Sintering of alumina powder compacts and their compressive mechanical properties

Sintering of alumina powder compacts and their compressive mechanical properties

Available online at www.sciencedirect.com CERAMICS INTERNATIONAL Ceramics International 41 (2015) 11449–11455 www.elsevier.com/locate/ceramint Sint...

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Available online at www.sciencedirect.com

CERAMICS INTERNATIONAL

Ceramics International 41 (2015) 11449–11455 www.elsevier.com/locate/ceramint

Sintering of alumina powder compacts and their compressive mechanical properties Yoshihiro Hiratan, Taro Shimonosono, Soichiro Sameshima, Hidehiro Tominaga Department of Chemistry, Biotechnology, and Chemical Engineering, Kagoshima University, 1-21-40 Korimoto, Kagoshima 890-0065, Japan Received 9 April 2015; received in revised form 13 May 2015; accepted 19 May 2015 Available online 29 May 2015

Abstract Three types of high purity alumina particles with diameters of 156, 210 and 351 nm equivalent to their BET surface areas were dispersed in aqueous solutions at pH 3 and consolidated via pressure filtration at 19 MPa. These alumina compacts were sintered in air at 700–1320 1C for 1 h. The compressive strengths and Young's moduli of the alumina compacts with relative densities of 57.6–81.3% increased as the grain boundary area increased. The shrinkage and decrease in the specific surface areas of the sintered alumina compacts during sintering indicated that the welldispersed alumina particles in acidic solutions were packed in a random close-packing structure with a particle coordination number (n) of 12. The grain boundary areas between two particles were calculated using the measured specific surface areas for n ¼ 12 and related to the measured compressive strengths and Young's moduli. This analysis revealed that the effective compressive strength for 0% porosity was 1.9 GPa, which was slightly lower than the reported compressive strengths (2.2–2.6 GPa) for highly dense, polycrystalline alumina. & 2015 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

Keywords: A. Sintering; B. Grain boundaries; C. Mechanical properties; D. Al2O3

1. Introduction Porous ceramics have been widely used as filters for exhaust gases from diesel engines [1,2], catalyst supports [3,4] and electrodes in solid oxide fuel cells [5,6]. Recently, we intensively studied the performance of porous ceramics as hydrogen separation membranes [7,8], in porous electrochemical cells for the production of a H2–CO mixed fuel from a 50% CH4 – 50% CO2 biogas [9–11] and to decompose carbon monoxide and carbon dioxide [12,13]. In addition to the above functions, a guarantee of strength is essential in porous ceramics. It has been known for a long time that the strength of porous ceramics increases exponentially with decreasing porosity [14,15]. However, we clarified that the strength of porous alumina compacts during the initial sintering stage is enhanced with an increase in the grain boundary area at a constant porosity [16]. The development of grain boundaries n

Corresponding author. Tel.: þ81 99 285 8325; fax: þ 81 99 257 4742. E-mail address: [email protected] (Y. Hirata).

http://dx.doi.org/10.1016/j.ceramint.2015.05.109 0272-8842/& 2015 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

with sintering was found to be related to a decrease in the specific surface area. The area (ASV) of the gas–solid interface and the grain boundary area (ASS) per particle shown in Fig. 1 are expressed using Eqs. (1) and (2), respectively [16]: ASV ¼ 4π r 2  nS1 ¼ 42=3 π r 20

ASS ¼

4 2np ð4  3np2 þ np3 Þ2=3

1 2p p2 nπ y2 ¼ 21=3 π r 20 n ; 2 ð4  3np2 þ np3 Þ2=3

;

ð1Þ

ð2Þ

where r0 is the radius of the starting particles, n is the particle coordination number and p is the ratio of the shortened distance (h) between two particles to the particle size (r) (p¼ h/r) during sintering. The p value can be determined from a specific surface area by assuming no change in the particle number in one sintered powder compact. In addition, the compressive strength of porous ceramics is related to the

Y. Hirata et al. / Ceramics International 41 (2015) 11449–11455 Ass: grain boundary area (i.e. cross section area of particle cut by the vertical plane through points A and B.) Asv: area of gas-solid interface

A

S1: disappeared surface area due to sintering

0

V1: transported volume due to sintering

h

y

r 2r h

B V2: volume of a residual part

Fig. 1. Schematic of grain boundary development in sintered alumina powder compacts with uniform microstructures.

