Kenetics of cristobalite growth on polycrystalline SiC film studied using high-temperature in situ X-ray diffractometry

Article abstract of DOI:10.1016/S0025-5408(98)00043-9

The kinetics of cristobalite growth on polycrystalline β-SiC films at 1803 and 1873 K were investigated. Sample films were synthesized on graphite strips via chemical vapor deposition and heated in air by their electric resistance. It was demonstrated that in situ X-ray diffractometry using imaging plate was useful for analyzing the growth of the oxide crystals with the coexistence of amorphous silica. The kinetics were found to obey parabolic laws. This is consistent with oxidation kinetics of SiC reported earlier.

Full text of DOI:10.1016/S0025-5408(98)00043-9

Materials Research Bulletin, Vol. 33, No. 5, pp. 731–738, 1998
Copyright © 1998 Elsevier Science Ltd
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025-5408/98 $19.00 ϩ .00
PII S0035-5408(98)00043-9
KINETICS OF CRISTOBALITE GROWTH ON POLYCRYSTALLINE SiC FILM
STUDIED USING HIGH-TEMPERATURE IN SITU X-RAY DIFFRACTOMETRY
1
2
3
4
T. Kingetsu *, K. Ito , M. Takehara , and H. Masumoto
Rigaku Corporation, X-ray Research Laboratory, 14–8 Akaoji-Cho, Takatsuki, Osaka
69–11, Japan
1
5
2
Steel & Technology Development Laboratories, Nisshin Steel Company Ltd., 4976
Nomura-minamimachi, Shin-nanyo, Yamaguchi 746, Japan
3
Carbon Materials Department, Nippon Steel Chemical Co., Ltd., 2–31-Shinkawa,
Chuo-ku, Tokyo 104, Japan
Japan Ultra-high Temperature Materials Research Institute, 573–3 Okiube, Ube,
4
Yamaguchi 755, Japan
(Refereed)
(Received July 10, 1997; Accepted October 13, 1997)
ABSTRACT
The kinetics of cristobalite growth on polycrystalline ␤-SiC films at 1803 and
873 K were investigated. Sample films were synthesized on graphite strips
1
via chemical vapor deposition and heated in air by their electric resistance. It
was demonstrated that in situ X-ray diffractometry using imaging plate was
useful for analyzing the growth of the oxide crystals with the coexistence of
amorphous silica. The kinetics were found to obey parabolic laws. This is
consistent with oxidation kinetics of SiC reported earlier. © 1998 Elsevier Science
Ltd
KEYWORDS: A. carbides, A. oxides, A. thin films, C. X-ray diffraction, D.
surface properties
INTRODUCTION
The oxidation behavior of SiC films is an important factor in the application of the material
as oxidation-resistant coatings in high temperature oxidizing atmospheres. Oxidation kinetics
*
To whom correspondence should be addressed.
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T. KINGETSU et al.
Vol. 33, No. 5
of various SiC samples have been studied extensively so far: SiC single crystals [1–3], SiC
polycrystalline synthesized through powder sintering [4] and chemical vapor deposition
(CVD) [5] methods, and SiC/SiC composite [6]. Many of those studies were concentrated on
the amorphous silica formation and growth at temperatures below 1780 K. The growth
kinetics of cristobalite with the coexistence of amorphous silica on SiC is not well under-
stood, since an overall feature, such as mass gains or oxide layer thicknesses, was used as a
measure of oxide growth in most of the previous studies.
As for studies on oxidation kinetics using in situ X-ray diffractometry (XRD), little
research work has been published to date. With conventional X-ray diffractometers, X-ray
detectors are ␪-scanned mechanically and, thus, it takes about a half hour to detect all
diffracted X-rays needed for analysis. Hence, the obtained XRD profile shows only an
average of the structural change of the sample crystal upon heating for such a long time of
scan. In contrast, the X-ray detection system in our study has an imaging plate that can detect
the X-ray signals diffracted at various angles simultaneously, and the cumulation of the
signals to the sufficient level requires only a few minutes or less. This enables us to detect
the structural change of a crystalline sample upon heating, nearly at real time. The aim of this
paper is to demonstrate the use of high temperature in situ XRD analysis for study of oxide
crystal growth and to present the results on growth kinetics of cristobalite with the coexist-
ence of amorphous silica on CVD-SiC films. In the present paper, growth of cristobalite
means increase in the amount of cristobalite and includes both forms of increase in a solid
phase: nucleation and growth.
EXPERIMENTAL
SiC films with a thickness of about 50 ␮m were deposited on isotropic graphite (IG-11, Toyo
Tanso Co., Japan) strips (7 mm in width and 1 mm in thickness) by thermally activated CVD.
Here, several substrate strips were loaded simultaneously in a CVD furnace for one batch of
CVD process in order to ensure the same quality of the SiC film for each substrate. SiCl and
4
CH gases diluted by H gas were employed as the gaseous precursors, and the growth
4
2
temperature was 1523 K. The crystal structure, surface morphology, microstructure in cross
section, and thickness of the films were characterized by conventional XRD analysis (␪–2␪
scans), optical microscopy, and scanning electron microscopy (SEM). SiC films in the
present study were confirmed to have no cracks. The films were characterized to have
␤
-(3C)–SiC crystal grains oriented nearly at random with sizes less than 5 ␮m, and the film
surfaces were less pebbled with pebbles less faceted. Details of specimen preparations and
features of the films will appear elsewhere [7].
Oxidation tests were conducted in open air by letting electric current pass directly through
the graphite specimen strips. Test temperatures were 1803 and 1873 K and duration was up
to 14.4 ks. The heating rate from room temperature to the test temperature was 0.83 K/s. The
specimen surfaces were observed directly during heating. XRD analyses (2␪ scans) with a Cu
K␣ X-ray source were performed in situ using a diffractometer with a so-called imaging plate
X-ray detector (DIP300/MXP18, MAC Science, Japan). The system consists of a Debye-
Scherrer camera with a radius of 150 mm, an X-ray sensitive two-dimensional detector
(photostimulable phosphor film), and a specimen heating system in a closed environment.
The incident angle (␪) of X-rays into the specimen surface is 6°, which corresponds to an
X-ray penetration depth of about 100 micrometers for SiO . Presence of oxygen atoms on the
2

