High-Temperature Rheology of Calcium Aluminosilicate (Anorthite) Glass-Ceramics under Uniaxial and Triaxial Loading

J. Am. Ceram. Soc., 84 [11] 2617–24 (2001)

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High-Temperature Rheology of Calcium Aluminosilicate (Anorthite) Glass-Ceramics under Uniaxial and Triaxial Loading Balakrishnan G. Nair*,† and Reid F. Cooper* Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, Wisconsin

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David Bruhn and David L. Kohlstedt* Department of Geology and Geophysics, University of Minnesota-Twin Cities, Minneapolis, Minnesota The high-temperature creep behavior of two fine-grained (⬃3 ␮m) anorthite-rich glass-ceramics was characterized at ambient pressure and under a confining pressure of ⬃300 MPa. Experiments were done at differential stresses of 15–200 MPa and temperatures of 1200°–1320°C. Of the two materials, one had a tabular (lathlike) grain structure with finely dispersed second phase of mullite, mostly in the form of ⬃3–5 ␮m grains comparable to that of the primary anorthite phase, whereas the other had an equiaxed grain morphology with fine (⬃400 nm) mullite precipitates concentrated at the anorthite grain boundaries. The results of creep experiments at ambient pressure showed that the material with the tabular grain structure had strain rates at least an order of magnitude faster than the equiaxed material. Creep in the tabular-grained material at ambient pressure was accompanied by a significant extent of intergranular cavitation: pore-volume analysis before and after creep in this material suggested that >75% of the bulk strain was due to growth of these voids. The equiaxed material, in contrast, showed a smooth transition from Newtonian (n ⴝ 1) creep at low stresses to non-Newtonian behavior at high stresses (n > 2). Under the high confining pressure, the microstructures of both materials underwent significant changes. Grain-boundary mullite precipitates in the undeformed, equiaxed-grain material were replaced by fine (⬃100 nm), intragranular precipitates of silliminate and corundum because of a pressure-induced chemical reaction. This was accompanied by a significant reduction in grain size in both materials. The substantial microstructural changes at high confining pressure resulted in substantially lower viscosities for both materials. The absence of mullite precipitates at the grain boundaries changed the behavior of the equiaxed material to non-Newtonian (n ⴝ 2) at a pressure of ⬃300 MPa, possibly because of a grain-boundary sliding mechanism; the tabular-grained material showed Newtonian diffusional creep under similar conditions. I.

F

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the high-temperature, low- to moderate-differential-stress conditions pursued for application of such composites, creep resistance of the matrix becomes an important element of component design.3,4 Therefore, there is a critical need to comprehend the rheology of the unreinforced matrix. Furthermore, deformation experiments on anorthite aggregates help to characterize the dynamics of natural deformation of plagioclase-containing rock in the earth’s crust. Although a considerable amount of work has been done on the deformation of natural granitic and anorthositic specimens,5 because natural rocks have complex chemistries and microstructures, it remains problematic to extrapolate these results to other assemblages. An alternate approach, then, is to study the rheology of engineered, synthetic aggregates having controlled compositions and microstructures. Barber6 suggests that the steady-state strain rate (ε˙ ss) of a crystalline aggregate can be expressed as ˙ε ss ⫽ ˙εss共␴,⌶共ε,˙ε兲,P,T兲

(1)

where ␴ is the differential stress (␴ ⫽ –(␴1 – ␴3)), P the hydrostatic pressure, T the absolute temperature, and ⌶ an internal state variable that characterizes the microstructure. Thus, ⌶ is a function of the strain and strain rate as well as material properties, such as grain size (d), hydroxyl-ion concentration or activity (aOH–), and distribution of secondary phases. In recent years, several studies have been reported in the literature on creep of anorthite-based ceramics.7–9 The earliest reported work was conducted by Montardi7 on synthetic, polycrystalline anorthite-rich aggregates, fabricated by cold pressing and sintering of An98‡ grains obtained from crushed rock. For this fine-grained anorthite (d ⬍ 25 ␮m), a distinct transition from Newtonian/diffusional creep (ε˙ ss ⬀ ␴1/d3; Coble creep11) at lower stresses to power-law creep (ε˙ ss ⬀ ␴3/d0; dislocation-controlled creep) at higher stresses is observed. Power-law creep is generally attributed to the motion of lattice dislocations.12 Diffusional creep has a thermal activation energy (Q) of ⬃740 kJ䡠mol⫺1, whereas power-law creep has a Q of ⬃1100 kJ䡠mol⫺1. Such a transition also has been reported by Wang et al.9 in a similar material (polycrystalline aggregate hot-pressed from anorthite glass). In a later study reported by the same group,13Q for diffusional creep has been reported to be a strong function of the water content (i.e., the concentration of OH⫺) in the aggregate: Q increases from ⬃370 kJ䡠mol⫺1 for specimens with high OH⫺ concentration (⬎1000 ppm H/Si) to ⬃570 kJ䡠mol⫺1 for “dry” specimens (⬍100 ppm H/Si). Although this value of Q for diffusion creep is lower than that reported by Montardi,7 the Q observed for dislocation creep (⬃1150 kJ䡠mol⫺1) agrees well with the earlier study. Mercer and Chokshi8 have