circular grain boundary area (πy2, y: radius of the circular grain boundary shown in Fig. 1) according to Eq. (3) [16]:  2=3 N σ ¼ σ 0 π y2 ; ð3Þ V where σ0 is the compressive strength of dense ceramics without pores [17,18], N is the particle number in one sintered powder compact and V is the bulk volume of a sintered powder compact. The (N/V)2/3 value represents the particle number per unit area of the compressive plane. Therefore, the strength of a porous ceramic compact is increased by the increase in the packing density and enlargement of the grain boundary area. Herein we report the effect of particle size on (1) the densification of alumina compacts, (2) the development of the grain boundary area during the initial to intermediate stages of sintering and (3) the compressive strength of porous sintered compacts using three types of high purity alumina powders. 2. Experimental 2.1. Fabrication of porous alumina compacts Three types of alpha-alumina particles (Al2O3, purity499.99 mass%, Sumitomo Chemical Co. Ltd., Japan) were consolidated via pressure filtration to make powder compacts with uniform microstructures: AKP50 (specific surface area S0=9.61 m2/g, equivalent diameter d0=156 nm, isoelectric point pH 6.37), AKP30 (S0=7.24 m2/g, d0=210 nm, isoelectric point pH 6.76) and AKP20 (S0=4.28 m2/g, d0=351 nm, isoelectric point pH 5.31). The alumina powders were dispersed at a solid content of 10 vol% in double distilled water adjusted to pH 3 with an HCl solution. In addition, the alumina particles were positively charged in order to produce a strong repulsive energy between them. The suspensions were stirred for 24 h and then consolidated to form a 20-mmdiameter and 5-mm-thick disk using pressure filtration equipment [19–21] at a crosshead speed of 0.2 mm/min up to 19 MPa. A three-layered membrane filter with a pore size of 100 nm was attached to the bottom of the piston in order to exhaust the solution through the internal piston pore. The consolidated powder compacts were dried at 100 1C in air for 24 h and then sintered at 700–1320 1C in air for 1 h. The bulk and apparent densities of the sintered alumina compacts were measured using the Archimedes method [22] with double distilled water. The

microstructures were observed using a field-emission scanning electron microscope (FE-SEM, S-4100H, Hitachi HighTechnologies Co., Japan). The pore size distributions of the sintered alumina compacts were determined using a mercury penetration method and a nitrogen adsorption method at the Saga Ceramics Research Laboratory (3037-7 Kuromuta, Arita-cho, Nishimatsuura-gun, Saga 844-0024, Japan). The Brunauer– Emmett–Teller (BET) specific surface areas of the sintered alumina compacts were determined using a nitrogen gas adsorption method (FlowSorb II 2300, Shimazu Co., Japan). 2.2. Measurement of compressive strength Each sintered porous alumina compact was cut into a rectangular prism with a length of 5 mm, a width of 4 mm and a height of 5 mm. The alumina sample was then sandwiched between two three-layer laminates composed of two copper plates (20  20  1 mm3) with a sintered SiC plate (20  18  7 mm3) between them. The sample was then compressed at a crosshead speed of 0.5 mm/min while the strain along the compressive direction was measured using a strain gauge attached to the sample. The detailed configuration for the compressive test has been reported elsewhere [16,23]. The compressive test was repeated with five samples for each sintering condition. 3. Results and discussion 3.1. Sintering behaviour of the porous alumina compacts Fig. 2(a) shows the dependence of the relative densities of the alumina compacts on the sintering temperature. No significant difference in the packing densities of sintered alumina compacts with different particle sizes was observed at 700 1C (61.9% for AKP50, 60.9% for AKP30 and 60.8% for AKP20). In addition, although only minor densification occurred at 700–1000 1C, the relative density increased from 90

Relative density (%)

y

Decrease in specific surface area, ΔS (m2/g)

11450

80

AKP50 AKP30 AKP20

70

60 50 8 6

AKP50 AKP30 AKP20

4 2 0

600

800

1000

1200

1400

Sintering temperature (ºC) Fig. 2. (a) Relative density and (b) decrease in the specific surface area of the alumina compacts as a function of the sintering temperature.

