sic composites

Acta metall, mater. Vol. 43, No. 12, pp. 4357~,370, 1995

~

Pergamon 0956-7151(95)00129-8

Elsevier Science Ltd Copyright 9 1995 Acta Metallurgica Inc. Printed in Great Britain. All rights reserved 0956-7151/95 $9.50 + 0.00

VISCOUS BEHAVIOR OF INTERFACES IN FLUORINE-DOPED Si3N4/SIC COMPOSITES G. PEZZOTTI1"f,K. OTA2, H.-J. KLEEBE3, Y. OKAMOTO4 and T. NISHIDA 4 IDepartment of Materials Science,Toyohashi University of Technology, Hibarigaoka, Tempaku-cho 1-1, Toyohashi 441, Japan, 2Institute of Scientificand Industrial Research, Osaka University, Mihogaoka 8-I, Ibaraki-shi, Osaka 567, Japan, 3Institut fur Materialforschung, Universitfit Bayreuth, Ludwig-Thoma Strasse 36B, D-95440 Bayreuth, Germany and 4Department of Materials, Kyoto Institute of Technology, Matsugasaki, Kyoto 606, Japan (Received 3 January 1995; in revisedform 7 March 1995)

Abstract--The influence of fluorine addition

on the grain/phase boundary structures and their viscous behavior at high temperature were systematically investigated in Si3N4/SiC composites. As a reference, a simple system densified by hot isostatic pressing (HIP) and containing only SiO2 at the boundaries was selected for this basic investigation. In addition, increasing amounts of F dopant were incorporated into the composite bodies by adding Teflon during the mixing procedure of the raw powders and then pre-firing the mixture under high vacuum at 1200~ Analytical transmission electron microscopy showed that fluorine remained localized at the grain boundary films and triple points, constituting an amount up to a few percent by weight of the intergranular glassy-SiO2 phase. Detailed structural characterizations of both grain and phase boundaries were performed by using high-resolution electron microscopy (HREM) and atomic force microscopy (AFM). The high-temperature mechanical behavior of the undoped and F-doped SiO2 phases was characterized by both measurements of torsional creep rate and variation of internal friction at temperatures up to 1600~ F-doped materials showed creep rates several orders of magnitude higher compared to the undoped sample and damping temperature curves markedly shifted to lower temperature values. According to the above set of microstructural and mechanical data, the inherent viscosityof the SiO2 intergranular phase could be quantitatively evaluated and the viscous-sliding mechanism under stress modeled.

1. INTRODUCTION Since the pioneering work of Zener and K~ [1-4] on metals, it is known that, at relatively high temperatures, the damping-temperature curve of most polycrystalline materials first starts to increase, shows a peak, and then rises continuously to very large values of internal friction; the peak and the successive rise being commonly denominated grain-boundary peak and high-temperature background, respectively. The existence of the grain-boundary peak (and background) is based on the idea that the relaxation of shear stress across incoherent interfaces, such as large angle grain boundaries and interfaces between different phases, constitutes a source of damping. This effect has been attributed [5, 6] to sliding at the interface corners where the stress is concentrated after relaxation and, accordingly, it has been shown to depend consistently upon the viscosity of the grain boundary. The same phenomenon results in a permanent setting when a static stress is applied, for example in a creep test. Internal friction studies of polycrystalline ceramics, which focussed on the grain-boundary relaxation of ~-To whom all correspondence should be addressed.

Si3N 4 materials at elevated temperature, have been performed by Raj and coworkers [7-11]. These researchers showed that, due to the low-viscosity of the eutectic phases present at the grain boundaries of Si3N4 materials doped with oxide additives, a grainboundary peak may appear in the internal friction behavior at relatively low temperatures. The phases present at the grain boundaries of Si3N4 materials sintered with adding mixtures of oxide densification agents are, however, of very complex composition and liable to crystallization and other diffusional processes during exposure to high temperature. These phenomena may overlap the sliding behavior of the grain boundaries and make the internal friction as well as the creep data difficult to interpret [12]. In previous studies [13-17], internal friction and creep measurements were performed on simple Si3N4/SiC systems with pure SiO: as the only boundary phase. The internal friction behavior showed an exponential background, but no grain-boundary peak was found up to 1350~ [13]. The background, however, showed a clear shift toward lower temperature when trace amounts of impurities were present. Evidently, the range of temperature which could be ultimately examined in those studies was too low for detecting sliding effects at the highly viscous SiO2

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boundaries without uncertainties. As a matter of fact, SiO2 boundaries in the highly pure status melt at around 1730~ Systematic work has been recently performed by Tanaka et al. [18-20] on a "pure" Si3N4 system containing glassy SiO2 at the grain boundaries doped with a few hundred ppm cation or anion impurities. Besides the importance of such a basic experimental approach on this simple system, however, those studies were also markedly limited by the too low temperature range regarding both investigations of internal friction and creep behavior. Thus, the damping temperature curves could not be rationally related to the creep data and the sliding mechanism at high temperature could not be clarified. In this work, we have attempted to overcome the problems related to the temperature range and investigated the torsional creep and the internal friction behavior up to 1600~ which is closer to the melting point of pure SiO2 glass. The simple Si 3N4/SiC system containing only pure SiO2 at the boundaries was intentionally doped with increasing amounts of fluorine in order to systematically decrease the inherent viscosity and, consequently, to increase the self-diffusion coefficients of the constituents ions in the SiO2 phase. This basic investigation was aimed to understand the role of the intrinsic grain-boundary viscosity on the overall high-temperature behavior of the material.

