Int. J. Appl. Ceram. Technol., 7 [5] 574–586 (2010) DOI:10.1111/j.1744-7402.2009.02448.x

Ceramic Product Development and Commercialization

A Screening Design Approach for the Understanding of Spark Plasma Sintering Parameters: A Case of Translucent Polycrystalline Undoped Alumina Yann Aman* Laboratoire MATEIS UMR CNRS 5510, Universite´ de Lyon, INSA Lyon, , F-69621 Villeurbanne, France Laboratoire LEPMI UMR CNRS 5631, INP, Universite´ Joseph Fourier Grenoble, Domaine Universitaire, 38402 Saint Martin d’He`res, France

Vincent Garnier Laboratoire MATEIS UMR CNRS 5510, Universite´ de Lyon, INSA Lyon, F-69621 Villeurbanne, France

Elisabeth Djurado Laboratoire LEPMI UMR CNRS 5631, INP, Universite´ Joseph Fourier Grenoble, Domaine Universitaire, 38402 Saint Martin d’He`res, France An experimental screening design was used to evaluate the effects of spark plasma sintering (SPS) parameters such as heating rate, sintering temperature, dwell duration, and green-shaping processing on the relative density, grain size, and the optical properties of polycrystalline alumina (PCA). It is shown that heating rate and sintering temperature are the most critical factors for the densification of PCA during SPS. Green-shaping processing could prevent grain growth at low SPS sintering temperatures. No predominant SPS parameters are observed on the optical properties. Hence, the optical properties of PCA are controlled by microstructural evolution during the SPS process.

Introduction This work was supported by the ‘‘Re´gion Rhoˆne Alpes – MACODEV.’’ *[email protected] r 2009 The American Ceramic Society

Spark plasma sintering (SPS) is an emerging consolidation technique that combines uniaxial applied

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pressures and pulsed direct currents to densify a wide range of various materials.1 A considerable number of papers have demonstrated the benefits of this process, such as the ability of retaining the nanostructural features, producing fully dense materials at lower temperatures, and shorter processing times compared with other conventional sintering techniques.2–4 In the case of SPS, pulsed electric currents pass through a graphite die-punch assembly, which acts as a direct heating source of the green compact. This allows rapid heating and cooling during the SPS process. Many hypothetical mechanisms were proposed to explain the enhancement of sintering kinetics. Among them, the controversial plasma effect1,2 or the external electrical field effect5 are assumed to clean the particle surfaces or grain boundaries, therefore facilitating the activation of sintering by reducing the activation energies for densification. In a recent paper, Hulbert et al.6 attempted, without success, to detect highly transient voltage anomalies associated with plasma or spark generation with a high time resolution oscilloscope. Their results clearly challenge this hypothesis of spark plasma generation, suggesting that one should pay more attention to the specific features of the SPS process such as heating rate, applied pressure, sintering temperature and dwell duration, or pulsed current patterns. Alumina is a common nonconductive ceramic material that has attracted the interest of many researchers in order to establish sintering models of SPS7–9 or to produce high optical and mechanical properties of alumina ceramics with fully dense submicrometer-grain microstructures.7,9–14 To achieve these goals, opposite and unexpected results on the SPS of alumina ceramics were published in the literature. In particular, in Kim et al.’s study,14 a fully dense and fine grain size (0.29 mm) transparent alumina was obtained at 11501C with a very low heating rate (21C/min), while, a high heating rate (1201C/ min) was needed to achieve the same density for SPS of alumina at 12001C with a higher average grain size (1.7 mm) in Shen’s work.7 Shen and colleagues proposed the first systematic study of SPS parameters on densification, grain growth, and mechanical properties. However, the use of one factor at a time variation approaches in these previous works could have led to an incomplete interpretation of their results. This could explain their contrasting conclusions. Thus, the aim of the present paper is to investigate, with an unbiased design of experiments approach, the influence of the most important SPS parameters like heating rate, sintering temperature, dwell

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duration, and green compact-shaping processing on the microstructural features and optical properties of spark plasma-sintered undoped polycrystalline alumina (PCA). Experimental Procedure Powder and Fixed Parameters of the SPS Process