Y. Hirata et al. / Ceramics International 41 (2015) 11449–11455

approximately 60% to 80% at 1000–1320 1C. Furthermore, during sintering at 1160–1320 1C, the sintering rate increased for the samples with smaller particles, indicating that the diffusion rate and the distance of the diffusion path for the component atoms controlled the sintering rate [24]. In Fig. 2 (b), a decrease in the specific surface area (ΔS) of the alumina compacts with heating can be seen. Interestingly, a gradual increase in ΔS was observed with heating at 700–1000 1C, which is the temperature range in which the bulk density was not sensitive to the heating temperature. The changes in the surface area are related to the initial stage of neck growth (formation of grain boundaries) between the alumina particles, as shown in Fig. 1. The dependence of the densification rate on the particle size at 1160–1320 1C in Fig. 1(a) is well reflected

Relative density (%)

100

d

c

b

a

90

80 70

in the ΔS values, with higher densification rates accompanied by larger ΔS values. Fig. 3 shows the relative density as a function of linear shrinkage (q) during sintering based on the starting diameters or heights of the alumina disks. The solid lines represent the theoretical relationship between the relative density (D) and the linear shrinkage (q) as described in Eq. (4): D ¼ D0

1 ð1  qÞ3

ð4Þ

The value of D0 is 0.524, 0.637, 0.680 and 0.741 for spherical particles with a simple cubic structure (sc), a random close packed structure (rcp), a body-centred cubic structure (bcc) and a cubic close packed structure (ccp), respectively. The initial packing densities (60.8–61.9%) for the AKP50, 30 and 20 particles near q¼ 0% were close to the D0 value for an rcp structure. The q values for the diameters and heights of the disks during sintering were distributed along the rcp and sc curves for the D–q relationship, respectively. These results suggest that the alumina particles were packed in mixed sc and rcp structures. 3.2. Microstructures of the sintered alumina compacts

Powder Diameter Height AKP50 AKP30 AKP20

60 50 0.00

11451

0.05

0.10

0.15

0.20

Shrinkage, q (-) Fig. 3. Relative density as a function of linear shrinkage (q) based on the initial diameter or height of the alumina compacts. The solid lines show an increase in the relative density with an increase in the linear shrinkage for spherical particles with (a) a simple cubic structure, (b) a random close packing structure, (c) a body-centred cubic structure and (d) a cubic close packing structure.

Fig. 4 shows typical microstructures for AKP30 sintered at (a, b) 800 and (c, d) 1180 1C. The alumina particles in (a) and (c) were uniformly packed, and the cumulative distributions of the grain and pore sizes were well fitted using normal distribution curves (solid lines), which supports the formation of uniform microstructures. The median size of the alumina grains changed in the following range: 123 nm (800 1C)–170 nm (1190 1C) for AKP50 (starting equivalent diameter for the specific surface area, d0 ¼ 156 nm), 181 nm (800 1C)–207 nm (1260 1C) for AKP30

800 ºC

1180 ºC

Cumulative percent (%)

1 μm

1 μm

100 80 60 40

Pore size D50 = 38.0 nm Particle size D50 = 180.8 nm

20 0

0

Pore size D50 = 55.1 nm Particle size D50 = 205.9 nm

100 200 300 400 0 100 200 300 400 500 Pore size or particle size (nm) Pore size or particle size (nm)

Fig. 4. (a, c) Microstructures and (b, d) pore and particle size distributions for the AKP30 compacts sintered at (a, b) 800 1C and (c, d) 1180 1C.

Y. Hirata et al. / Ceramics International 41 (2015) 11449–11455

Cumulative pore volume (cm3/g)

