J. Am. Ceram. Soc., 94 [9] 2825–2833 (2011) DOI: 10.1111/j.1551-2916.2011.04424.x r 2011 The American Ceramic Society

Journal

Spark Plasma Sintering Kinetics of Pure a-Alumina Yann Aman,*,w,z,y Vincent Garnier,z and Elisabeth Djuradoy z

Laboratoire MATEIS UMR CNRS 5510, INSA Lyon, Universite´ de Lyon, Jean Capelle F-69621 Villeurbanne, France y

Laboratoire LEPMI UMR CNRS 5631, Grenoble INP, UJF, Domaine Universitaire, F-38402 Saint Martin d’He`res, France

The microstructure development of sintered alumina at different stages in the spark plasma sintering process has been investigated. Based on classical kinetics laws and adapted Coble creep models of hot pressing, the densification and grain growth kinetics were analyzed as a function of various parameters such as heating rate, sintering temperature, and dwell duration. It is found that sintering kinetics are greatly influenced by heating rates. The local temperature gradients at interparticle contacts during high heating rate can be from three to 10 times higher than in low heating rate cycles. Plastic yield might lead to instantaneous densification at an early stage of sintering. However, grain-boundary diffusion probably dominates at low heating rate whereas grain coarsening, in respect of thermal equilibrium establishment, is unavoidable with high heating rate during the initial-stage sintering at low temperatures. During the final-stage sintering, fast grain growth mechanisms such as surface diffusion and pore-controlled grain-boundary migration may dominate over densification controlled by grain-boundary sliding or lattice diffusion. The grain size–density trajectory corroborates that low heating rate is much favorable to achieve near full density with fine grain size at low sintering temperatures.

min) and moderate applied pressures (generally o100 MPa) due to the limited mechanical strength of graphite. Previous works have shown that unsuitable SPS conditions can yield heterogeneous microstructures with large grain sizes deteriorating the ceramics performance.5,7,8 In a recent investigation,8 the present authors have used a powerful statistical design to show that at a moderate constant pressure of 80 MPa, SPS heating rate and sintering temperature are the key parameters on the final density and grain size of spark plasma-sintered pure alumina. It was thus suggested that the microstructure development during SPS is controlled by the sintering kinetics and mechanisms. In a recent comparison study, Langer et al.9 suggested that during SPS and HP, densification of a-Al2O3 was controlled by grain-boundary diffusion. They attributed the beneficial SPS effect on densification to a higher total neck area at low temperatures caused by local temperature overshoot during the heating regime. In an other investigation based on a modified creep law of dense metals, Bernard-Granger and Guizard.10 proposed grain-boundary sliding accommodated by oxygen grain-boundary diffusion as the governing densification mechanism in SPS of a-alumina codoped with CaO and TiO2. Faced with the lack of extensive analysis of SPS sintering kinetics in the literature review, the aim of the present work is to report detailed evolution and analysis of microstructure development during SPS. For this purpose, existing analytical models of HP were adapted to SPS of undoped submicrometer a-alumina in order to establish sintering trajectories, densification, and grain growth mechanisms and kinetics, as a function of various SPS parameters such as heating rate, sintering temperature, and dwell duration.

I. Introduction

T

benefit of very fine-grained microstructures with submicrometer grain sizes and high density for obtaining components with improved hardness, wear resistance, strength, and optical performance is well known for alumina ceramics1 but hardly achieved with conventional sintering or one-step hot pressing (HP). Although high-purity grade of a-alumina nanopowders and increased green-state homogeneity provided by the shaping method2 are some necessary requirements but not sufficient, the sintering step remains the most critical processing step for obtaining high-performance polycrystalline alumina ceramics, because it greatly affects the microstructural evolution and the related properties. A recent emerging consolidation technique called spark plasma sintering (SPS) or field-assisted sintering technique has attracted the interest of many researchers because it offers the possibility to densify a wide range of various materials3,4 including alumina ceramics,5–11 while retaining the submicrometer structures at low sintering temperatures. In the SPS process, the powdered materials are loaded in a graphite die-punches system, then uniaxially pressed, and directly heated by pulsed direct currents passing through the graphite assembly. These specific SPS features allow high heating and cooling rates (up to 6001C/ HE

II. Experimental Procedure (1) Raw Materials A high-purity commercial corundum powder (BMA-15, 499.99% a-Al2O3, Baı¨ kowski Chemicals, Annecy, France) was used in the experiments. The as-received powder had an average particle size of 170 nm, and a specific surface area of 14 m2/g, as reported by the manufacturer. The raw powder was used directly, with no special treatment before SPS, although it has been shown previously that the green shaping method influences the SPS sintering behavior.11 An approximate amount of 2 g of powder was loaded in the SPS graphite die. Three samples were characterized for each sintering condition in order to ensure reproducibility of microstructural analysis. (2) SPS Conditions The SPS apparatus type HD P 25/1 (FCT Gmbh, Rauenstein, Germany) was used in the present investigation. The as-received powders were loaded in a 20 mm inner diameter graphite die, with a thermal insulating carbon felt to limit the heat radiation loss during the heating regime. Two full graphite punches were also used. The pulses pattern was constant and it consisted of two pulses lasting 10 ms, followed by a pause duration of 5 ms.