Ultra-high-purity commercial a-Al2O3 powder (BMA-15, purity 499.99%, Baı¨kowski Chemicals, Annecy, France) was used in the experiments. The as-received (AsR) powder had an average particle size of 0.170 mm and a specific surface area of 14 m2/g, as reported by the manufacturer. The SPS apparatus used in this study was type HP D 25/1 (FCT Systeme, Rauenstein, Germany). The green sample weights were approximately 2 g. All the samples were sintered in a 20 mm cylindrical graphite die and punches assembly, with a thermal insulating carbon felt. The temperature was controlled using a horizontal pyrometer focusing on a nonthrough hole closed at about 2 mm from the sample side in the graphite die. The cooling rate was 1201C/min, with an annealing step at 10001C for 10 min for all the experiments. In the present investigation, the pulse pattern and the applied pressure factors remained constant for the following reasons: the pulse pattern was constant at 10:5 (10 ms pulses ON, 5 ms OFF) because no important effect of DC pulsing variations has been reported in the literature.15 In addition, the applied uniaxial pressure was maintained at 80 MPa throughout the heating and dwell steps, and then progressively released during the cooling step. The application of a high uniaxial pressure during SPS has been shown to decrease the sintering temperature and to limit grain growth.15,16 Methodology: Screening Design Approach Principle: Factor screening design is the process of determining the subset of factors in a design of experiments that exert the greatest impact on the set of response variables. This approach is based on an orthogonal array of a set of experiments combining different levels of factors, so that the subset experimental points are homogeneously and optimally distributed in the experimental domain, with the smallest number of experiments possible. This optimal array ensures the minimization of the polynomial model regression coefficients, and allows unbiased analysis of the estimation and comparison of each factor-isolated contribution and effect.17,18

Shen et al.7 Kim et al.14 NC 46%–0.2% 95.8–100 0.5–1.7 B100 0.29–0.54 0–20 20 1200 1150

NC NC NC NC 99 0.58 99.6–99.4 3.17–1.98 99 410 99 3–4 5 5 0 2

120 2–100

NC, not cited; RIT, real in-line transmittance; SPS, spark plasma sintering.

Factors’ and Levels’ Description: In this study, three main factors relative to the SPS process were selected because their influence on SPS has generally been recognized in the literature (Table I): heating rate, sintering temperature, and sintering dwell duration. To these SPS-specific factors, we added the green-shaping processing factor because it can considerably influence the solid-state sintering of transparent alumina as shown by Krell et al.21 The green samples were prepared by colloidal or dry routes, as follows: Dry route: The AsR alumina powder was directly cold pressed in a 20 mm graphite die in the SPS apparatus, under a constant uniaxial pressure of 80 MPa, without any treatment or additives.

50 80

The box plots characterize the distribution of the experimental results for each response variable. The main effect plots present a graphical display that enables a comparison of the average effect of a change of factor level on the response variables. In practice, the main effect is the average value of the responses for the same level of factor repeated in the experimental domain. This represents, to some extent, the weighting of a factor level on the measured response.20

1250 1300–1400 1650 1100

i¼1

ð3Þ

a2i

200 50–300 600 250

k P

15 47 40 45

a2j

TemperDwell ature duration (1C) (min)

Wj ¼

Applied Heating pressure rate (MPa) (1C/min)

This model (Eq. (2)) assumes the additivity of mean effects without taking into account possible interactions between factors. In practice, the experimental design treatments (candidate experiments) were selected and analyzed using the statistical software Nemrod-W.19 The least mean square method allows the determination of the polynomial coefficients ai. Treatment data were graphically displayed using Pareto charts, box plots, and main effect plots of each factor. From the polynomial expression (1), one can evaluate the contribution Wj of the jth factor (Eq. (3)). This allows us to display the Pareto chart.

