# The Effect of Particle Shape on Sintering Behavior and Compressive Strength of Porous Alumina

^{*}

## Abstract

**:**

## 1. Introduction

_{porous}is the Young’s modulus of partially sintered porous ceramics with porosity (P), E

_{dense}is the Young’s modulus for fully dense ceramics, and P

_{green}is the porosity of the green body before sintering. The exponent n is fitted to be 1.15 in Reference [2] and E

_{porous}approaches E

_{dense}at P = 0%. Kim et al. reported the compressive strength of microcellular mullite where small spherical cells (≤ 20 μm) were distributed homogeneously. The controlled cell size and porosity are key factors to fabricate a strong porous structure [14]. In our previous papers [15,16,17,18], we proposed Equation (2) for the compressive strength (σ

_{p}) of partially sintered porous alumina,

_{0}value corresponds to the strength needed to fracture the several grain boundaries (n) surrounding three-dimensionally one grain at 0% porosity, and is expressed by Equation (3),

_{gb}) for one grain layer per unit area (1 m

^{2}) of a porous ceramics perpendicular to the compressive direction is given by Equation (4) from Equations (2) and (3).

_{gs}) of the gas–solid interface and the grain boundary area (A

_{pp}) of the particle–particle interface per particle of radius r are expressed by Equations (5) and (6), respectively,

_{1}is the disappeared surface area due to sintering, r

_{0}is the radius of the starting particles and p is the ratio of the shortened distance (h) between two particles to the particle size (r) (p = 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 using Equation (7) [16].

_{0}represents the specific surface area before sintering and S represents the specific surface area after sintering, A

_{0}is equal to 4πr

_{0}

^{2}, and p is obtained from the ratio of the specific surface area before and after sintering. Another way to determine the p value is to apply Equations (8) and (9) regarding the relative density D and the linear shrinkage q, respectively, for p value [15,18],

_{0}represents the relative density before sintering. The relative density (D) of sintered porous compact is approximated by Equation (10) [18].

_{0}

^{3}) in Equation (10) is connected to the (N/V)

^{2/3}value in Equation (2), giving the relation of (N/V)

^{2/3}≈ D

^{2/3}/(2.599r

_{0}

^{2}). This relation is substituted for Equation (2) to give Equation (11).

_{0})

^{2}value is expressed by Equation (12) as a function of shrinkage p.

_{2}O

_{3}whiskers with 100–200 nm length and 20 nm width to matrix WC particles enhanced the flexural strength as compared with the powder composite of the 10 mass% Al

_{2}O

_{3}–90 mass% WC system [21]. The strengthening mechanisms were attributed to crack deflection, crack bridging, and ligamentary bridging between crack surfaces. However, few papers have reported the mechanical properties of porous ceramics prepared from whiskers or rod-like particles. In this paper, the sintering behavior and the compressive strength were examined for the alumina porous compacts prepared from spherical, rod-like and disk-like alumina particles. The goal of this paper is to identify the key factors affecting the mechanical properties of the partially sintered porous ceramics by comparing the measured strength and the proposed theoretical analysis. It is clearly demonstrated that the compressive strength, which is greatly affected by the shape of starting particles, depends on the number (n

_{f}) of grain boundaries which originally surround one grain and are fractured by a compressive stress. The uniform distribution of the applied load over many grain boundaries is a key factor to increase the compressive strength of partially sintered porous ceramics.

