Journal
J. Am. Ceram. Soc., 92 [2] 445–451 (2009)
DOI: 10.1111/j.1551-2916.2008.02879.x
r 2009 The American Ceramic Society
Mechanical and Thermophysical Properties of Zr–Al–Si–C Ceramics
Ling-Feng He,z,y Yi-Wang Bao,z Jing-Yang Wang,z Mei-Shuan Li,z and Yan-Chun Zhou*,w,z
z
Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences,
Shenyang 110016, China
y
Graduate School of Chinese Academy of Sciences, Beijing 100039, China
d
M
l
n
r
r2
h
kB
NA
R
Lo
The mechanical and thermophysical properties of quaternarylayered carbides, Zr2[Al(Si)]4C5 and Zr3[Al(Si)]4C6 have
been investigated and compared with those of Zr2Al3C4 and
Zr3Al3C5. These four carbides are generally alike in mechanical
and thermophysical properties due to their similar crystal structures that consisting of alternatively stacked ZrC layers and
Al3C2/[Al(Si)]4C3 slabs. The layer thickness of zirconium
carbide and aluminum carbide has effects on their properties.
Thicker layer of zirconium carbide and/or thinner layer of
aluminum carbides are in favor of stiffness, hardness, thermal,
and electrical conductivities, but go against density, specific stiffness, Debye temperature, and coefficient of thermal expansion.
density (g/cm3).
molecular weight (g/mol).
linear density of crystal structure of materials (cm1).
number of atoms in the molecule.
electrical resistivity (mO m).
correlation factor.
Plank’s constant, 6.626 1034 J s.
Boltzmann’s constant, 1.380 1023 J/K.
Avogadro’s number, 6.023 1023 mol1.
gas constant, 8.314 J/K.
Lorenz number, 2.45 108 W O/K2.
Nomenclature
I. Introduction
wavelength of CuKa radiation (nm).
sample length for the measurement of Young’s modulus(m).
sample wide for the measurement of Young’s modulus (m).
sample thickness for the measurement of Young’s modulus
(m).
m sample weight for the measurement of Young’s modulus (kg).
ff flexural resonant frequency (Hz).
Q1 internal friction.
k exponential decay parameter of the amplitude of the
flexural vibration component.
E Young’s modulus (GPa).
G shear modulus (GPa).
B bulk modulus (GPa).
v
Poisson’s ratio.
T1 correction factor in the calculation of dynamic Young’s
modulus.
T temperature (1C or K).
cP molar heat capacity at constant pressure J (mol K)1.
cV molar heat capacity at constant volume J (mol K)1.
ktotalthermal conductivity W (m K)1.
ke electron contribution to thermal conductivity W (m K)1.
kph phonon contribution to thermal conductivity W (m K)1.
tp Peierls shear stress (GPa).
b Burgers vector.
s
spacing between atomic slip planes (nm).
yD Debye temperature (K).
vm average sound velocity (m/s).
vl longitudinal sound velocity (m/s).
vs shear sound velocity (m/s).
l
L
w
t
Zr2Al3C4 and Zr3Al3C5 were recently developed by adding Al
into ZrC; these ternary zirconium aluminum carbides show
superior oxidation resistance, strength, specific stiffness, and
toughness to ZrC.1–8 Furthermore, Zr–Al–C ceramics exhibit
high retained stiffness at elevated temperatures. For instance,
the Young’s modulus of Zr3Al3C5 ceramic decreases slowly with
increasing temperature and the elastic stiffness at 16001C
remaines 78% of that at room temperature.3 However, as
high-temperature structural materials the oxidation resistance
of Zr–Al–C ceramics at high temperature is still unsatisfactory.6–8 The oxidation kinetics of Zr2Al3C4 follow the linear law
above 8001C because no protective Al2O3 scales formed on the
substrate. Recently, we improved the high temperature oxidation resistance of Zr2Al3C4 by silicon pack cementation.8 It was
found that a series of protective oxidation products, such as
aluminosilicate glass, mullite, and ZrSiO4, retarded inward
diffusion of oxygen during the oxidation of siliconized
Zr2Al3C4. Achievements in siliconized Zr2Al3C4 imply that
the oxidation resistance of Zr–Al–C ceramics can possibly be
improved by incorporating Si into the Zr–Al–C system.
Very recently, Zr2[Al3.56Si0.44]4C5 (denoted as Zr2[Al(Si)]4C5)
and Zr3[Al3.56Si0.44]4C6 (denoted as Zr3[Al(Si)]4C6) were identified in the Zr–Al–Si–C system.9,10 Moreover, it was reported
that quaternary Zr–Al–Si–C ceramics possessed thermoelectric
properties superior to those of Zr–Al–C ceramics. We also
synthesized Zr2[Al(Si)]4C5 and Zr3[Al(Si)]4C6 ceramics using a
hot-pressing method and characterized their elastic and oxidation properties.11,12 The theoretical and experimental elastic
properties are comparable to those of Zr–Al–C and ZrC. In
addition, the Young’s modulus of Zr2[Al(Si)]4C5 at 15801C is
293 GPa, which is about 81% of that at room temperature.
The oxidation resistance of Zr2[Al(Si)]4C5 and Zr3[Al(Si)]4C6
has been improved compared with Zr2Al3C4, and is much better
than ZrC due to the formation of larger fraction of protective
oxidation products, Al2O3 and aluminosilicate/mullite.12 The
high stiffness at elevated temperatures and relatively good oxidation resistance endow these Zr–Al–Si–C ceramics as potential
high-temperature structural materials. However, no mechanical
R. Naslain—contributing editor
Manuscript No. 25170. Received July 29, 2008; approved November 6, 2008.
*Member, The American Ceramic Society.
Supported by the National Outstanding Young Scientist Foundation (No. 59925208 for
Y. C. Zhou and No. 50125204 for Y. W. Bao), Natural Science Foundation of China under
Grant No. 50232040, 50302011, 90403027, 50832008 and ‘‘Hundred-Talent Plan’’ program
of Chinese Academy of Sciences.
w
Author to whom correspondence should be addressed. e-mail: [email protected]
445
446
Journal of the American Ceramic Society—He et al.
Vol. 92, No. 2
II. Experimental Procedure
decay parameter of the amplitude of the flexural vibration
component.