R. Bordia—contributing editor

Manuscript No. 28019. Received May 13, 2010; approved January 5, 2011. This work was financially supported by the Re´gion Rhoˆne-Alpes—MACODEV. *Member, The American Ceramic Society. w Author to whom correspondence should be addressed. e-mail: [email protected]

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The applied uniaxial pressure was constant to 80 MPa from the beginning of the heating step to the end of the dwell. It was generally observed that the samples are split into two pieces when the mechanical pressure is maintained at the maximum during cooling, probably due to residual stresses. Therefore, the mechanical pressure was progressively released to 10 MPa during the cooling step in order to preserve the samples. For all sintered samples, the initial heating step was approximately controlled at a rate of 3001C/min up to 6001C by a gradual increase of the input power, then an horizontal optical pyrometer focusing on a nonthrough hole in the graphite die (1 mm diameter), closed at about 2 mm from the sample side, was used to control the heating rate up to the desired sintering temperature. This graphite die/punches configuration and temperature control with the horizontal pyrometer were chosen to reduce the radial temperature difference during the heating and the dwell steps.12 Depending on the heating schedule, several trial and error attempts were necessary to empirically evaluate the ratio of power input to the maximum nominal power in order to limit the effect of local overheating at the sintering temperatures. In this investigation, two heating rates regimes were chosen: 81C/min (low heating rate) and 6001C/min (high heating rate) with different sintering temperatures (11501 and 13001C). An intermediate heating rate of 501C/min was arbitrary chosen for the isothermally treated samples at 9301C. Dwell durations up to 5 h under vacuum (0.7 mbar) were experimented. After the dwell step, all the samples were cooled at room temperature at a rate of 1201C/min.

(3) Microstructural Characterizations The average relative density (r) for each sintered sample was evaluated using the Archimedes method, assuming a theoretical density of 3.987 g/cm3 of alumina. The immersion liquid was water at a temperature of 221C, with a density of 0.9978 g/cm3. This balance method (NF EN 23369-1993) allowed a precision of 70.5% on the measured relative density. The initial relative green density after die compaction was ro 5 5071.25% (measured by mercury intrusion porosimetry). Diverse strategies of revealing grains boundaries on polished and postthermally etched samples failed, probably owing to clean boundaries devoid of impurities. Hence, SEM microstructural observations on fracture surfaces were achieved using SEM (JSM 840A, JEOL, Tokyo, Japan). The average grain size and grain size distribution for each sample were measured by random linear intercepts on at least 500 grains, using the public domain image analysis software Image J (NIH Image J). Because the grain sizes on fracture surfaces can be underestimated due to the presence of some transgranular fractures, attention was focused on the improvement of the image contrast, in order to reveal as much as possible the grain boundaries.13 A statistical correction factor was applied to the measured apparent grain size depending on

the shape of the grains. When the approximation of spherical grain could be performed (generally during the initial stage of sintering or at low sintering temperatures), the statistical correction factor was 1.225,14 whereas in the other cases for the approximation of tetrakaidecahedral grains, the apparent grain size was multiplied by 1.56.15 The errors bars of the average grain size measurements have been determined using Student’s test with a confidence interval of 95%. Horovistiz13 observed that the estimation of grain size from fractures surfaces were around 7% lower than that from polished etched surfaces; this falls within the error bars estimation. Moreover, the previous author observed that both characterizations lead to a similar distribution; hence, the estimated grain sizes are satisfactory for comparison of sintering kinetics in the present investigation.

III. Results (1) Densification Behavior The evolution of the relative densities of SP-sintered alumina during the constant heating regime (CHR), as a function of the sintering temperature, is plotted in Fig. 1(A). Whatever the heating rate, the increase in the SPS sintering temperature led to an increase in the relative density; this observation suggests that densification mechanisms during SPS are thermally activated phenomena. However, it is observed that high heating rate generally led to lower relative densities of SP-sintered alumina compared with low heating rate sintering cycle. This trend agrees well with the observations of Guillon and Langer16 for a heating rate range of 35–1501C/min. However, in the present investigation, it was possible to achieve almost full density at high temperatures ( 12001C) for low heating rate in contrast to the fast-heated alumina samples. Moreover, an enhanced degree of densification at low sintering temperature (9001CrTr11001C) is also observed for low heating rate. Kim et al.17 also obtained highly dense and fine transparent alumina at 11501C with a low SPS heating rate (81C/min). In a previous study, Aman et al.8 suggested that low SPS heating rate could favor diffusion mechanisms such as grain boundary and/or lattice diffusion, which bring closer the centers of contacting particles and can promote shrinkage in electrically non-conductive materials in contrast to high heating rates cycles. Figure 1(B) depicts the influence of the dwell duration on the densification behavior. At low sintering temperature (9301C), a moderate increase in the relative density is observed when the dwell duration is increased. At 11501C, long dwell duration has a little positive influence on density for high heating ratesintered samples, while for the alumina samples sintered at 81C/min, near full density was reached for dwell time ranging from 50 to 100 min. At 13001C, dwell duration had no marked effect on the relative density of slowly heated samples, whereas for fast-heated samples, a slight decrease in the relative density

Fig. 1. (A) Densification behavior during constant heating rate regime (CHR). (B) Densification behavior during the dwell.

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could be observed with the increasing dwell time. It was also observed that for high SPS temperatures (T 1  11501C), an increased sintering dwell time beyond 150 min was accompanied by a decrease in relative density, probably due to pore growth during grain coarsening, which is in good agreement with Kim et al.18 data.