## 2. Experimental Procedure

#### 2.1. Analysis of Starting Alumina Powders

_{2}O

_{3}: 99.8, SiO

_{2}: 0.03, FeO

_{2}: 0.02, Na

_{2}O: 0.02, Ig. loss: 0.12; (c) spherical particles, Al

_{2}O

_{3}purity > 99.99 mass%. The phases of alumina powders were identified by X-ray diffraction analysis (RINT 2200PCH/KG, Rigaku Co. Ltd., Tokyo, Japan). Particle morphology of alumina was observed by transmission electron microscope (TEM, JEM-3010, JEOL Ltd., Tokyo, Japan) and field emission electron microscope (S-4100H FE-SEM, Hitachi High-Tech Technologies Co., Tokyo, Japan). The dilute aqueous suspensions of the alumina particles at pH 3 were prepared and dropped on collodion membranes for TEM observation. The specific surface areas of alumina powders were measured by the Brunauer–Emmett–Teller (BET) method at P (equilibrium N

_{2}pressure)/P

_{0}(saturated N

_{2}pressure) = 0.30 using a mixed gas of 30% N

_{2}–70% He (Flow Sorb II 2300, Shimadzu, Co., Kyoto, Japan). The sample was heated at 100 °C for 24 h to eliminate the adsorbed gas before BET measurement. The median size of alumina particles was measured by centrifugal sedimentation method of a dilute alumina suspension (CAPA-700; Horiba Ltd., Kyoto, Japan). The true density of α-alumina powder was measured with pycnometer using double-distilled water. The isoelectric point of alumina particles was measured in a 0.001 M NH

_{4}NO

_{3}solution (Rank Mark II, Rank Brothers Ltd., Cambridge, UK). Figure 1 shows particle morphology of (a) rod-like particles, (b) disk-like particles, and (c) spherical particles. The length and width of rod-like particles were 200–400 nm and 100–200 nm, respectively. The diameter and thickness of disk-like particles were 1–10 μm and 1 μm, respectively. Although the median size measured by centrifugal sedimentation method was 1.47 μm, large particles above 10 μm were included in the disk-like particles. The spherical particles possessed a narrow particle size distribution of median size 0.60 μm.

#### 2.2. Sintering of Porous Alumina Compacts

_{3}solution. The positively charged alumina particles were stirred for 24 h at room temperature and then consolidated in a cylindrical vinyl chloride pipe mold (inner diameter of 15 mm, outer diameter of 18 mm, height of 30 mm) placed on a gypsum board for one week. The dried powder compacts were heated at 5 °C/min and sintered at 700–1600 °C in air for 1 h (SPM 6512 electric furnace, Marusho Denki Co. Ltd., Himeji, Japan). The sintered density and porosity were measured by the Archimedes method using double-distilled water. The specific surface area of sintered compact was measured by Brunauer–Emmett–Teller (BET) method (Flow Sorb II 2300, Shimadzu, Co., Kyoto, Japan). The microstructures of sintered alumina compacts were observed by field emission electron microscope (S-4100H FE-SEM, Hitachi High-Tech Technologies Co., Tokyo, Japan).

#### 2.3. Young’s Modulus and Compressive Strength of Sintered Porous Alumina

^{3}). The sample was then compressed at a crosshead speed of 0.5 mm/min (Tensilon RTC, A&D Co. Ltd., Tokyo, Japan) while the strain along the compressive direction was measured using a strain gauge (4 mm × 3 mm) attached to the sample. The compressive test was performed with more than five samples for each sintering condition [15]. The Young’s modulus of the sintered compact was evaluated from the stress-strain curve up to 0.05% strain. The loading and unloading test was repeated more than five times for each sample. The sudden decrease of the compressive strain as shown in Section 3.3 reflected the compressive fracture.

## 3. Results and Discussion

#### 3.1. Sintering Behavior

#### 3.2. Microstructures of the Sintered Alumina Compacts

^{2}/g, Table 1) and small sizes (0.55 μm median size, Figure 1) were densified with grain growth. The grain growth of primary rod-like particles occurred below 1200 °C without significant densification. The shape of rod-like particles changed to more spherical particles at a high sintering temperature. On the other hand, no significant change of the relative density and the microstructure was observed for the disk-like particles with a low specific surface area (1.16 m

^{2}/g) and the large particle sizes (1.47 μm median size). As compared with the rod-like particles or disk-like particles, the spherical particles were densified faster (Figure 2a) with little significant grain growth. As observed in Figure 2 and Figure 3, the particle shape provided great influence on the sintering behavior and grain growth rate.