(d0 ¼ 210 nm) and 287 nm (800 1C)–289 nm (1320 1C) for AKP20 (d0 ¼ 351 nm). The ratios of the median sizes during sintering to the d0 values were 0.79–1.09 for AKP50, 0.86–0.99 for AKP30 and 0.82 for AKP20, indicating that grain growth had little effect on the densification observed in Fig. 2(a). As can be seen in Fig. 4(b) and (d), open pores were also uniformly formed among the alumina grains. Because the initial packing densities at q¼ 0% for AKP50, 30 and 20 in Fig. 3 were close to the packing density (63.7%) of an rcp structure, two types of pores were formed in the alumina compacts: four particle-coordinated pores and six particle-coordinated pores [25]. The diameters of the pores were estimated to be 0.225d0 (47.2 nm for AKP30) and 0.414d0 (87.0 nm for AKP30) for the four-coordination pores and six-coordination pores, respectively. In addition, the ratio of the theoretical volumes for the four particle-coordinated pores and six particles-coordinated pores was 0.242:0.758 [25]. Furthermore, the pore sizes in the cumulative 0–80% range for AKP 30 (Fig. 4 (b) and (d)) were less than  100 nm and matched the pore sizes for an rcp structure. Additional quantitative measurements of the pore size distributions for the AKP30 compacts are shown in Fig. 5, which shows the cumulative pore volumes for the sintered AKP30 compacts measured using an Hg porosimeter. The distribution curves rose sharply in the pore size range 50– 100 nm. In addition, the pore volumes decreased at sintering temperatures greater than 1000 1C, which is in agreement with the sintering behaviour shown in Fig. 2(a). In the AKP30 sintered compact, the median sizes of the pores were 81.8–90.3 nm at sintering temperatures of 800–1180 1C and decreased to 59.7 nm at 1260 1C. Notably, the median sizes at 800–1180 1C were very close to the calculated value (87 nm) for the pores coordinated by six particles. On the other hand, pores with diameterso 50 nm (corresponding to four particlecoordinated pores, 47.2 nm diameter) were barely detected using the Hg-porosimeter. That is, the pores in Fig. 5 were mainly associated with six particle-coordinated pores, and thus, it is thought that the smaller four particle-coordinated pores may have rapidly shrunk during heating. Determination of the pore volumes in AKP30 samples sintered at 800–1260 1C using a nitrogen adsorption method revealed the formation of smaller pores with median sizes of 10.6– 10.0 nm (pore volumes of 0.015–0.005 cm3/g). These small pores likely formed from four particle-coordinated pores 0.20

0.15

0.10

Sintering Median Key temp. (ºC) size (nm) 800 81.8 1000 85.4 1180 90.3 1260 59.7

a b

c d

during sintering. The above pore size distribution results thus lead to the following conclusions: (1) the strongly dispersed submicrometer-sized alumina particles were consolidated via pressure filtration to form high-density, uniform microstructures characterised by a random close-packing structure of spherical particles; (2) during heating, smaller four particlecoordinated pores shrunk faster than larger six particlecoordinated pores and (3) during the initial to intermediate stages of sintering, little grain growth occurred. 3.3. Analysis of densification of the alumina powder compacts using the specific surface area The relationship between the shrinkage and relative density of the alumina compacts is shown in Fig. 3. In addition, little grain growth during heating at 700–1320 1C was shown in Fig. 4. Using these results, the relationship between the decrease in the specific surface area (ΔS m2/g) of the sintered alumina compacts and the formation of the grain boundaries seen in Fig. 1 without any change in the number of particles was determined. Fig. 6 shows the relationship between the linear shrinkage (q) and the normalised decrease in the specific surface area for the sintered alumina compacts. The q values represented by three solid lines were calculated using the following equation with h and p derived according to Eqs. (1) and (2), respectively [16]:  1=3 h 4 q¼ ¼p : ð5Þ r0 4  3np2 þ np3 The theoretical values for ΔS/S0 were calculated using Eq. (6): ΔS S0  S A0  ASV 4  2np ¼ ¼ ¼ 1 1=3 S0 S0 A0 4 ð4 3np2 þ np3 Þ2=3 2 ðA0 : 4π r 0 ; ASV : see Eq:ð1ÞÞ ð6Þ From Eqs. (5) and (6), the theoretical q–ΔS/S0 relationship was calculated for an arbitrary p value and a constant n value. Fig. 6 shows the three solid lines for n ¼ 6 (sc structure), 8 (bcc structure) and 12 (rcp and ccp structures). It is understood that the calculated linear shrinkage of sintered powder com0.25 Powder Diameter Height

Linear shrinkage, q (-)

11452

AKP50

0.20 AKP30 AKP20

0.15

(b) n = 8

(c) n = 12

0.10 0.05

0.00 0.0

0.05

(a) n = 6

0.2

0.4

0.6

0.8

1.0

Decreased rate of specific surface area, ΔS/S0 (-) 0.00 0.001

0.01

0.1

1

10

100

1000

Pore size (μm) Fig. 5. Cumulative pore volumes measured using an Hg porosimeter for the AKP30 compacts sintered at 800–1260 1C.

Fig. 6. Linear shrinkage of the sintered alumina compacts as a function of the rate of decrease for the specific surface area at sintering temperatures ranging from 700–1320 1C. The solid lines represent the calculated linear shrinkage for sintered alumina compacts with particle coordination numbers (n) of 6, 8 and 12.

