Full text of DOI:10.1111/j.1151-2916.2000.tb01683.x

J. Am. Ceram. Soc., 83 [12] 3065–69 (2000)
journal
Effect of Microstructure on High-Temperature
Compressive Creep of Self-Reinforced Hot-Pressed Silicon Nitride
Martha A. Boling-Risser,*,†,‡ K. C. Goretta,*,† J. L. Routbort,*,† and K. T. Faber*,‡
Argonne National Laboratory, Argonne, Illinois 60439-4838
Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208-3108
mechanism that determines deformation.4–6 A new model for
tensile creep of Si3N4 suggests that the rate of formation and
growth of cavities in the deformable second phase controls creep.7
The model predicts that tensile creep increases exponentially with
stress, is independent of grain size, is inversely proportional to the
effective viscosity of the deformable phase, and is proportional to
the cube of the volume fraction of deformable phase. However, it
is not clear that the model developed for tensile creep can be
applied to this investigation which concentrates on compressive
deformation mechanisms in relation to grain size.
An experimental self-reinforced hot-pressed silicon nitride was
used to examine the effects of microstructure on high-
temperature deformation mechanisms during compression
testing. At 1575–1625°C, the as-received material exhibited a
stress exponent of 1 and appeared to deform by steady-state
grain-boundary sliding accommodated by solution-
reprecipitation of silicon nitride through the grain-boundary
phase. The activation energy was 610 ؎ 110 kJ/mol. At
1450–1525°C for the as-received material, and at 1525–1600°C
for the larger-grained heat-treated samples, the stress expo-
nent was >1. Damage, primarily in the form of pockets of
intergranular material at two-grain junctions, was observed in
these samples.
II. Experimental Procedure
The starting material used in this study was an experimental
hot-pressed Si3N4 fluxed with Y2O3, MgO, and TiO2, produced by
Dow Chemical USA (Midland, MI). The room-temperature four-
point flexure strength and chevron-notch fracture toughness mea-
sured by Dow were 811 MPa and 7.0 MPa⅐m1/2, respectively.8
The material was received as two 15.25 cm ϫ 15.25 cm ϫ 0.6
cm billets. The largest surface was oriented perpendicular to the
hot-pressing direction. The original billets were sectioned into four
blocks each. To promote grain growth, six blocks were returned to
Dow for additional heat treatment at 1900°C under a nitrogen
pressure of 5.17 MPa for two different times: 2.67 and 24 h. The
resulting three materials were designated as-received (AR) mate-
rial, short-heat-treatment (SH) material, and long-heat-treatment
(LH) material.
The grain-size distributions for the materials were determined
from scanning electron microscopy (SEM) of plasma-etched sur-
faces and were calculated from a diameter based on a spherical
approximation of the area measured for each grain.9 The materials
appeared to have a bimodal grain-size distribution with smaller,
equiaxed grains surrounding larger, acicular grains. The average
grain sizes, based on the diameter of the spherical approximation
of the area, are listed in Table I; Ϸ2000 grains per sample were
counted. The large standard deviations were the result of neglect-
ing the bimodal distribution. While the heat treatment increased
the average grain size, it can be seen from the photomicrographs in
Fig. 1 that as grain growth proceeded, the largest acicular grains
impinged on surrounding grains, which prevented them from
extending in length, and hence they grew mostly in width. Growth
of the large grains occurred at the expense of the small grains. This
is consistent with grain-growth studies by Kramer et al.,10 Pyzik
and Carroll,11 and Lai and Tai12 in similar silicon nitrides. The
microstructures and the grain boundaries were examined by
transmission electron microscopy (TEM) and X-ray energy-
dispersive spectrometry (XEDS).
I. Introduction
ILICON NITRIDE (Si3N4) has potential use in many high-
temperature environments. Effective use of Si3N4 is hampered
by a lack of full characterization of high-temperature mechanical
behavior, including integration of failure mechanisms with plastic
deformation mechanisms. In this paper, the results of an investi-
gation of compressive creep are reported.