The Vickers hardness was measured at a load of 50 N with a
dwell time of 15 s. The measured value is the average of 10
separate measurements. The flexural strength of the samples
(3 mm 4 mm 36 mm) was measured using a three-point
bending method in a universal testing machine. The fracture
toughness of the samples (4 mm 8 mm 36 mm) was determined using the single-edge notched beams. The notch
machined by electrical discharged method was 4 mm in length
and 0.1 mm in width with a notch radius of 0.03 mm. The
as-machined samples were degreased in acetone before test. The
crosshead speeds in strength and toughness measurements were
0.5 and 0.05 mm/min, respectively and five samples were used in
both strength and toughness measurements.
(1) Sample Preparation
Polycrystalline Zr2[Al(Si)]4C5 and Zr3[Al(Si)]4C6 samples were
fabricated by hot-pressing zirconium (zirconium hydrides),
aluminum, silicon, and graphite powders at 19001C for 1 h in
Ar and then at 16001C for 0.5 h in low vacuum ( 102 Pa)
under a pressure of 30 MPa. The synthesis procedure of
Zr2[Al(Si)]4C5 and Zr3[Al(Si)]4C6 is similar to that of Zr2Al3C4.4
The molar ratios of Zr:Al:Si:C for the synthesis of Zr2[Al(Si)]4C5
and Zr3[Al(Si)]4C6 were 2:3.6:0.5:4.9 and 3:3.6:0.5:5.8, respectively. Excess Al and Si powders were added to compensate for
the loss of them during the heating process. Deficient carbon in
the starting materials is properly related to intrinsic carbon
vacancy in the two carbides. The samples for microstructure
and property characterization were cut from the as-synthesized
samples by electrical-discharge machining, ground using SiC
emery paper, and polished down to a 1 mm diamond suspension.
The density of sintered samples (+50 mm 10 mm) was
determined by the Archimedean method (ISO 1875413) using ion
exchanged water as immersion liquid without surfactant. The
measured density was the average of three measurements. Phase
identification was conducted via a step-scanning X-ray
diffractometer (Rigaku D/max–2400, Tokyo, Japan). Scan was
made with CuKa radiation (l 5 1.5418 nm, 56 kV and 182 mA)
at an angular step of 0.021 and a fixed counting time of 0.6 s/step.
The microstructures of the samples were studied by a SUPRA
35 scanning electron microscope (SEM) (LEO, Oberkochen,
Germany). The samples were etched for 1 h in a 1:1:5 (by volume) solution of HF (23 mol/L), HNO3 (15 mol/L) and H2O
before SEM observation.
(3) Thermophysical Properties
Disk samples (+12.7 mm 1.5 mm) were used to measure the
constant pressure molar heat capacity cp and thermal conductivity ktotal. The thermal diffusivity from 1001 to 12001C was
determined by a Flashlinet 5000 thermophysical instrument
(Anter, Pittsburgh, PA). Before the thermal diffusivity test the
samples were sprayed with a thin layer of colloidal graphite
approximately 10-mm-thick to ensure complete and uniform
absorption of the laser pulse. Three measurements were taken
at each temperature (2001, 4001, 6001, 8001, 10001, and 12001C)
and the data were calculated using software (Anter FL5000).
Using a multi-sample configuration system, and testing a reference sample (graphite) adjacent to Zr2[Al(Si)]4C5 and Zr3[Al
(Si)]4C6, the heat capacity can be obtained parallel with thermal
diffusivity.16 Then, the thermal diffusivity results were converted
to thermal conductivities using the heat capacity results and
measured density of Zr2[Al(Si)]4C5 and Zr3[Al(Si)]4C6.
The coefficient of thermal expansion (CTE) was measured using a Setsys–24 thermal mechanical analyzer (Setaram, Caluire,
France) from 1001 to 12001C with a heating rate of 21C/min under flowing Ar. The dimensions of the sample for CTE measurement are +5 mm 10 mm. The electrical resistivity at room
temperature was measured by the standard four-probe technique
in a superconducting quantum interference device (Quantum Design, San Diego, CA) using samples with dimensions of 1 mm 1
mm 10 mm. Four probes (two inner Cu current probes and two
outer Cu voltage probes) with equal spacing of 2.5 mm were fixed
on the sample with silver paste.
and physical properties other than elastic and thermoelastic
properties have been reported.
In the present work, the mechanical and thermophysical
properties, including hardness, strength, toughness, high-temperature Young’s modulus and internal friction, thermal expansion, Debye temperature, heat capacity, electrical resistivity, and
thermal conductivity of Zr2[Al(Si)]4C5 and Zr3[Al(Si)]4C6 were
studied and compared with those of Zr2Al3C4, Zr3Al3C5, and
ZrC. It was found that other than their best oxidation resistance,
Zr–Al–Si–C ceramics have comparable mechanical and thermophysical properties to Zr–Al–C ceramics, and superior toughness and strength to ZrC.
(2) Mechanical Properties
To reveal the temperature dependence of Young’s modulus and
internal friction of Zr3[Al(Si)]4C6 ceramic, a rectangular beamlike sample with dimensions of 3 mm 15 mm 40 mm was
suspended in the nodes of their first bending vibration mode
(0.224 L apart from both ends of the rectangular beam, where L
is the sample length), and measured in a graphite furnace (HTVP
17501C, IMCE, Diepenbeek, Belgium) at a heating rate of 31C/
min in vacuum on the order of 103 mbar. The vibration signal,
captured by a laser vibrometer was analyzed with the resonance
frequency and damping analyzer.14 The Young’s modulus was
calculated from the flexural resonant
ff, according to
2 frequency,
3
mf
ASTM E 1876–97:15 E ¼ 0:9465 wf Lt3 T1 , with m, L, w and
t, the sample weight, length, width, and thickness, respectively.
T1 is a correction factor, depending on the Poisson’s ratio v and
the thickness/length ratio t/L.
