Nanodomain structure of carbon-rich silicon carbonitride polymer-derived ceramics

Article abstract of DOI:10.1111/j.1551-2916.2009.03558.x

The presence of nanodomains in polymer-derived ceramics constitutes one of the most intriguing features of this class of materials. In the present work, the nanostructure of novel carbon-rich silicon carbonitride (SiCN) ceramics synthesized via thermolysis of poly(methylphenylsilylcarbodiimide), -[Ph(CH ₃) Si-NCN]_n-, at 1300°, 1500°, 1700°, and 2000°C is investigated by micro-Raman spectroscopy, X-ray powder diffractometry, and small-angle X-ray scattering (SAXS). The structural information obtained from these experimental methods is combined together with theoretical modeling of the SAXS data to obtain a detailed model of the temperature-dependent evolution of nanodomains comprised of free carbon, SiC, and Si₃N₄ in SiCN-based ceramics.

Full text of DOI:10.1111/j.1551-2916.2009.03558.x

J. Am. Ceram. Soc., 93 [4] 1169–1175 (2010)
DOI: 10.1111/j.1551-2916.2009.03558.x
r 2010 The American Ceramic Society
ournal
J
Nanodomain Structure of Carbon-Rich Silicon Carbonitride
Polymer-Derived Ceramics
Gabriela Mera,w,z Aitana Tamayo,z Hong Nguyen,z Sabyasachi Sen,y and Ralf Riedelz
zTechnische Universitat Darmstadt, Institut fur Materialwissenschaft, Darmstadt, D-64287, Germany
¨
¨
yDepartment of Chemical Engineering and Materials Science, University of California at Davis, Davis, California 95616
The presence of nanodomains in polymer-derived ceramics con-
stitutes one of the most intriguing features of this class of
materials. In the present work, the nanostructure of novel car-
bon-rich silicon carbonitride (SiCN) ceramics synthesized via
thermolysis of poly(methylphenylsilylcarbodiimide), –[Ph(CH3)
Si-NCN]n–, at 13001, 15001, 17001, and 20001C is investigated
by micro-Raman spectroscopy, X-ray powder diffractometry,
and small-angle X-ray scattering (SAXS). The structural in-
formation obtained from these experimental methods is com-
bined together with theoretical modeling of the SAXS data to
obtain a detailed model of the temperature-dependent evolution
of nanodomains comprised of free carbon, SiC, and Si3N4 in
SiCN-based ceramics.
gram.5,6 Several attempts were made to model the SiCN micro-
structure, with reverse Monte Carlo simulations showing that
graphite and silicon nitride do indeed tend to phase separate on
a nanodomain scale. Preliminary work revealed that even
deliberate additions of large amounts of oxygen have no appa-
rent influence on the crystallization behavior of SiCN.
Carbon-rich SiCN ceramics are novel derivatives of PDC
materials possessing exceptional properties such as resistance
against crystallization and decomposition up to high tempera-
tures as well as semiconducting properties. The precursors for
carbon-rich SiCN PDCs are polyorganosilazanes and polyorga-
nosilylcarbodiimides. Recent investigations7 show that phenyl-
containing polysilylcarbodiimides are thermally more stable
than the low-carbon-content polysilylcarbodiimides reported
in the literature, and that the thermal degradation of these
precursors occurs along a different pathway.8 Polysilylcarbodii-
mides in general yield SiCN ceramics containing two amorphous
phases, Si3N4 and carbon, when thermolyzed between 11001 and
14001C, as has been confirmed by solid-state NMR spectro-
scopic measurements.1,7,8 The analyzed compositions also re-
quire the presence of small amounts of SiC. These findings
strongly suggest the formation of a microstructure where amor-
phous Si3N4 regions are embedded in an interconnected matrix
of amorphous carbon together with a few amorphous SiC
regions as proposed previously in a microstructural model.7,9
The aim of the present work is to investigate the nanostruc-
ture of carbon-rich polysilylcarbodiimide-derived SiCN cera-
mics by means of modeling of the SAXS data combined with the
constraints obtained from the results of other characterization
techniques such as micro-Raman spectroscopy and powder
X-ray diffraction (XRD).
I. Introduction
OLYMER-DERIVED CERAMICS (PDCs) based on SiCO and
silicon carbonitride (SiCN) systems are a class of high-
P
temperature-resistant ceramics prepared from polymers by con-
trolled thermolysis.1 These refractory materials are amorphous
with considerable resistance to crystallization and to creep
deformation, exhibit viscoelasticity at high temperatures, and
contain persistent nanodomains as measured by several techni-
ques.2 One of the main features of PDCs is the incorporation of
high quantities of bonded and free carbon in the structure. The
amount of free carbon in PDCs plays an important role in the
tuning of the high-temperature, electrical, and mechanical prop-
erties of the materials. Moreover, the free carbon phase strongly
influences the microstructural arrangement of the various amor-
phous and crystalline phases in these ceramics.
In particular, SiCN PDCs are structurally and chemically
stable up to 15001C, are X-ray amorphous, do not show steady-
state creep despite their amorphous structure, and exhibit
viscoelasticity at high temperatures. Recent small-angle X-ray
scattering (SAXS) studies have shown the presence of persistent
nanodomains up to 3 nm in size in these PDCs.3,4 However, the
chemical nature and the morphology of these nanodomains as
well as how they evolve from the preceramic organosilicon-
based polymer during thermolysis have remained unknown.
The nanodomains in SiCN PDCs persist to ultrahigh tem-
peratures of up to 20001C as shown by the recent work
II. Experimental Procedure
(1) Characterization Techniques
The compositions of the sample S2 obtained at 13001, 15001,
17001, and 20001C were determined by means of quantitative
elemental analysis using a carbon analyzer (Leco C-200, Eltra
GmbH, Neuss, Germany) for the determination of the carbon
content and an N/O analyzer (Leco, Type TC-436) Leco T-436
for the nitrogen and oxygen traces.