S
Many creep studies have been performed on self-reinforced
silicon nitrides containing an oxide grain-boundary phase.1–6
However, most of these tests were conducted in either tension or
flexure; neither is directly comparable to results from compression,
in which cavitation is greatly reduced. Of the few compression
studies, a majority reported testing at low temperatures (i.e.,
Ͻ1400°C), where deformation is invariably accompanied by
damage accumulation. Some tests were further complicated by
having been conducted in an oxidizing atmosphere, which can
enhance cavitation and, in turn, influence creep response.2,3
The dominant creep mechanism for Si3N4 containing a grain-
boundary phase is generally accepted to be grain-boundary sliding
(GBS). It has been proposed that GBS occurs by viscous flow of
the grain-boundary phase (which acts as a lubricant between the
Si3N4 grains) or by solution-reprecipitation of Si and N (which
occur by diffusion through the grain-boundary phase).4–6 In
addition, cavitation at either two-grain or multiple-grain junctions
can occur within Si3N4 containing a grain-boundary phase; the
nucleation and growth of voids are controlled by the same
S. M. Wiederhorn—contributing editor
Steady-state creep behavior can usually be described by an
equation of the form13,14
Manuscript No. 189354. Received May 7, 1999; approved June 22, 2000.
Based in part on the thesis submitted by M. A. Boling-Risser for the Ph.D. degree
in materials science and engineering, Northwestern University, Evanston, Illinois,
1998.
Ϫp
ε ϭ Ad ␴neϪQ/RT
(1)
˙
This research was supported by the U.S. Department of Energy, and by Argonne
National Laboratory’s Division of Educational Programs, under Contract No. W-31-
109-ENG-38.
˙
where ε is the steady-state strain rate, A is a constant, d is the grain
size, p is the grain-size exponent, ␴ is the stress, n is the stress
exponent, Q is the activation energy, R is the gas constant, and T
*Member, American Ceramic Society.
†Argonne National Laboratory.
‡Northwestern University.
3065

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Journal of the American Ceramic Society—Boling-Risser et al.
Vol. 83, No. 12
Table I. Average Grain Size and Average x-Axis and y-Axis
Square-column compressive creep samples Ϸ2.3 mm ϫ 2.3
mm ϫ 6.0 mm were prepared, with the cross-sectional area 5.6
mm2 to avoid exceeding the limit of the Instron load cell. The
length:width ratio was 2:1–3:1 to allow for measurable strain
without buckling.16 The temperature range was 1450–1625°C.
Gross fracture occurred at Ͻ1450°C.
Approximations for the Three Materials†
AR Material
SH Material
LH Material
Avg grain size (nm) 0.26 Ϯ 0.24 0.55 Ϯ 0.51 1.01 Ϯ 0.69
Avg x-axis (nm)
Avg y-axis (nm)
0.53 Ϯ 0.52 0.94 Ϯ 1.17 1.61 Ϯ 1.26
0.25 Ϯ 0.17 0.43 Ϯ 0.35 0.89 Ϯ 0.48
Samples were heated at 10°C/min to the test temperature under
a small cyclic load (10 N minimum, 20 N maximum). Each sample
was held at the test temperature for 15 min to ensure thermal
equilibrium. Data were acquired as load P versus time t and
normalized to true stress ␴ versus permanent true strain ⑀. Strain
†Ϯ values represent 1 standard deviation.
rates were 5 ϫ 10Ϫ7 to 1 ϫ 10Ϫ5 Ϫ1; they were established in
s
reference to the initial specimen length. Strain rates of Ն1 ϫ 10Ϫ5
Ϫ1 caused the samples to fracture; strain rates of Ͻ5 ϫ 10Ϫ7 sϪ1
s
could not be reliably maintained. Tests were limited to total strains
Յ10%. After the deformation was complete, the samples were
cooled at 10°C/min to room temperature under no load.
Samples were compressed between platens machined from the
same material as the test specimens. No measurable reaction
occurred between the platens and the thoriated-tungsten tooling in
the Instron. In all tests, the sample was easily separated from the
platens. However, comparison of the measured strain with the
strain calculated from the time of the test and known crosshead
displacement velocity revealed that at Ն1575°C both the sample
and the platens deformed. The resulting depression in each platen
was measured optically. Platen deformation was taken into account
by treating the platen/sample assembly as a single deforming unit.