Pulse pattern

ð2Þ

Raw powder (average particle size)

ðmi ÿ 1Þ

i¼1

Different SPS Conditions of Alumina Reported in the Literature

k X

Table I.

p¼1þ

Relative Average Transparency density grain size RIT-640 nm (%) (lm) (%)

j¼1

where xi , j is the jth factor level for ith treatment response yi. The number of unknown variables p, depending on the numbers of factors k and levels mk, is defined as

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TM-DAR (0.21 mm) 12:2 TM-DAR (0.15 mm) 36:6 UA5105 (0.4 mm) NC Sumitomo Chemicals NC (0.1 mm) Ceralox APA05 (0.4 mm) 10:9/3:1/36:2 TM-DAR (0.15 mm) 12:2

Authors

In the present paper, a first-order polynomial model (Eq. (1)) was used to describe the responses as a function of the factor variables: p X yi ¼ a0 þ ai xi;j ð1Þ

Jayaseelan et al.10 Zhou et al.9 Gao et al.12 Stanciu et al.13

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Table II. Factors levels Level Level Level Level Level Level

1 2 3 4 5 6

577

Factors and Levels Description

Shaping process

Heating rate (1C/min)

Sintering dwell (min)

Sintering temperature (1C)

as-received powder 37 vol% DC 23 vol% DC 47 vol% DCC

8 50 300 600

0 5 20 60

1100 1150 1200 1250 1300 1350

DC, direct casting; DCC, direct coagulation casting.

Colloı¨dal routes: The powder was dispersed in aqueous slurries with different solid contents and different states of agglomeration: (a) 23 vol% electrostatic dispersion with HCl; (b) 37 vol% electrosteric dispersion with 2phosphonobutane-1,2,4-tricarboxilic acid (PBTCA, Lanxess-Bayer, Courbevoie, France)22; and (c) 47 vol% electrosteric dispersion with PBTCA. The dispersed slurries (a) and (b) were directly cast in a 20 mm cylindrical mold on a porous support at room temperature, whereas (c) was coagulated23 with the addition of acetate aluminum on a nonporous support and placed at steam room temperature of 551C for 1 h. After 24 h of drying, (b) and (c) were calcined in air at 7501C for 10 h in order to burn out the organic additive. These green samples, which have been characterized in another investigation,24 present different green densities and pore-size distributions. In this screening design approach, the selected factors and levels are summarized in Table II. The number of unknown variable p is 15, and the total number of experiments with all possible levels and factors combinations should be 384. The screening design approach allowed a reduction to 32 different experimental treatments. All the experiments were repeated twice in order to ensure reproducibility. The results’ data showed good reproducibility over repeated treatments. The SPS cycles tested in this design approach are presented in Table III. Screening Design Responses: The experimental responses were the relative sintered densities, the final average grain sizes, the in-line transmittances, and the subsequent scattering coefficients (g) at 640 nm. In this study, the relative sintered density was evaluated using the Archimedes method, assuming a theoretical density (TD) of alumina of 3.987 g/cm3. The immersion liquid was water at temperature of 221C, with a density of 0.9978 g/cm3. The balance method (NF EN 23369-

1993) allowed a density precision of 70.5%. Microstructural observations were achieved using SEM (JEOL 840, Tokyo, Japan). Because it was difficult to observe grains precisely on thermally etched polished surfaces of spark plasma-sintered alumina samples, fracture surfaces of samples were observed to determine grain sizes with the statistical correction factor 1.56.25 Apetz et al.26 proposed the real in-line transmittance (RIT) as the real evaluation of transparency of sintered PCA, because it only takes into account the unscattered light through the sample (i.e., the real transmitted light). In this investigation, we only measured the inline transmitted light as a function of the wavelength using a common commercial double-beam spectrophotometer UV-Visible light (Perkin-Elmer Lambda 35, Shelton, CT). Strictly speaking, our measurements do not evaluate the transparency because of the large aperture of the incident beam. Indeed, with an opening angle in the range of 3–51, one cannot exclude the scattered amounts from the measured intensity.27 Nevertheless, the technique used in the present study is suitable for a qualitative comparison of the optical scattering properties of the sintered samples. For this purpose, all the sintered specimens were polished on both sides with a 0.500 mm diamond disk. The final thickness of the polished samples ranged from 0.80 to 1 mm. To enable a direct comparison of the samples at the same thickness of the sample (dcorr 5 0.80 mm), the measured in-line transmittances were corrected28 as follows: Tcorr



T1 ¼ ð1 ÿ RÞ 1ÿR

dcorr =d1

ð4Þ

where Tcorr (%) represents the corrected in-line transmittance of the measured one T1, whose initial thickness is d1 (mm). R (B14%) represents the reflection losses

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Table III.