T1 ¼1 þ 6:585ð1 þ 0:0752v þ 0:8109v2 Þðt=LÞ2 0:868ðt=LÞ4
"
#
:
8:340ð1 þ 0:2023v þ 2:173v2 Þðt=LÞ4
2
2
1:000 þ 6:338ð1 þ 0:1408v þ 1:536v Þðt=LÞ
The internal friction corresponding to the flexural vibration
mode was calculated as Q1 5 k/pff, where k is the exponential
III. Results and Discussion
(1) Microstructure
Figure 1 shows the XRD patterns of as-prepared Zr2[Al(Si)]4C5
and Zr3[Al(Si)]4C6 samples. All the diffraction peaks correspond
well to Zr2[Al(Si)]4C5 and Zr3[Al(Si)]4C6, indicating that both
carbides are predominantly single-phase. In addition, the measured densities of Zr2[Al(Si)]4C5 and Zr3[Al(Si)]4C6 samples are
4.4470.03 and 4.8170.02 g/cm3, which are about 99% of their
theoretical values (4.50 and 4.85 g/cm3 for Zr2[Al(Si)]4C5 and
Zr3[Al(Si)]4C6, respectively). Figures 2(a) and (b) show the SEM
micrographs of the polished and etched surface for Zr2[Al
(Si)]4C5 and Zr3[Al(Si)]4C6, respectively. The microstructure
of both carbides consists of mainly plate-like or elongated grains
as well as some equiaxed grains. The average grain sizes of
Zr2[Al(Si)]4C5 and Zr3[Al(Si)]4C6 are 1074 and 1275 mm,
respectively, and the aspect ratio of their elongated grains are
about 8 and 3, respectively. Compared with Zr2[Al(Si)]4C5,
Zr3[Al(Si)]4C6 shows the grains of less anisotropic which is
most probably related with the difference in liquid phase content during the sintering process. In our previous work,3,4 it was
also found that the grain of Zr2Al3C4 showed much more anisotropic than that of Zr3Al3C5. Liquid-phase Al triggers the
formation of Zr–Al–C4,6 and thus we can expect that higher Al
content in Zr2[Al(Si)]4C5 and Zr2Al3C4 make their grains more
anisotropic. The measurements of properties were conducted on
February 2009
Properties of Zr-Al-Si-C
Fig. 1. X-ray diffraction patterns of as-synthesized (a) Zr2[Al(Si)]4C5
and (b) Zr3[Al(Si)]4C6 samples. Scan was made with Cu Ka radiation
(l 5 1.5418 nm, 56 kV and 182 mA) at an angular step of 0.021 and a
fixed counting time of 0.6 s/step.
these fine-grain and dense Zr2[Al(Si)]4C5 and Zr3[Al(Si)]4C6
samples. The obtained values are compared with those of
Zr2Al3C4 and Zr3Al3C5, and summarized in Table I.
(2) Mechanical Properties
The room-temperature stiffness of Zr–Al–Si–C is very close to
that of Zr–Al–C, e.g., the Young’s modulus of Zr2[Al(Si)]4C5
(361 GPa) is 99.7% of that of Zr2Al3C4 (362 GPa) and the
Young’s modulus of Zr3[Al(Si)]4C6 (367 GPa) is 98.1% of that
of Zr3Al3C5 (374 GPa). Zr2[Al(Si)]4C5 shows the highest specific
447
stiffness (81.3 GPa cm3/g), i.e, the ratio of Young’s modulus to
density, among the four carbides. Figure 3 shows the temperature dependence of Young’s modulus and internal friction of
Zr2[Al(Si)]4C5 and Zr3[Al(Si)]4C6. The Young’s modulus of both
carbides decreases slowly and almost linearly with increasing
temperature up to about 14501C. The Young’s modulus
decreases at a much faster rate and the internal friction increases sharply when the temperature reaches about 14501C.
Moreover, during the heating and cooling process, no relaxation
peak but only a high temperature damping background was
observed, which is similar to mechanical spectroscopy of (B1C)doped SiC17 and high-purity SiAlON18 materials. Like (B1C)doped SiC and high purity SiAlON, the grain boundary of
Zr–Al–Si–C ceramics was absence of glass phase11 and therefore
relaxation resulting from grain-boundary sliding was suppressed
and the internal friction curve simply experienced an exponential-like increase. It is conceivable to expect a low viscoelastic
response and high macroscopic deformation resistance at
elevated temperatures from the Zr–Al–Si–C ceramics with
directly bonded grain boundaries. The remaining Young’s modulus of Zr2[Al(Si)]4C5 at 15801C (293 GPa) and of Zr3[Al(Si)]4C6
at 16001C (292 GPa) is much higher than those for most refractory compounds,19,20 which renders Zr–Al–Si–C ceramics
potential high-temperature structural materials.
The Vickers hardnesses of Zr2[Al(Si)]4C5 and Zr3[Al(Si)]4C6
under 50 N are 11.770.2 and 12.470.4 GPa, respectively,
which are higher than that of Zr2Al3C4 (10.170.3 GPa), but
slightly lower than that of Zr3Al3C5 (12.570.2 GPa). The
flexural strength of Zr2[Al(Si)]4C5 (302710 MPa) and Zr3[Al
(Si)]4C6 (312712 MPa) is lower than that of Zr2Al3C4 (405741
MPa) and Zr3Al3C5 (488743 MPa). Zr2[Al(Si)]4C5 exhibits
relatively low fracture toughness, 3.8870.16 MPa m1/2, which
is about 84% of Zr3[Al(Si)]4C6 (4.6270.45 MPa m1/2), but is
still two times higher than that of ZrC (1.6570.36 MPa m1/2).21
In addition, the fracture toughness of both quarternary carbides
is comparable to that of ternary carbides, Zr2Al3C4 (4.2070.52
Fig. 2. Scanning electron microscopy micrographs of the polished and etched surface of (a) Zr2[Al(Si)]4C5 and (b) Zr3[Al(Si)]4C6 as well as (c) the
fracture surface of Zr2[Al(Si)]4C5.
448
Vol. 92, No. 2
Journal of the American Ceramic Society—He et al.