It was assumed that because the platens were of the same
heat-treated material, they would deform at the same rate as the
sample. Adding the initial thickness of each platen to the initial
sample length yielded an effective initial sample length; adding the
depth of each platen depression to the measured sample strain
yielded the total strain. Measured strains then agreed with strains
calculated from crosshead velocity and time to within 5% of each
other. No barreling of the samples was obvious.
SEM of deformed samples indicated that volatilization damage
to the samples was limited to the exposed surfaces and affected
less than 1% of the material; it was therefore considered to be
insignificant. Grain growth did not occur during creep testing.
Deformed samples were also examined by TEM and XEDS.
III. Results
(1) Creep Data
Typical ␴ versus ⑀ curves are shown in Fig. 2. True steady-state
stress was achieved, as indicated by the work-hardening rate,
d␴/d⑀, being zero and the path independence of the stress value.
After a new steady-state stress was established in the AR sample
at 1600°C at a new strain rate of 2.17 ϫ 10Ϫ6 sϪ1, it was possible
to return to the initial steady-state stress of 22 MPa when returning
to the initial strain rate of 8.7 ϫ 10Ϫ7 sϪ1
.
Fig. 1. SEM photomicrographs showing the microstructures of the (a)
AR, (b) SH, and (c) LH materials for the surface perpendicular to the
hot-pressing direction.
is the absolute temperature. The values of p, n, and Q were
determined for steady-state creep in this material system under
compressive creep conditions at a constant crosshead speed in an
Instron universal tester previously described.15 All compressive
creep experiments were conducted in static N2 at a pressure of 105
Pa to minimize oxidation and to inhibit volatilization of the
grain-boundary material.
Fig. 2. Characteristic true stress as a function of true strain. This sample
of the AR material was tested at 1600°C.

December 2000
High-Temperature Compressive Creep of Self-Reinforced Hot-Pressed Si3N4
3067
For most strain rates, steady state was achieved within 2%
permanent true strain. In a few instances, apparent steady states
could not be achieved because of obvious damage accumulation;
the measured load decreased with strain. Data from these tests
were not included in our analyses.
Table II. Stress Exponents as a Function of Temperature
for the AR, SH, and LH Materials†
Stress exponent
Test temperature (°C)
AR Material
SH Material
LH Material
Strain rate versus steady-state stress for the AR material is
shown in Fig. 3(a). The AR material was tested at 1450°, 1525°,
1575°, 1600°, and 1625°C. We determined that the stress exponent
for the AR material was temperature dependent; n Ϸ 1.5–2 at
1450–1525°C, but n Ϸ 1 at Ն1575°C. A stress exponent of 1 is
consistent with a diffusional GBS creep mechanism.17 The in-
crease in stress exponent with decrease in temperature indicated
1450
1525
1575
1600
1625
1.9 Ϯ 0.35
1.5 Ϯ 0.3
0.8 Ϯ 0.2
0.9 Ϯ 0.2
1.4 Ϯ 0.3
1.4 Ϯ 0.3
1.5 Ϯ 0.3
1.4 Ϯ 0.3
†Standard deviations are based on estimated uncertainties in stress, strain rate, and
temperature.
that either another creep mechanism became active or
a
temperature-dependent threshold stress existed.18
The SH material was tested at 1525°C and the LH material was
tested at 1525° and 1600°C (Fig. 3(b)). At 1525°C, the stress
exponent was Ϸ1.5 for all three materials. Note that the SH and
˙
LH ε versus ␴ data were nearly identical. The stress exponent for
the LH material was Ϸ1.4 at 1600°C. Results are summarized in
Table II.
(2) Microscopy
TEM and SEM of samples deformed at Յ1525°C revealed
consistent features. Dislocations were present in the deformed
samples (Fig. 4), but not in the undeformed samples. There was
some indication of grain translation, but little evidence of cavita-
tion.
Fig. 4. TEM photomicrograph of AR material crept at 1450°C, showing
evidence of dislocation activity (primarily in large central grain) and grain
translations (examples marked by arrows).