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The 32 Treatments Tested in the Screening Design Approach

No. of sample

Heating Sintering Sintering Relative Average T corr Green rate dwell temperdensity grain size (640 nm) shaping processing (1C/min) (min) ature (1C) (%) (%) (lm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

As-received powder As-received powder As-received powder As-received powder As-received powder As-received powder As-received powder As-received powder 37 vol% DC 37 vol% DC 37 vol% DC 37 vol% DC 37 vol% DC 37 vol% DC 37 vol% DC 37 vol% DC 23 vol% DC 23 vol% DC 23 vol% DC 23 vol% DC 23 vol% DC 23 vol% DC 23 vol% DC 23 vol% DC 47 vol% DCC 47 vol% DCC 47 vol% DCC 47 vol% DCC 47 vol% DCC 47 vol% DCC 47 vol% DCC 47 vol% DCC

300 8 50 600 50 600 300 8 600 50 8 300 8 300 600 50 8 300 600 50 600 50 8 300 50 600 300 8 300 8 50 600

5 20 0 60 20 5 60 0 0 60 5 20 60 0 20 5 60 0 20 5 0 60 5 20 20 5 60 0 5 20 0 60

1100 1150 1200 1250 1300 1350 1100 1150 1100 1150 1200 1250 1300 1350 1100 1150 1100 1150 1200 1250 1300 1350 1100 1150 1100 1150 1200 1250 1300 1350 1100 1150

96.2 99.3 96.2 99.2 99.2 99.6 97.5 98.6 91.7 99.4 98.7 99.1 99.7 98.7 96.4 95.8 99.1 97.3 98.1 99.3 97.2 99.6 97.9 98.9 99.1 94.0 99.0 99.3 99.2 99.5 96.1 94.9

0.51 0.72 0.41 5.01 2.64 4.61 0.89 0.36 0.31 0.43 0.67 0.72 0.95 1.05 0.30 0.32 0.58 0.53 7.81 1.48 1.93 15.64 0.35 1.36 0.44 0.90 0.96 0.61 0.94 1.10 0.26 0.24

12.29 21.52 10.56 1.05 10.92 0.10 33.50 12.85 1.15 38.45 2.23 30.62 23.51 15.56 32.58 21.88 25.48 1.28 6.39 1.06 10.67 16.56 25.27 19.98 27.11 27.48 30.52 31.13 33.03 37.88 14.20 27.80

c (640 nm) (m ÿ1 ) 2423 1723 2613 5498 2571 8423 1170 2368 5389 997 4556 1282 1612 2129 1204 1702 1512 5251 3241 5484 2600 2051 1522 1816 1434 1417 1286 1261 1187 1016 2242 1403

DC, direct casting; DCC, direct coagulation casting.

for two alumina surfaces. From the Beer–Lambert expression of the measured in-line transmittance26 for a sample thickness d, one can express the scattering coefficient g (mÿ1) as follows:   R ln 1 ÿ T ð5Þ g¼ d In this work, the scattering coefficient was calculated from the measurement data. This coefficient accounts

for the different contributions of scattering centers as grain boundaries, pores, and impurities.26 Results Effects of SPS Parameters on the Density

Figure 1 shows the box plots of the experimental results on the final density. Q25, Q50, and Q75 are, respectively, the quartile values of 25%, 50%, and 75% of

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Exp6: AsR − 600°C/min 5 min dwell − 1300°C − 99.6% Exp9: 37vol% − 600°C/min − 0 min dwell − 1100°C − 91.7%

Exp23: 23vol% − 8°C/min 5 min dwell − 1100°C − 97.9%

relative density 97.931 (%) Q50 Q75 Q25 max 98.800 97.000 99.225

min

Fig. 1.

Box plot of the experimental results on the final density.

Sintering temperature

Heating rate

Sintering dwell

1.53%

6.80%

42.27%

100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%

49.40%

the distribution of the experimental results. From this figure, one can note that high heating rates or low ones, with or without the sintering dwell step, can induce similar or opposite densification. From the observation of the large distribution of experimental final densities, it seems that the combined effects of SPS parameters influence the densification of PCA. However, Fig. 2 shows the Pareto chart of the SPS parameters on the final density. This chart allows the analysis of the magnitude and importance of each parameter effect. The Pareto chart shows that B90% of the SPS parameter effects on the final density can be attributed to the sintering temperature and the heating rate. This is also confirmed by the main effect plots of each parameter on the density (Fig. 3). This figure highlights the strong effects of low SPS heating rates (o501C/min) and high