Table I. Comparison of Some Properties of Zr2[Al(Si)]4C5, Zr3[Al(Si)]4C6, Zr2Al3C4, and Zr3Al3C5
Properties
Lattice parameters a, c (nm)
Molar weight (g/mol)
Theoretical density (g/cm3)
Measured density (g/cm3)
Young’s modulus (GPa)
Specific stiffness (GPa cm3/g)
Shear modulus (GPa)
Poisson’s ratio
Bulk modulus (GPa)
Hardness (GPa)
Bending strength (MPa)
Fracture toughness (MPa m1/2)
Coefficient of thermal expansion ( 106 K1)
Debye temperatures (K)
Molar heat capacity J (mol K)1
Thermal conductivity W (m K)1
Electrical resistivity (mO m)
Zr2[Al(Si)]4C5
Zr3[Al(Si)]4C6
Zr2Al3C44,5
Zr3Al3C53
0.3311, 4.09459
350.9
4.50
4.4470.03
36111
81.3
15311
0.1811
18811
11.770.2
302710
3.8870.16
8.1
841
199
12.0
1.3670.01
0.3314, 4.900810
454.1
4.85
4.8170.02
36711
75.8
15611
0.1811
19111
12.470.4
312712
4.6270.45
7.7
813
214
14.7
0.8670.04
0.3347, 2.223923
311.4
4.80
4.7370.01
362
76.5
152
0.19
195
10.170.3
405741
4.2070.52
8.1
830
157
15.5
1.1070.01
0.3343, 2.760922
414.7
5.14
5.0270.01
374
74.5
157
0.19
202
12.570.2
488743
4.6870.74
7.7
806
193
14.3
1.4570.03
MPa m1/2) and Zr3Al3C5 (4.6870.74 MPa m1/2). The fracture
surface of Zr2[Al(Si)]4C5 shown in Fig. 2(c) delineates a rough
and flaky surface morphology with many jagged fractured
grains, indicating that Zr2[Al(Si)]4C5 experiences mixed interand intragranular fracture modes at room temperature. The inset
in Fig. 2(c) displays the delamination of grains, which is another
important energy dissipation mechanism during fracture.
The crystal structures of four carbides generally can be described as ZrC slabs interleaved by Al3C2 or [Al(Si)]4C3
blocks.22–25 Zr2[Al(Si)]4C5 and Zr3[Al(Si)]4C6 have the similar
crystal structure to Zr2Al4C5 and Zr3Al4C6, respectively, although the later two ternary carbides have not been found in the
Zr–Al–C system. We can expect Zr2[Al(Si)]4C5 and Zr3[Al
(Si)]4C6 have similar properties to Zr2Al4C5 and Zr3Al4C6,
respectively due to the identical crystal structure and small Si
replacement of Al (11%). The properties of ternary carbides
should have close relation to the properties of ZrC and aluminum carbide. In other words, the layer thickness of ZrC and/or
aluminum carbide may have obvious influence on their mechanical properties. The measured Vickers hardness of Al4C3 with
a load of 2.94 N is 12 GPa,26 while that for ZrC is above
20 GPa.27,28 The calculated bulk and shear moduli of Al4C3 are
170 and 129 GPa, respectively, and the values of ZrC are 229
and 170 GPa, respectively.29,30 Because ZrC is stiffer and harder
than Al4C3, increasing the thickness of ZrC layer or decreasing
the thickness of aluminum carbide layer can endow these
ternary layered carbides with higher stiffness and hardness. It
is followed that the stiffness and hardness of ternary carbides
should follow the sequence of Zr3Al3C54Zr2Al3C44Zr2Al4C5,
Zr3Al3C54Zr3Al4C64Zr2Al4C5. Interestingly, the hardness of
Zr2[Al(Si)]4C5 is higher than that of Zr2Al3C4, and the hardness
of Zr3[Al(Si)]4C6 is very close to that of Zr3Al3C5. A possible
explanation is that the replacement of Al with Si can improve
the hardness and stiffness of aluminum carbide slabs, and thereafter the ternary layered carbides. This sounds reasonable
according to the difference of lattice constant a between
Zr–Al–Si–C and Zr–Al–C. Zr–Al–Si–C has a smaller lattice
constant a,9,10,23,24 indicating that the average bond length
of Al(Si)–C in Zr–Al–Si–C is shorter than that of Al–C in
Zr–Al–C, which is in favor of higher stiffness and hardness. In
addition, Si has one more valance electron than Al, which can
strengthen the Al4C3-type structure and thereby the layered carbides. Our previous work confirmed that ternary layered carbide
Ti3AlC2 could be strengthened by substituting partial Al with
Si.31 The Vickers hardness of Zr–Al–Si–C is about half that of
ZrC. Compared with Zr–Al–Si–C, ZrC possesses a stronger
covalent bond, which endows it with a stronger resistance
against permanent plastic deformation. Using the calculated
lattice and mechanical parameters, we estimated the maximum
value of Peierls shear stress to initiate the movement of a dislocation on glide plane of ZrC, Zr–Al–C, and Zr–Al–Si–C by32
tp ¼
Fig. 3. Temperature dependence of Young’s modulus and internal friction for Zr2[Al(Si)]4C511 and Zr3[Al(Si)]4C6 samples.
2G
2pg
exp 1n
b
(1)
where g ¼ ½ð3 2nÞ=4ð1 nÞs, G is the shear modulus, b the
Burgers vector, s the spacing between atomic slip planes, and n
the Poisson’s ratio. Following Krenn et al.,33 we use s by 1/6
/111S and b by 1/2/110Sfor ZrC with the NaCl-type structure. Since shear slips in Zr3Al3C530 occur by breaking Zr–C
bonds, the interplanar distance between Zr–C atomic planes is
used as s to calculate their Peierls stress. Additionally the b of
hexagonal crystal structure is set as the lattice constant along the
basal plane. The calculated tp of Zr2Al3C4, Zr3Al3C5, Zr2[Al
(Si)]4C5, and Zr3[Al(Si)]4C6 are 69%, 71%, 78%, and 77%,
respectively, of ZrC, indicating that Zr–Al–C and Zr–Al–Si–C
ceramics still mainly conserves strong covalent bond of ZrC. In
addition, the strong covalent bond in Zr–Al–Si–C intrinsically
contributes to its high stiffness at high temperature up to 16001C.
The measured flexural strengths of Zr–Al–Si–C are lower
than that of Zr2Al3C4, and much lower than that of Zr3Al3C5 at
ambient temperature, which is mainly ascribed to larger average
gain size of Zr–Al–Si–C. The loss in strength appears to be
February 2009
aggravated by generation of clusters of the large grains, which
serve as a fracture origin.34 The fracture toughness of Zr2[Al
(Si)]4C5 and Zr3[Al(Si)]4C6 is comparable to that of Zr2Al3C4
and Zr3Al3C5, but superior to that of ZrC. Improved toughness
of layered carbides with respect to ZrC should mainly be associated with the grain morphology. The as-synthesized layered
carbides contain elongated and plate-like grains, while the arcmelted ZrC contains large equiaxed grains.21,35 As in the cases of
Si3N436,37 and SiC,38,39 elongated grains benefit high energy dissipation during fracture and consequently lead to high fracture
toughness. Thus, the irregular fracture surface topography of
layered carbides containing the elongated grains may be the
main reason for their relatively high fracture toughness. However, the fracture strength and fracture toughness of Zr–Al–Si–C
and Zr–Al–C are much lower than those of self-reinforced
Si3N434–37 and SiC38,39 although all their microstructures are
composed of elongated and plate-like grains. Like in Si3N4,34
higher fracture strength combined with higher fracture toughness can be developed in Zr–Al–Si–C and Zr–Al–C by control of
the grain size and amount of well-dispersed large elongated
grains in a fine-grained matrix. The microstructure of Zr–Al–
Si–C and Zr–Al–C with improved strength and fracture toughness should be investigated in the near future.