Y. Hirata et al. / Ceramics International 41 (2015) 11449–11455

pacts increases as n decreases at a similar ΔS/S0 ratio. The experimentally determined q–ΔS/S0 plots are distributed around the theoretical curve for n¼ 12. This result supports the densification of the alumina compacts along the solid line for an rcp structure as shown in Fig. 3. The relative density–ΔS relationships for the AKP50, 30 and 20 compacts can be seen in Fig. 7. The three solid lines represent the theoretical relationships in Eqs. (6) and (4) for an arbitrary p value and with n=12 (rcp structure). The q values used in Eq. (4) were determined using Eq. (5). The experimentally determined D–ΔS relationships are also plotted in Fig. 7. Although further analysis is required to establish quantitative agreement between the calculated and measured curves, the behaviour of the experimentally obtained data matches well that of the theoretical curves. Neck formation (ASS in Fig. 1) decreased the distance between two particles, which was accompanied by a decrease in the specific surface area of the sintered particles (ASV in Fig. 1). The calculated density therefore increased more rapidly for the larger particles (AKP50 o AKP30 o AKP20) at a similar ΔS during heating. The experimentally measured relative densities also increased in the following order: AKP50 E AKP30 o AKP20, as indicated by the theoretical D–ΔS relationship. The small difference in the sintered densities for AKP50 and AKP30 may be due to the close median sizes of the starting particles (156 and 210 nm, respectively). However, the heating temperature needed to achieve a similar ΔS value increased for the larger particles in the AKP20 compact (Fig. 2(b)). The calculated ratios for the neck (2y in Fig. 1) and starting particle diameters are plotted as a function of the ΔS values in Fig. 8. The 2y value was expressed using Eq. (7): sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2p  p2 2y ¼ 2 r 2  ðr  hÞ2 ¼ 25=3 r 0 : ð7Þ ð4  3np2 þ np3 Þ2=3 Fig. 8 is closely related to the D–ΔS relationship seen in Fig. 7. When the ΔS value increased, the neck diameter increased, causing densification of the alumina compacts (Fig. 7). In addition, the 2y/2r0 ratio increased for larger particles at a similar ΔS value. (f) AKP20 (cal.)

Fig. 9 shows the relationship between the compressive stress and strain for AKP30 compacts sintered at (a) 1000 1C, (b) 1180 1C and (c) 1260 1C. The stress–strain curves for the porous alumina compacts often exhibited zigzag-like deformation. Although a relatively wide distribution of fracture strengths was measured at each sintering temperature, the average fracture strength increased as the sintered density increased. The Young's modulus of each sintered compact was determined from the slope of the linear approximation of the corresponding stress–strain curve up to 0.05% strain. Fig. 10 shows the dependence of the (a) compressive strength, (b) Young's modulus and (c) strain at fracture on the sintering temperature. It was shown above that the sintering temperature widely affected the relative density (Figs. 2 and 3), pore size (Fig. 5) and neck diameter (Fig. 8) of the alumina compacts. In Fig. 10(a) it can be seen that the strength of the compacts tended to increase at higher sintering temperatures but was not significantly influenced by the initial particle size. In addition, comparing the data in Fig. 2 to the results in Fig. 10(b) revealed that the Young's modulus was nearly constant at a relative density of 60–70% and increased to greater than 200 GPa at a relative density of 80%. Furthermore, the strain at fracture was small (0.1–0.2%) in the compacts sintered at 1000 1C, but increased to 0.4% in the samples sintered at 1160–1320 1C. As mentioned above, each mechanical property exhibited a different dependency on the sintering temperature. The measured properties in Fig. 10 are plotted in Fig. 11 against the ratio (T) of the total grain boundary area to the unit area of the compressive plane in each alumina compact, where T is equal to πy2(N/V)2/3 in Eq. (3). Fig. 11(a) shows the relationship between the compressive strength and the grain boundary area of the sintered alumina compacts. The compressive strength increased linearly with increasing grain boundary area. On the other hand, the initial particle size had no influence on the strength–grain boundary area relationship (Fig. 11(a)). The slopes of the linear approximations of the plots represent the compressive strength of dense alumina without pores (effective compressive strength, σ0, in Eq. (3)). The σ0 values for AKP50, AKP30 and AKP20 were all 1.91 GPa, which was slightly less than

(e) AKP30 (cal.) (d) AKP50 (cal.)

90

1.0 0.8

(a) AKP50

70

(c) AKP20 (b) AKP30 (a) AKP50

(b) AKP30

80 (c) AKP20

60 50

3.4. Mechanical properties of the sintered alumina compacts

2y / 2r0 (-)

Relative density (%)

100

11453

0.6 0.4 0.2

0

2

4

6

8

ΔS (m2/g) Fig. 7. Relative densities of sintered alumina compacts as a function of the decrease in the specific surface area. The solid lines in (d), (e) and (f) represent the calculated relative densities for a random close packing structure with a particle coordination number of 12.