Introduction

glass-ceramics and glass-ceramics having other tektosilicates as the majority phase have been applied heavily as matrix materials in fiber-reinforced ceramic composites.1,2 Under ELDSPAR

S. M. Wiederhorn—contributing editor

Manuscript No. 188213. Received October 12, 2000; approved June 29, 2001. Supported in part by the National Science Foundation through Grant Nos. CMS-9414756 (Civil and Mechanical Systems Program in Mechanics and Materials) and EAR-9706213 (Earth Sciences Program in Geophysics). *Member, American Ceramic Society. † Currently at Ceramatec, Inc., Salt Lake City, UT 84119.

‡ Plagioclase feldspars constitute a complete solid solution between NaAlSi3O8 (albite; Ab) and CaAl2Si2O8 (anorthite; An).10 Nomenclature in the earth-sciences literature is to describe plagioclase according to either its Ab or An content. An98 thus represents a composition that is 98 mol% An and 2 mol% Ab.

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reported that fine-grained synthetic aggregates of an anorthitebased glass-ceramic (CAS-II, Corning Incorporated, Corning, NY) show Newtonian creep with large-scale cavitation under compression at ambient pressure, leading the authors to suggest solution– precipitation creep as the rate-controlling mechanism. Although these studies, along with previous work in our group,3 have laid a foundation for understanding the rheology of polycrystalline anorthite, variations in behavior of material so revealed— e.g., factors of 102 differences in absolute strain rates for the same conditions of T and ␴ for materials believed to be similar microstructurally (see Refs. 3 and 8)—suggest much room for further investigation. The current experimental work has been directed at studying the plastic rheology of two different, finegrained anorthite aggregates that, despite having very similar chemistries, produce distinctly different microstructures. Relative to Eq. (1), this work examines the creep response at high temperatures (T ⫽ 1200°–1320°C) and at medium to high differential stresses (–(␴1 – ␴3) ⬇ 20 –200 MPa) as well as probes the impact of confining pressure (P ⬇ 0.1 MPa and P ⬇ 300 MPa). II.

Materials and Methodology

The anorthite-rich aggregates used in this study were fabricated by the uniaxial hot pressing and consequent crystallization of pulverized glass powder. Commercial-grade oxide raw materials (many having a purity higher than analytical-reagent (AR) grade) were used, and the component powders were mixed by tumbling, melted in air in a platinum crucible at 1650°C for 16 h, quenched from the melt into a cold-water bath (drigaged), and pulverized (zirconia media ball milling followed by fluid energy milling) to ⬍10 ␮m dust. Hot pressing was accomplished in a molybdenumlined graphite die in flowing argon for 10 min at 1350°C under a stress of 15 MPa. Two different chemical compositions were considered in this investigation: CAS-II and CAS-III (Corning Incorporated). The chemical compositions of both processed polycrystalline solids were analyzed using X-ray florescence spectroscopy, and the results are indicated in Table I along with the calculated chemical composition for stoichiometric anorthite. The rules for calculation of a phase assembly in an igneous rock were followed,14 and the distribution of phases based on the compositions indicated that both materials would constitute ⬃87 vol% anorthite and ⬃10 vol% mullite. Powder X-ray diffractometry (XRD) of crushed, as-hot-pressed material indicated that both aggregates had anorthite and mullite as the primary phases with the ratio of peak intensities ⬃8:1. The As2O3 added to CAS-II acted as a fining agent for the glass; however, there was no unique arsenic-rich phase apparent. CAS-II and CAS-III had ⬃5% and 4% porosity, respectively, in the as-processed state, as estimated from image analysis of low-magnification optical micrographs. The pores were dispersed and approximately the same size as the grains. Despite very similar chemistries, scanning (secondary) electron images (SEIs) of as-hot-pressed, etched specimens of CAS-II and CAS-III reveal significant differences in microstructure (Fig. 1). CAS-II is a two-phase mixture of anorthite with mullite. The anorthite grains have a randomly oriented, tabular (lathlike) morphology, similar to the structure of plagioclase in many extrusive igneous rocks; energy dispersive spectroscopy (EDS)

Table I. Bulk Composition of Anorthite Glass-Ceramics Oxide

CAS-II†

SiO2 Al2O3 CaO MgO ZrO2 As2O3

39.8 40.3 16.9 0.4 2.3 0.3

†

Composition (wt%) CAS-III† Anorthite (CaAl2Si2O8)‡

41.6 40.6 17.5 0.3 0.1

43.2 36.7 20.1

X-ray fluoresence spectroscopy (XRAL Labs, Hamilton, Ontario). ‡Theoretical.

