Gel Casting$ JP Pollinger, AlliedSignal Ceramic Components, Torrance, CA, USA YE Khalfalla, University College Dublin, Dublin, Ireland KY Benyounis, Dublin City University, Dublin, Ireland r 2016 Elsevier Inc. All rights reserved.
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Introduction Gelcasting Technology Gelcasting Process Slurry Preparation Mold Materials Gelation Solvent Removal Polymer Removal Gelcasting Capabilities Gelcasting Limitations Other Gelcasting Systems Summary
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Introduction
Gelcasting is an advanced ceramic powder compact forming process capable of fabricating complex near-net shapes. The principal gelcasting process was originally developed by Oak Ridge National Laboratory (ORNL) scientists during the 1980s and is based on free-radical polymerization of acrylamide. It has the capabilities for short forming time, uniform powder packing densities, high green strength, and short binder pyrolysis times. The traditional ceramic powder compact forming processes of slip casting, isostatic or uniaxial pressing of spray-dried powder, and injection molding are widely used manufacturing processes for a variety of industrial (e.g., whitewares, sanitary ware) and technical (e.g., electronics, structural) applications. Although relatively mature and widely used, these forming processes have significant limitations for specific applications, especially for use with nonclay (powder systems not exhibiting plastic properties) materials and fine (o1 mm) particle size powders. Slip casting limitations include the need for molds with porous dewatering surfaces, which is a difficulty for complex shaped molds for parts such as turbine wheels, significant powder packing density gradients for fine powders, long forming times when using submicron powders due to the very small pore channels, and low green strength. Injection molding of fine, relatively monodisperse powders requires 40–60 vol.% wax/plastic binder as the carrier medium. The high binder concentration and small pore size results in the need to pyrolyze the binder very slowly (up to 2–3 weeks for some components) and significantly limits part thickness. In isostatic or uniaxial pressing of spray-dried powders, the small amount of binder results in relatively weak powder compacts, requiring careful handling. Pressing of fine powders can also result in relatively nonuniform powder compaction, generating packing density gradients, and leaving vestiges of the spraydried granule agglomerates in the powder compact. With the progress in the development of high-performance ceramic materials and their requirement for fine monodisperse powders and defect-free powder compacts, there is a significant need for improved ceramic powder forming processes.
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Gelcasting Technology
Gelcasting is a novel near-net shaping method with a homogeneous microstructure and low cost in fabricating ceramics with largesized and/or complicated-structural parts versus other techniques (Sun et al., 2015). The first gelcasting technology was developed during the 1980s by ORNL scientists (Omatete et al., 1991) to address the need for an improved process for making complexshaped ceramic powder compacts. The basic concept of gelcasting is that a fluid slurry of ceramic powder and a solvent/monomer solution is poured into a mold and rapidly polymerized to form the powder in the shape of the mold. The part is removed from ☆
Change History: November 2015. Y.E. Khalfalla and K.Y. Benyounis added an Abstract, added a list of keywords, expanded the text with review of additional articles, and extended the list of references accordingly.