2050~ while the two specimens containing F achieved the same density at 1900~ LECO analysis was employed for characterizing the oxygen contents both in the starting powders and in the sintered bodies. Analysis of cation impurities was performed using an inductively coupled radiofrequency plasma emission spectrometer (ICP) after dissolving the powders into HF. The grain boundaries of the materials were characterized by HREM experiments using a 400 kV microscope (Model 4000EX, JEOL, Tokyo, Japan) whose point-to-point resolution was 0.18 nm. TEM foils were prepared by the successive procedures of grinding, dimpling, and argon-ion-beam thinning the sintered bodies, followed by light carbon coating to avoid charging during observation. The technique adopted to measure the grain boundary thickness has been described previously [21]. The presence of F in the glassy-SiO2 intergranular phase was determined by both energy-dispersive Xray spectroscopy (EDS) and by electron energy loss spectroscopy (EELS) with the spectrometer (Gatan Model 666, Warrendale, Pa) attached to a Philips CH20FEG scanning transmission electron microscope, operating at 200 kV and with a probe size of 1-2 nm. In order to characterize the phase boundaries by AFM, the SiC crystallites were first extracted by a chemical treatment (18-20h at 190~ in dilute NaOH aqueous solution from the dense SiaN4 composite body. This chemical process was previously 2. EXPERIMENTAL PROCEDURES optimized in order to dissolve the amorphous SiO2 Three materials were investigated in the present boundary-phase with negligible damage of the SiC report. In comparison with a "pure" (undoped) crystallites [22]. Then, the platelets were attached to a metallic support and scanned with a contamination SiaN4/SiC system, two materials with the same phase composition but doped with different amounts of tip of ~ 40 nm radius grown in the scanning electron fluorine were analyzed. The raw powders were: a microscope onto a standard pyramidal tip. The scan high-purity Si3N4 powder (E-10, Ube Ind. Lid, Ube, speed was typically 9 Hz, or 1 min per image. Further Japan) and a SiC single-crystal platelet powder details of the AFM technique adopted for character(Grade-M, C-axis Co., Jonquiere, Canada). All the izing the Si3N4/SiC boundaries were reported in composites contained the same nominal fraction of previous studies [23, 24]. The apparatus used for measuring simultaneously 25 wt% SiC platelets. The F dopant was incorporated into the composite bodies by adding pulverized the internal friction, Q - l, and the shear modulus, G, Teflon (Teflon, E. I. du Pont de Nemours, Wilming- was of the torsion pendulum type and was similar to ton, Del.) during the mixing procedure of the raw that used by K6 [2-4]. The test specimen was powders and then pre-firing the mixture in high 2 x 3 x 50 mm in dimensions. The apparatus differed vacuum at 1200~ in order to depolymerize first the from that used by K6 since it was enclosed in a Teflon structure (to tetrafluoroethylene C2F4) and, vacuum-tight system in which a controlled argon successively, via the elimination of CO gas. The atmosphere could be maintained during the experaddition of the Teflon compound was thought to be iments. Also, a carbon heater, surrounding the specthe most suitable for the present experiments since it imen, was employed to raise the testing temperature does not involve the incorporation of H into the SiO2 up to 1600~ The absolute strain amplitude was structure and hence allows for easier modeling of the calibrated prior to testing by a strain gage attached grain-boundary structure. Details of the mixing and to the sample surface. It corresponded to an outerforming procedures were described previously [14]. fiber maximum stress of 10 MPa. Measurements were performed at the frequency of 10 Hz and the free Sintering was performed by HIP after encapsulating the specimens in a borosilicate glass tube evacuated decay method [25] was used for the measurement of to 0.1 Pa. The HIP cycles were conducted under Ar Q -1. All the materials showed almost the same shear gas pressure of 180 MPa for 2 h. The undoped spec- modulus at room temperature, the measured value imen was fully dense (>99.5%) by sintering at being 140 GPa. Calibration by strain-gage method at

PEZZOTTI et al.: VISCOUS BEHAVIOR OF INTERFACES room temperature revealed a confidence of + 1 GPa for the measured G values. High temperature torsional creep experiments were carried out with the same torsional pendulum apparatus used for measuring internal friction. The constant momentum was applied to the specimen by a magnetic force through a stiff transverse rod. The strain was detected by a high sensitivity eddy current type displacement detector after amplifying and filtering the signal. This allowed us to obtain a quite high precision in the strain measurement. The confidence in the strain measurement was about +4.0 • 10 40/0. 3. BACKGROUND AND MICROSTRUCTURAL CHARACTERIZATIONS 3.1. Background on the material