Fig. 1. SEI images of undeformed, polished, and etched (37% HCl, 10 min) specimens of (a) CAS-II and (b) CAS-III. Anorthite in CAS-II has a tabular (lathlike) structure, whereas CAS-III has a more equiaxed grain structure. Mullite grains appear in CAS-III as the fine (⬃400 nm) precipitates on all grain boundaries. Mullite in CAS-II is widely distributed as grains of similar size to the anorthite.

imaging reveals that the mullite grains are, for the most part, distributed among the anorthite grains with a grain-size comparable to the anorthite grains, although some mullite is distributed as ⬍500 nm precipitates within anorthite grains and along grain boundaries. Line-intercept analysis15 of micrographs of CAS-II give a grain-size of d ⫽ 3.3 ⫾ 1.4 ␮m, where the relative magnitude of the uncertainty (standard deviation of means) indicates the distinct aspect ratio (⬃2) of the grains. CAS-III, in contrast, has an equiaxed morphology with d ⫽ 3.8 ⫾ 0.4 ␮m. Mullite in CAS-III is concentrated at the anorthite grain boundaries in the form of precipitates ⬃400 nm in diameter. The microstructures of both undeformed materials show a significant

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amount of twinning within the individual grains, which is a common feature in plagioclase.16 Creep experiments were conducted in two different apparatus. Ambient pressure, low-differential-stress experiments (␴ ⫽ 15– 45 MPa) were conducted in a dead-weight creep rig in an atmosphere of either flowing argon or flowing dry air. Compression specimens (approximate dimensions of 3 mm ⫻ 3 mm ⫻ 6 mm) were cut from the hot-pressed ceramic billet. The apparatus is described in detail elsewhere.4 Its unique features include a frictionless, dynamic oil-seal for the top piston, which reduces errors introduced in stress calculations due to frictional forces. Temperatures in these experiments ranged from 1300° to 1320°C. The small specimen height (⬃6 mm), combined with the maintenance of a uniform hot zone ⬃4 –5 cm in length contributed to a virtually constant temperature profile across the length of the specimen. Vertical translation of a type-C thermocouple, whose tip was displaced horizontally by 3 mm from the specimen, revealed the temperature change across the length of the specimen to be ⬍0.5°C. The accuracy of the temperature measurement was estimated to be 0.5°C; during a test, the fluctuation in temperature was always within ⫾1°C. The specimens were annealed at the test temperature for 4 –5 h before the application of load to ensure equilibrium among the phases. A compressive stress was applied to the specimens by addition of a precalculated weight to a load pan attached to the top piston. The downward displacement of the top piston was monitored using a pair of direct-current differential transducers (DCDTs) mounted in parallel. Digital displacement– (voltage–) time data were collected using data-acquisition software and stored on a microcomputer. High-stress experiments were performed in an internally heated, servo-controlled, triaxial deformation apparatus that included an internal load cell.17 Specimens were core drilled from the hot-pressed ceramic billets and ground to form cylindrical specimens 8 –9 mm in diameter and 15–18 mm in length. A deformation specimen was positioned between specially designed alumina spacers and pistons, and this whole assembly was enclosed in a close-fitting nickel jacket. ⫺␴2 and ⫺␴3 were applied by pressurizing the specimen chamber with argon gas to a confining pressure of ⬃300 MPa. Because the gas temperature and pressure were related, maintaining the pressure was crucial to maintaining the temperature and, thus, ensuring a useful creep test. In these experiments, the fluctuations in pressure were always less than ⫾10 MPa, and the corresponding fluctuations in temperature were less than ⫾2°C; the accuracy of the temperature measurement was ⫾2°C. The internal and external load cells were monitored and controlled via a servo-actuator (Model 8500, Instron Corp., Canton, MA); the precision of the load measurements was within 0.05 kN. The high-pressure deformation experiments were conducted at constant load with the loads corresponding to initial differential stresses ((⫺(␴1 – ␴3)) ranging from 30 to 225 MPa. Three to six constant-load tests were performed at each temperature (in the range of 1200°–1300°C) to determine the stress exponent, after which the temperature was changed and the procedure was repeated, so as to evaluate the activation energy. Data analysis was conducted using an algorithm that corrected for the mechanical energy dissipated by flow of the nickel jacket. After each experiment, the nickel jacket was removed by dissolving in aqua regia. In an effort to characterize the deformation mechanisms predominant in these materials, microstructural/chemical analyses using optical/electron microscopy and XRD were conducted to complement the rheological data. III. Experimental Results (1) Experiments at Ambient Pressure The experimental data were analyzed using the standard, semiempirical equation that describes steady-state creep as a thermally activated process.18 The steady-state strain rate can be expressed as ˙ε ss ⫽ ⌶␴n exp