(3) Thermophysical Properties
(A) Thermal Expansion: Figure 4 shows the thermal
expansion of Zr2[Al(Si)]4C5 and Zr3[Al(Si)]4C6 in the temperature range of 1001–12001C during heating. A least-squares fit
of the data yields CTE of 8.1 106 and 7.7 106 K1 at
1001–12001C for Zr2[Al(Si)]4C5 and Zr3[Al(Si)]4C6, respectively.
The CTE of Zr3[Al(Si)]4C6 and Zr3Al3C5 is higher than that of
Zr2[Al(Si)]4C5 and Zr2Al3C4, indicating that higher layer thickness of ZrC can suppress the thermal expansion of these carbides. Thus, it is expected that Zr2Al4C5 and Zr3Al4C6 have
lower CTE than Zr2Al3C4 and Zr3Al3C5, respectively. Interestingly, the CTE of Zr2[Al(Si)]4C5 is the same as that of Zr2Al3C4,
and the CTE of Zr3[Al(Si)]4C6 is the same as that of Zr3Al3C5,
indicating that the bonding in Zr–Al–C is strengthened by substituting Al with Si. This is in good agreement with the stiffness
and hardness results.
(B) Debye Temperature: The Debye temperatures, yD
for Zr2[Al(Si)]4C5 and Zr3[Al(Si)]4C6 were calculated from the
average sound velocity, nm, based on the given equation40:
h 3n NA d 1=3
vm ¼ Clvm
yD ¼
kB 4p M
449
Properties of Zr-Al-Si-C
(2)
where h, Plank’s constant, kB, Boltzmann’s constant, n, the number of atoms in the molecular, NA, Avogadro’s number, d, the
Fig. 4. Thermal expansions of Zr2[Al(Si)]4C5 and Zr3[Al(Si)]4C6 ceramics during heating at a rate of 21C/min.
3N 1=3
density, M, the molecular weight. C ¼ khB 4pA
is a constant
1=3
and l ¼ nd
is
defined
as
the
linear
density
of
crystal
structure
M
of the materials. The average sound velocity is defined as40:
"
3ðvs vl Þ3
vm ¼
2v3l þ v3s
#1=3
(3)
where vl, vs are longitudinal and shear sound velocities, respectively, which can be calculated from the shear modulus G
and bulk modulus B using the following equations:41
1=2
B þ 4G
3
vl ¼
d
1=2
G
and vs ¼
d
(4)
As shown in Table I, Zr2[Al(Si)]4C5 has the highest Debye
temperature (841 K) and Zr3[Al(Si)]4C6 has the Debye temperature (813 K) being higher than Zr3Al3C5 (806 K), but lower
than Zr2Al3C4 (830 K). The calculated linear densities of the four
carbides are the same (0.52 cm1), thus the divergence of yD
mostly originates from the difference in vm. The ratio of yD between four carbides is approximately equivalent to their corresponding ratio of vm. It is known that the average sound velocity
of a material is related to its elastic properties (stiffness) and
density (weight). Thus, the specific stiffness, i.e. the stiffness-toweight ratio or E/d predominantly determines vm and therefore
yD. The highest specific stiffness, E/d of Zr2[Al(Si)]4C5 (81.3 GPa
cm3/g) is in good agreement with its highest yD, as shown in
Table I. In addition, all four layered carbides have higher specific
stiffness and Debye temperature than ZrC (the specific stiffness
and Debye temperature of ZrC are 61 GPa cm3/g and 707 K,
respectively5), indicating that these layered carbides conserve the
strong covalent bonding of their binary counterpart but simultaneously lowers the density by incorporating Al into ZrC, which
is of great significance for its engineering applications.
(C) Heat Capacity: Temperature dependences of molar
heat capacities of Zr2[Al(Si)]4C5 and Zr3[Al(Si)]4C6 are plotted
in Fig. 5. For comparison, those of Zr2Al3C4,5 Zr3Al3C53 and
ZrC27 are also given. Curve fitting of the experimental data for
Zr2[Al(Si)]4C5 yields:
cP ¼ 226 þ 51:3 103 T 38:1 105 T 2
(5)
with a r2 of 0.99, and that for Zr3[Al(Si)]4C6 yields:
cP ¼ 336 þ 6:43 103 T 112 105 T 2
(6)
Fig. 5. Temperature dependence of heat capacity of Zr2[Al(Si)]4C5 (m)
and Zr3[Al(Si)]4C6 (). Also plotted are values for ZrC, Zr2Al3C4, and
Zr3Al3C5.
450
Journal of the American Ceramic Society—He et al.
with a r2 of 0.98. The molar heat capacities of Zr2[Al(Si)]4C5 and
Zr3[Al(Si)]4C6 at 300 K are extrapolated to be 199 and 214 J/mol
K, respectively, and those at 1600 K are 307 and 342 J/mol K,
respectively. The molar heat capacity of Zr2[Al(Si)]4C5 is very
close to that of Zr3Al3C5, and smaller than that of Zr3[Al
(Si)]4C6, but much higher than that of Zr2Al3C4.