Raman spectra were recorded on a confocal Horiba HR800
micro-Raman spectrometer (Bensheim, Germany) using an ex-
citation laser wavelength of 514.5 nm. For the evaluation of free
carbon cluster size in ceramics, Gaussian–Lorentzian curve fitting
of the Raman bands (LabSpec 5.21.08 Software) was applied.
XRDs of our samples were measured by an STOE X-ray
diffractometer (Darmstadt, Germany) using Ni-filtered CuKa
radiation at a scan speed of 11/min.
published by Durr et al.3 and by Saha et al.4 Tentative thermo-
¨
dynamic modeling suggests that the amorphous SiCN phase
separates into carbon and silicon carbide with a composition
that lies along the Si3N4–SiC tie line in the composition dia-
P. Colombo—contributing editor
The SAXS experiments were carried out in an Anton Paar
SAXSess system (Graz, Austria) using monochromatic CuKa
radiation. The primary beam was focused through the powder
sample mounted on a thin Si wafer. The voltage and current of
the X-ray source were 40 kV and 50 mA. The scattered signal
Manuscript No. 26610. Received July 28, 2009; approved November 14, 2009.
This work was financially supported by Deutsche Forschungsgemeinschaft, Bonn,
Germany, (DFG-NSF research initiative), and the Fonds der Chemischen Industrie,
Frankfurt (Germany).
wAuthor to whom correspondence should be addressed. e-mail: mera@materials.
tu-darmstadt.de
1169

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Journal of the American Ceramic Society—Mera et al.
Vol. 93, No. 4
was collected in a 2D PSP over an angular range of 0.141–141C
with step intervals of 0.0651 and subsequently radially integrated
in order to obtain the wave-vector (q) dependence of intensity.
For quantitative investigations the absolute SAXS intensity was
determined using low-density polyethylene Lupolent (BASF,
Tokyo, Japan) as a reference sample.
Table I. Elemental Analysis of Sample S2 at 13001, 15001,
17001, and 20001C
Composition (wt%)
Empirical formula
Sample
Si
C
N
O
normalized on Si
The modeling of the nanostructure of the synthesized SiCN
ceramics was performed using the Igor program,10 which pro-
vides a convenient interface for the reduction of the SAXS data
and for modeling microstructures. The Irena 2 package11 allows
the manipulation of any scattering data for evaluation and
modeling.
S2 13001C 25.33 54.09 19.53 1.06 Si1C4.98N1.54O0.07
S2 15001C 24.52 55.62 18.98 0.87 Si1C5.29N1.55O0.06
S2 17001C 33.76 65.77
S2 20001C 32.96 66.81
0.46 0.00 Si1C4.44N0.03
0.16 0.07 Si1C4.73N0.01
reaction according to Si3N4 (a)13C (a)-3SiC (c)12N2m has to
be taken into account in order to explain the formation of
crystalline SiC phases. As can be seen from Fig. 2, after crystal-
lization of SiC from the amorphous matrix at 17001C, all
compositions of the annealed samples are lying almost perfectly
on the tie line between C and SiC. In conclusion, we can
distinguish between two types of compositions of S2 during
thermal annealing: samples annealed at 13001 and 15001C result
in compositions close to the tie line between C and Si3N4, while
materials heat treated at 17001 and 20001C give compositions
around the tie line between C and SiC. It is obvious to expect for
these samples different nanostructure formation and materials
properties as for the samples situated inside the SiC–C–Si3N4
triangle as reported in the literature.8 The microstructure of
SiCN-ceramics having a composition in the SiC–C–Si3N4 trian-
gle is composed of a-Si3N4 and C phases in the amorphous state
and of b-Si3N4, b-SiC, and graphite at temperature 414501C.8
III. Results and Discussion
(1) Synthesis of Carbon-Rich SiCN Samples
The synthesis of the preceramic poly(phenylmethylsilylcarbodii-
mide) S2 was performed, as reported recently,7 by the reaction
of phenylmethyldichlorosilane with bis(trimethylsilyl)carbodii-
mide in the presence of a catalytical amount of pyridine (Fig. 1).
A similar synthesis was reported by Durr and collea-
¨
gues5,6,12,13 by the reaction of methyldichlorosilane with bis(tri-
methylsilyl)carbodiimide in toluene or THF to produce
poly(methylsilylcarbodiimide)–[(CH3)HSi–NCN]n–, the low-
carbon analogue of S2. The polymer reported by Durr and
¨
colleagues was thermolyzed at 13001C and its nanostructure was
investigated by SAXS. Both polymers, S2 and the one reported
by Durr and colleagues, contain a methyl group attached to the
¨
silicon and differ by the second R group bonded to the Si atoms,
namely phenyl for S2 and hydrogen (H) for the latter one. It is of
interest to compare the SAXS data of the SiCN ceramics derived
from these two polymeric systems with low and high carbon
contents that should allow one to investigate the influence of
carbon content on the microstructural development and on the
nanodomain composition of SiCN ceramics.
Several SiCN samples were prepared by thermolysis of the S2
polymer in an Ar atmosphere at different temperatures, namely
13001, 15001, 17001, and 20001C, in order to investigate the
thermal stability of the SiCN phase with respect to decomposi-
tion, phase evolution, and crystallization. The characterization
of the nanostructure is a challenging task and most of the
spectroscopic methods as well as transmission electron micro-
scopy cannot resolve the nanostructural features of PDCs in the
amorphous state. Here, the ceramic samples derived from S2 are
investigated by means of elemental analysis, micro-Raman
spectroscopy, XRD, and SAXS.