(2) Grain Growth The influence of heating rate on the average grain size-temperature dependence is shown in Fig. 2(A). Two distinct behaviors can be observed. At low temperatures (T 1o12001C), increasing sintering temperatures have a negligible influence on the grain growth for the low heating rate samples in contrast to the fastheated samples. The difference in average grain size between the two regimes increased with sintering temperatures up to 11501C but it considerably decreased at 12001C when significant grain growth occurred for slowly heated samples. At higher sintering temperatures (13001C), the average grain size in slowly heated samples dramatically increased and became higher than in the fast-heated ones. These results suggest that besides being thermally activated at high sintering temperatures, grain growth kinetics may depend on the heating rates. This grain growth behavior with high heating rate was also observed by Murayama and Shin19 and was attributed to high defect concentration during rapid heating. It has been argued by previous researchers that the accuracy of temperature measurements during SPS cycle was questionable and that, macroscopic temper-

ature differences between the center and the edge of the graphite die could reach 1501C at 13001C.20 Nevertheless, the decrease in grain growth kinetics at high temperatures for fast-heated samples compared with slowly heated ones may supports the hypothesis of different competitive sintering mechanisms. The evolution of the average grain size with the dwell duration is represented in Fig. 2(B). At low sintering temperatures (9301C), negligible grain growth is observed. In contrast, at 13001C significant grain growth occurred with the increase of dwell duration, irrespective of the heating schedule. At intermediate sintering temperatures (11501C), the average grain size of fast-heated samples was approximately three times larger than the slowly heated ones. This difference in grain size at moderate sintering temperatures remained nearly constant for a dwell time beyond 60 min (Fig. 3). The latter observation suggests that throughout the isothermal treatment, the mechanisms of grain growth of alumina might be the same, irrespective of the heating rate.

(3) Microstructural Features and Sintering Trajectory At high sintering temperatures, (Fig. 4) significant grain growth occurred regardless of the heating rate. Intragranular pores can be seen on SEM observations, suggesting that pore boundary separation may have occurred at high temperatures, regardless of the heating schedule. After 1 h of dwell duration at 13001C, fast-heated samples resulted in heterogeneous microstructures with few exaggerated grains and ‘‘stick-like’’ grains, suggesting that impurities atoms may have segregated at grain boundaries or free surfaces. The curve showing the nature of the microstructure development during SPS of alumina is shown in Fig. 5. Contrary to Bernard-Granger21 and Guillon and Langer,16 the sintering trajectory of alumina during SPS does not follow a single path, and thus rationalization by master sintering curve approach16 is no more valid for high heating rates (41501C/min). In the present investigation, low SPS heating rate seems to be much favorable to achieve high-density and fine undoped alumina ceramics because pore/boundary separation is delayed at high sintering temperatures. However, codoping the starting alumina powder21,22 can be a fruitful strategy to influence the sintering mechanism, and hence the sintering path, as shown on Fig. 5. From the previous observations, the microstructure development of submicrometer undoped alumina powder during SPS seems to be controlled by densification and grain growth mechanisms and kinetics. In the next section, the nature of sintering mechanisms and kinetics will be analyzed and discussed using adapted existing models of creep and pore-dragged grain growth model. IV. Analysis and Discussions (1) Initial-Stage Sintering (qo0.90) Similarly to HP, densification during SPS is enhanced by pressure application at low sintering temperatures as recently shown by Chakravarty and Sundararajan.23 In the present investigation, for the sake of simplification, we assume two different sintering stages instead of the three ones commonly found in sintering literature. We define the initial stage for ro0.90 and the final stage for 0.90oro1, where r is the relative density of sintered samples. Because the applied uniaxial pressure was maintained constant to 80 MPa throughout the heating and dwell step, it is possible that particle rearrangement under the uniaxial compaction stress during the initial stage may have occurred at low sintering temperatures (o6001C); this contribution was not estimated in the present investigation due to the inaccuracy of temperature control with the optical pyrometer under 6001C. Because mass transport by diffusion is usually the dominant mechanism in HP of ceramics, and assuming that the applied stress is much greater than the sintering stress, the densification rate can be written24

Fig. 2. (A) Grain growth behavior during constant heating rate regime (CHR). (B) Grain growth behavior during the dwell.

1 dr HDðFPa Þl ¼ r dt RTGm

(1)

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Fig. 3. SEM micrographs of sintered alumina at 11501C. (A) 6001C/min without dwell. (B) 6001C/min after 1-h dwell duration. (C) 81C/min without dwell. (D) 81C/min after 1-h dwell duration. Arrows indicate the presence of interconnected porosities for (C), intergranular, and triple junctions pores for (A), (B), and (D).

Fig. 4. SEM micrographs of sintered alumina at 13001C. (A) 6001C/min without dwell. (B) 6001C/min after 1-h dwell duration. (C) 81C/min without dwell. (D) 81C/min after 1-h dwell duration. Arrows indicate the presence of intergranular and intragranular pores.

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SPS Kinetics of Pure a-Alumina Table I. Properties Data for a-Alumina Properties

a-Al2O3 27

Melting temperature Tm (K) Yield strengh syo (MPa)48 at 9001C Heat capacity Cfd (J
(m3
K)ÿ1)35 Electrical conductivity lefd ((Ohm
m)ÿ1)49

2327 80 2:311107 Tþ249 þ 21:6T ÿ
26 62:7  exp ÿ29T970

Meyers et al.,26 the yield stress–temperature dependence follows in first approximation a linear relationship expressed as: Fig. 5. Grain size–density trajectories of spark plasma-sintered alumina as a function of the heating rate.

where H is a numerical constant, D is the diffusion coefficient of the rate-controlling species, F is the stress intensification factor, Pa the applied pressure, G is the grain size, R is the Boltzmann constant, and T is the absolute temperature. The l and m exponents depend only on the mechanisms of densification. Because of the presence of pores, the magnitude of stress in the material within the compact is greater than the nominal pressure applied to the external surface of the compact. Assuming that the heated compact is an ideal powder composed of monosize spherical particles in which neck growth occurred during initial stage of sintering (ro0.90), the stress intensification factor can be expressed as24: F¼

ð1 ÿ ro Þ2 rðr ÿ ro Þ2

(2)

Equation (2) is applied in the case of isothermally treated samples at low sintering temperatures (9301C). For this calculation, r is ranged between 0.70 and 0.80, while grain growth is negligible (Fig. 2(B)). A linear relationship of   1 dr ln r dt vs ln (FPa) is found (Fig. 6), its slope is estimated to l 5 0.93 ( 1) suggesting that the SPS densification mechanisms may be governed by diffusional processes.24 This is consistent with Langer et al.’s investigation,9 and it was expected regarding strong bonding in alumina and limited dislocation motion at low temperatures. However, because a moderate mechanical pressure is applied throughout the heating and the dwell step, thus according to Helle et al.,25 the limiting pressure for yielding (Plim) is given by:   2sy ðTÞ 1 ln Plim ðT; rÞ ¼ (3) 3 1ÿr where r is the relative density, and sy(T) is the temperature-dependent yield stress for the fully dense alumina. According to

Fig. 6. Stress intensification factor exponent during initial-stage sintering (ro0.90).