0.0

0

2

4

6

8

ΔS (m2/g) Fig. 8. Calculated neck size to initial particle diameter ratios as a function of the decreasing in the specific surface area of the alumina compacts.

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Y. Hirata et al. / Ceramics International 41 (2015) 11449–11455

200

No. 2 No. 3 No. 4

No. 1

0 600

No. 5 No. 3

400

No. 4

No. 2

200

No. 1 No. 5

0 600

No. 2 No. 1

No. 4

400

No. 5

No. 3

Young's modulus (GPa)

Stress (MPa) Stress (MPa) Stress (MPa)

400

Compressive strength (MPa)

1000

600

200

0.0

0.1

0.2

0.3

0.4

400 200 0 600

Fig. 9. Stress–strain curves for AKP30 alumina compacts sintered at (a) 1000 1C, (b) 1180 1C and (c) 1260 1C. 1000

AKP50 AKP30 AKP20

500

0 400

400

200

0.5

0.0

0.0

0.1

0.2

0.3

Fig. 11. (a) Compressive strength and (b) Young's modulus as a function of the grain boundary area per unit area of the compressive plane (See Eq. (3)).

size once again appeared to have no influence on the Young's modulus for a given grain boundary area. This result indicates that the likelihood of deformation in sintered alumina compacts at a given applied stress is largely determined by the grain boundary area. 4. Summary

AKP50 AKP30 AKP20

200 0 1.0

AKP50 AKP30 AKP20

π y2(N/V)2/3 (-)

0.5

Strain (%)

Young's modulus Compressive Strain at strength (MPa) (GPa) fracture (%)

600

0

0

AKP50 AKP30 AKP20

800

AKP50 AKP30 AKP20

1000

1100

1200

1300

Sintering temperature (ºC) Fig. 10. (a) Compressive strength, (b) Young's modulus and (c) strain at fracture for the alumina compacts as a function of the sintering temperature.

previously reported values for dense, polycrystalline alumina (σ0 ¼ 2.2 GPa [17] and 2.6 GPa [18]). In addition, in previous work [16] the σ0 value determined for alumina compacts with relative densities of 60–63% was calculated to be 0.83 GPa. The increase in the value of σ0 with densification in alumina compacts reflects closely their fracture behaviour under compressive stress (Fig. 9). The present σ0 value for the sintered alumina compacts includes all of the complex information related to the compressive, tensile and shear stress applied to the weak grain boundaries. Fig. 11(b) shows the Young's modulus as a function of the grain boundary area. The Young's modulus of the sintered alumina compacts increased linearly as the grain boundary area increased. This tendency of the Young's modulus is similar to that of the compressive strength in Fig. 11(a). On the other hand, the initial particle

Alumina powder compacts with uniform microstructures were consolidated from aqueous suspensions of three types of submicrometer-sized particles (particle diameters 156, 210 and 351 nm) at pH 3.0 using pressure filtration. The sintering rate was higher for the smaller particles, and thus, the diffusion rate and distance of the diffusion path for the component atoms controlled the sintering rate. In addition, higher densification rates were accompanied by greater decreases in the specific surface area (ΔS) of the alumina compacts. Notably, the cumulative grain and pore size distributions were well fitted by normal distribution curves. Furthermore, during heating, the smaller four particle-coordinated pores shrunk faster than larger six particle-coordinated pores, and during the initial to intermediate stages of sintering, little grain growth occurred during heating. Specifically, the calculated linear shrinkage of the sintered compacts increased as the particle coordination number (n) decreased at a similar ΔS/S0 ratio (S0: starting specific surface area of the alumina compacts). Densification of the alumina compacts with initial packing densities of 60.8–61.9% proceeded along the calculated densification curve for spherical particles with a random close-packing structure (n ¼ 12) and neck formation between two particles decreased the distance between them, leading to a decrease in the specific surface area of the sintered particles. It should also be noted that the sintered density or the ratio of the neck and initial particle diameters increased during heating for larger particles at a similar ΔS, although achieving a similar ΔS value with larger particles required higher temperatures. Importantly, the compressive strength and Young's modulus increased linearly with an increase in the grain boundary area, while the initial

Y. Hirata et al. / Ceramics International 41 (2015) 11449–11455

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