Reference Module in Materials Science and Materials Engineering
doi:10.1016/B978-0-12-803581-8.03556-6
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the mold, the solvent removed by drying, and the remaining polymer removed by pyrolysis. The part is then processed as any other typical ceramic powder compact through densification. The initial ORNL gelcasting system was based on free radical-initiated polymerization of acrylamide monofunctional monomer. The gel system consisted of acrylamide, methylene bisacrylamide (MBAM) – a difunctional monomer cross-linker, and ammonium persulfate (APS) – the free radical initiator. Tetramethylethylenediamine (TEMED) was typically added as a catalyst to break down the APS and speed up the cross-linking reaction. The total amount of monomer and cross-linker used is 2–4 wt.% of the slurry ceramic powder content. The cross-linker/monomer ratio used ranges typically from 1:2 to 1:8, depending on the specific powder system used, its unique chemical interactions with the gel constituents, and the desired balance of wet gel powder compact strength and dried (green) part strength. Increasing monomer content and a higher ratio of cross-linker/monomer increases gel strength. Conversely, increasing cross-linker/monomer ratio decreases dried powder compact strength. Very small amounts of initiator and catalyst are required, typically B0.01 wt.% initiator and B0.001 wt.% catalyst. The resulting cross-linked polymer–solvent gel contains approximately 85–90 wt.% solvent and 10–15 wt.% polymer. The polymerization process is started by heating the slurry to 35–85 1C, although the polymerization process can also be initiated chemically at room temperature depending on the concentrations of initiator and catalyst. The gelation process can be very rapid, in the order of minutes for relatively small parts. The gelled part is then removed from the mold and dried to remove the solvent system. The 2–4 vwt.% polymer that remains in the powder compact is then removed by oxidative pyrolysis at temperatures up to 600 1C in air. After pyrolysis the powder compact is ready for densification by the appropriate means for that material system. The acrylamide-based gelcasting system was very effective and robust as a powder compact forming process. It resulted in rapid forming (8 cm diameter Si3N4 turbine wheels gelled in less than 15 min), high green strength – up to 3–4 MPa (Nunn et al., 1994), rapid drying, and rapid pyrolysis due to the open pore channel network and the need to remove only 2–4 wt.% polymer. The acrylamide system did have two major factors limiting its ultimate potential as a viable forming process: acrylamide is a neurotoxin which requires very careful handling not usually desirable in manufacturing; and it forms carbon–nitrogen bonds during polymerization which are very difficult to break, requiring oxidative pyrolysis to 600 1C or above. Two low-toxicity gelcasting systems have subsequently been developed by ORNL, which have been commercialized by ceramic manufacturers. Methacrylamide (MAM) is an effective replacement for acrylamide, and again typically utilizes MBAM as the cross-linker, APS as the initiator, and TEMED as a catalyst (Janney et al., 1998). A novel nontoxic system for gelcasting of alumina suspensions was investigated using curdlan as gelling agent. The rheological and gelling behavior of curdlan suspensions in the temperature range 10–85 1C either on heating or cooling were studied. Influences of concentration of curdlan and solid loading of alumina suspension on the rheological properties and gelling behavior of alumina suspension were investigated. Complex shaped green bodies with compressive strength around 3.7 MPa were obtained by heating 50 vol% alumina suspensions with 0.625–0.750 wt% curdlan (based on alumina powder) at 80 1C for 1 h and by subsequently cooling to room temperature. Dense alumina parts with relative density above 98% have been prepared by curdlan gelation with homogeneous microstructures and good mechanical properties (Xu et al., 2015). The polymerization is again triggered by heating the slurry to 35–50 1C. Another variant of the acrylamide gelcasting technology has been developed: hydroxymethacrylamide (HMAM) (Omatete and Nick, 1999). HMAM self-cross-links and does not require a cross-linker. Experimentation has shown that HMAM can be initiated by APS, but exhibits relatively weak gel strengths. A more effective initiator, azobis[2-(2-imidazolin-2-yl)propane] 2HCl (AZIP), was discovered that generates very strong gels with HMAM. However, AZIP requires a higher temperature to begin dissociating, so the HMAM–AZIP gel system requires gelation temperatures of 60–85 1C. The HMAM system has shown an advantage over the MAM–MBAM system in that higher slurry solids contents are achievable for the same desired slurry viscosity, presumably because HMAM also further enhances powder dispersion. Both the MAM–MBAM and HMAM gelcasting systems are in commercial use. Very recently, a nontoxic water-soluble copolymer of isobutylene and maleic anhydride (Isobam) system was developed by Yang et al. (2013) and Qin et al. (2014). The merits of this new gelling system are environmental friendly (low exhaustion), and the procedure can be carried out under air atmosphere and humidity conditions. Most importantly, only one additive is needed and it is easy to completely remove.
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Gelcasting Process
The gelcasting process uses similar equipment and process steps to those used in standard ceramic powder compact forming processes such as slip casting. The generic flowchart for the gelcasting process is shown in Figure 1 and the individual steps are discussed below.