  T ÿ To sy ðTÞ ¼ so 1 ÿ Tm ÿ To

(4)

where syo is the ‘‘pseudo’’ yield stress at initial temperature To. In the present calculations, To 5 1173 K was arbitrary chosen (see Table I), and Tm 5 2327 K is the melting temperature of alumina.27 Figure 7 depicts the evolution of the limiting pressure for plastic flow as a function of the SPS sintering temperature. According to these calculations, the moderate uniaxial pressure of 80 MPa is sufficiently high to lead to an instantaneous densification during the initial-stage sintering at 9001CrT 1r10501C via plastic flow, whereas it is not expected at higher temperatures due to insufficient applied pressures. Initial-stage densification via plastic flow has been observed by some researchers in rapid heating or SPS of some nanocrystalline ceramics. Indeed, Meng et al.28 attributed the full densification of nanograined alumina subjected to self-propagating high-temperature synthesis (SHS) at T 1416001C and 120 MPa to instantaneous and time-independent plastic yield mechanisms. Chaim and Margulis29 found a good agreement between experimental SPS data and calculated densification maps on nanocrystalline MgO, showing that SPS densification of may proceed by plastic flow and other diffusion processes. More recently, Morita et al.30 provided experimental evidence of the nonnegligible amount of stacking faults and dislocations in substructures of low-density SP-sintered MgAl2O4, attributed to a high-stress exponent caused by plastic flow due to dislocations motion. Regarding the large intensification factor in low-density region (Eq. [2]), it is possible that high effective stress at small particle contact areas might contribute to a glide-climb dislocation mechanism in the neck region, producing some densification in sintering of alumina, as observed by Ogbuji.31 HRTEM observations are now performed to confirm or invalidate this hypothesis. On the other hand, in agreement with previous works of Felten,32 and Coble33 on hot-pressed alumina, plastic flow may not be a predominant mechanism in the observed enhanced sintering of SPS alumina. Assuming the effective stress (FPa) constant for isothermally treated samples at low sintering temperatures,   1 dr ln r dt

Fig. 7. Limiting pressure for plastic flow as a function of the sintering temperatures.

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Fig. 9. Local temperature gradients at interparticle contacts as a function of the sintering temperatures.

Fig. 8. Densification kinetics at initial-stage sintering (ro0.90).

vs ln (G) allows the evaluation of the slope 5 ÿm and the grain size exponent m of the densification mechanism. For the nonisothermally treated samples, assuming that the densification mechanisms are governed by diffusional process, and that a thermal quasiequilibrium is achieved during the constant heating rate regime, because ro0.90 for T1 o11001C, it is possible to plot the same linearization of (1) for a given relative density, because G and r are interrelated. The different linear relationships found between the relative densification rates and the normalized grain sizes are illustrated in Fig. 8. According to this analysis, densification during the initial stage of SPS seems to be controlled by grain-boundary diffusion24 (m 3) during constant low heating rate up to 11001C and all over the dwell step at 9301C after moderate heating rate of 501C/min. These results are consistent with Langer et al.9 and they are not surprising in view of the very fine starting grain size of alumina powder (170 nm). However, more outstanding is the positive slope (m 5 ÿ1.75) obtained for the fast-heated samples at low temperatures, suggesting that grain growth mechanism may be predominant during the high heating rate regime. It was proposed by Shen et al.34 that at high heating rates, a strong chemical driving force of grain growth is created by a dynamic ripening mechanism, which consists of bringing nanosized microstructures compacts and a liquid phase that roughly deviates from thermodynamic equilibrium to higher temperatures. In the present work, such a liquid or viscous phase was not observed in alumina SP-sintered with high heating rate cycles. On the other hand, some researchers35,36 have pointed out the possibility of a thermal gradient at interparticle contact area during SPS. According to Olevsky and Froyen’s35 model, it is possible to estimate this local interparticle thermal gradient, assuming no heat losses, as follows: jHTjlocal ¼

1 G þ rp

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DtðE2 le To Þ 2Cn

(5)

where Dt (s) is the pulse sequence duration (ON-OFF), E (V/m) the electric field intensity, To (K) the starting temperature, n the number of pulses for achieving the desired sintering temperature from To and le ((Ohm
m)ÿ1) the electrical conductivity dependence on porosity C (J (m3
K)ÿ1) the heat capacity dependence on porosity. G and rp are the grain size and the pore radius, respectively. The heat capacity dependence on porosity for powdered materials can be approximated by35 (Cfd is the heat capacity of the fully dense materials, y the porosity): Cðy; TÞ ¼ ð1 ÿ yÞCfd ðTÞ

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(6)

The electrical conductivity dependence on porosity for powdered materials is expressed as35 (lefd is the electric conductivity

of the fully dense material): le ðy; TÞ ¼ lefd ðTÞ

ð1 ÿ yÞ ð1 þ 2yÞ

(7)