Based on the Neumann–Kopp law,42 the heat capacity of
Zr–Al–Si–C can be determined as a sum of the atomic heat
capacities of the constituent elements. At temperatures above
the Debye temperature, the molar heat capacity at constant volume, cV of each atom is about 3R ( 25 J/mol K) according to
the Dulong-Petit law,43 where R is the gas constant. Therefore,
the heat capacity of Zr2[Al(Si)]4C5 and Zr3[Al(Si)]4C6 above the
Debye temperature is approximately 275 and 325 J/mol K, respectively, which are a little bit higher than the experimental
values at their Debye temperature (264 and 324 J/mol K for
Zr2[Al(Si)]4C5 and Zr3[Al(Si)]4C6, respectively) without taking
into account of the difference between cP and cV (at room temperature, (cP–cV) for a typical solid is about 1–8 J/mol K and it
reaches a maximum at the melting point with a value of about
10% of cV).44
Generally, the cP of Zr2[Al(Si)]4C5 is close to that of Zr3Al3C5
in the whole measured temperature range, which is reasonable in
terms of the Dulong–Petit law. The deviation of heat capacity of
these two carbides in high temperature range is probably related
to the impurities (about 2.8 wt% Y3Al5O12) in Zr3Al3C5.3 In
addition, the molar heat capacity of Zr2[Al(Si)]4C5 and Zr3[Al
(Si)]4C6 is about four to five and six to seven times that of ZrC,
respectively, mainly due to the difference in the number of atoms
in the molecular.
(D) Electrical Resistivity and Thermal Conductivity: Like
Zr–Al–C, Zr–Al–Si–C ceramics are also good electrical conductor (the electrical resistivities of Zr2[Al(Si)]4C5 and Zr3[Al(Si)]4C6 are 1.3670.01 and 0.8670.04 mO m, respectively) and
the samples with different dimensions in the present tests were
readily machined by an electrical discharge method. Considering
the
dielectric character
of
Al4C3
(the
electrical
resistivity of 60% dense Al4C3 in the range of 990–1240 K is
on the order of 106–108 mO m and decreases linearly with increasing temperature),45 the electrical conduction of layered carbides should dominantly originate from the ZrC layers. Previous
first-principles calculation indicated that at around Fermi level,
the density of state (DOS) of Zr3Al3C5 mainly originates from
Zr 4d state, which contributes to its metallic bonding.30 Due to
the similar crystal structure between Zr3Al3C5 and Zr–Al–Si–C,
it is reasonable to conclude that the electrical conduction of Zr–
Al–Si–C is caused by the Zr 4d state. Therefore, thicker ZrC
and/or thinner aluminum carbide layer are in favor of electrical
conductivity, which can reasonably account for the higher electrical resistivity of Zr2[Al(Si)]4C5 than Zr3[Al(Si)]4C6.
The thermal conductivity, ktotal, of Zr2[Al(Si)]4C5 and
Zr3[Al(Si)]4C6 are plotted in Fig. 6. For comparison, those of
Zr2Al3C4,5 Zr3Al3C53 and ZrC27 are also given. A least squares
fit of the data for Zr2[Al(Si)]4C5 yields the following relationship:
ktotal ¼ 9:14 þ 870:9=T
(7)
with a r2 of 0.96, and that for Zr3[Al(Si)]4C6 yields:
ktotal ¼ 8:85 þ 1751:7=T
(8)
with a r2 of 0.97. The thermal conductivities of Zr2[Al(Si)]4C5 at
300 and 1600 K are extrapolated to be 12.04 and 9.68 W/m K,
respectively, and those of Zr3[Al(Si)]4C6 at 300 and 1600 K are
extrapolated to be 14.69 and 9.95 W/m K, respectively. Zr2[Al
(Si)]4C5 has the lowest thermal conductivity at room temperature,
while Zr3[Al(Si)]4C6 show the second highest thermal conductivity in the whole temperature range among the four carbides.
In general, ktotal is given by:
ktotal ¼ ke þ kph
(9)
Vol. 92, No. 2
Fig. 6. Temperature dependence of thermal conductivity of Zr2[Al(Si)]4C5
(m) and Zr3[Al(Si)]4C6 (). Also included are values for Zr2Al3C4 and
Zr3Al3C5.
where ke and kph are the electronic and phonon contributions to
ktotal. ke can be calculated from the Wiedemann–Franz law46:
ke ¼
Lo T
r
(10)
where r is the electrical resistivity at temperature T, and Lo is the
classic Lorenz number, 2.45 108 W O/K2.
Zr2[Al(Si)]4C5 has relative low stiffness and high electrical
resistivity, which results in its low phonon and electron contribution of thermal conductivity. Therefore, Zr2[Al(Si)]4C5 has the
lowest thermal conductivity among the four layered carbides.
Zr3[Al(Si)]4C6 show high stiffness and lowest electrical resistivity,
which should have best thermal conductivity. However, its
thermal conductivity is lower than that of Zr2Al3C4. The mechanism of lower thermal conductivity of Zr3[Al(Si)]4C6 than
Zr2Al3C4 is not well-understood at present and more work is
needed. A possible reason is that Zr3[Al(Si)]4C6 has more defects,
especially carbon vacancy. The molar ratio of Zr:Al:Si:C in the
starting materials of Zr3[Al(Si)]4C6 is 3:3.6:0.5:5.8, while the molar ratio of Zr:Al:C in the staring materials of Zr2Al3C4 is
2:3.1:3.9.3 Nonstoichiometric binary transition metal carbides
show the relatively lower thermal conductivity than stoichiometric ones due to high concentration of carbon vacancies, which can
produce high residual resistivity and also strong phonon-point
defect interaction.47–49 Therefore, layered carbides, like ZrC,
should be defective crystals and the effects of defects on electron
and phonon scattering cannot be ignored. Among four carbides,
the synthesis processing of Zr3Al3C5 is unique because Y2O3 was
used as additive to densify the sample at 17501C.3 As a result, the
grain boundary of Zr3Al3C5 is not as clean as those in other three
carbides and about 2.8 wt% Y3Al5O12 exists, which lower the
thermal conductivity as well as electrical conductivity of Zr3Al3C5
sample.5,50 The intrinsic thermal and electrical conductivity
of Zr3Al3C5 should be higher than those of Zr2Al3C4 due to
higher stiffness and thicker conductive ZrC blocks in crystal
of the former.
IV. Conclusions
Zr2[Al(Si)]4C5 and Zr3[Al(Si)]4C6 have comparable mechanical
and thermophysical properties to those of Zr2Al3C4 and
Zr3Al3C5 due to their similar crystal structures that consisting
of alternatively stacked ZrC layers and Al3C2/[Al(Si)]4C3 slabs.
In addition, the properties of these layered carbides are dominated by the characteristics of composed structural blocks, ZrC
and aluminum carbide. Thicker layer of zirconium carbide
and/or thinner layer of aluminum carbides are in favor of
February 2009
Properties of Zr-Al-Si-C
stiffness, hardness, thermal, and electrical conductivities, but go
against density, specific stiffness, Debye temperature, and CTE.