3.1
Slurry Preparation
Water is the solvent of choice for most gelcasting applications because of the ability to strongly enhance dispersion of ceramic powders using the polar nature of the water molecule to generate electrostatic repulsion, principally by pH adjustment. Organic solvents have also been effectively demonstrated. Steric repulsion using long-chain polymers is the primary powder dispersion mechanism for organic solvents and it is also used with water-based systems. The acrylamide, MAM, and HMAM gelcasting
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Figure 1 Flowchart and details of typical ceramic powder gelcasting process.
monomers also provide some component of dispersion (they are similar in steric repulsion capability to the polyacrylate dispersants used in ceramic powder processing) and thus serve an added benefit. Most slurries for gelcasting have been prepared using the traditional ball milling process, which provides effective mixing of powders and allows aging time for hydroxylation of particle surfaces to achieve stable slurry dispersions. Ball milling also allows for controlled particle size reduction, if required. High-energy milling techniques such as turbomilling and attrition milling have also been used effectively to prepare slurries, but care must be taken to allow suitable time for slurry stabilization to take place. The monomer and cross-linker gelcasting system components are added at the slurry preparation step to assure they are intimately mixed with the powder in the slurry and also to provide added dispersion, as described above. Because the slurry is subsequently poured or pumped into a mold, low viscosity (o500 mPa s) is desirable. Since the solids content of the slurry becomes essentially the resulting gelcast part powder packing density, maximizing solids content while keeping the slurry viscosity low enough to be readily pourable is a typical optimization requirement. High solids contents are achievable with coarse powders (larger than B5 mm) and powders with graded particle size distributions to optimize packing and rheology. Some fine powders can be dispersed effectively to achieve high solids contents, for example, 62 vol.% for 1 mm Al2O3 (Young et al., 1991), but maximum achievable solids contents below 50 vol.% are typical of many fine powders due to high surface area and surface chemistry/dispersivity limitations. Omatete and Nick (1999) demonstrated that for a 0.8 mm-sized silicon nitride powder, a maximum solids content of only 45 vol.% was achievable before exceeding maximum slurry flowability (o500 mPa s) for effective mold filling. After mixing/milling, the slurry may be deaired to remove entrapped air generated by the slurry preparation process. The initiator and catalyst (if used) are added after the slurry has been prepared. Since APS, AZIP, and TEMED are all strongly acidic, they are added to basic pH slurries while the slurries are rapidly mixing to prevent coagulation and spot-gelation. Porous g-Y2Si2O7 ceramic with good mechanical and thermal properties is prepared by the in situ reaction sintering foam-gelcasting method using Y2O3 and SiO2 as the starting powders and non-toxic gelatin as the gel former. The porous sample has interconnected large pores (40–230 mm) and small pores (0.1–2 mm) in the skeleton. The porosity can be controlled from 64.3 to 89.3% by adjusting the solid content and amount of the slurry. The corresponding strength ranges from 46.5 to 3.4 MPa. Porous g-Y2Si2O7 with a porosity between 57.2 and 90.0% shows a low thermal conductivity in the range of
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0.918–0.147 W (m K) 1 at room temperature. Porous g-Y2Si2O7 has excellent mechanical property at high temperature (the strength at 1100 and 1200 1C is maintained above 71% and 50%, respectively, of the value at room temperature) and good thermal stability (the reheating shrinkage is 1.3–1.7%) (Wu et al., 2015). A nontoxic, water-soluble copolymer consisting of isobutylene and maleic anhydride (PIBM) was used as both dispersant and gelling agent to mold MgAl2O4 green body by gelcasting at room temperature in air. MgAl2O4 slurries with solid loadings from 43 to 50 vol% were prepared by adding PIBM. They reported that as the solid loadings increased from 43 to 50 vol%, the linear shrinkage in the drying and pre-sintering process decreased from 6.9 to 2.8% and from 16.0 to 14.7%, respectively. The bending strength of the green body with 50 vol% solid loading can reach 2.62 MPa. The in-line transmission of the MgAl2O4ceramics gradually increased from 61 to 86.9% (1100 nm) with the solid loadings increasing (Zhang et al., 2015).