(3) Micro-Raman Spectroscopy
Raman spectroscopy is an important nondestructive tool for
investigating the structural evolution of the free carbon phase in
materials.14–18 Free carbon appears in the Raman spectra of
PDCs in the form of disorder-induced D and D0 bands at
B1350 and 1620 cmꢀ1, the G band at B1582 cmꢀ1 due to in-
plane bond stretching of sp2 carbon, as well as the G0 band that
is the overtone of the D band at B2700 cmꢀ1, characteristic of
defect-free samples.14–18 In amorphous carbon phases, the D
and G bands vary in the intensity, position, and width, depen-
ding on the structural organization of the sample under inves-
tigation. The intensity ratio of the D and G bands, I(D)/I(G),
enables the evaluation of the carbon-cluster size using the
formula reported by Ferrari and Robertson14
IðDÞ
¼ C0ðlÞL2a
(1)
IðGÞ
(2) Elemental Analysis of the SiCN Ceramics
The compositions of the sample S2 obtained at 13001, 15001,
17001, and 20001C were determined by means of quantitative
elemental analysis and the values are listed in Table I.
where La is the size of carbon domains along the sixfold ring
plane (lateral size; see Fig. 4) and C0 is a coefficient that depends
on the excitation wavelength of the laser. The value of the
coefficient C0 for the wavelength of 514.5 nm of the Ar-ion laser
As can be seen from Table I and from the composition
diagram (Fig. 2), the elemental composition of sample S2 at
13001 and 15001C is almost the same. At 13001 and 15001C, the
sample composition lies almost perfectly on the tie line between
Si3N4 and C. Accordingly, the samples are carbon-rich SiCN
ceramics. Compared with the reported low-carbon SiCN cera-
mic synthesized from –[(CH3)HSi–NCN]n–, sample S2 annealed
at 15001C does not contain a crystalline Si3N4 phase, and on an
increase in the temperature up to 20001C, little formation of
crystalline silicon carbide and carbon is observed. From a
thermodynamic point of view, at T414501C, the carbothermal
used here is 0.0055 Aꢀ2. Gaussian–Lorentzian curve fitting of
˚
the Raman bands was performed in order to extract the I(D)/
I(G) intensity ratios and to determine the size of the free carbon
cluster formed in the SiCN ceramics. Raman spectra of samples
S2 thermolyzed at 13001, 15001, 17001, and 20001C are pre-
sented in Fig. 3(a). The samples annealed at 13001 and 15001C
exhibit broad signals and a strong overlap as a consequence of
the pronounced structural disorder of the carbon phase. At
17001C, very distinct and narrow peaks of the D and G modes
are observed due to an enhanced graphite-like structure
Ph
[pyridine]
CH
CH
3
Ph
3
Si N C N
H C S i N C N Si CH
n
3
n
+
Cl Si Cl
3
n
− 2n (CH ) SiCl
3 3
CH
CH
CH
3
3
CH
3
3
Fig. 1. Synthesis reaction of the poly(phenylmethylsilylcarbodiimide) S2.

April 2010
Nanodomain Structure of C-Rich SiCN PDCs
1171
Table II. Nanodomain Sizes Determined by Means of Micro-
Raman Spectroscopy and XRD Analysis
XRD
Raman
Sample
C La (nm)
b-SiC (nm)
C Lc (nm)
S2 13001C
S2 15001C
S2 17001C
S2 20001C
2.01
1.59
1.35
1.11
—
—
—
—
5.67
11.26
14.27
57.23
XRD, X-ray diffraction.
plane crystallite size (for crystalline carbon) or lateral cluster size
(size of carbon domains along the sixfold ring plane) La for
amorphous and crystalline systems can be calculated using Eq.
(1) as discussed above. Such calculations indicate that La
decreases with increasing thermolysis temperature, from 2.01
nm at 13001C in the amorphous state to 1.11 nm at 20001C due
to the reorganization of the carbon phase from an amorphous
and disordered state to the turbostratic state (see Table II). By
means of XRD, the crystallite thickness Lc or stacking for all
types of carbon phases (Fig. 3) can be derived.19 The particle size
of the b-SiC phase and turbostratic carbon was determined by
means of Rietveld refinement of the XRD patterns using the
approximation of spherical particles. These results are listed in
Table II. The low intensities of the Bragg reflections associated
with the a-SiC domains did not allow such an analysis for this
phase.
Fig. 2. Composition diagram of S2 at 13001, 15001, 17001, and 20001C,
compared with the reported silicon carbonitride ceramic by Durr and
colleagues.
¨
(graphene layers). At 20001C, turbostratic carbon is formed, as
indicated primarily by the increase in the intensity of the G band
and the concomitant decrease of the D band, as well as by the
overtone band profile.
Spherical particles comprised of Si3N4 and/or SiC and em-
bedded in the carbon network represent the possible domains in
the nanostructure of SiCN ceramics (Fig. 4).
(4) XRD
The crystallization behavior of the SiCN ceramics derived from
the precursor system S2 was studied by X-ray powder diffrac-
tion (Fig. 3(b)). In contrast to the previous studies on poly-
silylcarbodiimide-derived ceramics, no crystalline Si3N4 phases
were detected in our system. The ceramic S2 is amorphous up to
15001C when a fraction of amorphous Si3N4 transforms to
crystalline SiC. At this temperature, the composition can be
expressed as a mixture of three phases comprising a-Si3N4, a-C,
and a- and b-SiC.7 This result is consistent with those reported
in a previous study indicating that a significant amount of
carbon can hinder the crystallization of amorphous Si3N4.7,8
The separation of b-SiC was detected at 17001C. At
T ꢁ 17001C, the S2 ceramic crystallizes to yield b-SiC and a
small fraction of a-SiC, while at 20001C, the presence of
turbostratic carbon is also detected (Fig. 3(b)).