Previous works [13 17], focussed on developing a Si3N4 material with high fracture and creep resistance up to around 1500~ a fully dense composite constituted of high-purity Si3N 4 with 25 wt% SiC platelets was sintered by HIP without external addition of sintering additives. A SiO2 impurity, generally present in Si-based ceramics (i.e. as a consequence of oxidation process during exposure of the powders to the atmosphere) constituted the grain-boundary phase. Detailed image analysis data [26] showed that the SiC platelets were randomly distributed inside the sintered body, their average thickness and average diameter being 3.2 and 24.2 pm, respectively. A peculiarity in the mechanical behavior of this "pure" system was the almost complete absence of plasticity up to 1520~C; as a matter of fact, very low creep rates (i.e. in the range 10 -9 t o 10-SS -I) were measured under stresses of 400-500MPa [14, 15]. Furthermore, it was suggested that this composite system was suitable as a model material for basic investigations since it showed neither significant dislocation activity inside the grains nor significant modification of its grain-boundary structure, such as cavitation or crystallization, after up to several hundred hours exposure in air at high temperature. The original idea for improving the mechanical performance at high temperature of this simple ceramic system was to (slightly) modify the grain-boundary structure in order to achieve some plasticity effect (i.e. a better reliability with loading at fast rates) without a significant enhancement of the boundary-phase cavitation process. This first report describes some basic finds related to the above attempt. 3.2. Chemical analyses

The results of LECO and ICP analyses of the starting powders are shown in Table 1. The Si3N 4 and SiC starting powders contained 2.5 and 0.2 wt% SiO2, respectively, as calculated from the respective O contents (measured by LECO analysis). Oxygen analyses, also performed on the sintered bodies, revealed the presence of a SiO2 amount which is in

4359

good agreement with the value calculated from the respective constitutive fractions found in the starting powders. No difference was detected in the amounts of oxygen between the undoped and F-doped samples. 3.3. Microscopy

HREM observation revealed that in all the materials investigated the SiO2 glass phase was localized at both the grain boundaries and at the triple-grain junctions [Fig. I(A) and (B)]. The Si3N 4 grains showed a similar grain size, d, (~ 1 pm) in all the materials. The geometry of both triple points and grain-boundary films in the F-doped materials was found to be the same as that of the undoped materials. Triple-grain junctions were typically 10-50 nm in size and electron diffraction analyses found systematically only halo-patterns due to the glassy status of the SiO2 structure present inside them. The thickness of the grain-boundary films was precisely measured to be 1.1 ___0.1 nm in the 5.8 wt% F-doped material, as compared to 1.0 + 0.1 nm for the pure system [20]. The F species is a known modifier of SIO2, forming non-bridging Si--F bonds in the glass structure. According to the measured thickness of the grain boundary, the SiO2 structure should be basically constituted of few SiO4 tetrahedra. The small increase in film thickness with the addition of F should be considered to be a result theoretically conceivable according to the following considerations. The F and the O atoms, the latter being replaced by the former in the present experiments, have almost identical ionic radii (1.32/~ against 1.33/~) but different ionic valency. To compensate for ionic valency one 02- ion must be replaced by two F-ions, which leads to the observed widening of the interlayer. Since similar spectra were detected by EELS from both the grain boundaries and the triple grain junctions, it was assumed that they contained, in the average, SiO2-glass with the same composition [Fig. I(C)]. The local F amount was measured at about ten triple junctions per each material. The average values for the two F-doped specimens were respectively 2.4 and 5.8 wt% of the SiO2 phase as determined by EDS. No presence of F was detected from the grain boundary phase of the undoped sample. The guessed grain-boundary structure of the F-doped samples is shown in the inset of Fig. I(B). The structures of the glassy phase for which, in addition to the thickness of the intergranular film, almost no information was available from the HREM images, have been represented according to the structure of pure and F-doped SiO2 glass reported in the literature [26-28]. The structures of the adjacent Si3N 4 grains were constructed from the HREM image according to the structural model given by Hiraga et al. [29]. Intergranular film thickness, F amount and other salient microstructural characteristics of the materials are summarized in Table 2.

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Table 1. Oxygenand cation impuritycontents as detected by LECO and ICP analyses, respectively,from the raw Si3N4 and SiC powders 0 Fe Cr Ca A1 (%) (ppm) (ppm) (ppm) (ppm) Si3N4 powder 1.45 36 < 50 < 20 < 30 SiC platelet 0,14 100 < 50 40 4300 Table 2. Sintering conditions and salient microstructural characteristics of the materials under investigation Sint. T~ d 2 6 Materials (~ Phases (#m) (pm) (#m) Si3N4/SiC no dopant

2050

Si3NJSiC+ 2.4wt%F

1900

Si3N4/SiC + 5.8wt%F

1900

fl-Si3N34 or-SiC fl'Si3N4 or-SiC Si3N4 ~t-SiC

The phase boundaries were not easily observable by H R E M . This was due to the markedly different ion thinning rate o f the Si3N4 and SiC structures during the T E M - f o i l preparation which led to interfaces too thick for H R E M imaging. In order to characterize also the phase boundaries in a quantitative manner, A F M experiments were carried out on the SiC platelets after extracting them from the respective sintered bodies. The surface morphology of the SiC platelets could be mapped with nanometer resolution by A F M and this characterization revealed the systematic presence of permanent marks by the matrix grains and wrinkles at the phase boundaries as

1.4

45.5

1.0 + 0.1

1.2

5.0

--

1.2

--

1.1 + 0.1

a consequence of the high pressure applied during sintering [Fig. 2(A)]. Profilometric analyses were automatically performed to determine the average depth of the marks as shown in Fig. 2(B). Crystallites extracted both from the material containing 5.8% F and from the undoped material were characterized. The results, averaged over about 15 platelets per material (i.e. over ~ 5 • 10 3mm2), are shown in Table 2. The SiC crystals extracted from the material containing undoped SiO2 at the phase boundaries showed sintering damages with an average depth about nine times larger than that measured on crystals from the F-doped sample. N o damages were

Fig. IA.