TEM of samples deformed at Ϸ1600°C stood in contrast. Few
dislocations were observed. Grain-boundary sliding was suggested
by regions of apparent grain translation. These translations were
most obvious at triple points (Fig. 5). Grain faceting could, in
principle, impart a similar appearance. However, the apparent
translations were not observed in the uncrept AR material, and so
GBS is the more likely explanation for the feature shown in Fig. 5
TEM indicated the possibility of grain-boundary buckling and
strain whorls caused by grain impingement at some boundaries.
These features were most prevalent in the AR material tested at
1450°C, or in the SH and LH samples. Strain whorls have been
Fig. 3. Logarithmic strain rate as a function of logarithmic steady-state
stress for (a) AR (open circles ϭ 1625°C, closed circles ϭ 1600°C, open
squares ϭ 1575°C, open diamonds ϭ 1525°C, and open triangles ϭ
1450°C) and for the (b) SH (closed triangles ϭ 1525°C) and LH (open
circles ϭ 1600°C, open diamonds ϭ 1525°C) materials. Slope resulting in
n ϭ 1 is shown for comparison.
Fig. 5. TEM photomicrograph of AR material crept at 1600°C showing
evidence of grain-boundary sliding, as indicated by the white arrow, and no
evidence of dislocations.

3068
Journal of the American Ceramic Society—Boling-Risser et al.
Vol. 83, No. 12
seen under compressive creep conditions in “pure” and 0.5 wt%
Al2O3 ϩ 0.5 wt% Y2O3 Si3N4 materials that were hot-pressed at
1500° to 1600°C.19 Strain whorls have also been observed in crept
samples of Si3N4/MgO alloys20 and in sintered Si3N4 deformed in
flexure.21
Figure 6 shows a characteristic TEM photomicrograph of a
sample deformed under conditions where n Ͼ 1. The LH material
was compressed at 2 ϫ 10Ϫ6 sϪ1 and 1600°C. The SH and LH
materials, and the AR materials tested at Յ1525°C, showed
development of lenticular-shaped pockets along two-grain junc-
tions. These pockets were not present in the undeformed material.
These pockets were filled with grain-boundary-phase material. The
lenticular shape intruded into the neighboring grains, evidence that
grain material was being removed from the area through a
solution-reprecipitation mechanism.
An XEDS examination of triple points in deformed AR and LH
samples indicated no apparent change in the grain-boundary phase
due to deformation. Magnesium and zirconium were detected in
the triple points. However, examination of the pockets revealed
preferential migration of zirconium. The pockets that were most
isolated from one another showed the highest concentrations of
zirconium.
into the analysis of the steady-state data, the results were not
consistent. An apparent temperature-dependent ␴0 was calculated.
Insertion of the values of ␴0 into Eq. (2) led to contradictory results
in which the compensated strain rates were then faster at lower
temperatures than were the AR rates at Ն1575°C. Therefore, it
seems clear that the two categories of creep response represent
steady-state creep and a regime in which damage accumulation
was significant. It has been shown that cavitation, at least in
tension, can lead to a creep rate that depends exponentially on
temperature.7
The activation energy Q for the AR material was determined in
the temperature regime in which the stress exponent was Ϸ1. Data
from two strain rates were used; it was necessary to interpolate
data for 1600°C (Fig. 7). The average value of Q was calculated to
be 610 Ϯ 110 kJ/mol; the error bars in the figure reflect estimates
of the accuracy of the measurements and the standard deviations of
the line fits. This Q value agrees closely with that for grain-
boundary sliding accommodated by solution-reprecipitation given
by Raj and Morgan,23 which was based on the heat of solution for
Si3N4 in the grain-boundary-phase material. Solution-
reprecipitation as the primary mechanism of deformation is con-
sistent with the types of pockets formed in the damage regime.