The mean pore sizes were estimated from SEM image analysis (Section II(3)). The electric field is assumed to be E 5 300 V/m (cf. maximum applied tension of 5 V over the approximate sample height of 2 mm), Dt 5 0.015 s, and the starting temperature To 5 873 K. Thus, depending on the sintering temperatures and material properties data for alumina (Table I), the calculation of (5) was plotted in Fig. 9. The first noteworthy point of this estimation is that the magnitude of the local temperature gradient is negligible compared with that found by Olevsky and and Froyen.35 The maximum calculated thermal gradient does not exceed 41C/m at 12001C, which is seemingly insufficient to melt alumina particles (see Table I Tm 5 20541C). Hence, there is no reason to expect melting or liquid phase at grains surfaces or boundaries. The second point is that high SPS heating rate resulted in local temperature gradients at interparticle contacts of alumina from three to 10 times higher than for the low SPS heating rate. The plots of the ratio of temperature gradient between high and low heating rates as a function of the grain size ratio (Fig. 10) indicate that an increase in the grain size relating to high heating rate is favorable to the decrease of the local temperature gradients comparatively to low heating rate. Poulier et al.37 have reported that the formation of grain boundaries during sintering, with larger contact areas between the grains, increases the thermal conductivity of the material, and that larger average grain sizes strongly increase the intrinsic thermal conductivity of the grains in the porous alumina ceramics. Hence, we can put forth the assumption that grain growth during high heating rate of SPS of alumina may be a required condition to establish thermal equilibrium, and simultaneously the reduction of the particles’ specific surface energy. Therefore, at high heating rates, SPS mechanisms of undoped fine alumina powder can be predominated by grain growth or coarsening at low sintering temperatures. In addition, because faceted grains were observed from 10501C up to 11501C in alumina SP-sintered at high heating rates instead of rounded grains in slowly heated samples for the same sintering temperatures (Fig. 3), it could be suggested that the corresponding mechanism of grain growth is probably linked to a surface diffusion mechanism38 that retain the initial adhesion structure while it increases the interparticle contact areas to achieve thermal equilibrium.

(2) Final-Stage Sintering (0.90oqo1) As sintering proceeds, both the density and the grain size of the compact increase. Because these processes occur simultaneously,

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Fig. 10. Ratio of local temperature gradients between high and low heating rate (HR/LR) as a function of the ratio of grain size.

interaction between them must be considered if the microstructural development of alumina during SPS has to be understood. At final stage of sintering, it is generally observed that the pores are isolated, and particularly they are located at grain boundaries or triple junctions (Figs. 3 and 4). Accordingly, these isolated pores would move together with the grain boundary during grain growth. Therefore, the relative mobility of pores compared with boundaries mobility would determine the microstructure development. Because grain growth mechanisms are not influenced by the applied mechanical pressure during HP or SPS, the grain growth rate can be approximated by a derived model of ‘‘pore-dragged’’ as proposed by Kang39: 1 dG K ¼ G dt RTGn ð1 ÿ rÞj

(8)

where K is a constant containing various parameters (diffusivity, surface energy, molar volume), G, R, T, and r have the same definition as in (1). The exponent n, j are related to the grain growth mechanism. Because r and G are interrelated, plotting   1 dG ln G dt vs ln (G) for a given density allows the evaluation of the grain size exponent, and thus the grain growth mechanism. At finalstage sintering, with the reduction of pore surface area, the sintering stress due to isolated pore curvature is no more negligible. Accordingly, the stress intensification factor should be modified40 as follows: F¼

1 r

(9)

Assuming that SPS mechanisms are still governed by a diffusional mechanism and do not change throughout the final stage, the linearization of expression (1) is still valid to approximate the densification kinetics. The curves representing   1 dr ln r dt and   1 dG ln G dt vs ln (G) are plotted for constant heating rate regime CHR (Figs. 11(A) and (B)) and dwell step (Figs. 12(A) and (B). The corresponding exponents m and n are determined similarly as in Section III(1). According to Fig. 11(A), the grain size exponents for the densification rates (m) are 2.16 and 1.25, which tend to

Fig. 11. Sintering kinetics at final-stage sintering during constant heating rate regime (CHR). (A) Densification kinetics. (B) Grain growth kinetics.

lattice diffusion and grain-boundary sliding24 for high heating rate and the low heating rate, respectively. Bernard-Granger and Guizard.10 suggested that grain-boundary sliding accommodated by oxygen grain-boundary diffusion could govern the densification mechanism in CaO–TiO2-codoped alumina SP-sintered at 1001C/min between 8501 and 12001C. Instead, based on nanopore shrinkage model at constant grain size, Chaim et al.41 showed that grain-boundary diffusion may be associated to fast densification kinetics at low temperatures when pores are isolated during the final-stage SP-sintering of nano-Y2O3 and MgO. In Fig. 11(B), the higher values of grain growth relative rates compared with the densification ones in the temperature range of 11501–13001C suggest that grain growth is expected to predominate during CHR at r40.90. Because the grain size exponent values for the relative growth rates (Fig. 11(B)) are almost zero, it can be suggested that the grain growth mechanism strongly depends on porosity and temperature, i.e. pore controls the boundary migration. This is consistent with the observed SEM microstructures (Fig. 4) showing large pores trapped at triple junctions in the fast-heated samples instead of few small pores in low heating rate samples at high temperatures. Accordingly, it is expected that by using suitable additive compounds (e.g., doping with La, Y, Mg), which lower the boundary migration and enhance the densification via lattice diffusion during sintering of large initial particles, it would be possible to achieve highly dense submicrometer polycrystalline alumina with SPS high heating rates, as recently attempted by Stuer et al.22 Figure 12(A) depicts the relative densification rates versus the normalized grain size during the dwell step. Except for the sample (D-6001C/min–11501C), the densification kinetics are very slow during the dwell, probably due to slow grain-boundary sliding mechanisms (mA–B  1) for A (81C/min–11501C) and B (6001C/min–13001C). For the slowly heated sample C at 13001C, the almost full density obtained before the dwell can explain the very low grain size exponent of densification rate (mC  0.17). Indeed, pores located at grain boundaries triple