冉 冊 ⫺Q RT

(2)

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where ⌶ is a constant, ␴ the applied stress, n the stress exponent, Q the activation energy for creep, R the universal gas constant, and T the absolute temperature. The results of creep experiments conducted at ambient pressure are shown in Fig. 2. Under the ␴,T conditions studied, CAS-II and CAS-III showed a transition behavior (see Fig. 2(a)). At low stresses (␴ ⬇ 20 MPa), the materials showed Newtonian behavior (i.e., n ⬇ 1). n increased with stress, however, and at stresses of ⬃40 MPa, the behavior was distinctly non-Newtonian with n ⬎ 2 for CAS-II and CAS-III. The activation energy for both materials also increased with ␴ (see Fig. 2(b)): For CAS-II, Q increased from ⬃900 kJ䡠mol–1 at 15 MPa to ⬃1100 kJ䡠mol–1 at 35 MPa; for CAS-III, Q increased from ⬃600 kJ䡠mol–1 at 20 MPa to ⬃810 kJ䡠mol–1 at 40 MPa. The strain rates for CAS-II were always more than an order of magnitude higher than those observed for CAS-III under similar temperatures and stresses. (2) Experiments under Confining Pressure (P ⬇ 300 MPa) Under a confining pressure of 300 MPa, the rheologies of CAS-II and CAS-III were very different from that observed at 1

Fig. 2. Creep data for CAS-II and CAS-III at ambient pressure. Transition from Newtonian to non-Newtonian behavior appears in both materials: (a) variation of strain rate with stress and (b) variation of activation energy with stress.

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atm. The results of these experiments are shown in Fig. 3. For similar ␴,T, the absolute strain rates observed for CAS-II and CAS-III were higher under the confining pressure by at least an order of magnitude. Moreover, the rheology was characterized by distinctly different values of n and Q. The creep behavior of CAS-II was essentially Newtonian (n ⬇ 1) under these conditions over a wide range of differential stress (30 –170 MPa), and there was no indication of a transition to non-Newtonian behavior at higher stresses (see Fig. 3(a)). CAS-III, in contrast, clearly showed a non-Newtonian rheology with a constant n ⬇ 2 (see Fig. 3(b)). A specimen of CAS-III annealed at 1300°C for a week at ambient pressure before its being subjected to deformation at P ⫽ 300 MPa showed behavior virtually identical to that of the nonannealed material under similar ␴,T conditions. The activation energy for creep of CAS-II under confining pressure was ⬃300 ⫾ 40 kJ䡠mol⫺1 (Fig. 3(c)), much lower than that observed at 1 atm (see Fig. 2(b)), while Q for creep of CAS-III was ⬃640 ⫾ 30 kJ䡠mol⫺1. (3) Characterization: Optical Microscopy, Electron Microscopy, and X-ray Diffractometry CAS-II deformed at 1 atm showed a significant increase in porosity: image analysis of the optical micrograph of the deformed specimen presented in Fig. 4(b) suggests that 8% plastic strain resulted in a specimen having 24 vol% porosity. Because a specimen subjected to the same temperature for approximately the same amount of time (4 h) showed only 6% porosity (see Fig. 4(a)), most of the cavitation was clearly creep induced. CAS-III,

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however, did not show an observable change in porosity after deformation at ambient pressure. For specimens deformed under the high confining pressure, however, optical microscopy revealed a significant decrease in porosity with CAS-II ⬃2 vol% porous and CAS-III ⬃1 vol% porous. SEI images of deformed CAS-II specimens are presented in Fig. 5. Figure 5(a) shows a micrograph of a CAS-II specimen deformed at 1 atm to 8% total strain, from a nominally coherent region (i.e., not having a large pore volume): The material deformed at 1 atm showed no significant differences in grain morphology as compared with the undeformed specimen (see Fig. 1(a)). In the ambient-pressure-deformed specimen, there was considerable evidence for cavity nucleation at the grain-boundaries. In several areas of the micrograph, grains could be seen clearly separated from their nearest neighbors by intergranular voids. The microstructure of the CAS-II specimen deformed at high confining pressure was significantly different (Fig. 5(b)): There was no evidence of the intergranular cavitation observed in CAS-II deformed at ambient pressure, and the grain size was considerably smaller (1.8 ⫾ 0.3 ␮m). Moreover, a finely dispersed phase had precipitated within the grains in the form of particles ⬃200 nm in size: EDS concentrating on these particles revealed them as CaO-free aluminosilicates. SEI images of deformed CAS-III are presented in Fig. 6. As in the case of CAS-II, the microstructure of the CAS-III specimen deformed at 1 atm (Fig. 6(a)) was essentially the same as that of

Fig. 3. Stress–strain rate relationship for CAS-II and CAS-III at P ⬇ 300 MPa: (a) CAS-II and (b) CAS-III ((▫) CAS-III response for a specimen annealed at 1300°C, in air, at ambient pressure, for a week before the high-P deformation experiment). (c) Arrhenius plot for creep of CAS-II and CAS-III at P ⬇ 300 MPa.