PEZZOTTI et al.:

VISCOUS BEHAVIOR OF INTERFACES

4361

Fig. 1. HREM micrographs of the 5.8 wt% F-doped composite. (A) A triple junction and (B) a grain boundary with an intergranular film thickness of I. Inm. In (C), the EELS spectrum detected at grain-boundary film is shown. The local F : O ratio in the EELS spectrum is about 0.30. The inset of (B) shows the guessed structure of the F-doped SiO2 boundary film. SoIid circles represent the Si atoms, small and large open circles represent the N and O atoms, respectively, while the half-open circles are the F atoms.

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PEZZOTTI et al.: VISCOUS BEHAVIOR OF INTERFACES

Fig. 2. AFM image of the surface of a SiC platelet extracted from the undoped sample after sintering at 2050~ (A). The profilometric analysis performed between the points located with U and V in (A) is shown in (B) with the axis perpendicular to the platelet scaled up for clarity. detected in the SiC platelets before HIP sintering [22, 24]. Despite the possibly limited statistical significance of the A F M data, a rationale for these data may reside both in the lower sintering temperature adopted for densifying the F-doped materials and in the lower viscosity of the SiO2 phase, which allows an easier sliding and rearrangement of the matrix grains during the sintering process. It should be noted that the local plastic damages on the SiC surfaces may act as interlocks and inhibit sliding processes at elevated temperatures. This important microstructural feature is likely to play a predominant role also in the internal friction and creep behaviors of the materials at high surface

temperature. This point will be discussed in some detail afterwards. 4. MECHANICAL CHARACTERIZATIONS 4. I. D a m p i n g temperature curves

The damping temperature curves as measured in the undoped and F-doped samples are shown in Fig. 3. These curves were stable with respect to further measurement runs. The F-addition produced a definite shift of the curve towards low temperatures. An important find was that all three curves relaxed above a certain temperature value which was decreasing by increasing the amount of F present in the intergran-

PEZZOTTI et al.: 30 -9 SiO2+5.8%F O SiO2+ 2.4%F

~'_ ~

20

i~

lO

-

/ __,~

-

800

1000

1200

1400

1600

Temperature (~ Fig. 3. Damping temperature curves as measured in the undoped and F-doped samples.

ular SiO2 phase. In other words, the rising Q - l behavior, believed in previous studies [13, 18-20] to be simply part of an exponential background, represented instead the low-temperature foot of a broad internal friction peak. In Fig. 4(A) the peaks are 15 --

4"

(A) ITr- = 1434~

I~['T= 1506~

['P

7

~

[E-= 146 kJ/mol

10

o

~

5

1000

30

1200 1400 1600 Temperature (~

4363

VISCOUS BEHAVIOR OF INTERFACES

1800

/

(B)

better shown after subtracting the respective background curves. According to works from the literature dealing with polycrystalline metals [1-4, 25], the contribution of the background to the overall value of internal friction was first fitted by an exponential curve [Fig. 4(B)] and then subtracted to characterize the net contribution of the peak responsible for the relaxation process. The background curves were fixed by imposing the mathematical condition that the last data point constitutes an inflection point of the damping temperature curve. The peaks seem to become less broad and achieve a higher intensity with decreasing F content of the material, as they are enclosing a constant area. In Fig. 5 the peak-top temperature, Tp, and the apparent activation energy, E, (calculated from each Q-~ peak shape by the peak-width method [25]), are plotted as a function of the average amount of F detected from the intergranular phase. It is seen that the activation energy decreases linearly as the fraction of F incorporated into the SiO2 structure increases. These values are almost coincident with those given by Hetherington et al. [30] for viscous flow of vitreous SiO~ containing increasing contents of chlorine. Also, the E value of the undoped sample is found to be the same as that given by Williams for self-diffusion of oxygen in highly pure SiO2 [31] and about half of that reported by other authors [32, 33]. Two main factors should be pointed out before coming to discuss the above activation energy results. The first is the unknown diffusion behavior of the silicon ions in SiO2 as well as that of other trace amounts of various cation impurities in the raw materials (Table 1) which also remain segregated at the grain boundaries after sintering [15]. The presence of these latter impurities may alter the SiO:glass structure with respect to the highly pure status. Also, it should be noted that typically 5-10at.% nitrogen are dissolved in SiO2based glasses present in Si3N4 materials. Secondly, a more important factor may be the somewhat arbitrary choice, of the internal friction background

SiO2 + 5.8% F "~ 20 -

SiO2 + 2.4% 150

1 5 0 0 ~

SiO2 undoped

::o~

"~ 1o

i125 o 0

100 '-~ I t~

1000

I

I

1400

1800

Temperature (~

< 1350

I

J

r

I

2

4

6

8

75 10

Amount of F in SiO2 (%) Fig. 5. Peak-top temperature, Tp, and apparent activation

Fig. 4. Internal friction data for various materials are separated into peak (A) and background (B) contributions according to the mathematical criterion explained in the text.

energy, E, as a function of the F content detected from the grain-boundary glassy-SiO2phase. Error bars represent the error possibly involved in the determination of the peak-top temperature.