#### 3.3. Compressive Mechanical Properties

#### 3.4. Analysis of Compressive Strength

_{0}= 0.335, q = 0.306, and p = 0.271, F = 0.8130 for rod-like particles at n = 12, D

_{0}= 0.335, q = 0.306, and p = 0.244, F = 0.3488 for disk-like particles at n = 12, D

_{0}= 0.623, q = 0.146, and p = 0.138, and F = 0.3639 for spherical particles at n = 12, D

_{0}= 0.610, q = 0.152, and p = 0.143. The calculated σ(dense) value was 0.346 (n = 6)–0.366 GPa (n = 12) for the rod-like particles, 0.288 GPa for the disk-like particles (n = 12), and 1.320 GPa for the spherical particles (n = 12). The calculated σ(dense) value for the spherical particles was 40–60% of the reported compressive strength (2.2–3.3 GPa) of dense alumina ceramics [22,23], and was discussed in latter part of this section. However, the above calculated σ(dense) values should be close to each other at 0% porosity. The difference in the above σ(dense) values for different particle shape is interpreted as follows. The compressive strength of porous ceramics (σ

_{p}) is expressed by Equation (15) and related to the compressive strength of fully dense ceramics, f(p) value defined by Equation (13) (=3.046(2p − p

^{2}) D

^{2/3}/(4 − 3np

^{2}+ np

^{3})

^{2/3}) and the number (n

_{f}) of grain boundaries which originally surrounded one grain and were fractured by a compressive stress.

_{f}value at fracture is distinguished from the coordination number (n) in f(p) value related to the sintering process. That is, the σ

_{0}value in Equation (13) is expressed by Equation (16).

_{f}(dense) values for the spherical particles were calculated to be 0.3639 and n

_{f}= 2/F = 5.50, respectively. The ratio of n

_{f}to n (coordination number = 12) resulted in 0.458. The ratio of σ

_{0}(porous)/σ

_{0}(dense) is calculated from Equations (16) and (17) as follows.

_{0}values for dense and porous compacts are measured, the ratio provides the n

_{f}(porous) value. Similarly, Equation (16) is useful to analyze the n

_{f}(porous) of partially sintered porous alumina for two kinds of particles as expressed by Equation (19).

_{0}(porous, rod, n = 12)/σ

_{0}(porous, spherical, n = 12) resulted in 0.124, suggesting that the number of grain boundaries fractured by an applied stress was significantly smaller for rod-like particles or disk-like particles as compared with spherical particles. That is, the applied load concentrates on a few grain boundaries of rod-like particles, causing the fracture at a low compressive stress. The uniform distribution of the applied load over many grain boundaries of spherical particles contributes to the increase in the compressive strength of the partially sintered porous ceramics.

#### 3.5. Observation of Fractured Surfaces

_{f}(porous) value is smaller than the coordination number (n) in the sintering process.