3.2
Mold Materials
Gelcasting molds require impervious surfaces, good part release characteristics, and tight sealing. Many mold materials have performed very effectively with the gelcasting technology. Suitable metal mold materials include aluminum and stainless steel. Anodized aluminum offers a more wear- and corrosion-resistant surface, especially with basic pH slurries, and has improved part release compared to unanodized aluminum. Aluminum and steel can be readily machined into complex molds. Glass has been shown to be an effective mold material, due to its combination of very smooth surface and resistance to corrosion, but is difficult to generate complex molds from and too fragile for typical handling. Plastics such as PVC have made effective gelcasting molds, and they take advantage of what is many times a disadvantage for acrylamide-based gelcasting systems – that oxygen inhibits the free-radical polymerization process. PVC has a slightly oxygenated surface and thus generates a small (o0.1 mm) ungelled layer (typically referred to as a reaction layer) on the surface of the part which acts as a lubricant allowing part removal. Many plastics and waxes evaluated for mold materials have much more oxygenated surfaces and generate significant surface reaction layers (41 mm) which is undesirable because these thicker reaction layers spall off and generate cracks and stresses during drying and pyrolysis. Sensitivity to oxygen can be adjusted with the monomer/cross-linker ratio. For example, in the MAM/MBAM system, higher cross-linker concentrations increase reaction layer thicknesses. Because of the sensitivity to oxygen during gelation, molds should be designed to contact all part surfaces that are desired to be near-net-shape. Relatively fluid slurries are used in gelcasting, so molds must be very close fitting to prevent leaking. Since molds are heated to initiate the gelation process, it is usually desirable also to use mold materials with high thermal conductivity to minimize process heating and cooling times. The effective use of dissolvable or meltable cores (analogous to the lost-wax process for metal casting processes) has also been demonstrated for gelcast parts. Waxes dissolvable in solvent and low-melting metal alloys have been used to form gelcast powder compacts with complex internal features (Pollinger, 1997) such as gas turbine combustor cans. The cores must be removed prior to drying of the gelcast part due to the typical 1–3% shrinkage that occurs during drying. To enhance part removal from molds, release agents are frequently used. A number of mold releases have been evaluated, with release agents used for injection molding of plastics being typically effective. Mold release agents vary in effectiveness depending on particular ceramic powders, gelcasting systems, and mold materials, thus some trial and error is usually required when evaluating release agents for each application. Materials that have demonstrated effective release for specific systems include cooking spray, petroleum jelly, and spray lubricants. The ability of a mold release to provide effective part release must also be balanced with the fact that many release agents contain potential contaminants and that they function by preventing wetting by the gelcasting slurry, thus increasing the potential for incompletely filled molds and air pockets.
3.3
Gelation
Gelation itself is triggered by heating the molds. Since the temperatures to which the molds must be heated are moderate (35– 85 1C), there is a variety of heating techniques that have proven effective: static air ovens, forced air ovens, water baths, water jacketed molds, and infrared heating of molds. The mold material and heating method should be selected based upon the desired gelling time and size of component, which controls the amount of heat flux needed. An important characteristic of the gelled part is that the gelcasting process results in powder compacts with very uniform powder packing densities. The gelation process ‘freezes in place’ the homogeneously distributed powder in the slurry. Freeze gelcasting of hydrogenated vegetable oil-in-aqueous alumina slurry (HVO-in-AAS) emulsions has been studied for the preparation of macroporous ceramics. The emulsions with HVO to AAS volume ratios in the range of 1.34–2.69 prepared from a 30 vol.% AAS containing carrageenan using sodium dodecyl sulfate emulsifying agent at 85 1C undergo gelation on cooling to room temperature due to the solidification of HVO and physical crosslinking of carrageenan. Macroporous ceramics obtained by drying, HVO removal followed by sintering at 1500 1C of the gelled emulsion bodies had porosity in the range of 70.7–84% and contain cells of spherical to polygonal shape. The average cell size (13.24–3.6 mm) decreased and the cell interconnectivity increased with an increase in HVO to AAS volume ratio and mixing speed. The macroporous alumina bodies had high compressive strength (6.5–39.6 MPa) and Young's modulus (350–2352 MPa) (Vijayan et al., 2014).
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Solvent Removal
After gelation the solvent is removed by standard drying practices. For large particle size powder compacts with corresponding large pore sizes, static or circulating air drying suffices. For finer particle size (o1 mm) powder compacts, drying must be performed more carefully due to submicron pore channels and the potential to crack parts as a result of internal solvent thermal expansion and/or increasing vapor pressure before open pore channels to the surface are achieved. In this case, controlled humidity dryers are typically used. Because the gel provides enhanced strength to the powder compacts during drying, they can handle more rapid drying rates than corresponding slipcast parts. This is balanced with the fact that the gel shrinks as the water is removed from its structure. Gelcast parts with submicron powder and B45–50 vol.% powder packing can shrink 1–3% during drying, which generates large stresses if not carefully controlled (Ghosal et al., 1999). For example, drying times for silicon nitride parts using 0.5 mm powder and with 50 vol.% packing are B20 h for an 8 cm diameter turbine wheel, and B80 h for a 15 cm diameter wheel. The dried parts have also been shown to be readily green machined (Nunn and Kirby, 1996) due to the high dried gel strength.