Vol. 33, No. 5
SILICA ON SILICON CARBIDE
733
FIG. 1
a) XRD profiles (2␪ scans, Cu K␣ rays), obtained in situ, of the same CVD-SiC film at a time
(
step of 0, 0.6, 2.1, 3.6, 7.2, and 14.4 ks after the steady state temperature of 1803 K was
reached, during one heating procedure. (b) Similar profiles for a separate specimen film taken
at a time step of 0, 0.3, 0.6, 1.8, 3.6, and 5.4 ks, upon heating at 1873 K. A profile (RT) taken
at room temperature is shown as a reference.
film surfaces was confirmed by electron probe X-ray microanalysis after cooling the speci-
mens down to room temperature.
RESULTS AND DISCUSSION
Figure 1a shows XRD profiles of a CVD-SiC film obtained during heating at 1803 K in open
air. Each profile was obtained for the same specimen at one of various time steps in the course
of heating. It is observed that the SiO peak appeared upon heating and its height increased
2
gradually with increasing heating time, as seen in this figure. This SiO peak corresponds to
2
the cristobalite structure. Similar results for a separate specimen heated at 1873 K are shown
in Fig. 1b. A profile taken at room temperature is also shown as a reference in this figure. It

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T. KINGETSU et al.
Vol. 33, No. 5
FIG. 2
XRD profile (␪–2␪ scan, Cu K␣ rays) of the bubbles formed upon heating at 1873 K for 5.4
ks in air. The sample was obtained by scrapping bubbles from the SiC film. The profile
indicates that its structure is amorphous.
is seen that the SiO peak intensity also increases with time, and the rate of increase is much
2
larger compared to that shown in Figure 1a.
During heating of the specimens, it was observed that the SiO overlayers formed on the
2
SiC films melted and that bubbles of SiO were generated due to gaseous products (presum-
2
ably CO, SiO, and/or CO ) upon oxidation. These SiO bubbles were scraped off from the
2
2
SiC films after cooling down to room temperature, to confirm their crystal structure by
conventional XRD analysis. The XRD profile indicates that the substance is amorphous, as
shown in Figure 2. The oxidation tests showed that cristobalite coexisted with amorphous
silica at high temperatures. Moreover, SEM observations revealed that the surface of pebbles
which existed on the SiC film before heating became considerably smoother after heating,
suggesting that the surface is covered with amorphous silica.
It is observed in Figures 1a and b that each of the ␤-SiC peak intensities decreased slightly
upon heating with increasing heating time. The reduction rates for each of the peaks are
similar. This reduction of the intensities is attributed to the formation and growth of SiO2
overlayers consisting of cristobalite and amorphous silica. The reduction is smaller in Figure
1
a than that in Figure 1b. This is due to the lower growth rate of SiO layers at the lower
2
temperature, as will be discussed later.
In addition, it is observed in Figure 1b that small peaks at angle (2␪) positions of about 34°,
3
8°, 66°, and 73° decrease in intensity. These small peaks are located at the diffraction angles
of ␣-(6H)–SiC and indicate the presence of stacking faults on {111} planes [7]. This
suggests, therefore, that the stacking faults were healed by the prolonged heating. This
phenomenon is not seen in Figure 1a, presumably because of the lower temperature.
The background intensities are considerably high in the XRD profiles of Figures 1a and b,
since the profiles were obtained in 2␪-scan mode with a fixed value of ␪ because of the
restriction of the diffractometer geometry. The absolute heights of SiO peaks were obtained
2
by subtracting the background signals from the counted signals of the peaks. In order to make
a comparison between SiO peak intensities in different specimens, each SiO peak intensity
2
2
was normalized by the 111SiC peak intensity in the XRD profile at the zero time for each
specimen. It is emphasized that comparison of SiO peak intensities between different
2