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Fig. 12. Sintering kinetics at final-stage sintering during dwell. (A) Densification kinetics. (B) Grain growth kinetics.

junctions are almost annihilated (Fig. 4), therefore few vacancies are provided to increase the chemical potential gradient at grain boundaries. Consequently, the corresponding densification mechanism can be assumed to be independent of the grain size, and probably owing to a power-law creep39 mechanism. For the fast-heated sample at 11501C (D), the negative coefficient of the grain exponent (mD  ÿ0.98) highlights the predominance of grain growth as discussed in SectionIV(1). This agrees well with the high value of grain size exponent for the growth rate (nD  4 in Fig. 12(B)), which tends to a surface diffusion mechanism.39 For the slowly heated samples at 11501C, the grain size exponent of growth rate during the dwell is also high (nA  3), which might correspond to a gas phase diffusion.39 During the dwell at high temperatures (13001C), close values of grain size exponents for grain growth rate (nB–C  2), are obtained regardless of the heating rates. In view of the low relative porosities for B and C when the dwell starts, the mechanisms responsible of grain growth seem to be governed by grainboundary migration, regardless of the heating rates. Finally, it is also critical to note that, irrespective of the heating rates, because the grain size exponents for densification rate are smaller than the growth rate ones during the dwell, it can be expected that the use of fine particles at this stage of sintering will not be favorable to achieve high density and fine alumina due to fast grain growth.

(3) Grain Size–Density Trajectory According to the previous discussions, the enhancement of densification during low heating rate is attributed to grain-boundary diffusion at low sintering temperature, followed by grain-boundary sliding at high temperatures. The use of suitable codoping system (e.g., CaO–TiO2)10 can significantly modify the sintering path and delays the pore/boundary separation to higher density

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by reducing the grain growth rate. In contrast for the high heating rate, the required condition of thermal equilibrium probably enhances the surface diffusion coefficient, thus grain growth dominates at low sintering temperatures and pore/boundary separation occurs earlier. The enhanced grain growth kinetics at an early stage of sintering when using high heating rate (6001C/min) is particularly marked when comparing with the ultrafine alumina powder freely sintered at 301C/min as reported by Zuo et al.42 First, one must note that in Zuo’s investigation, the green samples were, however, first uniaxially pressed at 100 MPa, before cold isostatic pressing at 250 MPa before sintering. This subsequent reduce of pore size and pore size distribution in the green pressed matrix in Zuo’s investigation, concomitantly to the increase in the green density (58.470.2%) could have shifted the onset of grain growth to higher temperature as discussed elsewhere.2 Nevertheless, in the present study, the observed enhancement of grain growth during early stage of sintering when using extremely high heating rate seems opposed to what is generally proposed in the literature, namely that by increasing the heating rate, the detrimental effect of surface diffusion can be reduced by getting quickly to high temperatures where grain boundary or lattice diffusion beneficial effect of high heating rate.43 This latter consideration was formerly emphasized by Harmer and Brook,44 for rapid heating of material in which activation energy of densification is higher than that of grain growth. Indeed, in the case of conventional free sintering of ultrafine a-alumina powder (TM-DAR), Bernard-Granger et al.45 reported an activation energy of grain growth of 810 kJ/ mol in the early stage of isothermal sintering, and an apparent activation energy of densification of 1095 kJ/mol at heating rate of B1.61C/min. However, based on the master sintering concept, Guillon and Langer16 calculated a global activation energy of densification of 290 kJ/mol for the ultrafine alumina (TM-DAR) spark-plasma sintered at high heating rates (351 to 1501C/min). This latter value seems consistent with the activation energies of surface diffusion16 and interface reaction,46 and it is considerably smaller than those of grain growth reported previously for conventional sintering. Surface diffusion mechanism during the initial stage of SPS of ultrafine a-alumina at a heating rate of 501C/min was also reported by Stanciu et al.47 Accordingly, in the particular case of SPS of ultrafine a-alumina, extreme high heating rate would not be beneficial to reduce the extent of grain growth at an early stage of sintering. On the other hand, it has been stated by Bernard-Granger et al.45 that grain growth in ultrafine a-alumina powder is controlled by Frenkel disorders formation, before diffusion through grain boundaries of Al31 cations associated to these Frenkel defects. Because the driving force of grain growth is the decrease in free energy of the grain-boundary region, it can be supposed that thermal gradients that accompany extremely high heating rates might promote structural interfacial rearrangements, i.e. a higher rate of elimination of Frenkel disorders through surface diffusion mechanism, which could enhance grain growth during the early stage of sintering. This hypothesis, however, requires more advanced experimental investigations to confirm or invalidate it.

V. Conclusion Highly dense and fine pure polycrystalline a-alumina can be obtained with SPS in very short sintering times compared with conventional powder metallurgy processing. Based on a detailed report on microstructure development, and by the mean of classical kinetics laws and adapted HP models, this study analyzed sintering kinetics of pure a-alumina sintered by SPS at different heating rates, sintering temperatures, and dwell durations. Heating rates strongly influenced the sintering mechanisms and kinetics. At low sintering temperatures, densification is much favored by low heating rate probably due to grain-boundary diffusion. Instead, a required condition of thermal equilibrium, due to the large thermal gradient at interparticle contacts, could enhance surface diffusion coefficient and thus grain growth

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SPS Kinetics of Pure a-Alumina

during the initial-stage sintering of fine alumina powder sintered with high heating rates. Regardless of the heating rates, plastic yield might lead to instantaneous densification at an early stage of sintering. At high sintering temperatures (T1  11501C), grain coarsening is unavoidable because of surface diffusion and pore-controlled boundary migration during the dwell. At high sintering temperatures, densification rate is much lower for low heating rate samples, probably due to grain-boundary sliding and power-law creep, in contrast to lattice diffusion and grain-boundary sliding for the high heating rate samples.