3.5
Polymer Removal
The polymer remaining after drying of the gel is typically removed by oxidative pyrolysis. Where the initial acrylamide monomer gel system required 600 1C or greater to achieve complete polymer removal, the MAM–MBAM and HMAM systems pyrolyze at much lower temperatures due to their weaker bonds and the polymers can be removed at temperatures as low as 400 1C in air. Since the part has open pore channels because of previous removal of the solvent which constitutes 85–90% of the gel, the pyrolysis can be performed very rapidly, usually in less than a day. For larger and thick cross-section components, pyrolysis times are lengthened to assure complete removal of polymer from the interior. For those materials requiring inert pyrolysis to prevent oxidation, nitrogen and vacuum pyrolysis at temperatures up to 600 1C show that B0.5–1 wt.% carbon residue is left. After polymer pyrolysis, gelcast components are then treated as any other powder compact for subsequent densification.
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Gelcasting Capabilities
The acrylamide-based gelcasting technology results in a number of demonstrated capabilities as a powder compact forming process. The gelation process is rapid, for example, an 8 cm diameter part can be gelled in 10 min. The process results in very uniform powder packing densities, minimizing stresses and potential cracking during subsequent drying and pyrolysis and maintaining near-net-shape during densification. A variety of mold materials, many of them relatively inexpensive and easily machined into tight tolerances, can be used. Green strengths on the order of 3–4 MPa allow for robust handling, the ability to green machine, and faster drying. Pyrolysis is rapid because 85–90% of the gel system is removed during drying, leaving an open pore network and only 2–4 wt.% polymer. The combination of ease of mold filling by fluid slurry, tight tolerance mold capability, uniform packing densities, and high as-gelled and green strength results in the ability of the gelcasting process to form readily complex and near-net shapes. The mold filling process, the chain reaction capability of the free radical polymerization to initiate gelation uniformly, the high green strength, uniform packing density, and removal of most of the gel system by low stress evaporation also results in the ability to form and process both large and thick cross-section powder compacts. The gelcasting process is also automatable, as has been demonstrated for Si3N4 turbine wheels (Nick et al., 1999).
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Gelcasting Limitations
Although the acrylamide-based gelcasting technology and its improvements have a number of desirable powder compact forming capabilities, there are number of potential limitations that must be considered. Because low-viscosity slurries are used, sealing of molds is a potential issue. The mold tooling must be tightly sealed, which is potentially difficult with complex shape molds. Many mold materials have some oxygenated surface content and can cause inhibition of gelation and formation of reaction layers. Higher cross-linker content increases sensitivity to oxygen-induced inhibition of gelation, which can limit the ability to generate high gel strengths. Many mold releases will provide effective release but generate high wetting angles with the slurry, making complete mold filling without air entrapment a potential problem. Although uniform powder packing densities are achieved, high surface area/fine particle size powders present a significant problem in that they generate high slurry viscosities at relatively low solids contents. The resulting low powder packing densities present potential problems of extensive shrinkage during drying, pyrolysis, and densification which can cause significant stresses and cracking, part distortion, and reduced dimensional reproducibility. Additionally, low powder packing densities reduce the driving force for densification and can inhibit achievement of full density and desired microstructures. Finally, inert pyrolysis cannot completely remove the polymer, leaving residual carbon char.