(5) SAXS
SAXS provides structural information and composition fluctua-
tions over a wide range of lengthscales typically ranging from
one nanometer to up to about one hundred nanometers. It has
been widely used for the structural characterization of a wide
range of materials including polymers, biomaterials, and colloi-
dal systems.20–25 Particle-size distributions obtained by SAXS
have been often compared with the one obtained from TEM.26
However, in our amorphous SiCN systems, TEM images are
featureless and do not allow a detailed characterization of the
nanodomain structure.
(6) Diffraction Experiments
The SAXS experiments were carried out in an Anton Paar
SAXSess system using monochromatic CuKa radiation. The
intensity profile is measured in the detector in terms of photons/
s. Conversion of scattered photons per second into the intensity
in units of cmꢀ1 involves the measurement of the transmission of
Regarding the behavior of carbon in these ceramics, Raman
spectroscopy and XRD results provide the opportunity to
determine two important parameters for the characterization
of the carbon phase. First of all, by means of Raman, the in-
Fig. 3. Micro-Raman spectroscopy (a, left) and X-ray diffraction analysis (b, right) of S2 thermolyzed at 13001, 15001, 17001, and 20001C.

1172
Journal of the American Ceramic Society—Mera et al.
Vol. 93, No. 4
during the pyrolysis process. However, the Porod prefactor
shows a decrease in the surface area of the primary particles
with the thermal treatment. The radius of gyration increases with
the temperature as well. The high polydispersity index, defined as
the dimensionless ratio of BpR4g/Gp, has been interpreted as a sign
of the coexistence of multiple phases in the system.
The calculation of Rg of the primary particles from the
scattering curves using Guinier’s Law comprises one of the first
steps in the basic analysis of SAXS results. In a polydisperse
system, only an average value of Rg can be obtained in the
Guinier regime (qRg ꢃ 1) from the slope of log I(q) versus q2
plot, which is equal to R2g/3. In the specimen thermolyzed at
13001C, the Rg is around 1.04 nm, which can be equated to a
sphere of radius 1.34 nm. The Rg of the scatters at 15001C is 1.85
nm, corresponding to spherical particles with a radius of B2.23
nm. However, no distortion of the spheres or the appearance of
rod-like particles has been taken into account in this calculation.
The Rg increases upon an increase in the thermolysis tempera-
ture, and for the specimens treated at 17001 and 20001C, it
reaches higher values of up to 3.79 and 3.89 nm, respectively. It
may be noted that despite the importance of the determination
of Rg at the first stage of SAXS data analysis, interparticle
interferences may influence the initial part of the scattering curve
in Guinier’s approach. The Rg calculated by means of the unified
fit30 doesnot differ from that calculated with the application of
Guinier’s Law in the specimens pyrolyzed at 13001 and 15001C
in the first structural level. In the log–log plot, the knee observed
at the medium-q range describes the Guinier regime, which
occurs at q values of the order of 1/d, where d is the diameter
of the primary particle. The approximation to spherical particles
in the specimens thermolyzed at 13001 and 15001C sets the
Guinier region in the q range obtained experimentally. The
SAXS data of the specimens thermolyzed at higher temperatures
show a clearly different trend in which the knee appears at larger
q values and between power-law regions that indicate multiple
structural levels. In these samples, the Rg obtained by applica-
tion of Guinier’s Law and in the first structural level of the
unified fit corresponds to the primary aggregates.
In the high q range, corresponding to short length scales,
carbon-rich materials show a deviation from the Porod Law by
the superimposition of different structural scales. The interla-
mellar distance d002, interlamellar distance fluctuations, and
structural defects of the graphene layers contribute to the
SAXS in a modified Porod’s Law where a qꢀ2 term is included.31
The fitting of the SAXS scattering to a Porod expression yields a
power law of 2.54–2.52, indicative of layered structures in all the
samples. In the high q range, the Porod power-law prefactor in
combination with the integral over the scattering intensity in the
reciprocal space (invariant), can be used to determine the surface
to volume ratio. This ratio does not depend on particle sym-
metry and is directly related to the mean square fluctuation of
electron density. The specific surface area of the particles in the
sample thermolyzed at 13001C is 1.67 g/cm2, with a contribution
of B2 vol% of voids to the total scattering intensity. The surface
Fig. 4. Free carbon in polymer-derived ceramics ceramic network
containing spherical nanoparticles of Si3N4 and/or SiC embedded in
the carbon network (top left). Magnification of the carbon chain
(bottom right) (La 5 in-plane crystallite size (for crystalline carbon) or
lateral cluster size (size of carbon domains along the sixfold ring plane)
(for amorphous and crystalline systems) and Lc 5crystallite thickness
(for crystalline carbon) or stacking for all types of carbon phases). The
spherical particles embedded in the carbon network form the other
domains present in the silicon carbonitride ceramics.
the sample under the incident flux and data reduction proce-
dures as described elsewhere.27 The intensity in absolute units
allows quantitative evaluation of the electron density fluctua-
tions as well as comparison with other sets of data.
The total scattered intensity Ip(q) is the result of the interac-
tion of the incident X-rays with any heterogeneities in the
electron density in the specimens. The scattering curves of the
specimens treated at different temperatures are shown in Fig. 5
and are analyzed using the unified equation proposed by
Beaucage,28,29 where the scattering intensity can be approxi-
mated by
!
!
pffiffi
p
R2gq2
3
½erffqRg= 6gꢂ
IpðqÞ ¼ Gp exp
þ Bp
(2)
3
q
In this equation, Rg is the radius of gyration of the nanopar-
ticles, Gp is the exponential prefactor, and Bp is a prefactor
specific of the power-law scattering. This unified equation
describes the material in terms of various structural levels,
with each level being characterized by a Guinier regime related
to the characteristic particle size Rg and a power-law regime that
describes the mass- or surface-fractal scaling of Ip(q) with q for
that structural level.
In the analysis through the unified fit, the obtained value of
the Guinier prefactor does not show significant differences with
temperature, which indicates slight particle volume variations
Fig. 5. Small-angle X-ray scattering curves (left) and the unified fit (right) of the S2 sample thermolyzed at 13001, 15001, 17001, and 20001C.