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Fig. 4. Optical micrographs of a CAS-II specimen (a) annealed at 1300°C for 4 h and (b) deformed at ambient pressure to ε ⬇ 0.08. Total time at temperature was ⬃4 h. Figure illustrates extensive cavitation that occurs during creep at ambient pressure. Image analysis indicates that the porosity of this specimen is ⬃24 vol%.

the undeformed CAS-III (see Fig. 1(b)). The grain-boundarysegregated mullite phase was present, and there was no obvious change in the morphology of these particulates. However, the CAS-III specimen deformed at 300 MPa had a significantly different microstructure: the grain size was finer (2.4 ⫾ 0.5 ␮m), and there was no indication of precipitates at the grain boundaries (Fig. 6(b)). The grain-boundary precipitates were replaced by a widely distributed, CaO-free intragranular aluminosilicate phase essentially identical to that in the CAS-II specimen deformed at high confining pressure. Comparison of the X-ray spectra for powdered, as-hot-pressed CAS-III with that of a specimen deformed at 300 MPa indicated new peaks in the spectrum of high-temperature-deformed material that corresponded to corundum (␣-Al2O3). IV.

Discussion

Scrutiny of the creep data on CAS-II and CAS-III at ambient and high confining pressures reveals behavioral trends that need to be addressed explicitly to gain a comprehensive understanding of the rheology of anorthite-based glass-ceramics. (1) The viscosity of these fine-grained anorthite aggregates is strongly affected by pressure. The absolute strain rates observed for CAS-II and CAS-III are much higher (by at least an order of magnitude) under confining pressure than under similar ␴,T

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Fig. 5. SEI images of deformed CAS-II. (a) Specimen deformed at ambient pressure to ε ⬇ 0.08. Lathlike microstructure of CAS-II leads to the opening of intergranular voids during deformation, shown as wedge cracks in the micrograph. (b) Specimen deformed at P ⫽ 300 MPa to ε ⬇ 0.20. Finer grain size as compared with the specimen deformed at ambient pressure as well as the precipitation of fine (⬍200 nm) intragranular particles.

conditions at ambient pressure. Furthermore, conventional considerations of pressure dependence of creep predict that the plastic strain rates of polycrystalline solids are lower at high-pressure because of increases in activation energy (i.e., because of the effect of a positive activation volume19,20). This suggests that one of the basic assumptions used in these treatments, i.e., the maintenance of a constant structure, is not valid in the case of these fine-grained polycrystalline anorthite aggregates. (2) There is a clear change in mechanisms of deformation of CAS-II and CAS-III with the increase in confining pressure: n and Q show significant variation for both materials as a function of the confining pressure. CAS-II and CAS-III display a Newtonian (n ⫽ 1) to non-Newtonian (n ⬎ 2) transition at differential stresses ⬍40 MPa at ambient pressure, with corresponding increases in activation energy with stress. At high confining pressure, however, there has been no indication of such a transition: Here, CAS-II shows Newtonian creep to very high levels of differential stress (⬃130 MPa), and CAS-III shows a very steady n ⫽ 2 in the differentialstress regime of 30 –220 MPa. (3) Despite the similarities in composition and phase constitution, the rheologies of CAS-II and CAS-III are strikingly

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the observation seems counterintuitive; it would appear to indicate the reverse of the Oswald ripening process,21 i.e., the larger particles at the grain boundaries (300 – 400 nm) become smaller (and disappear), whereas the smaller intragranular precipitates become larger in size. However, this contradiction can be resolved if a phase transformation occurs under the application of a high confining pressure. XRD of the high-P CAS-III specimens indicates the presence of corundum; such can occur only in these materials by the reaction of mullite to form one of the high-P polymorphs of Al2O3–SiO2. (Because triclinic anorthite produces many peaks, and the XRD spectra for mullite and the three Al2O3–SiO2 compounds— kyanite, andulusite, and sillimanite— are very similar, it is not possible to confirm or deny the presence of the polymorph in the high-P specimens; thus, we have to consider the formation of corundum to verify the occurrence of this phase transformation.) Sillimanite is the stable polymorph of the 1:1 aluminosilicate compound at 1300°C and 300 MPa; the reaction is P,T