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el al.:

VISCOUS BEHAVIOR

curves, which affects the calculated activation energy values. Underestimation of 50-100kJ/mol in our measurements can be due to the uncertainty in the morphology of the background curve. The consequences of such a low confidence in the E values on evaluating the inherent viscosity of the intergranular phase are discussed in the next section. 4.2. Intrinsic viscosity o f the g l a s s y - S i O 2 f i l m s

The damping peaks shown in Figs 3 and 4 were correlated to the viscosity of the grain-boundary phase at the respective peak-top temperatures by means of the procedure proposed by Mosher and Raj [8]. The basic equation adopted for relating the externally applied shear stress, z, to the viscosity, r/, of the polycrystalline materials with a SiO2 grainboundary phase is = (0/6)~

(l)

where 6 and C are the grain boundary thickness and the sliding velocity, respectively. The latter parameter is related to the microstructural and elastic characteristics of the material by means of the equation (J = U / t * = c~d[(l - v ) / G ] r / t *

(2)

where 0 and t* are the average displacement of two adjacent grains and the time required for such a displacement to occur, respectively; e is a numerical factor which varies according to the shape of the grain and phase boundaries; aT, v, and G are the average grain size, Poisson's ratio and the shear modulus of the polycrystal, respectively. Combining equations (1) and (2) and considering that during internal friction measurements at a frequency f0, at the peak-top temperature, Tp, the time t* corresponds to 1/2r~f0, the grain boundary viscosity can be expressed as tl = G f /2nfo~(1 - v)d.

(3)

This constitutes a basic relation which allows evaluation of the grain-boundary viscosity in a polycrystalline material. However, two main problems generally hamper a precise determination of r/. They are: the uncertainty in determining experimentally the grain-boundary thickness 6 and the estimate of the boundary-shape factor c~. Regarding the former parameter, there are some basic, physical models [34] (recently also proved experimentally [35-37]) supporting the existence of an equilibrium grain-boundary film thickness in Si3N4 ceramics. According to this thesis, 6 should remain constant throughout the polycrystal since the film thickness is determined only by a balance between attractive and repulsive forces acting across and within the boundary, independently of the relative grain orientation. Hence, since in the present work 6 was precisely determined, the uncertainty related to the grain-boundary geometry was eliminated. The value of boundary-shape factor, a, has been theoretically calculated for a homogeneous polycrystalline structure by several authors [1, 2, 7]

OF INTERFACES

according to various grain geometries. However, besides the inherent inhomogeneity of the present composites consisting of two different phases of different size and morphology, the microstructural characterization by AFM, shown in a previous section, has also en,~isaged the different geometry of the phase boundaries formed under different sintering conditions. This morphological difference, however, lies on a scale much smaller than that of the grain size. With this in mind, rather than a theoretical estimate, we have attempted to determine a experimentally. Following K~ [3], the total strain, ~tot, of the polycrystal under the external shear stress can be expressed by the sum of the elastic and anelastic components according to the relation ]}tot ( z / G ) + ( O / a ) = z /G R =

(4)

where G and GR are the unrelaxed and relaxed shear modulus values, respectively, obtained from macroscopic measurements and the d value represents the average grain-size of the matrix (Table 2). Substituting from equation (2) and rearranging, we find ot = [(G /GR) - 1]/(1 - v)

(5)

which gives the boundary-shape factor as a function of the shear modulus relaxation determined experimentally. The dependence of the modulus GR/G on temperature, as measured in the present composites, is plotted in Fig. 6. Strictly speaking we have not found in any of the present materials a constant value for the relaxed modulus GR, since the G value was a monotonically decreasing function in the range of temperature investigated. In calculating ~ from equation (5), the values of GR/G at the respective damping peak-top temperatures (indicated by arrows in Fig. 6) were assumed. Considering the quite small absolute values of modulus relaxation found in the present materials, this experimental evaluation of

+5.8% F

F

+2.4%

SiO 2 undoped

~-" 1.00

.2

,-

.o

0.98

0.96

0.94

0.92

J

I

I

I

t0

12

14

16

Temperature/100 (~ Fig. 6. Relaxation strength ratio, GR/G, of various materials as a function of temperature. The respective peak-top temperature and the temperature at which each internal friction curve starts to increase [from Fig. 5(A)] are indicated by arrows.