April 2010
Nanodomain Structure of C-Rich SiCN PDCs
1173
Table III. Characteristic Values of the Scattering Curves. Rg is the Radius of Gyration of the Scattered Particle, Q is the
Invariant, and V is the Volume of the Scatters Calculated from the Area Under the Curve; f1, f2, and f3 Represent the Volume Fraction
of Each Phase
T
Rg (nm)
Q (cmꢀ4
)
V (nm3)
f1
f2
f3
13001C
15001C
17001C
20001C
1.04
1.85
4.87
4.43
1.42ꢄ 1022
1.07ꢄ 1021
1.18ꢄ 1021
1.32ꢄ 1021
25.23
567.78
772.59
712.80
SiCam
SiCam
a,bSiC
a,bSiC
0.44
0.73
0.13
0.11
Cam
Cam
C
0.28
0.25
0.01
0.01
Si3N4
Si3N4
Cturb
Cturb
0.28
0.02
0.86
0.88
C
area of the particles at 15001C increases to up to 2.3 g/cm2 with
B0.1 vol% of voids. For the specimens prepared at 17001 and
20001C, the estimated specific surface area of the aggregates is
4.97 and 7.2 g/cm2, respectively. Table III summarizes the
characteristic values of the SAXS analysis obtained directly
from the scattering curves.
the length of very elongated particles. It is also important to
consider the physical meaning of the results and the applicable
range of the model.
The volume fraction of each phase was previously estimated
from the Porod invariant (Table III) using a three-phase model.
Modeling of the sample thermolyzed at 13001C SAXS yields
the presence of three different types of spherical domains.
Amorphous carbon clusters with diameter of B2.08 nm and
small SiC clusters with a diameter of B0.98 nm are found as
oblate spheroids at this temperature. The third type of nanodo-
main is spheroidal Si3N4, taking up nearly 14 vol% of the
amorphous nanostructure. At this temperature, the microstruc-
ture can be described as primarily a matrix of layered carbon
domains and amorphous Si3N4 embedded in the matrix. The
SiC nanodomains are found to exist at the interface of Si3N4 and
C domains. The slope of Porod’s region at high q reaches a value
close to 3, which suggests a rough interface between the particles
and the carbon matrix. With increasing temperature, the SiC
nanodomains become spherical and reduce in size as Si3N4
reacts with the adjacent carbon to form small spheres and
rods of SiC. At 15001C, the average C nanodomain size is o1
nm, but the aspect ratio remains almost constant. In the model,
there are 3.9 and 10 mol of carbon nanodomains per mole of
Si3N4 at 13001 and 15001C, respectively. The volume fraction
calculated either from the invariant with a three-phase model or
from the modeling results points out that up to 15001C, 25 vol%
of nanodomains are C. At temperatures 415001C, Si3N4 no
longer exists.
(7) Modeling
The modeling of the nanostructure of the synthesized SiCN
ceramics based on our experimental SAXS data is the most
important objective of this work and it was performed using the
Igor program,10 which provides a convenient interface for the
reduction of the SAXS data and for modeling microstructures,
together with the Irena 2 package,11 which allows the manipula-
tion of any scattering data for evaluation and modeling. Here,
we report for the first time the application of this simulation
package for detailed structural modeling of the SAXS data for
the PDCs. Each set of data has been independently analyzed and
fitted to the structural parameters including form, size, shape,
and volume fractions of the constituent crystalline and amor-
phous phases in the SiCN PDCs. Electron densities for each
phase were calculated from its density and chemical composition
(see Table IV). The form factor, which comprises the intrapar-
ticle effects, includes the main shape of the domain as well as the
estimated volume fraction and radius. The standard expressions
for form factors of homogeneous rods and spheres have been
used in this modeling.
The radius of gyration that formally corresponds to the
radius of inertia in mechanics is defined by the root mean square
of the distances of all electrons from their center of gravity. The
distortion of the quasi-spherical size along the equatorial axis
and the appearance of rod-like domains produce an increase of
the radius of gyration even though the actual radius of the single
domains becomes slightly reduced. The new SiC particles
formed through the reaction of the a-Si3N4 and a-C are sup-
posed to grow in the interphase of the domains along the axial
axis of the domain, which produces an increase of the aspect
The results of the model-independent analysis obtained
in the previous section are used as input parameters for
the nonlinear model fitting. Igor Pro uses the Levenberg–
Marquardt algorithm to fit the modeling results to the experi-
mental curve. The goodness of fit is reported as w2. An
iterative method is used to fit the modeled SAXS curve to
the experimental data; any change of the physical parameters
of the model affects the scattering curve. Changes in the shape
of the scatters are described by different form factors that are
very sensitive in small particles but are not largely affected by
Table IV. Form, Shape, and Size of the Various Phases Present in the SiCN PDC at Each Thermolysis Temperature as Obtained
from Modeling of SAXS Data
C (amorphous)
(r 5 2.09 g/cm3)
SiC (amorphous)
(r 5 2.85 g/cm3)
Si3N4 (amorphous)
(r 5 3.2 g/cm3)
a,b SiC
C turbostratic
(r 5 2.25 g/cm3)
T
(r 5 3.22 g/cm3)
13001C
Form
Aspect ratio
Diameter (nm)
Spheroid
0.90
2.08
Spheroid
0.52
0.98
Spheroid
1.00
2.33
15001C
17001C
20001C
Form
Aspect ratio
Diameter (nm)
Spheroid
1.10
0.79
Spheroid
1.10
0.74
Spheroid
1.10
1.45
Rods
4.60
1.56
Form
Aspect ratio
Diameter (nm)
Spheroid
4.58
2.41
Rods
31.4
2.61
Spheroid
0.44
1.13
Rods
9.85
0.75
Form
Aspect ratio
Diameter (nm)
Spheroid
6.80
3.09
Rods
84.34
5.14
Spheroid
0.69
1.01
Rods
12.48
0.99
PDC, polymer-derived ceramic; SAXS, small-angle X-ray scattering; SICN, silicon carbonitride.