Vol. 33, No. 5
SILICA ON SILICON CARBIDE
735
FIG. 3
2
Square of normalized intensity, I , of the SiO peak in XRD profiles of CVD-SiC films as
n
2
a function of oxidation test duration, t, at a given temperature, T. F T ϭ 1803 K, f T ϭ 1873
K.
specimens in this way is reasonable, because the specimens were prepared in the same CVD
run and values of the hklSiC/111SiC peak ratios were confirmed to be very similar for all
samples prepared, showing that the film qualities were the same.
Furthermore, it is noted that the thickness of the cristobalite crystals and other overlayers
must be thin enough to be penetrated by X-rays (typically less than a few tens of microme-
ters), for evaluation of the crystal content by XRD peak intensities. Otherwise, the crystals
in the depth cannot be detected by XRD and thus the intensities do not give true content. In
other words, the amount of the crystals is underestimated in the case of thick crystals since
the intensity of diffracted X-rays is not proportional to the thickness of the crystals because
of the absorption of X-rays (see Appendix for details). In the present study, SiC peaks are
visible even after the SiC films were covered by oxide overlayers, indicating that X-rays
penetrate to the SiC through the overlayers. This justifies our use here of the peak intensities
as a measure of the cristobalite content.
2
The variations of square of the normalized SiO peak intensities (peak heights), I , as a
2
n
function of the oxidation test duration, t, at a given temperature, T, were plotted as shown in
2
Figure 3. It is found that a linear relationship between In and t is established in both plots,
although considerable deviations are seen in the plot for 1873 K. This relationship indicates
that the kinetics of cristobalite growth obey parabolic laws, suggesting that the cristobalite
growth is mostly diffusion controlled. The values of the parabolic kinetics constant, k,
2
defined by the parabolic equation In ϭ kt were calculated by the least-squares linear fitting,
which gives the slope of the straight lines shown in Figure 3. The values of k are listed in

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T. KINGETSU et al.
Vol. 33, No. 5
TABLE 1
Values of the parabolic Kinetics
Constant K
Ϫ1
Temperature (K)
Value of k [(ks)
]
1
1
803
873
111
899
Table 1. The present result that the kinetics of cristobalite growth obeys parabolic laws is
consistent with the results on oxidation kinetics of SiC reported previously [1–6,8,9].
It is noted that, in the case of 1873 K, the XRD SiO peak intensity was finite even at zero
2
time and that the straight line does not pass through the origin. This indicates the very fast
formation of cristobalite: cristobalite was formed with temperature rising, before the test
temperature was reached. If the straight line is shifted by 197 s rightwards in the plot, the line
passes through the origin. Hence, the effective time for the formation of cristobalite during
temperature rising is about 200 s.
In addition, the cristobalite peaks at the start of heating are small. Hence, there is a
possibility that the estimation of a kinetics constant may include some error at the initial stage
of heating. In the case where a nucleation step exists at this stage, a change in a kinetics
constant might not be detectable.
In principle, when an Arrhenius plot, 1/T vs. ln k, indicating the dependence of the
parabolic kinetics constant k on temperature T, is taken, the apparent activation energy of
cristobalite growth can be calculated from the slope of the plot. In the present results,
however, only two points are available in the plot. Hence, it is difficult to obtain an exact
value of the activation energy, and the estimation is not made here.
SUMMARY
In conclusion, the results obtained here are summarized as follows. It was demonstrated that
in situ X-ray diffractometry using an imaging plate is suitable for analyzing the growth of
crystalline oxide on the SiC films at real time. Under the coexistence of silica overlayers, the
growth kinetics of cristobalite on polycrystalline ␤-SiC films at temperatures of 1803 and
1
873 K were successfully determined. The kinetics of cristobalite growth obeys parabolic
laws, which is consistent with the results on oxidation kinetics in earlier reports.
APPENDIX
Estimation of a Relative Amount of Cristobalite in Silica Overlayer Based on X-ray
Diffraction Intensities. Here, we estimate the X-ray diffraction intensities originating from
the cristobalite grains in amorphous silica overlayer on the SiC film. The grains are assumed
to be distributed uniformly in the overlayer. Incident X-ray intensity I(x) at depth x from the
surface of the silica overlayer is lower than the original X-ray intensity I at the surface
0
because of absorption during travel in the overlayer, and is given by [10]:
I(X) ϭ I exp(Ϫ␮x/sin ␪1
0

