)441 K.
6x1(T2
I I I
2 4 6 8 10 12 14 2 4 6 8 10 12 14
(e) 478 K. (f) 517 K.
Wavelength, (xm
Figure 2.—Surface emission spectrum of SIC compared with calculated spectrum and Planck curve for same
temperature.
.•*•••; 2
Temperature,
K
124 6 . 8 1 0
Wavelength, |tm
Figure 3.—Spectral reflectivity of SiC at temperatures from
358 to 517 K.
1.0
tt;
.8
.4
.2
6 8 10
Wavelength, \im
12 14
Figure 4.—Spectral emissivity of SIC at temperatures from
358 to 517 K.
Calculated
Equipment
1.0
.8
/
fr
"* -„tr .4
.2
2 4 6 8 10
Wavelength, |im
Figure 5.—Experimentally determined reflectivity compared
with calculated reflectivity using the classical dispersion
theory with v0 = 2.35 x 1013 Hz, p = 0.045, y = 0.08, and
3
'
00
2.75
2.50
2
-
25
2.00
§ 1.75
1.50
Data
Least-squares fitted
curve, 0.0585 x T3"*
exp(-415/T)
350 375 400 425 450 475 500 525 550
Temperature, K
Figure 6.—Relative resonance strength vs temperature.
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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE
February 1992
3. REPORT TYPE AND DATES COVERED
Technical Memorandum
4. TITLE AND SUBTITLE
Temperature-Dependent Reflectivity of Silicon Carbide
6. AUTHOR(S)
•••Daniel Ng
5. FUNDING NUMBERS
WU-510-01-50
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135 - 3191
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REPORT NUMBER
E-6618
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National Aeronautics and Space Administration
Washington, D.C. 20546-0001
10. SPONSORING/MONITORING
AGENCY REPORT NUMBER
NAS ATM-105287
11. SUPPLEMENTARY NOTES
Responsible person, Daniel Ng, (216) 433-3638.
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13. ABSTRACT (Maximum 200 words)
The spectral reflectivity of a commercial silicon carbide (SiC) ceramic surface was measured at wavelengths from
2.5 to 14.5 pm and at temperatures ranging from 358 to 520 K using a NASA-developed multiwavelength pyrometer.
The SiC surface reflectivity was low at the short wavelengths, decreasing to almost zero at 10 um, then increasing
rapidly to a maximum at approximately 12.5 jam, and decreasing gradually thereafter. The reflectivity maximum
increased in magnitude with increasing surface temperature. The wavelength and temperature dependence can be
explained in terms of the classical dispersion theory of crystals and the Lorentz electron theory. Electronic transitions
between the donor state and the conduction band states were responsible for the dispersion. The concentration of the
donor state in SiC was determined to be approximately 4 x 1018 and its ionization energy was determined to be
approximately 71 meV. 1
14. SUBJECT TERMS
Silicon carbide; Reflectivity; Emissivity activation energy; Temperature; Pyrometry
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10
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