_{f}value in Equation (16) for the increased strength. The comparison of the microstructures between Figure 3f (sintered surface) and Figure 7f (fractured surface) for the disk-like particles suggests little formation of apparent grain boundaries, resulting in the low compressive strength. The above observation agreed basically with the analysis of strength in Section 3.4.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Wan, P.; Wang, J. Highly porous nano-SiC with very low thermal conductivity and excellent high temperature behavior. J. Eur. Ceram. Soc.
**2018**, 38, 463–467. [Google Scholar] [CrossRef] - Fukushima, M.; Yoshizawa, Y.-I. Fabrication and morphology control of highly porous mullite thermal insulators prepared by gelation freezing route. J. Eur. Ceram. Soc.
**2016**, 36, 2947–2953. [Google Scholar] [CrossRef] - Bruzzoniti, M.C.; Appendini, M.; Rivoira, L.; Onida, B.; Bubba, M.D.; Jana, P.; Soraru, G.D. Polymer-derived ceramic aerogels as sorbent materials for the removal of organic dyes from aqueous solutions. J. Am. Ceram. Soc.
**2018**, 101, 821–830. [Google Scholar] [CrossRef] - Ma, H.; Hei, Y.; Wei, T.; Li, H. Three-dimensional interconnected porous tablet ceramic: Synthesis and Pb(II) adsorption. Mater. Lett.
**2017**, 196, 396–399. [Google Scholar] [CrossRef] - Pechenkin, A.A.; Badmaev, S.D.; Belyaev, V.D.; Sobyanin, V.A. Performance of bifunctional CuO–CeO
_{2}/γ-Al_{2}O_{3}catalyst in dimethoxymethane steam reforming to hydrogen-rich gas for fuel cell feeding. Appl. Catal. B Environ.**2015**, 166–167, 535–543. [Google Scholar] [CrossRef] - Ishiyama, T.; Kurimoto, K.; Kita, M.; Otsuka-Yao-Matsuo, S.; Omata, T. Enhancement by praseodymium addition of catalytic activity of nickel supported on cerium–zirconium oxide in methane steam reforming. J. Ceram. Soc. Jpn.
**2014**, 122, 537–542. [Google Scholar] [CrossRef] - Shikazono, N.; Kanno, D.; Matsuzaki, K.; Teshima, H.; Sumino, S.; Kasagi, N. Numerical assessment of SOFC anode polarization based on three dimensional model microstructure reconstructed from FIB-SEM images. J. Electrochem. Soc.
**2010**, 157, B665–B672. [Google Scholar] [CrossRef] - Cronin, J.S.; Wilson, J.R.; Barnett, S.A. Impact of pore microstructure evolution on polarization resistance of Ni-yttria-stabilized zirconia fuel cell anodes. J. Power Sources
**2011**, 196, 2640–2643. [Google Scholar] [CrossRef] - Abo-Almaged, H.H.; Gaber, A.A. Synthesis and characterization of nano-hydroxyapatite membranes for water desalination. Mater. Today Commun.
**2017**, 13, 186–191. [Google Scholar] [CrossRef] - Bukhari, S.Z.A.; Ha, J.-H.; Lee, J.; Song, I.-H. Oxidation-bonded SiC membrane for microfiltration. J. Eur. Ceram. Soc.
**2018**, 38, 1711–1719. [Google Scholar] [CrossRef] - Ryshkewitch, E. Compression strength of porous sintered alumina and zirconia. J. Am. Ceram. Soc.
**1953**, 36, 65–68. [Google Scholar] [CrossRef] - Rice, R.W. Comparison of stress concentration versus minimum solid area based mechanical property relations. J. Mater. Sci.
**1993**, 28, 2187–2190. [Google Scholar] [CrossRef] - Ostrowski, T.; Ziegler, A.; Bordia, R.; Rodel, J. Evolution of Young’s modulus, strength and microstructure during liquid phase sintering. J. Am. Ceram. Soc.
**1998**, 81, 1852–1860. [Google Scholar] [CrossRef] - Kim, Y.-W.; Kim, H.-D.; Park, C.B. Processing of microcellular mullite. J. Am. Ceram. Soc.
**2005**, 88, 3311–3315. [Google Scholar] [CrossRef] - Hirata, Y.; Shimonosono, T.; Sameshima, T.; Sameshima, S. Compressive mechanical properties of porous alumina compacts. Ceram. Int.
**2014**, 40, 2315–2322. [Google Scholar] [CrossRef] - Hirata, Y.; Shimonosono, T.; Sameshima, S.; Tominaga, H. Sintering of alumina powder compacts and their compressive mechanical properties. Ceram. Int.
**2015**, 41, 11449–11455. [Google Scholar] [CrossRef] - Hirata, Y.; Takehara, K.; Shimonosono, T. Analyses of Young’s modulus and thermal expansion coefficient of sintered porous alumina compacts. Ceram. Int.
**2017**, 43, 12321–12327. [Google Scholar] [CrossRef] - Hirata, Y.; Fujita, H.; Shimonosono, T. Compressive mechanical properties of partially sintered porous alumina of bimodal size system. Ceram. Int.
**2017**, 43, 1895–1903. [Google Scholar] [CrossRef] - Dong, X.; Wang, M.; Guo, A.; Zhang, Y.; Ren, S.; Sui, G.; Du, H. Synthesis and properties of porous alumina ceramics with inter-locked plate-like structure through the tert-butyl alcohol-based gel-casting method. J. Alloys Compd.
**2017**, 694, 1045–1053. [Google Scholar] [CrossRef] - Faber, K.T.; Evans, A.G. Crack deflection processes—I. Theory. Acta. Metall.
**1983**, 31, 565–576. [Google Scholar] [CrossRef] - Dong, W.; Zhu, S.; Bai, T.; Luo, Y. Influence of Al
_{2}O_{3}whisker concentration on mechanical properties of WC–Al_{2}O_{3}whisker composite. Ceram. Int.**2015**, 41, 13685–13691. [Google Scholar] [CrossRef] - STC Corporation, Alumina (AL998, AL998E). Available online: http://www.ceramics.net/ (accessed on 13 June 2018).
- Accuratus Corporation, Alumina Oxide. Available online: http://accuratus.com/alumox.html (accessed on 28 June 2018).