1174
Journal of the American Ceramic Society—Mera et al.
Vol. 93, No. 4
Fig. 6. Results of the simulation of the particle size distributions in the SiCN ceramics annealed at different temperatures as based on the experimental
small-angle X-ray scattering data.
ratio (from oblate to prolate spheroids), together with an
increment of the radius of gyration (Fig. 6).
crystals of 60.8 nm (calculated from the aspect ratio) were also
found and around 1.5 vol% of amorphous carbon still remains
in the nanostructure.
SAXS intensity curves significantly change at a thermolysis
temperature of 17001 and 20001C. Lamellar carbon aggregates
cause the main distortion of the curves, yielding, as a result,
scattering functions defined by rod-like and elongated particles.
Amorphous and structured carbons coexist at this temperature
with large SiC particles. Amorphous carbon evolves with tem-
perature to turbostratic structures where graphene layers are
stacked with no graphitic order. The length of the rod can be
associated with Lc in a crystalline system or in-plane crystallite
size La correlates with the diameter. SAXS measurements allow
the determination of the number of graphene layers present in
the cluster if the plane-to-plane gap is known. According to our
modeling results, the turbostratic carbon domains are present as
rod-like domains with the axial planes of graphene in the
elongated direction. The diameter of the carbon domains at
17001C is 2.41 nm for amorphous and 0.75 nm for turbostratic
carbon. The aspect ratio, which defines the length of the particle
in relation to its radius, is double in size for turbostratic carbon
as compared with that of amorphous carbon, with values of the
turbostratic layers up to 7.4 nm in length. The volume fraction
of the carbon domains decreases to 12% C at 17001C and
spheroidal crystallites of ab-SiC become the most prominent
particle type in the SiCN nanostructure. The presence of about
1.1 nm (diameter) nanocrystalline SiC rods is also noticeable.
The domain spheroidization loss was reported by Schmidt
et al.32 in SiC films deposited on glassy carbon by means of
XRD and TEM analysis. The presence of ellipsoidal SiC crystal-
lites was related to the crystallization kinetics of amorphous SiC.
The length of the rods is correlated with the crystal size in the X-
ray pattern. In the transition to the highest thermolysis tem-
perature, ab-SiC predominates in the nanostructure with the
ordered forms of carbon. The diameter of the ab-SiC domains is
1.01 and 0.99 nm in the case of turbostratic carbon, whose layers
can grow up to 12.3 nm in this kind of material. Large SiC
Therefore, amorphous and turbostratic carbon, in addition to
two types of SiC domains, are the distinct phases present in the
nanostructure of carbon-rich SiCN at the highest temperatures.
The coexistence of amorphous and turbostratic carbon and SiC
domains leads to the necessity of using multiple structural
lengthscales in the modeling of the SAXS data. The tempera-
ture-dependent evolution of the size and shape of the various
amorphous and crystalline phases present in the SiCN PDC as
obtained from modeling of SAXS data is listed in Table IV.
IV. Conclusions
In conclusion, several characterization techniques have been
used in order to investigate the nanostructure and nanodomains
present in poly(methylphenylsilylcarbodiimide)-derived cera-
mics synthesized at 13001, 15001, 17001, and 20001C. At
13001C, the sample is X-ray amorphous. By Raman spectro-
scopy, a lateral carbon particle size La of 2.01 nm was deter-
mined, and the value coincides with the 2.08 nm (spheroid
shape) evaluated by modeling the SAXS data. Moreover,
nanodomains of amorphous Si3N4 (2.33 nm, spheroid shape)
and an amorphous interphase of SiC domains (0.98 nm, spheroid
shape) were identified. At 15001C, the amorphous SiCN
starts to crystallize to yield rod-like b-SiC (1.56 nm), while the
remaining Si3N4 phase continues to be amorphous (1.45 nm,
spheroid shape). Nanodomains of spherical SiC domains (0.79
nm) are still present at this temperature. The divergence between
the nanodomain size calculated from the Raman spectra and
that derived from the SAXS data is probably due to experi-
mental and modeling errors. At 13001 and 15001C, the modeled
shape of the samples is predominantly spherical. At 17001C, the
clusters of crystalline a- and b-SiC are embedded in the matrix

April 2010
Nanodomain Structure of C-Rich SiCN PDCs
1175
J. Schuhmacher, K. Muller, J. Q. Peng, H. J. Seifert, F. Aldinger, ‘Precursor-
¨
of carbon. The amorphous nanodomains of rod-like carbon
determined by SAXS modeling are 0.75 nm and 7.4 nm in
length, while the Raman-determined cluster size of carbon is
1.35 nm. No more amorphous SiC and Si3N4 nanodomains are
present after annealing of the SiCN sample at this temperature.
The crystalline SiC phases are analyzed as rods and spherical
particles, 2.61 and 1.12 nm in size, respectively. Rod-like
particles of SiC (15.99 nm length) simulated from SAXS are
assimilated into crystallites of 14.27 nm lateral size determined
by Rietveld refinement. Moreover, the SAXS simulation shows
the presence of rods of turbostratic carbon of 0.75 nm lateral
size and 9.85 nm length. XRD analysis is probably not sensitive
enough to detect such small sizes and, therefore, the presence of
t-C cannot be experimentally identified. At the highest tempera-
ture of 20001C, the nanostructure is composed of amorphous
carbon (3.09 nm by SAXS), crystalline SiC (rods of 5.14 nm and
spheroids of 1.01 nm size), and turbostratic rod-like carbon of
0.99 nm in size. The Raman analysis yields a carbon cluster size
of 1.11 nm. The length of the crystallite obtained from the
Rietveld refinement is 57.23 nm, while particles of 60.8 nm size
were determined from the SAXS data. In general, the results
derived from XRD are similar to that of the SAXS measure-
ments; the differences in the particle size determination are due
to the impossibility to distinguish the shape of the particles.