Generally, layered carbides show high hardness, stiffness, strength,
indicating that they conserve the strong covalent bonding of ZrC,
and superior fracture toughness to ZrC due to their anisotropic
microstructure. To be short, like ZrC, Zr–Al–Si–C ceramics are
potential high temperature structural materials, which should be
further systematically investigated in the near future.
References
1
U. Leela-adisorn, S. M. Choi, N. Tera, T. Takeuchi, S. Hashimoto, S. Honda,
H. Awaji, K. Hayakawa, and A. Yamaguchi, ‘‘Sintering and Mechanical Properties of AlZrC2,’’ J. Ceram. Soc. Jpn., 113, 188–90 (2005).
2
U. Leela-adisorn, S. M. Choi, S. Hashimoto, S. Honda, H. Awaji, K. Hayakawa, and A. Yamaguchi, ‘‘Sintering and Characterization of Zr2Al3C5 Monolith,’’ Key. Eng. Mater., 317–18, 27–30 (2006).
3
L. F. He, Y. C. Zhou, Y. W. Bao, Z. J. Lin, and J. Y. Wang, ‘‘Synthesis,
Physical and Mechanical Properties of Bulk Zr3Al3C5 Ceramic,’’ J. Am. Ceram.
Soc., 90, 1164–70 (2007).
4
L. F. He, Z. J. Lin, J. Y. Wang, Y. W. Bao, M. S. Li, and Y. C. Zhou, ‘‘Synthesis and Characterization of Bulk Zr2Al3C4 Ceramic,’’ J. Am. Ceram. Soc., 90,
3687–9 (2007).
5
L. F. He, J. Y. Wang, Y. W. Bao, and Y. C. Zhou, ‘‘Elastic and Thermal
Properties of Zr2Al3C4: Experimental Investigation and Ab initio Calculations,’’
J. Appl. Phys., 102, 043531 (2007).
6
L. F. He, Y. C. Zhou, Y. W. Bao, J. Y. Wang, and M. S. Li, ‘‘Synthesis and
Oxidation of Zr3Al3C5 Powders,’’ Int. J. Mater. Res., 98, 3–9 (2007).
7
L. F. He, Z. J. Lin, Y. W. Bao, M. S. Li, J. Y. Wang, and Y. C. Zhou, ‘‘Isothermal Oxidation of Bulk Zr2Al3C4 at 500 to 10001C in Air,’’ J. Mater. Res., 23,
359–66 (2008).
8
L. F. He, Y. W. Bao, M. S. Li, J. Y. Wang, and Y. C. Zhou, ‘‘Improving the
High-Temperature Oxidation Resistance of Zr2Al3C4 by Silicon Pack Cementation,’’ J. Mater. Res., 23, 2275–82 (2008).
9
K. Fukuda, M. Hisamura, T. Iwata, N. Tera, and K. Sato, ‘‘Synthesis, Crystal
Structure, and Thermoelectric Properties of a New Carbide Zr2[Al3.56Si0.44]C5,’’
J. Solid State Chem., 180, 1809–15 (2007).
10
K. Fukuda, M. Hisamura, Y. Kawamoto, and T. Iwata, ‘‘Synthesis, Crystal
Structure, and Thermoelectric Properties of a New Layered Carbide (ZrC)3[Al3.56Si0.44]C3,’’ J. Mater. Res., 22, 2888–94 (2007).
11
Z. J. Lin, L. F. He, J. Y. Wang, M. S. Li, Y. W. Bao, and Y. C. Zhou,
‘‘Atomic-Scale Microstructures and Elastic Properties of Quaternary Zr–Al–Si–C
Ceramics,’’ Acta Mater., 56, 2022–31 (2008).
12
L. F. He, W. Bao, M. S. Li, J. Y. Wang, and Y. C. Zhou, ‘‘Oxidation of
Zr2[Al(Si)]4C5 and Zr3[Al(Si)]4C6 in Air,’’ J. Mater. Res., 23, 3339–46 (2008).
13
ISO 18754 , Fine Ceramics (Advanced Ceramics, Advanced Technical Ceramics)—Determination of Density and Apparent Porosity. International Organization
for Standards, Geneva, Switzerland, 2003.
14
G. Roebben, B. Bollen, A. Brebels, J. Van Humbeeck, and O. Van der Biest,
‘‘Impulse Excitation Apparatus to Measure Resonant Frequencies, Elastic Moduli, and Internal Friction at Room and High Temperature,’’ Rev. Sci. Instrum., 68,
4511–5 (1997).
15
ASTM E 1876-97, Standared Test Method for Dynamic Young’s Modulus,
Shear Modulus, and Poisson’s Ratio by Impulse Excitation of Vibration. American
Society for Testing Materials, West Conshohocken , PA, 1998.
16
P. S. Gaal, M. A. Thermitus, and D. E. Stroe, ‘‘Thermal Conductivity Measurements Using the Flash Method,’’ J. Therm. Anal. Calorim., 78, 185–9 (2004).
17
G. Pezzotti, H.-J. Kleebe, and K. Ota, ‘‘Grain-Boundary Viscosity of Polycrystalline Silicon Carbides,’’ J. Am. Ceram. Soc., 81, 3293–9 (1998).
18
G. Pezzotti, H.-J. Kleebe, K. Okamoto, and K. Ota, ‘‘Structure and Viscosity
of Grain Boundary in High-Purity SiAlON Ceramics,’’ J. Am. Ceram. Soc., 83,
2549–55 (2000).
19
T. Rouxel, J. Sangleb!uf, M. Huger, C. Gault, J. Besson, and S. Testu,
‘‘Temperature Dependence of Young’s Modulus in Si3N4-Based Ceramics: Roles
of Sintering Additives and of SiC-Particle Content,’’ Acta Mater., 50, 1669–82
(2002).
20
J. B. Wachtman Jr., and D. G. Lam Jr., ‘‘Young’s Modulus of Various
Refractory Materials as a Function of Temperature,’’ J. Am. Ceram. Soc., 42, 254–
60 (1959).
21
451
C. C. Sorrell, V. S. Stubican, and R. C. Bradt, ‘‘Mechanical Properties of ZrC–
ZrB2 and ZrC–TiB2 Directionally Solidified Eutectics,’’ J. Am. Ceram. Soc., 69,
317–21 (1986).