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Other Gelcasting Systems
Another significant gelcasting technology being developed is the polymerization of existing polymers in solution. Morrisette and Lewis (1999) have developed and demonstrated the effective gelcasting of alumina powder aqueous slurries by cross-linking poly (vinyl alcohol) (PVA) with organotitanates to form strong gels at room temperature. PVA has the added powder processing benefits of being extensively used in current powder processing applications as a binder for spray drying and in being an effective powder dispersant in water suspensions. The gelation process occurs rapidly at room temperature, so slurries are cooled after crosslinker addition to temperatures below room temperature (5–20 1C) to slow the gelation process, and provide workable lowviscosity slurries for mold filling. Direct coagulation casting (DCC) is a new forming technology that also converts an aqueous slurry into a ceramic green body in a nonporous mold – similar to gelcasting, but in this case by coagulation of the powder suspension. Two approaches have been developed to achieve in situ suspension coagulation, using enzyme-catalyzed reactions: (1) to change suspension pH by forming acids or bases to drive pH toward the powder suspension isoelectric point (IEP); or (2) to form salts to reduce double layer thickness. Baader et al. (1995) demonstrated the coagulation casting of alumina through the decomposition of urea to generate ammonia and increase suspension pH. The alumina powder, which has an IEP of B8.5, was first dispersed in water with a small amount of urea at pH 4 to generate a low-viscosity suspension for casting. Urease enzyme was then mixed into the suspension and the casting mold filled. The urease catalyzed the decomposition of the urea to generate ammonia and shift the pH higher, to pH 9. The alumina suspension is then effectively coagulated into a green body as the pH approaches the alumina IEP. The rate of urea decomposition can be controlled by temperature (decreasing the suspension temperature from 25 to 5 1C) and increased working time (no appreciable increase in viscosity) from 10 to 60 min, and decreasing the urease concentration by an order of magnitude increases both working time and coagulation time by an order of magnitude. Granule et al. (1995) also demonstrated the use of in situ salt generation to coagulate silicon carbide aqueous suspensions. In this case silicon carbide has an IEP of two and welldispersed suspensions are generated at pH 9–11. It is very difficult to decrease pH to such a low value to coagulate the suspension. Here the urease enzyme-catalyzed decomposition of urea was used to form ammonium carbonate salt to decrease the silicon carbide particle double layer thicknesses to achieve coagulation. Approximately 2 mol l 1 salt concentration was needed to achieve complete destabilization of the silicon carbide suspension, while the suspension pH stayed at about pH 9–10. For both of these coagulation processes, high solids content suspensions result in higher green strength parts and binder burnout is not needed because less than 1 vol.% organic material is added to generate the coagulation process.
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Summary
Gelcasting is an advanced ceramic powder compact forming process that has demonstrated the capability for fabricating complex near-net shapes. The principal gelcasting process of polymerization of acrylamide monomer using a cross-linker and free radical initiator has been improved through the development of a low toxicity monomer (MBAM) and a self-cross-linking monomer (HMAM). The capabilities of these gelation processes include short forming time, uniform powder packing densities, high asgelled and green strength, short binder pyrolysis times, and the ability to form both thick cross-section powder compacts and complex shaped compacts with both thin and thick sections. Limitations include difficulty in sealing complex molds against leaking of the low-viscosity slurries, the potential for low powder packing densities with fine powders, the sensitivity of the polymerization process to oxygen exposure, and incomplete polymer pyrolysis in nonoxidative environments. Gelcasting technology has been demonstrated for a variety of ceramic materials and commercial applications have been initiated.
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Sun, Y., Qin, X., Zhou, G., et al., 2015. Gelcasting and reactive sintering of sheet-like YAG transparent ceramics. J. Alloy. Compd. 652, 250–253. Vijayan, S., Narasimman, R., Prabhakaran, K., 2014. Freeze gelcasting of hydrogenated vegetable oil-in-aqueous alumina slurry emulsions for the preparation of macroporous ceramics. J. Eur. Ceram. Soc. 34 (16), 4347–4354. Wu, Z., Sun, L., Wan, P., Wang, J., 2015. Preparation, microstructure and high temperature performances of porous g-Y2Si2O7 by in situ foam-gelcasting using gelatin. Ceram. Int. 41 (10), 14230–14238. Xu, J., Zhang, Y., Gan, K., et al., 2015. A novel gelcasting of alumina suspension using curdlan gelation. Ceram. Int. 41 (9), 10520–10525. Yang, Y., Shimai, S., Wang, S., 2013. Room-temperature gelcasting of alumina with a water-soluble copolymer. J. Mater. Res. 28 (11), 1512–1516. Young, A.C., Omatete, O.O., Janney, M.A., Menchhofer, P.A., 1991. Gelcasting of alumina. J. Am. Ceram. Soc. 74, 612–618. Zhang, P., Liu, P., Sun, Y., et al., 2015. Microstructure and properties of transparent MgAl2O4 ceramic fabricated by aqueous gelcasting. J. Alloy. Compd. 657, 246–249.