Information on the size, composition, shape, orientation, and
volume fraction of the nanodomains is provided by SAXS
analysis. The Rietveld refinement of the XRD data assumes
that all the particles are spherical, which is not true. Therefore, a
dissimilarity of the sizes can be observed. However, an excellent
correlation in the determination of the particle size exists
between the Raman spectroscopy and the SAXS analysis.
To conclude, Raman spectroscopy, XRD, and SAXS results
indicate that the structure of polymer-derived carbon-rich SiCN
ceramics consists of nanodomains. The carbon-rich ceramics
derived from [PhMeSi–NCN]n reveal the presence of more than
one type of nanodomain in the microstructure, compared with
the low-carbon poly(methylsilylcarbodiimide)-derived ceramics
obtained from [HMeSi–NCN]n. These results clearly show that
excess carbon in the SiCN composition plays an important role
in the temperature-dependent formation of the nanodomain
structure of these PDCs. An increase in the nanodomain volume
fraction in the SiCN ceramics implies an increase in the inter-
granular surface area and consecutively in the ‘‘reactivity’’ of the
PDCs. However, despite the pronounced nanodomain structure,
the PDCs are thermally stable, resistant to corrosion, and
chemically inert as has been shown by a number of experimental
studies reported in the past. According to these studies, nanos-
tructured PDCs such as these carbon-rich PDCs are excellent
candidate materials for high-temperature applications in the
fields of catalyst supports, MEMS/NEMS, or advanced ceramic
fibers and protective coatings. Therefore, further studies are
needed in future to understand the relationship between the
nanodomain structure of PDCs and their unusual physical–
chemical properties.
Derived Si–(B–)C–N Ceramics—Thermolysis, Amorphous State and Crystalliza-
tion,’ Appl. Organomet. Chem., 15 [10] 777–93 (2001). (c) W. Gruber, O. Starykov,
W. Oppermann, H. Schmidt, ‘Growth of Amorphous Domains in Precursor
Derived Si–C–N-Ceramics Studied with Small Angle X-Ray Scattering,’ Diffus.
Fundam., 8 [9] 1–7 (2008). (d) W. Gruber, O. Starykov, H. Schmidt, ‘Nanodomain
Growth in Amorphous Si–C–N,’ Phys. Status Solidi (RRL—Rapid Res. Lett., 3
[2–3] 85–7 (2009).
4A. Saha, R. Raj, and D. L. Williamson, ‘‘A Model for the Nanodomains in
Polymer-Derived SiCO,’’ J. Am. Ceram. Soc., 89 [7] 2188–95 (2006).
5S. Schempp, J. Durr, P. Lamparter, J. Bill, and F. Aldinger, ‘‘Study of the
¨
Atomic Structure and Phase Separation in Amorphous Si–C–N Ceramics by
X-Ray and Neutron Diffraction,’’ Z. Naturforsch. A, 53 [3-4] 127–33 (1998).
6J. Bill, J. Schuhmacher, K. Muller, S. Schempp, J. Seitz, J. Durr, P. Lamparter,
¨
¨
J. Golczewski, J. Peng, H. J. Seifert, and F. Aldinger, ‘‘Investigations on the
Structural Evolution of Amorphous Si–C–N Ceramics from Precursors,’’
Z. Metallkd., 91 [4] 335–51 (2000).
7G. Mera, R. Riedel, F. Poli, and K. Muller, ‘‘Carbon-Rich SiCN Ceramics
¨
Derived from Phenyl-Containing Poly(Silylcarbodiimides),’’ J. Eur. Ceram. Soc.,
29 [13] 2873–83 (2009).
8Y. Iwamoto, W. Volger, E. Kroke, and R. Riedel, ‘‘Crystallization Behavior of
¨
Amorphous Si–C–N Ceramics Derived from Organometallic Precursors,’’ J. Am.
Ceram. Soc., 84 [10] 2170–8 (2001).
9R. M. Morcos, G. Mera, A. Navrotsky, T. Varga, R. Riedel, F. Poli, and K.
Muller, ‘‘Enthalpy of Formation of Carbon-Rich Polymer-Derived Amorphous
¨
SiCN Ceramics,’’ J. Am. Ceram. Soc., 91 [10] 3349–54 (2008).
10S. R. Kline, ‘‘Reduction and Analysis of SANS and USANS Data using
IGOR Pro,’’ J. Appl. Cryst., 39, 895–900 (2006).
11J. Ilavsky and P. Jemian, ‘‘Irena: Tool Suite for Modeling and Analysis of
Small-Angle Scattering,’’ J. Appl. Cryst., 42, 347–53 (2009).
12J. Durr, P. Lamparter, J. Bill, S. Steeb, and F. Aldinger, ‘‘X-Ray and Neutron
¨
Scattering Investigations on Precursor-Derived Si24C43N33 Ceramics,’’ J. Non-
Cryst. Solids, 234, 155–61 (1998).
13J. Durr, S. Schempp, P. Lamparter, J. Bill, S. Steeb, and F. Aldinger, ‘‘X-Ray
¨
and Neutron Diffraction Investigation on Amorphous Silicon Carbonitrides’’;
pp. 224–33 in Precursor-Derived Ceramics, Edited by J. Bill, F. Wakai, and
F. Aldinger. Wiley-VCH, Weinheim, Germany, 1999.
14A. C. Ferrari and J. Robertson, ‘‘Interpretation of Raman Spectra of
Disordered and Amorphous Carbon,’’ Phys. Rev. B, 61, 14095–107 (2000).
15A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S.
Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, ‘‘Raman Spectrum
of Graphene and Graphene Layers,’’ Phys. Chem. Lett., 97, 187401, 4pp (2006).
16M. A. Pimenta, G. Dresselhaus, M. S. Dresselhaus, L. G. Can@ado, A. Jorio,
and R. Saito, ‘‘Studying Disorder in Graphite-Based Systems by Raman Spectro-
scopy,’’ Phys. Chem. Chem. Phys., 9, 1276–90 (2007).
17A. C. Ferrari, ‘‘Raman Spectroscopy of Graphene and Graphite: Disorder,
Electron–Phonon Coupling, Doping and Nonadiabatic Effects,’’ Solid State
Commun., 143, 47–57 (2007).
18L. G. Can@ado, K. Takai, E. Enold, M. Endo, Y. A. Kim, H. Mizusaki, A.
Jorio, L. N. Coelho, R. Magalhaes-Paniago, and M. A. Pimenta, ‘‘General
Equation for the Determination of the Crystallite Size La of Nanographite by
Raman Spectroscopy,’’ Appl. Phys. Lett., 88, 163106, 3pp (2006).
19K. Dasgupta and D. Sathiyamoorthy, ‘‘Disordered Carbon—Its Preparation,
Structure, and Characterisation,’’ Mater. Sci. Technol., 19, 995–1002 (2003).
20G. Fritz and O. Glatter, ‘‘Structure and Interaction in Dense Colloidal
Systems Evaluation of Scattering Data by the Generalized Indirect Fourier
Transformation Method,’’ J. Physics: Cond. Matter., 18 [36] S2403–19 (2006).
21N. Dingenouts, J. Bolze, D. Potschke, and M. Ballauff, ‘‘Analysis of Polymer
Latexes by Small-Angle X-Ray Scattering,’’ Adv. Polym. Sci., 144, 1–29 (1999).
22R. A. Page, ‘‘Applications of Small-Angle Scattering in Ceramic Research,’’
J. Appl. Cryst., 21, 795–804 (1988).
23Y. Shi, Y. Wan, Y. Zhai, R. Lium, Y. Meng, B. Tu, and D. Zhao, ‘‘Ordered
Mesoporous SiOC and SiCN Ceramics from Atmosphere-Assisted in Situ Trans-
formation,’’ Chem. Mater., 19, 1761–71 (2007).
24D. R. Vollet, D. A. Donatti, and A. Ibanez Ruiz, ‘‘A SAXS Study of the
Nanostructural Characteristics of TEOS-Derived Sonogels upon Heat Treatment
up to 11001C,’’ J. Non Cryst. Solids, 306, 11–16 (2002).
25D. L. Williamson, ‘‘Microstructure of Amorphous and Microcrystalline Si
and SiGe Alloys using X-Rays and Neutrons,’’ Sol. Energy Mater. Sol. Cells, 78,
41–84 (2003).
26V. Goertz, N. Dingenouts, and H. Nirschl, ‘‘Comparison of nanometric
Particle Size Distributions Determined by SAXS, TEM and Analytical Ultracen-
trifuge,’’ Part. Part. Syst. Charact., 26, 17–24 (2009).
Acknowledgment
The authors acknowledge Prof. Rishi Raj for giving H. Nguyen the opportu-
nity to work in his lab on the SAXS machine, Prof. Don Williamson for the helpful
discussion about SAXS, and Dr. Liviu Toma for the Rietveld particle-size
determination.
27D. L. Williamson, ‘‘Nanostructure of Hydrogenated Amorphous Silicon
(a-Si:H) and Related Materials by Small-Angle X-Ray Scattering,’’ Mater. Res.
Soc. Symp. Proc., 377, 251–62 (1995).
28G. Beaucage, ‘‘Approximations Leading to a Unified Exponential/Power-Law
Approach to Small-Angle Scattering,’’ J. Appl. Cryst., 28, 717–28 (1995).
29G. Beaucage, ‘‘Small-Angle Scattering from Polymeric Mass Fractals of
Arbitrary Mass-Fractal Dimension,’’ J. Appl. Cryst., 29, 134–46 (1996).
30G. Beaucage, H. K. Kammler, and S. E. Pratsinis, ‘‘Particle Size Distributions
from Small-Angle Scattering using Global Scattering Functions,’’ J. Appl. Cryst.,
37, 523–35 (2004).
References
1R. Riedel, G. Mera, R. Hauser, and A. Klonczynski, ‘‘Silicon-Based Polymer-
Derived Ceramics: Synthesis Properties and Applications—A Review,’’ J. Ceram.
Soc. Jpn., 114 [6] 425–44 (2006).
2A. Saha, R. Raj, D. L. Williamson, and H.-J. Kleebe, ‘‘Characterization of
Nanodomains in Polymer-Derived SiCN Ceramics Employing Multiple Techni-
ques,’’ J. Am. Ceram. Soc., 88 [1] 232–34 (2005).
31B. Smarsly, M. Antonietti, and T. Wolff, ‘‘Evaluation of the Small-Angle
X-Ray Scattering of Carbons using Parametrization Methods,’’ J. Chem. Phys.,
116, 2618–27 (2002).
3(a)J. Durr, S. Schempp, P. Lamparter, J. Bill, S. Steeb, F. Aldinger, ‘‘X-Ray
¨
and Neutron Small Angle Scattering with Si–C–N Ceramics Using Isotopic
32H. Schmidt, E. R. Fotsing, G. Borchardt, R. Chassagnon, S. Chevalier, and
M. Bruns, ‘‘Crystallization kinetics of amorphous SiC films: Influence of Sub-
Substitution,’’ Solid State Ionics, 101, 1041–47 (1997). (b) J. Bill, T. W. Kam-
phowe, A. Muller, T. Wichmann, A. Zern, A. Jalowieki, J. Mayer, M. Weinmann,
strate,’’ Appl. Surf. Sci., 252, 1460–70 (2005).
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