Acknowledgment The authors gratefully acknowledge Prof. G. Fantozzi and G. Bonnefont from the SPS consortium at INSA Lyon.

References 1

A. Krell, P. Blank, H. Ma, T. Hutzler, and M. Nebelung, ‘‘Processing of HighDensity Submicrometer Al2O3 for New Applications,’’ J. Am. Ceram. Soc., 86 [4] 546–53 (2003). 2 A. Krell and J. Klimke, ‘‘Effects of the Homogeneity of Particle Coordination on Solid-State Sintering of Transparent Alumina,’’ J. Am. Ceram. Soc., 89 [6] 1985–92 (2006). 3 M. Omori, ‘‘Sintering, Consolidation, Reaction and Crystal Growth by the Spark Plasma System (Sps),’’ Mater. Sci. Eng A, 287, 183–8 (2000). 4 Z. A. Munir, U. Anselmi-Tamburini, and M. Ohyanagi, ‘‘The Effect of Electric Field and Pressure on the Synthesis and Consolidation of Materials: A Review of the Spark Plasma Sintering Method,’’ J. Mater. Sci., 41, 763–77 (2006). 5 Z. Shen, M. Johnsson, Z. Zhao, and M. Nygren, ‘‘Spark Plasma Sintering of Alumina,’’ J. Am. Ceram. Soc., 85 [8] 1921–7 (2002). 6 B.-N. Kim, K. Hiraga, K. Morita, and H. Yoshida, ‘‘Spark Plasma Sintering of Transparent Alumina,’’ Scr. Mater., 57, 607–10 (2007). 7 D. Doni Jayaseelan, S. Ueno, T. Ohji, and S. Kanzaki, ‘‘Differential Sintering by Improper Selection of Sintering Parameters during Pulse Electric Current Sintering,’’ J. Am. Ceram. Soc., 87 [1] 159–61 (2004). 8 Y. Aman, V. Garnier, and E. Djurado, ‘‘A screening Design Approach for the Understanding of Spark Plasma Sintering Parameters: A Case of Translucent Polycrystalline Undoped Alumina,’’ Int. J. Appl. Ceram. Technol., 7, 574–86 (2010). 9 J. Langer, M. J. Hoffmann, and O. Guillon, ‘‘Direct Comparison between Hot Pressing and Electric Field-Assisted Sintering of Submicron Alumina,’’ Acta. Mater., 57, 5454–65 (2009). 10 G. Bernard-Granger and C. Guizard, ‘‘Densification mechanism involved during spark plasma sintering of a codoped a-alumina material: Part I. Formal Sintering Analysis,’’ J. Mater. Res., 24 [1] 179–86 (2009). 11 Y. Aman, V. Garnier, and E. Djurado, ‘‘Influence of Green State Processes on the Sintering Behavior and the Subsequent Optical Properties of Spark Plasma Sintered Alumina,’’ J. Eur. Ceram. Soc., 29, 3363–70 (2009). 12 J. Ra¨thel, M. Herrmann, and W. Beckert, ‘‘Temperature Distribution for Electrically Conductive and Non-Conductive Materials During Field Assisted Sintering (FAST),’’ J. Eur. Ceram. Soc., 29, 1419–25 (2009). 13 A. L. Horovistiz, J. R. Frade, and L. R. O. Hein, ‘‘Comparison of Fracture Surface and Plane Section Analysis for Ceramic Grain Size Characterization,’’ J. Eur. Ceram. Soc., 24, 619–26 (2004). 14 R. Apetz and M. P. Bruggen, ‘‘Transparent Alumina: A Light Scattering Model,’’ J. Am. Ceram. Soc., 86 [3] 480–6 (2003). 15 M. I. Mendelson, ‘‘Average Grain Size in Polycrystalline Ceramics,’’ J. Am. Ceram. Soc., 52 [8] 443–6 (1969). 16 O. Guillon and J. Langer, ‘‘Master Sintering Curve Applied To Field-Assisted Sintering Technique,’’ J. Mater. Sci., 45 [19] 5191–5 (2010). 17 B.-N Kim, K. Hiraga, K. Morita, and H. Yoshida, ‘‘Effects of Heating Rate on Microstructure and Transparency of Spark-Plasma-Sintered Alumina,’’ J. Eur. Ceram. Soc., 29, 323–7 (2009). 18 B.-N Kim, K. Hiraga, K. Morita, H. Yoshida, T. Miyazaki, and Y. Kagawa, ‘‘Microstructure and Optical Properties of Transparent Alumina,’’ Acta Mater., 57, 1319–26 (2009). 19 N. Murayama and W. Shin, ‘‘Effect of Rapid Densification and Grain Growth in Hot Pressed Alumina,’’ J. Ceram. Soc. Jpn., 108 [9] 799–802 (2000).