Factor contribution (%)

Exp13: 37vol% − 8°C/min 60 min dwell –1300°C − 99.7%

Shaping process

Factors

Fig. 2. Pareto chart of spark plasma sintering parameters on the final density.

sintering temperatures (412001C) on high final relative densities of sintered PCA. Effects of SPS Parameters on the Average Grain Size

From the box plots of the experimental results on the grain size (Fig. 4), one can observe a narrow distribution of the results around the median value of 0.72 mm. From this figure, it is worth noting that the SPS process generally allows fine grain-sintered microstructures but it cannot prevent significant grain growth if the sintering parameters are improperly selected. Moreover, there is no direct evidence of a link between the heating rate and the final grain size. However, larger grain sizes were obtained at high sintering temperatures (  12001C), while smaller grain sizes were obtained with samples elaborated from well-dispersed slurries. The previous observations are well supported by the main average effect plots of each SPS parameter on grain size (Fig. 5), in which high solid content, homogeneous and well-dispersed samples (b), (c) promoted lower grain sizes. From the Pareto chart on grain size (Fig. 6), B90% of the SPS parameters effects on the final average grain size can be attributed to the sintering temperatures of the undoped PCA. Effects of SPS Parameters on the Optical Properties

Figures 7 and 8 show the box plots of the in-line transmittances and scattering coefficients, respectively. First, one can observe a large distribution of the in-line transmittances, which implies a priori no marked effect of a specific SPS parameter on the optical properties.

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99.5

relative density (%)

99 98.5 98 97.5 97 96.5 96 AsR

23% 37%

47%

Shaping process

8

50

300

600

Heating Rate (°C/min)

0

5

20

60

Sintering dwell (min)

1100

1150 1200 1250 1300 1350 Sintering temperature (°C)

Factors

Fig. 3.

Main effect plots of spark plasma sintering parameters on the final density.

From the Pareto chart (Fig. 9), the influence of the green-shaping processing cannot be neglected. This is well supported by the main average effect plots (Fig. 10) showing a trend according to which high solid content, homogeneous, and well-dispersed samples are favorable to higher in-line transmittances. However, there is no clearly distinguished effect of SPS parameters on the scattering coefficient (Figs. 11 and 12). From these observations, it is confirmed that optical properties of spark plasma-sintered alumina samples are only depen-

dent on the evolution of the sintered microstructures during the SPS cycle.

Discussion The present study enables us to provide new insights into the ‘‘contradictory’’ results reported in the literature (Table I), when the applied pressure and the pulse pattern are maintained constant.

Exp32: 47%vol% − 600°C/min 60 min dwell − 1150°C − 94.9% − 0.24 µm Exp11: 37%vol% − 8°C/min 5 min dwell − 1200°C − 98.7% − 0.67 µm

1.720 Q25 Q75 min Q50 0.720 0.4251.165

Fig. 4.

Box plot of the experimental results on the final grain size.

Exp22: 23%vol% − 50°C/min 60 min dwell − 1350°C − 99.6% − 15.6 µm

Average grain size (µm) max

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6

5

Grain size (µm)

4

3

2

1

0 AsR 23% 37% 47%

8

Shaping process

50

300

600

Heating Rate (°C/min)

0

5

20

60

1100 1150 1200 1250 1300 1350

Sintering dwell (min)

Sintering temperature (°C)

Factors

Fig. 5.

Main effect plots of spark plasma sintering parameters on the final average grain size.

Density of Spark Plasma-Sintered PCA

Sintering temperature

Sintering dwell

3.47% Shaping process

2.72%

87.80%

100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%

6.01%

Factor contribution (%)

From the previous section, it was shown that low SPS heating rates (o501C/min) and high sintering temperatures were more favorable to achieving fully dense sintered PCA. This is in good agreement with Kim et al.14 who achieved fully dense spark plasma-sintered PCA at low heating rates (21C/min). In contrast, our results are opposed to the recent paper of Olevsky et al.29 showing the beneficial influence on densification of thermal diffusion under a high thermal gradient due

Heating rate

Factors

Fig. 6. Pareto chart of spark plasma sintering parameters on the final average grain size.