Al6Si2O13(mullite) O ¡ 2Al2SiO5(sillimanite) ⫹ Al2O3(corundum)

Fig. 6. SEI images of deformed CAS-III. (a) Specimen deformed at ambient pressure to ε ⬇ 0.06; no significant change in microstructure is observed compared with undeformed CAS-III. (b) Specimen deformed at P ⬇ 300 MPa to ε ⬇ 0.015. Finer grain-size as compared with the specimen deformed at ambient pressure, loss of grain-boundary precipitates, and their replacement by the intragranular precipitates, similar to those seen in CAS-II deformed at high-P are shown.

different. Under any set of ␴,T,P conditions, the strain rates of CAS-II are always at least an order of magnitude higher than those of CAS-III. We target these issues in the following sections. (1) Impact of High Confining Pressure on the Rheology of Anorthite Glass-Ceramics The discontinuity in the magnitudes of strain rates of CAS-II and CAS-III in the deformation experiments under high confining pressures compared with the creep experiments at ambient pressure can be understood in terms of Eq. (1). However, contrary to the normally considered direct effect of pressure, which is to lower the absolute strain rates due to a pressure-induced increase in activation energy, the impact of pressure in our anorthite aggregates is to affect the microstructure of the materials (i.e., to change ⌶) in such a way as to subjugate the activation volume effect. Specimens of CAS-II and CAS-III subjected to a high-P, high-T environment experience a refinement in grain size and the precipitation of fine (⬍200 nm in diameter) aluminosilicate particles within the grains. In the case of CAS-III, this structural (and chemical) reaction is accompanied by a near-total removal of the mullite precipitates from the anorthite grain boundaries. If the internal precipitates in the high-P specimens are also mullite, then

(3)

As written, this reaction results in a ⬃7% decrease in volume (⌬V). The removal of the mullite grain-boundary phase has a tremendous impact on the absolute strain rates of the anorthite aggregates. The mullite particulates pin the grain boundaries in CAS-III at ambient pressure. The presence of the particulates obstructs the diffusion of matter along the grain boundaries and grain-boundary dislocation mobility, resulting in the relatively low strain rates for diffusional (Newtonian) creep and for grain-boundary sliding by a (secondary grain-boundary) dislocation mechanism.22 The removal of these grain-boundary particles by the high-P reaction results in the absolute strain rates being significantly higher than those at ambient pressure. As well as the specific effect due to the removal of mullite particles from the grain boundaries in CAS-III, the reduction in grain size in both materials at high-P—presumably related to the reaction creating intragranular precipitates— contributes directly to an increase in strain rate. The specific mechanisms that operate in CAS-II and CAS-III at ambient and high pressure are addressed immediately below. At this point, it is sufficient to note that a decrease in grain size by a factor of 2 (similar to that seen in CAS-II, where the mean grain size decreases from 3.3 to 1.8 ␮m) can cause an increase in absolute strain rate by a factor of 8 for a grain-boundary diffusion-controlled mechanism. (2) Deformation Mechanisms in Anorthite Glass-Ceramics: Effect of Confining Pressure (A) CAS-III: The differences in microstructure described above also result in changes in the rate-controlling mechanism of creep in the anorthite glass-ceramics. At ambient pressure, the behavior of CAS-III is characterized by a familiar Newtonian to non-Newtonian (n ⬎ 2) transition, well recognized in previous work.3,7,13 The activation energy, Q ⬇ 600 ⫾ 30 kJ䡠mol–1, observed for Newtonian creep (n ⫽ 1) at stresses ⬍30 MPa also agrees well with reported values as well as with previous work in our group.3 Newtonian behavior is characteristic of creep by ionic diffusion that is rate limited by transport either through individual grains (Nabarro–Herring creep; ε˙ ss ⬀ d–2)23,24 or through the grain boundaries (Coble creep; ε˙ ss ⬀ d–3).11 Recent work on dry, polycrystalline anorthite suggests that it is the latter mechanism that is active,13 because the grain-size exponent has been found to be 3. Although there is no direct data on activation energy for grain-boundary diffusion of Al3⫹ or Si4⫹ ions in anorthite, experimental studies of lattice diffusion in anorthite show activation energy values from 520 to 630 kJ䡠mol–1 for Al3⫹–Si4⫹ interdiffusion.25,26 In general, activation energy for grainboundary diffusion is only slightly lower than that of lattice diffusion. Our activation energy values in the low-stress regime are