**Figure 1.**Particle morphology of (

**a**) rod-like alumina, (

**b**) disk-like alumina and (

**c**) spherical alumina.

**Figure 2.**Relation between sintering temperature and (

**a**) relative density or (

**b**) specific surface area of sintered alumina compacts.

**Figure 3.**Microstructures of alumina compacts sintered from (

**a**–

**c**) rod-like particles, (

**d**–

**f**) disk-like particles, and (

**g**–

**i**) spherical particle at 1000–1600 °C.

**Figure 4.**Compressive stress–strain curves for the alumina compacts sintered from (

**a**) rod-like particles, (

**b**) disk-like particles, and (

**c**) spherical particles at 1000–1600 °C.

**Figure 6.**Relation between compressive strength and the right term of Equation (13) associated with grain boundary area.

**Figure 7.**Fractured surfaces of alumina compacts sintered from (

**a**–

**c**) rod-like particles, (

**d**–

**f**) disk-like particles, and (

**g**–

**i**) spherical particle at 1000–1600 °C.

Powder No. | L30N2-F1112 | ACLM-27 | AKP20 |
---|---|---|---|

Crystal structure | α-alumina | α-alumina | α-alumina |

Manufacturer | Asahikasei | Sumitomo Chemical | Sumitomo Chemical |

Particle shape | Rod-like | Disk-like | Spherical |

Specific surface area (m^{2}/g) | 10.96 | 1.16 | 4.28 |

Median diameter (μm) | 0.55 | 1.47 | 0.60 |

True density (g/cm^{3}) | 3.990 | 3.961 | 3.990 |

Isoelectric point | pH 6.45 | pH 5.28 | pH 5.31 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Miyake, K.; Hirata, Y.; Shimonosono, T.; Sameshima, S.
The Effect of Particle Shape on Sintering Behavior and Compressive Strength of Porous Alumina. *Materials* **2018**, *11*, 1137.
https://doi.org/10.3390/ma11071137

**AMA Style**

Miyake K, Hirata Y, Shimonosono T, Sameshima S.
The Effect of Particle Shape on Sintering Behavior and Compressive Strength of Porous Alumina. *Materials*. 2018; 11(7):1137.
https://doi.org/10.3390/ma11071137

**Chicago/Turabian Style**

Miyake, Kimiya, Yoshihiro Hirata, Taro Shimonosono, and Soichiro Sameshima.
2018. "The Effect of Particle Shape on Sintering Behavior and Compressive Strength of Porous Alumina" *Materials* 11, no. 7: 1137.
https://doi.org/10.3390/ma11071137