Additional support for the conclusion that the AR material
tested at Յ1525°C and the SH and LH materials did not achieve
steady state, despite the appearance of an apparent zero work
hardening rate in the ␴ versus ε data, was obtained from calcula-
tions of the apparent grain-size exponent p. The grain-size expo-
nent was determined to be zero at 1525°C for all materials. There
is no known steady-state diffusional creep mechanism that could
account for creep rates being independent of grain size. However,
the stress at which damage becomes significant is likely to be
nearly independent of grain size. Although flexure and compres-
sion tests cannot be directly compared, it has been shown that the
elevated-temperature fracture stress of this Si3N4 was a very weak
function of grain size.1
IV. Discussion
The data and observations for stress versus strain rate could be
separated into two categories. The AR material crept at Ն1575°C
exhibited a stress exponent that was Ϸ1, absence of dislocations,
and limited cavity formation. The AR material crept at Յ1525°C,
and the larger-grained SH and LH materials crept at Յ1600°C,
exhibited stress exponents that were Ϸ1.5–2, relatively high
concentrations of dislocations within many grains, and lenticular-
shaped pockets that were primarily at two-grain junctions. The
simplest explanation for the differences is that the AR material
tested at the higher temperatures achieved true steady-state creep,
but in the other tests, a combination of plasticity and damage
For a material deforming by steady-state GBS accommodated
by diffusion through a liquid phase, the grain-size exponent is
expected to be 1 to 3.24 All the creep tests were conducted well
above the softening point of the grain-boundary phase, as indicated
by the flexure results.1 It is reasonable to assume, and is consistent
with the TEM observations, that GBS occurred and was accom-
modated by some viscous flow of the boundary phase. However,
the strain due to viscous flow in Si3N4 has been shown to be
limited.25,26 Therefore, solution-reprecipitation most likely domi-
nated the deformation.
˙
accumulation occurred. For a given ε and T in fine-grained
materials, a certain steady-state stress may be achieved, in contrast
to coarser-grained materials in which the imposed ⑀˙ and T may
produce fracture before achieving steady state. Examination of
only the creep data may suggest that the n Ͼ 1 values could be
attributable to the existence of a threshold stress ␴0:22
ϪQ/RT
˙
ε ϭ A͑␴ Ϫ ␴ ͒e
(2)
0
˙
Reasonable linear plots of ε versus ␴ could then be used to
calculate ␴0.1 However, when a threshold stress was incorporated
In the AR materials at 1450–1525°C and the LH and SH
materials, GBS could not accommodate all the imposed stress.
Stress levels were high, as indicated by the generation of disloca-
tions, and cavitation occurred.
Fig. 6. TEM photomicrograph of LH material crept at 1600°C at an
initial ⑀˙ ϭ 2 ϫ 10Ϫ6
s
Ϫ1, which caused damage in the form of
lenticular-shaped pockets filled with Zr-rich/Mg-poor grain-boundary-
phase material, as indicated by white arrows. Dislocation activity is also
evident.
Fig. 7. Steady-state stress as a function of inverse temperature for AR
material at two strain rates (squares ϭ 2 ϫ 10Ϫ6 sϪ1 and circles ϭ 1 ϫ
10Ϫ6 Ϫ1).
s

December 2000
High-Temperature Compressive Creep of Self-Reinforced Hot-Pressed Si3N4
3069
4J. E. Marion, A. G. Evans, M. D. Drory, and D. R. Clarke, “Overview No. 28,
High-Temperature Failure Initiation in Liquid Phase Sintered Materials,” Acta
Metall., 31, 1445–57 (1983).
Before creep testing, the grain boundaries exhibited a uniform
thickness and the grain-boundary phase had a uniform composi-
tion. There was clear evidence that pocket formation was accom-
panied by redistribution of the grain-boundary phase. Most impor-
tant, zirconium migrated preferentially to the two-grain-junction
pockets. It has been reported that redistribution of the grain-
boundary phase from compressive two-grain junctions to tensile
two-grain junctions should require that stress be applied for Ͼ100
h.27 Our test periods were Յ24 h. We can at present offer no
credible explanation for why the zirconium and magnesium
concentrations of the grain-boundary phase changed with time and
location.
5W. Luecke, S. M. Wiederhorn, B. J. Hockey, and G. G. Long, “Cavity Formation
During Tensile Creep of Si3N4”; pp. 467–72 in Silicon Nitride Ceramics: Scientific
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7W. Luecke and S. M. Wiederhorn, “A New Model for Tensile Creep of Silicon
Nitride,” J. Am. Ceram. Soc., 82, 2769–78 (1999).
8D. Magley, private communication, 1997.
9J. C. Russ, Practical Stereology; p. 103. Plenum Press, New York, 1986.