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High-Temperature Rheology of Calcium Aluminosilicate Glass-Ceramics under Loading

in good agreement with the values for Al3⫹–Si4⫹ interdiffusion and much higher than those for diffusion of Ca2⫹ (⬃290 kJ䡠mol⫺1)27 or O2⫺ (100 –130 kJ䡠mol–1)28 in feldspars; therefore, we can conclude that diffusional creep is rate limited by the transport of the tetrahedral cations in these materials. Based on Ref. 13 and the fine-grained nature of our anorthite aggregates, we believe that creep of CAS-III under low-stress, ambient-pressure conditions is controlled by grain-boundary diffusion of tetrahedral species. Our previous transmission electron microscopy (TEM) studies on the CAS-III matrix in CAS-III/SiC composites show no evidence for a glassy phase on the anorthite grain boundaries.29,30 Indeed, the matrix in the composite has a greater chance of a glassy grain-boundary phase, because the reaction between fiber and matrix introduces additional SiO2 into the system. The absence of such a glassy phase is consistent with our interpretation of creep controlled by grain-boundary diffusion. In our ambient pressure experiments, at higher stresses, nonNewtonian rheology is possibly due to dislocation-controlled creep. The occurrence of dislocation-controlled creep in anorthite under high stresses has been confirmed recently through TEM studies of anorthite/SiC composites subjected to high-temperature creep.31 The transition from diffusional creep to dislocation creep with an increase in temperature at constant stress results specifically because of the higher activation energy of dislocation creep. Although the maximum activation energy we have observed for CAS-III is ⬃810 kJ䡠mol⫺1 at ␴ ⫽ 40 MPa, Q increases with ␴, and the transition to dislocation creep is clearly not complete. Thus, our result is not in conflict with the values of Q ⬇ 1100 –1150 kJ䡠mol–1 reported for non-Newtonian creep behavior (n ⫽ 3, most likely dislocation creep) in anorthite.7,13 The higher value of Q for dislocation creep results from the fact that Q is a sum of two terms in ceramics, Q ⫽ QF ⫹ QD, where QF describes the energy involved in the formation of charge-neutral (i.e., perfect) jogs on dislocations, and QD describes the temperature sensitivity of lattice diffusion of the least-mobile ionic species in the compound.18 Moreover, QD is higher than the activation energy for grainboundary diffusion for most species. The very steady n ⫽ 2 observed for creep of CAS-III under a confining pressure of 300 MPa, suggests that some grain-boundary sliding mechanism is active. Sliding is accomplished by motion of dislocations localized near the grain boundaries (i.e., secondary grain-boundary dislocations),32 or through an interface reactioncontrolled mechanism due to grain-boundary particles acting as obstacles to the motion of boundary dislocations.33 However, the segregated grain-boundary mullite phase is almost completely removed during the experiments at high pressure. The observed value of Q (⬃640 kJ䡠mol⫺1) in our deformation experiments on CAS-III under high confining pressure is again in good agreement with that expected for lattice diffusion of the tetrahedral cations.25 (B) CAS-II: Although the rheology of CAS-II seems similar to that of CAS-III at ambient pressure, there are important differences in absolute strain rates, in the magnitude of Q, and, most importantly, in the observed microstructure. Even in the low-stress/Newtonian regime (␴ ⬇ 15 MPa), the activation energy for creep of CAS-II is significantly higher (⬃900 kJ䡠mol–1) than those reported for diffusional creep in anorthite (570 –730 kJ䡠mol⫺1). This discrepancy can be attributed directly to the extensive cavitation that occurs during creep of CAS-II at ambient pressure. Lange and Davis34 have shown that cavitation can result in a higher value of activation energy for creep of ceramics. In their work, the activation energy of a Si3N4-based material that exhibits pure diffusional creep is 660 kJ䡠mol⫺1, whereas the material shown to exhibit extensive cavitational creep has an activation energy of 1080 kJ䡠mol–1. The higher activation energy is believed to be due to the energy required for creation of new surfaces (i.e., creation of the new cavities). Such cavitation has been observed previously in compressive creep of several finegrained ceramics:8,35,36 Creep enhanced by such cavitation is associated with non-Newtonian behavior (n ⬎ 3).37 The tabular grain structure of CAS-II results in localized stress concentrations at the grain boundaries during creep: such stress inhomogenities