20

2833

R. S. Dobedoe, G. D. West, and M. H. Lewis, ‘‘Spark Plasma Sintering of Ceramics: Understanding Temperature Distribution Enables More Realistic Comparison With Conventional Processing,’’ Adv. Appl. Ceram., 104 [3] 110–6 (2005). 21 G. Bernard-Granger and C. Guizard, ‘‘Spark Plasma Sintering of a Commercially Available Granulated Zirconia Powder: I. Sintering Path and Hypotheses About the Mechanism(s) Controlling Densification,’’ Acta Mater., 55, 3493–504 (2007). 22 M. Stuer, Z. Zhao, U. Aschauer, and P. Bowen, ‘‘Transparent Polycrystalline Alumina using Spark Plasma Sintering: Effect of Mg, Y and La Doping,’’ J. Eur. Ceram. Soc., 30, 1335–43 (2010). 23 D. Chakravarty and G. Sundararajan, ‘‘Effect of Applied Stress on IR transmission of Spark Plasma-Sintered Alumina,’’ J. Am. Ceram. Soc., 93 [4] 951–3 (2010). 24 M. N. Rahaman, Ceramics Processing and Sintering, 2nd edition, pp. 514–36. Marcel Dekker, New York, 2003. 25 A. S. Helle, K. E. Easterling, and M. F. Ashby, ‘‘Hot Isostatic Pressing Diagrams: New Developments,’’ Acta Metall., 33, 2163–74 (1985). 26 M. A. Meyers, E. A. Olevsky, J. Ma, and M. Jamet, ‘‘Combustion Synthesis/ Densification of an Al2O3–TiB2 Composite,’’ Mater. Sci. Eng. A, 311, 83–99 (2001). 27 B. Glorieux, F. Millot, J.-C. Rifflet, and J.-P. Coutures, ‘‘Density of Superheated and Undercooled Liquid Alumina by a Contactless Method,’’ Int. J. Thermophys., 20 [4] 1085–94 (1999). 28 F. Meng, Z. Fu, J. Zhang, H. Wang, W. Wang, Y. Wang, and Q. Zhang, ‘‘Rapid Densification of Nano-Grained Alumina by High-Temperature and Pressure with a Very High Heating Rate,’’ J. Am. Ceram. Soc., 90 [4] 1262–4 (2007). 29 R. Chaim and M. Margulis, ‘‘Densification Maps for Spark Plasma Sintering of Nanocrystalline MgO Ceramics,’’ Mater. Sci. Eng. A, 407, 180–7 (2005). 30 K. Morita, B.-N. Kim, H. Yoshida, and K. Hiraga, ‘‘Densification Behavior of a Fine-Grained MgAl2O4 Spinel During Spark Plasma Sintering (SPS),’’ Scr. Mater., 63, 565–8 (2010). 31 L. Ogbuji, ‘‘Plastic Flow in the Sintering of Alumina,’’ Ceram. Int, 12, 195–202 (1986). 32 E. J. Felten, ‘‘Hot-Pressing of Alumina Powders at Low Temperatures,’’ J. Am. Ceram. Soc., 44 [8] 381–5 (1961). 33 R. L. Coble and J. S. Ellis, ‘‘Hot-Pressing Alumina—Mechanisms of Material Transport,’’ J. Am. Ceram. Soc., 46 [9] 438–41 (1963). 34 Z. Shen, Z. Zhao, H. Peng, and M. Nygren, ‘‘Formation of Tough Interlocking Microstructures in Silicon Nitride Ceramics by Dynamics Ripening,’’ Nature, 417, 266–9 (2002). 35 E. A. Olevsky and L. Froyen, ‘‘Impact of Thermal Diffusion on Densification During SPS,’’ J. Am. Ceram. Soc., 92 [S1] 122–32 (2009). 36 X. Song, X. Liu, and J. Zhang, ‘‘Neck Formation and Self-Adjusting Mechanism of Neck Growth of Conducting Powders in Spark Plasma Sintering,’’ J. Am. Ceram. Soc., 89 [2] 494–500 (2006). 37 C. Poulier, D. S. Smith, and J. Absi, ‘‘Thermal Conductivity of Pressed Powders Compacts: Tin Oxide and Alumina,’’ J. Eur. Ceram. Soc., 27, 475–8 (2007). 38 J. E. Bonevics and L. D. Marks, ‘‘The Sintering Behavior of Ultrafine Alumina Particles,’’ J. Mater. Res., 7, 1489–500 (1992). 39 S.-J. L. Kang, Sintering, Densification, Grain Growth and Microstructure, pp. 145–62. Elsevier Butterworth Heinemann, Oxford, 2005. 40 R. L. Coble, ‘‘Diffusion Models for Hot Pressing with Surface Energy and Pressure Effects as Driving Forces,’’ J. Appl. Phys., 41 [12] 4798–807 (1970). 41 R. Chaim, R. Mardel, and C. Estourne`s, ‘‘Optically Transparent Ceramics by Spark Plasma Sintering of Oxide Nanoparticles,’’ Scr. Mater., 63 [2] 211–4 (2010). 42 R. Zuo, E. Aulbach, and J. Ro¨del, ‘‘Experimental Determination of Sintering Stresses and Sintering Viscosities,’’ Acta. Matter, 51, 4563–74 (2003). 43 E. A. Olevsky, S. Kandukuri, and L. Froyen, ‘‘Consolidation Enhancement in Spark-Plasma Sintering: Impact of High Heating Rates,’’ J. Appl. Phys., 102, 114913, 12pp (2007). 44 M. P. Harmer and R. J. Brook, ‘‘Fast Firing-Microstructural Benefits,’’ J. Br. Ceram. Soc., 80, 147–8 (1981). 45 G. Bernard-granger, C. Guizard, and A. Addad, ‘‘Sintering of an Ultra Pure a-Alumina Powder: I. Densification, Grain Growth and Sintering Path,’’ J. Mater. Sci., 42, 6316–24 (2007). 46 Z. He and J. Ma, ‘‘Constitutive Modeling of the Densification and Grain Growth of Fine-Grained Alumina Ceramics,’’ Mater. Sci. Eng. A, 361, 130–5 (2003). 47 L. Stanciu, D. Quach, C. Faconti, J. R. Grosza, and F. Raether, ‘‘Initial Stages of Sintering of Alumina by Thermo-Optical Measurements,’’ J. Am. Ceram. Soc., 90, 2716–22 (2007). 48 R. Chaim, ‘‘Densification Mechanisms in Spark Plasma Sintering of Nanocrystalline Ceramics,’’ Mater. Sci. Eng. A, 443, 25–32 (2007). 49 J. Pappis and W. D. Kingery, ‘‘Electrical Properties of Single-Crystal and Polycrystalline Alumina at High Temperatures,’’ J. Am. Ceram. Soc., 44 [9] 459–64 (1961). &