Vol. 33, No. 5
SILICA ON SILICON CARBIDE
737
FIG. 4
Comparison among two types of estimations (IDnom and IЈDnom)(see text for details) and the
true, relative cristobalite content I (ϭ␣(I /I111)d). Note that IDnom underestimates and IЈDnom
id
0
overestimates the amount for large d values although both estimations are good approxima-
tions for small d values.
where ␪ is an incident angle of the X-rays and ␮ is a linear absorption coefficient of the
1
oxide. Diffraction intensity at depth x of cristobalite I (x) is proportional to the incident
D
X-ray intensity there I(x), i.e., I (x) ϭ ␣I(x), where ␣ is a positive constant less than unity.
D
Then, diffracted X-ray intensity, dI , at the surface of the overlayer, arising from a depth
D
region between x and (x ϩ dx) is
dID ϭ I (x) exp( Ϫ ␮x/sin ␪ )dx ϭ ␣I exp( Ϫ ␮x/sin ␪ ) exp( Ϫ ␮x/sin ␪H )dx
D
2
0
1
2
where ␪ is a diffraction angle of cristobalite. This equation is rewritten as
2
dID ϭ ␣I exp( Ϫ ␮Јx)dx
0
Ϫ1
Ϫ1
where ␮Ј ϭ (sin ␪1 ϩ sin ␪2)␮.
The diffracted X-ray intensity I at the surface of the overlayer with a thickness of d is
D
d
ID ϭ
␣I exp( Ϫ ␮Јx)dx ϭ (␣I /␮Ј)[1 Ϫ exp( Ϫ ␮Јd)]
0 0
͐
0
Thus, let 111SiC peak intensity of SiC in the case of d ϭ 0 be I111, and then the cristobalite
diffraction intensity normalized by I111 is given by
IDnom ϭ (␣I /␮ЈI111)[1 Ϫ exp( Ϫ ␮Јd)]
0
On the other hand, if the cristobalite peak intensity is normalized by 111SiC peak (at
diffraction angle ␪ ) intensities in each XRD profile, the intensity IЈ
of 111SiC peak is
3
111
expressed as

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T. KINGETSU et al.
Vol. 33, No. 5
IЈ111 ϭ I111 exp( Ϫ ␮d/sin ␪ ) exp( Ϫ ␮d/sin ␪ ) ϭ I exp( Ϫ ␮Љd)
1
3
111
Ϫ1
Ϫ1
where ␮Љ ϭ (sin ␪1 ϩ sin ␪3)␮. Then, the normalized intensity IЈDnom (ϭIDnom/IЈ111) is
given by
IЈDnom ϭ (␣I /␮ЈI111){exp(␮Љd) Ϫ exp[(␮Љ Ϫ ␮Ј)d]}
0
ϭ (␣I /␮ЈI111)[exp(␮Љd) Ϫ 1]
0
Comparison of these two types of estimations and the true, relative cristobalite content is
illustrated in Figure 4. It is seen that IDnom underestimates and IϽϽDnom overestimates the
amount for large d values although both estimations are good approximations for small d
values.
ACKNOWLEDGMENTS
This work was supported by the grant from the New Energy and Industrial Technology
Development Organization (NEDO), Japan, on the basis of the Measures for Promotion of
Regional Technology proposed by the Ministry of Internal Trade and Industry (MITI) of
Japan.
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