to a high heating rate. Kim et al.14 discussed the effect of low heating rates by considering the final stage sintering, where a small grain size (0.21 mm) in the case of a low heating rate, associated with low porosity (2.4%) at a low temperature (11501C), could favor grain-boundary diffusion, grain sliding, and deformation-induced densification during the sintering dwell. However, these mechanisms are linked to surface tension and external stress-driven densification mechanisms under the isothermal conditions during the dwell. On the other hand, high heating rates associated with the thermal gradient that may locally enhance matter transport by the Soret effect29 led to lower sintered densities. Based on a classical two-sphere sintering model, Johnson30 demonstrated that, although mass transport can be favored by thermal gradient, it may rather enhance shortrange surface diffusion, and thus there may be no overall densification. This is also in good agreement with Huntington,31 who qualitatively showed a negligible effect of vacancy migration mechanisms on the heat of transport in nonmetal; hence the mass motion, because the effect of phonon scattering by vacancy is pratically negligible. Thus, from the previous considerations, low SPS heating rates would be more favorable to the densification of alumina. Thereby, it would be reasonable to consider an additional significant effect on surface tension, and external stress-driven mechanisms on the

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Exp11: 37vol% – 8°C/min 5 min dwell – 1200°C – 98.7% − 0.67 µm − 2%

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Exp29: 47vol% – 300°C/min 5 min dwell – 1300°C – 99.2% − 0.94 µm − 33% Exp10: 37vol% – 50°C/min 60 min dwell – 1150°C – 99.4% − 0.43 µm − 38%

Tcorr (%)

18.894 Q75

Q25 Q50

min 10.643

Fig. 7.

28.480

Box plot of the experimental results on the corrected in-line transmittances at 640 nm.

low-temperature densification of alumina at a low heating rate, compared with hot pressing and other conventional sintering techniques. This additional effect could be linked to the intrinsic properties such as thermal and electrical conductivities of spark plasma-sintered materials. Grain Size of the Spark Plasma-Sintered PCA

The present results showed that SPS sintering temperature is the most crucial factor for grain size. This is normally expected for (conventional or rapid) sintering of alumina because the activation energy of grain growth is lower than the densification one at a high temperature, as shown by Harmer and Brook.32 A significant

Exp10: 37vol% − 50°C/min 60 min dwell − 1150°C − 99.4% 0.43 µm − 997 m−1

Q25

increase in grain size is particularly emphasized at the temperature at which the densification rate reaches its maximum, and hence coarsening mechanisms become predominant.33 Otherwise, it is also worth noting the beneficial effect of green body-shaping processing on the final grain size. Well-dispersed and homogeneous green bodies, with small and narrow pore-sizes distribution are supposed to shift the onset of densification to higher temperatures and to impede grain growth.24,34 Optical Properties of the Spark Plasma-Sintered PCA

It was shown that optical properties of sintered PCA are linked to microstructural evolution during

Exp7: AsR − 300°C/min 60 min dwell − 1100°C − 97.5% − 0.89 µm − 1170 m−1 −

2511.438 Q75 Q50

min 1768.500 1373.000 2602.250

Fig. 8.

max

20.750

Box plot of the experimental results on the scattering coefficient at 640 nm.

Exp6: AsR − 600°C/min 5 min dwell − 1350°C − 99.6% 4.61 µm − 8423 m−1

γ (m−1) max

Shaping process

Sintering Heating rate Sintering dwell temperature Factors

Fig. 9. Pareto chart of spark plasma sintering parameters on inline transmittances at 640 nm.

SPS. High in-line transmittances and corresponding low scattering coefficients were obtained for well-prepared green samples with low heating rates and enough dwell duration. From the previous section (see ‘‘Grain Size of the Spark Plasma-Sintered PCA’’), green-shaping processings could allow finer sintered microstructures than the AsR powder. According to Apetz’s model,26 because the scattering coefficient of grain boundary ggb is pro-

583

7.92%

29.70%

31.12%

100% 90% 80% 70% 60% 50% 50% 40% 30% 20% 10% 0%

31.27%

Factor contribution (%)

0.39%

19.03%

20.61%

100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%

59.97%

Factor contribution (%)

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Heating rate

Sintering temperature

Shaping process

Sintering dwell

Factors

Fig. 11. Pareto chart of spark plasma sintering parameters on the scattering coefficient at 640 nm.