PEZZOTTI et aL: VISCOUS BEHAVIOR OF INTERFACES SiO2+

4.3. Torsional creep data and mechanisms o f grainboundary sliding

10 SiO 2 undoped

/

X /

b

/

/

SiO2+

8

> 7 5.0

I

I

f

I

5.5

6.0

6.5

7.0

1 / T x 10 4 ( l / K )

Fig. 7. Viscosity of the grain-boundary SiO2 phase, as determined from internal friction experiments, are compared with data from macroscopic measurements by Ohashi et al. [38].

was believed to provide a better approximation than using theoretically calculated values. The viscosity values of the SiO2 grain-boundary phase containing different fractions of F were calculated from equations (3) and (5). The results of this calculation are plotted in Arrhenius fashion in Fig. 7 at the respective damping peak-top temperatures. The maximum data scatter involved with the experimental error of 1 GPa in the measurements of G and G R is also indicated. For comparison, viscosity data from macroscopic measurements on SiO2 glass doped with the same respective amounts of F are replotted as a function of temperature from Ohashi et al. [38]. The agreement between the r/ values from internal friction and those from macroscopic measurements is fairly good considering the quite different experimental conditions under which they were obtained. The larger error involved in the measurement of the r/ value for undoped SiO 2 is due to the very small relaxation ratio that this material showed in the range of measured temperature. If desired, the viscosity data can be replotted in terms of oxygen self-diffusivity, Dox, according to the Stokes-Einstein equation. Based on this equation, it can be also shown that the increase in the inherent viscosity of the boundary film with increasing the fluorine content up to 5.8 wt%, leads to one order of magnitude increase in the oxygen self-diffusivity, Dox, in the SiO2 glass. The dependence of the viscosity of the SiO2 glass on the F-content, in the range investigated in the present study, experiences a linear dependence when plotted in logarithmic scale (Fig. 8). The slope fl of this plot is found to be quite sensitive to the temperature change, its variation being ~ 25% in the range 1400-1600~ The above viscosity data provide the experimental basis for the micromechanical analysis of viscous grain-boundary sliding discussed hereafter. AM43/12--K

4365

An open question resides about the origin of both the grain-boundary peak and the high-temperature internal friction background in SisN4 ceramics [18]. Previous HREM experiments on the present undoped composite [17] have revealed the formation of "wedge" type microcracks with few-ten-/~ amount sliding at the triple grain junctions only after ~ 100 h exposure at 1520~ under the high tensile stress of 220 MPa. It is conceivable, however, that the presence of impurities, reducing the inherent viscosity of the glass structure, can shorten significantly the time necessary for the formation of "wedge" type microcracks. Therefore, a focal point for deducing the origin of the damping temperature curve would be to ascertain directly as to whether wedge cracks were formed during the present internal friction measurements. For this purpose, exploiting the high precision in the strain measurement provided by the present torsional pendulum apparatus, we attempted to monitor the strain behavior of the materials under a constant shear stress being exactly the same (i.e. z = 10 MPa) as the maximum stress applied during the internal friction measurements. The strain vs time curves at 1430~ for the F-doped specimens are shown in Fig. 9. The strain curve of the undoped material was below the detection limit of the apparatus utilized (i.e. <10-8s-1). The macroscopic amount of creep strain, 7p, associated with the presence of an array of wedge-type microcracks inside the specimen, depends upon the average length of the microcracks, 2c, and the average extent of sliding of two adjacent grains, U [39, 40]. Assuming that the adjacent grains can slide only within the distance of their elastic deformation, which is in the area of interest herein, gives 7p = (z/G){1 -- Nc3[16(1 -- v 2) x (10 -- 3v)/45(2 -- v)]V} -l

(6)

9 -

•/•

1402~ = -1.21

o

F,434 c

"-~ 8 M

g

15 O6;.C6

7 2

I 3

I 4

I 5

I 6

Amount of F in SiO 2 (%) Fig. 8. Intrinsic viscosity of the grain-boundary glassy SiO2 film as a function of F-content and temperature. Data are plotted in log-log fashion to achieve linearity in the regions of F-content and temperature of interest.

PEZZOTTI et al.: VISCOUS BEHAVIOR OF INTERFACES

4366 x = 10 MPa

50 40

-

(A)

5SiO2+S

~

o 30

%

--

Si02+

~

20

strain[ 0

250

[

]

]

500

750

1000

formed extensively during the present internal friction tests, On the other hand, wedge-shaped microcracks were found by TEM inspection after long-term creep exposure at around 1500~ [17]. Similar arguments about whether wedge microcracks form or not can be provided in terms of strain rate considerations. Steady-state torsional strain rates, ~, as measured in the F-doped specimens are plotted in Arrhenius fashion in Fig. 10. They have to be compared with an upper bound strain rate value for wedge cracking given as [11]

~L = r~6/drl

(7)

Time (s) where we invoke the argument that the amount of sliding at the boundaries will become negligible if the polycrystal is deformed at a rate faster than the boundary can slide. This boundary value, calculated as a function of temperature and F content from the data in Figs 8 and 9, is shown in Fig. 10. As seen, the strain rate at which the shear stress is applied during the internal friction experiments, ~r, is well above the ~L limit over the entire temperature range of measurement. This would confirm that the formation of wedge microcracks is not the phenomenon originating the damping temperature curve in the present materials. The activation energy values deduced from the creep measurements coincide with some literature data reported for the oxygen self-diffusion in SiO2 glass [32, 33]. This may suggest that the enhanced diffusivity [corresponding to the lowered viscosity according to equation (6)] of the SiO2 phase owing to the presence of the F atoms, is at the origin of the

x = 10 MPa

15 F

(B) si~

/I

7c

"~

| 5~]

I

0

Elas!ic strain

"~ 2.4% V

10

20

30

Time (s)

x = 10 MPa ~tif value

Fig. 9. Torsional creep data as detected at 1430~ in the F-doped samples (A). In (B), the data are compared with the theoretically calculated strain value, Yc, for the formation of irreversible wedge-type microcracks at the triple grain junctions.