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result in nucleation of cavities at the grain boundaries and subsequent growth of these cavities through the diffusional transport of matter away from the grain boundaries. Such cavities appear in the SEI image of the CAS-II specimen deformed at ambient pressure (see Fig. 5(a)), specifically in the form of wedge cracks between the lathlike grains. The contribution of such cavitation to bulk specimen strain measured during creep experiments is difficult to estimate accurately. Weiderhorn et al.38 have qualitatively explained cavitational effects during tensile creep of ceramics as analogous to dilatational effects during flow of granular materials, such as sand. A simple analysis by Raj39 suggests that a third of the total volume change due to cavitation contributes to the strain in the axial direction. However, this is probably an overestimate, because it is unlikely that the strain in the axial and radial directions are partitioned equally. Lofaj et al.40 have assumed that, in compressive creep, cavitation contributes only to strain in the radial direction, and, in tensile creep, cavitation contributes only to strain in the axial direction. However, this assumption is probably an oversimplification. In fact, Lofaj et al. mention that their assumption that cavitation in tensile creep has no contribution to the radial strain component is not supported by the experimental evidence on tensile creep of Si3N4 by Xu and Solomon:41 by direct measurement, 25% of the cavitation in tension had to be partitioned to axial strain. Considering this lack of appropriate analytical tools to quantify the contribution of cavitation to creep strain, a quantitative analysis is not possible at this time. However, the significant cavitation accompanying compressive creep in these materials and the similarity of cavity volume fractions and creep curves to tensile creep of Si3N4 accommodated by cavitation suggests that cavitation is important in creep of these materials. The behavior of the CAS-II specimens at high P—Newtonian creep with Q ⬇ 300 kJ䡠mol⫺1— could be due to the presence of a residual glass phase in CAS-II. Arsenic has been added to CAS-II during processing as a fining agent for the glassmelt. As incompatible elements in mullite and anorthite, As3⫹,5⫹ and Mg2⫹ could be preferentially concentrated in a residual glass phase during crystallization. Such segregation of arsenic and magnesium into the glass phase could cause the evolution of the tabular microstructure of anorthite grains seen in CAS-II: Residual glass, confined to the triple junctions of anorthite aggregate, could also result. Recent TEM studies by Dimanov et al.42 suggest that anorthite aggregates processed similarly to the materials in this study show a residual glassy phase only at the triple junctions; two-grain boundaries are free of an amorphous phase. The extensive cavitation induced in CAS-II during creep at ambient pressure also suggests the presence of such a triple-junction glass phase: Lange et al.35 have shown that cavitation during compressive creep is significantly enhanced by residual glass. In fine-grained ceramics with a residual glass phase, solution– precipitation creep mechanisms are expected to rate limit the kinetics.43,44 The Newtonian behavior and low Q observed for high-P creep of CAS-II is consistent with solution–precipitation creep rate limited by transport of ions through the residual glass at three-grain junctions. Mercer and Chokshi8 have studied the creep behavior of a material with approximately the same chemical composition as the CAS-II in our experiments; their material was hot isostatically pressed (HIPed) to near full density before deformation. Intragranular precipitates have been observed on an SEM micrograph of the HIPed material, which suggests the completion of the pressure-induced reaction of mullite to sillimanite and corundum during HIPing. Intriguingly, the strain rates and creep observed on the HIPed material during creep at ambient pressure are similar to the strain rates seen in our high-P experiments: This result clearly reinforces that the impact of hydrostatic pressure is to affect the microstructure of the material.

V.

Summary and Conclusions

The following conclusions can be drawn from this study on creep of fine-grained CAS (anorthite) glass-ceramics.

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Journal of the American Ceramic Society—Nair et al.

(1) At ambient pressure, the rheologies of CAS-II (tabular anorthite morphology) and CAS-III (equiaxed anorthite morphology) are characterized by a transition from a Newtonian mechanism at low stresses to a non-Newtonian mechanism at high stresses. For CAS-II, this non-Newtonian behavior is simply due to the onset of cavitation: Most of the strain accumulated in the specimen is due to the nucleation and growth of cavities. For CAS-III, however, the transition to non-Newtonian behavior is due to a transition to dislocation-controlled creep at higher stress. The difference in behavior can be directly correlated to the microstructures of the two materials. (2) The rheology is strongly affected by confining pressure. At high P, the mullite precipitates are removed from the grainboundaries in CAS-III, and a finely distributed, ⬍200 nm sized phase—formed because of the pressure-induced reaction of mullite to sillimanite and corundum—is precipitated within the grains. Another important factor is the presence of an arsenic-rich triplejunction phase in CAS-II, which is absent in CAS-III. Because of the removal of the grain-boundary precipitates, CAS-III shows non-Newtonian (n ⬇ 2) behavior at high P, and the rate-limiting deformation mechanism is grain-boundary sliding accomplished by motion of grain-boundary dislocations. For CAS-II, under confining pressures, the intergranular cavitation mechanism that occurs at ambient pressure is suppressed, and the rate-controlling mechanism is Newtonian: Our data suggest solution–precipitation creep rate limited by intergranular transport of ions through a residual glass phase. Moreover, both materials show a refinement in grain size at high P that causes a further enhancement in the strain rates in the high-P experiments compared with those at 1 atm. Acknowledgments The glass-ceramic materials used in these experiments, while of our own design chemically, were fabricated at the Research and Development facility of Corning Incorporated, Corning, NY, and were provided to us by Dr. Kenneth Chyung. We thank Dr. Chyung, too, for helpful discussions and his continued interest in our work.

References 1

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