10M. Kramer, M. J. Hoffmann, and G. Petzow, “Grain Growth Studies of Silicon
Nitride Dispersed in an Oxynitride Glass,” J. Am. Ceram. Soc., 76, 2778–84 (1993).
11A. J. Pyzik and D. F. Carroll, “Technology of Self-Reinforced Silicon Nitride,”
Annu. Rev. Mater. Sci., 24, 189–214 (1994).
V. Summary
12K. R. Lai and T. Y. Tien, “Kinetics of ␤-Si3N4 Grain Growth in Si3N4 Ceramics
Sintered under High Nitrogen Pressure,” J. Am. Ceram. Soc., 76, 91–96 (1993).
13M. A. Meyers and K. K. Chawla, Mechanical Metallurgy Principles and
Applications, 1st ed.; p. 761. Prentice-Hall, Englewood Cliffs, NJ, 1984.
14W. D. Kingery, H. K. Bowen, and D. R. Uhlmann, Introduction to Ceramics.
Wiley, New York, 1976.
For this Si3N4 system, the as-received material deformed by the
mechanism of grain-boundary sliding at 1575–1625°C; the stress
exponent was Ϸ1 and the activation energy was 610 Ϯ 110 kJ/mol.
Data and observations were consistent with solution-
reprecipitation of the Si3N4 as the dominant mechanism of mass
flow. At 1450–1525°C for the as-received material, at 1525°C for
the short-heat-treated material, and at 1525–1600°C for the long-
heat-treated material, the apparent stress exponent increased to
1.5–2, and TEM revealed dislocations and enlarged pockets of
grain-boundary-phase material in the crept samples. In these tests,
steady state was not achieved and the apparent plasticity was due
in part to the damage accumulation.
15J. L. Routbort, “Work Hardening and Creep of MgO,” Acta Metall., 27, 649–61
(1979).
16J. M. Birch, B. Wilshire, D. J. R. Owen, and D. Shantaram, “The Influence of
Stress Distribution of the Deformation and Fracture Behaviour of Ceramic Materials
Under Compression Creep Conditions,” J. Mater. Sci., 11, 1817–25 (1976).
17W. R. Cannon and T. G. Langdon, “Review Creep of Ceramics: Part I,
Mechanical Characteristics,” J. Mater. Sci., 18, 1–50 (1983).
18B. Burton and G. L. Reynolds, “Creep of Uranium Dioxide: Its Limitation by
Interfacial Processes,” Acta Metall., 21, 1073–78 (1973).
19
M. Backhaus-Ricoult, P. Eveno, J. Castaing, and H. J. Kleebe, “High-
Temperature Creep Behavior of High Purity Hot-Pressed Silicon Nitride”; pp. 555–66
in Plastic Deformation of Ceramics. Edited by R. C. Bradt, C. A. Brookes, and J. L.
Routbort. Plenum Press, New York, 1994.
Acknowledgments
20F. F. Lange, D. R. Clarke, and B. I. Davis, “Compressive Creep of Si3N4/MgO
Alloys, Part 2, Source of Viscoelastic Effect,” J. Mater. Sci., 15, 611–15 (1980).
21G. D. Quinn and W. R. Braue, “Fracture Mechanism Maps for Advanced
Structural Ceramics, Part 2, Sintered Silicon Nitride,” J. Mater Sci., 25, 4377–92
(1990).
Thanks are extended to Alek Pyzik of Dow Chemical USA, who provided the
material for this research and arranged for the postprocessing heat treatments. Thanks
to Nestor Zaluzec at Argonne National Laboratory for performing the XEDS
experiments, to Craig Sperry for assistance in monitoring the experiments, and to
Antonio R. de Arellano-Lo´pez for his assistance in reviewing the manuscript.
22A. R. De Arellano-Lo´pez, A. Dom´ınguez-Rodr´ıguez, and J. L. Routbort,
“Microstructural Constraints for Creep in SiC-Whisker-Reinforced Al2O3,” Acta
Mater., 46, 6361–73 (1998).
23R. Raj and P. E. D. Morgan, “Activation Energies for Densification, Creep, and
Grain-Boundary Sliding in Nitrogen Ceramics,” J. Am. Ceram. Soc., 64, C-143–C-
145 (1981).
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Ⅺ