"

~

~Lf~ 5S8Oqf;

10-4

d 10-6

where N is the number of cracks in the volume V. For a wedge-type microcrack, c is equal to the grain-facet length ( ~ aT) and N~ V can be expressed as the number of triple points per unit volume, assuming the microstructure as an array of regular dodecahedra. An order-of-magnitude calculation based on the presence of one wedge microcrack at each triple point, gives a creep strain value of ~ 10-2%. The time required for the present F-doped specimens to achieve such a strain during the torsional creep experiments is in the range between 10 and few 10 s [Fig. 10(B)] namely, about three orders of magnitude longer than the time t* = 1/(2nf0) within which the maximum shear stress z = 10 MPa is applied to the specimen during the internal friction measurement. Thus, it can be argued that wedge-type microcracks should not have been

10 -8 ~/det value

o

L

I

I

[

I

5.6

6.0

6.4

6.8

7.2

1/Tx 104 (l/K)

Fig. 10. Torsional creep strain rate as a function of temperature as measured in the F-doped materials. Experimental data are compared with the respective upper limit strain rate values, ~L, for wedge cracking. Detection limit for the strain rate measurements, ~d0,, strain rate adopted during the internal friction measurements, ~f, and activation energy values, E, for the torsional creep process are also explicitly indicated.

PEZZOTTIet (A)

al.:

VISCOUSBEHAVIOROF INTERFACES

4367

(B)

/

Internalfriction experiments

~ ~ ~ Com~n~'~

Fluxof ox;ge; va;a;cy

\~ \ \

Ten.sie~

(C)

Torsionalcreep experiments (x= 10MPa) ,9 ' ~

w

~-U> IOA [ t* > lOs

\ \

Fig. 1I. Micromechanisms proposed in the present study to explain both the origin of the internal friction peak [(A) and (B)] and the formation of wedge-type microcracks (C) in the Si3N4 materials with glassy SiO2 at the grain boundaries.

creep process. We guess that the enhancement of diffusivity by fluorine impurity is the physical process also responsible for the grain-boundary peaks found in the present materials. According to the above results and calculations, we suggest the following mechanism to explain the origin of the grain-boundary peaks. Under the externally applied shear stress, z, in correspondence to each triple-grain junction, portions of the SiO2 interface on adjacent sides of the grains should be locally subjected to tension or compression stress components [Fig. l l(A)]. These stresses, whose

overall balance is provided by the elastic response of the individual grains, may produce the driving force for the oxygen diffusion process through the glassy interface from the side of interface in tension towards the side in compression. Such a diffusion process of oxygen atoms in the SiO2 glass is the common origin of both the internal friction peak and the creep deformation, showing similar activation energies. However, during the internal friction measurements, the external shear stress, z, is applied for quite a short time so that the Si02 boundaries can slide only within the maximum distance-

4368

PEZZOTTI et al.: VISCOUS BEHAVIOR OF INTERFACES

allowed by the elastic deformation of adjacent grains [7] Umax : 0~t~(l -- v ) / a ~ 1-10 A.

4.4. Relation between internal friction and creep experiments In some polycrystalline alloys with grain boundaries containing low melting non-metallic impurities [41-43], the internal friction background was recognized to be of viscoelastic nature. Accordingly, it was proposed that the build up of stress at the grain edges, due to the grain boundary relaxation, produces local irrecoverable (plastic) creep of a linear and thermally activated type. Considering the similarity of those alloys with the present materials (also containing boundary phases of lower refractoriness in comparison with the grains), this hypothesis was examined in the present study. A viscoelastic creep process at the grain boundaries involves the existence of a plastic strain, ~,p, accumulated into the specimen at a rate (9)

where R is a constant and AH is the activation energy of the creep process. If equation (9) can describe appropriately the overall creep behavior of the specimen (cf. Fig. 10), it follows that the material behaves as a Maxwell solid and the internal friction background, ~bB, can be expressed as [25] tan tk~ = (G/2nfo)R e x p ( - A H / k T ) .

(10)

Thus, assuming the same values of R and AH for the creep and internal friction processes, equations (9) and (I0) can be rearranged to relate the internal friction background, qSB,to the macroscopic torsional creep strain, ~p, as Cp = ~(2nfo/G)tan dpB.