22
J. C. Schuster and H. Nowotny, ‘‘Investigations of the Ternary Systems (Zr, Hf,
Nb, Ta)–Al–C and Studies on Complex Carbides,’’ Z. Metallkd., 71, 341–6 (1980).
23
Th. M. Gesing and W. Jeitschko, ‘‘The Crystal Structure of Zr3Al3C5,
ScAl3C3, UAl3C3 and Their Relation to the Structure of U2Al3C4 and Al4C3,’’
J. Solid State Chem., 140, 396–401 (1998).
24
K. Fukuda, S. Mori, and S. Hashimoto, ‘‘Crystal Structure of Zr2Al3C4,’’
J. Am. Ceram. Soc., 88, 3528–30 (2005).
25
Z. J. Lin, M. J. Zhuo, L. F. He, Y. C. Zhou, M. S. Li, and J. Y. Wang,
‘‘Atomic-Scale Microstructures of Zr2Al3C4 and Zr3Al3C5 Ceramics,’’ Acta Mater., 54, 3843–51 (2006).
26
T. Iseki, T. Kameda, and T. Maruyama, ‘‘Some Properties of Sintered Al4C3,’’
J. Mater. Sci. Lett., 2, 675–6 (1983).
27
P. T. B. Shaffer, Handbooks of High-Temperature Materials, pp. 142–6. Plenum Press, New York, NY, USA, 1964.
28
E. K. Storms, The Refractory Carbides, pp. 18–34. Academic Press, New
York, 1967.
29
T. Liao, J. Y. Wang, and Y. C. Zhou, ‘‘Atomistic Deformation Modes and
Intrinsic Brittleness of Al4SiC4: A First-Principles Investigation,’’ Phy. Rev. B, 74,
174112 (2006).
30
J. Y. Wang, Y. C. Zhou, Z. J. Lin, T. Liao, and L. F. He, ‘‘First-Principles
Prediction of the Mechanical Properties and Electrical Structure of Ternary Aluminum Carbide Zr3Al3C5,’’ Phy. Rev. B, 73, 134107 (2006).
31
Y. C. Zhou, J. X. Chen, and J. Y. Wang, ‘‘Strengthening of Ti3AlC2 by
Incorporating of Si to Form Ti3Al1-xSixC2 Solid Solutions,’’ Acta Mater., 54,
1317–22 (2006).
32
A. M. Kosevich, ‘‘Crystal Dislocations and the Theory of Elasticity’’; pp. 31–6
in Dislocations in Solids, Edited by F. R. N. Nabarro. North-Holland Publishing
Company, Amsterdam, The Netherlands, 1979.
33
C. R. Krenn, J. W. Morris Jr., S.-H. Jhi, and J. Ihm, ‘‘Relationships Between
Atomistic Bonding and Intrinsic Macroscopic Hardness’’; pp. 379–88 in Hard
Coatings Based on Boride, Carbide & Nitrides, Edited by A. Kumar, Y.-W. Chung,
and R. W. J. Chia. TMS, Warrendale, PA, USA, 1998.
34
P. F. Becher, E. Y. Sun, K. P. Plucknett, K. B. Alexander, C. H. Hsueh, H. T.
Lin, S. B. Waters, C. G. Westmoreland, E. S. Kang, K. Hirao, and M. E. Brito,
‘‘Microstructural Design of Silicon Nitride with Improved Fracture Toughness:
I, Effects of Grain Shape and Size,’’ J. Am. Ceram. Soc., 81, 2821–30 (1998).
35
R. Darolia and T. F. Archbold, ‘‘Arc Melting and Homogenization of ZrC
and ZrC1B Alloys,’’ Metallography, 6, 433–8 (1973).
36
F. F. Lange, ‘‘Relation Between Strength, Fracture Energy, and Microstructure of Hot-Pressed Si3N4,’’ J. Am. Ceram. Soc., 56, 518–22 (1973).
37
F. L. Riley, ‘‘Silicon Nitride and Related Materials,’’ J. Am. Ceram. Soc., 83,
245–65 (2000).
38
X. F. Zhang, Q. Yang, and L. C. De Jonghe, ‘‘Microstructure Development in
Hot-Pressed Silicon Carbide: Effects of Aluminum, Boron, and Carbon Additives,’’ Acta Mater., 51, 3849–60 (2003).
39
N. P. Padture, ‘‘In-Situ Toughened Silicon Carbide,’’ J. Am. Ceram. Soc., 77,
519–23 (1994).
40
O. L. Anderson, ‘‘A Simplified Method for Calculating the Debye Temperature from Elastic Constants,’’ J. Phys. Chem. Solids, 24, 909–17 (1963).
41
E. Schreiber, O. L. Aderson, and N. Soga, Elastic Constants and their Measurements. McGraw-Hill, New York, NY, USA, 1973).
42
E. S. R. Gopal, Specific Heats at Low Temperatures. Plenum Press, New York,
NY, USA, 1996).
43
P. L. Dulong and A. T. Petit, ‘‘Sur Quelques Points Importans de la Theorie
de la Chaleur,’’ Ann. Chim. Phys., 10, 395–413 (1819).
44
A. Cezairliyan, Specific Heats of Solids. Hemisphere Publishing Corporation,
New York, NY, USA, 1988.
45
W. R. King and R. C. Dorwardi, ‘‘Electrical Resistivity of Aluminum Carbide
at 990–1240 K,’’ J. Electrochem. Soc., 132, 388–9 (1985).
46
G. Weidemann and R. Franz, ‘‘The Thermal Conductivity of Metals,’’ Ann.
Phys., 89, 497–530 (1853).
47
R. E. Taylor and J. Morreale, ‘‘Thermal Conductivity of Titanium Carbide,
Zirconium Carbide, and Titanium Nitride at High Temperatures,’’ J. Am. Ceram.
Soc., 47, 69–73 (1964).
48
W. S. Williams, ‘‘High-Temperature Thermal Conductivity of Transition
Metal Carbides and Nitrides,’’ J. Am. Ceram. Soc., 49, 156–9 (1966).
49
W. S. Williams, ‘‘The Thermal Conductivity of Metallic Ceramics,’’ JOM, 50
[6] 62–6 (1998).
50
N. P. Padture and P. G. Klemens, ‘‘Low Thermal Conductivity in Garnets,’’
J. Am. Ceram. Soc., 80, 1018–20 (1997).
&