portional to the average grain radius r (ro10 mm), the submicrometer-scale grain size in the fully dense sintered microstructures would enhance the in-line transmittances, as verified by Kim et al.35 Moreover, dense sintered alumina samples could be obtained at low heating rates and low SPS temperatures (see ‘‘Density of Spark Plasma-Sintered PCA’’). This reduction of the heating rate and sintering temperature would lead to homogeneous and limited

30

Tcorr 640n m (%)

25

20

15

10 AsR 23% 37% 47% Shaping process

8 50 300 600 Heating Rate(°C/min)

0 5 20 60 Sintering dwell(min)

1100 1150 1200 1250 1300 1350 Sintering temperature(°C)

Factors Fig. 10.

Main effect plots of spark plasma sintering parameters on the in-line transmittances at 640 nm.

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Gamma 640nm (m–1)

3600

3100

2600

2100

1600

1100 AsR 23% 37% 47% 8 Shaping process

50

300

600

Heating Rate (°C/min)

0

5

20

60 1100 1150 1200 1250 1300 1350

Sintering dwell (min)

Sintering temperature (°C)

Factors

Fig. 12.

Main effect plots of spark plasma sintering parameters on the scattering coefficient at 640 nm.

residual pore growth as shown by Kim et al.35; hence, the in-line transmittances would be enhanced and the total scattering coefficient would be reduced. Validity of the First-Order Polynomial Model and Optimization

The model used to describe the results of this design of experiment is a first-order polynomial model that assumes the additivity of the effects, and does not take account of the possible interactions between factors. To characterize the validity limit of this additive model, a particular combination of the factors’ levels was tested: 23 vol% direct casting ÿ81C/min—60 min dwell—13001C. The experimental result of this partic-

Table IV.

ular combination is compared with the model result (Table IV). Closed values were obtained for the relative density and the in-line transmittance responses. Differences from predicted grain size and scattering coefficient values are observed and could be attributed to some strong interactions existing between factors. One can identify these possible interactions by plotting the effects of a variation of two factor-level combinations when all the other factors are assumed to be constant. Figure 13 shows a particular strong interaction plot between the shaping process factor and the heating rate on the grain size response. Thereby, for further optimization of the optical properties of spark plasma-sintered PCA, it would be useful to consider all the possible interactions between factors.

Validity Limit of the First-Order Polynomial Model without Interactions

Factors levels: 23 vol% ÿ81C/min ÿ60 min ÿ13001C First-order polynomial model result Experimental result

Relative density (%)

Grain size (lm)

T corr 640 nm (%)

c 640 nm (mÿ1 )

99 B100

1.75 3.78

17 B17

2254 2036

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INSA Lyon, and Dr. E. Beyou (LMPB ISTIL-Lyon) for the spectrophotometer measurements.

6 5 Grain size (µm)

585

References

4 3

1.

600°C/min

2.

2

3.

1 8°C/min 0 37 vol.%

4.

23 vol.% Shaping process

Fig. 13. Interaction plots on grain size response between shaping process and heating rate.

5. 6.

7.

Conclusion A powerful statistical tool has been applied to investigate the effects of some SPS parameters (heating rate, sintering temperature, sintering dwell) and the green-shaping processing. With this screening design approach, factors that exert the greatest impacts on densification, grain size, and optical properties of spark plasma-sintered alumina have been clearly identified; B90% of the SPS parameter effects on the final sintered density can be attributed to the heating rate and the sintering temperatures. In particular, it was shown that low SPS heating rates (o501C/min) were much more favorable for achieving full density at low temperatures. Otherwise, the sintering temperature factor exerts the greatest impact on the grain size, whereas green samples prepared by high solid content, homogeneous, and well-dispersed aqueous slurries may favor a fine submicrometer-scale grain size. Thus, green sample preparation could enhance the optical properties. Finally, no evidence directly connecting the heating rate to the optical properties could be observed. It was confirmed that the optical properties of sintered PCA are only dependent on the microstructural evolution during the SPS process. The present results allow an optimization of the optical transparency of spark plasma-sintered alumina. That will be the subject of a forthcoming investigation.

Acknowledgements The authors gratefully acknowledge Prof. G. Fantozzi and G. Bonnefont from the SPS consortium at

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