-6 --

f

Theoretical r o

(11)

Since the present torsional creep experiments were conducted under a shear stress, z, which is the same as the maximum shear stress amplitude applied during internal friction, it was possible to compare without any extrapolation the Cp values determined experimentally with those theoretically calculated from equation (11) under the assumption of Maxwell solid-like behavior. This comparison is shown in Fig. 12 for the experiments conducted at 1430~ In the

m

~

/

(8)

Accordingly, this sliding, occurring in times of about 10 -2 s, is almost completely reversible since obeying the elastic law the grains will push the boundaries back to their original position once the external stress is removed. Loading the specimen for a time longer than ~ I0 s will lead to an irreversible sliding process with the formation of wedge microcracks with increasing size, as observed during the creep experiments. This model is summarized in Fig. 1 I(B and C). The possibility of a partial irreversibility in the "elastic-range" sliding occurring during the internal friction measurements will be discussed in the next section.

Cp= Rz e x p ( - A H / k T )

,-,

= "~

/ ~ //

-10

-12

/

Experimental creep data 1430 ~ = 10 MPa

I

I

I

1

3

5

Amount of F in SiO 2 (%) Fig. 12. Torsional strain rates experimentally measured at 1430~ as a function of the F-content are compared with the respective strain rate values theoretically calculated from the internal friction background curves under the hypothesis of Maxwell solid-like behavior. The experimental data for the undoped sample is from Ref. [14].

calculation, we have assumed ~bB= Qff~, where these latter internal friction values are that corresponding to the background curves of Fig. 4(B). This assumption is correct since, in the present experiments, q~B= Qffl<< 1 [25]. A fairly good agreement is found for the F-doped specimens. The comparison between the experimental and theoretical [equation (11)] creep data, could not be done directly in the case of the undoped material, for which torsional creep data were not available. The results in Fig. 12 suggest that the internal friction back-grounds are, in the present materials, the consequence of an irreversible (plastic) component of strain built up at the grain boundaries during the measurements at increasing temperatures. The microscopic origin of such a plastic deformation in the glassy-SiO2 phase is presently unknown. Some recent studies by small-angle neutron scattering experiments on silicate ceramics containing glassy phase at the grain boundaries [44] have suggested that very small cavities (i.e. not easily detectable even by high-resolution microscopy) can nucleate rapidly within the glassy films at a very early stage of the entire cavitation time. Although further experimental work is required for clarifying the microplastic mechanisms occurring in the present materials under internal friction/creep experiments, we argue here that, according to the "open structure" of the glass SiO2 interfaces containing F atoms [Fig. 13(A)], cavities of about 10/~ should be necessarily formed. Rupture of adjacent Si--O bonds under even small "elastic" short-range slips is likely to give rise to slit-like cavities whose dimension would be of a couple of SiO~- tetrahedra. Although these cavities may have not enough time to coalesce forming larger (observable) damages, their formation can explain

PEZZOTTI et al.: VISCOUS BEHAVIOR OF INTERFACES

Fig. 13. Micromechanism of cavity formation proposed in the present study to relate the "open structure" of the SiO2 film (due to the presence of F atoms) to the measured drop-down in the apparent grain-boundary viscosity with increasing the F-content. The average displacement, U, is still within the "elastic" range of deformation of the adjacent grains and of the order of one SiO4 tetrahedron, Symbols are the same as that in Fig. 2. the drop-down in the measured viscosity of the grain boundary film. According to this process [schematically shown in Fig. 13(B)], the number of cavities inside the boundaries will be directly increasing with increasing amount of F in the SiO2 structure. Hence, this model would also allow one to explain why the ~bB values increase with increasing the macroscopic creep strain and, ultimately, why the present internal friction and creep data can be fitted by the same Arrhenius equation. 5. CONCLUSION Internal friction and torsional creep experiments were conducted on a model Si3N4/SiC material up to temperature close to the melting point of the intergranular phase. This simple material contained only a few percent of glassy SiO2 at both the grain and the phase boundaries. In order to systematically decrease the intrinsic viscosity (i.e. increase the diffusivity) of the SiO2 phase, modifier F atoms which, segregated at the boundaries, formed non-bridging S i - - F bonds in the glassy structure, were added for increasing

4369

amounts up to about 5.8 wt% of the SiO 2 content. Detailed characterizations by HREM, A F M and analytical microscopy, allowed determining precisely both the geometry and the composition of the phase and the grain boundaries. It has been shown that the damping temperature curves of all materials consist generally of a grain-boundary peak superimposed on an exponential-like background, increasing continuously with increasing temperature. The peak, of a common (anelastic) diffusive origin, showed a linearly decreasing activation energy and was shifted to lower temperatures with increasing F content. The background, higher for increasing F contents, was found instead to be of viscoelastic (irreversible) nature. Torsional creep tests, conducted inside the same apparatus used for the internal friction experiments, helped to identify a common origin between the creep plastic strain and the internal friction background curve which could be expressed by the same Arrhenius equation. Exploiting the present precise microstructural characterizations, providing information up to the sub-nanometer scale, a micromechanical model including sliding and cavity formation at the boundaries was proposed for explaining both the anelastic relaxation phenomenon, responsible for the internal friction peak, and the viscoelastic behavior of the grain-boundary phase under stresses applied for prolonged times. Finally, this study suggests that the internal friction technique, when applied up to sufficiently high temperatures, can provide unique insights for characterizing the micromechanical response of the grain boundary phase of Si3N4 ceramics. Acknowledgements--The Authors gratefully thank Pro-

fessor M. Sakai for the critical review of the manuscript. Part of this work has been supported by the Mitsubishi Foundation.

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