Ceramic materials such as alumina are widely used in diverse engineering applications including electric insulators, catalysts, filters, abrasives, and protective coatings, due to its high mechanical strength, excellent chemical inertness, wear resistance, and high working temperature [1] [2] [3] . For example, Qian et al. coated alumina on graphene nanosheets to make composites with high thermal conductivity [4] . Based on the research from Gestel et al., an alumina layer was added into titanium dioxide membrane to help it survive in strong acid and alkali due to its excellent chemical stability [5] . Chakravarty et al. used alumina as necessary materials and doped with magnesia to obtain high hardness fracture toughness property [6] . McElwain et al. utilized alumina as the reinforcement to improve the wear resistance of PTFE (polytetrafluoroethylene) by fabricating nanocomposites [7] . However, the relatively low electrical conductivity at room temperature limits its broader application in electronic devices [2] .
Fabricating composites is a standard method to improve the properties of a pure substance [8] . By introducing conductive materials such as multi-walled carbon nanotubes into a nonconductive ceramic matrix, ceramics matrix composites have been fabricated to improve the electrical properties. For example, Ahmad et al. used multi-walled CNTs (MWCNTs) as the reinforcement to enhance the electrical conductivity and dielectric properties of alumina. With 1.74 vol.% MWCNT, electrical conductivity increased eleven orders of magnitude (from 10 -12 to 10 -1 S/m), and the dielectric increased around 500 times [9] . Flahaut et al. synthesized CNT/Fe/alumina nanocomposites to improve the electrical conductivity of alumina [10] .
Conventional methods for processing of ceramics composites include powder processing, colloidal processing, sol-gel processing, powder derived ceramics, and spark plasma sintering (SPS) [11] . For example, Dusza et al. used the powder processing method to manufacture CNT/zirconia composites at a pressure of 41 MPa [12] . An et al. produced CNT/silicon
Ceramic materials such as alumina are widely used in diverse engineering applications including electric insulators, catalysts, filters, abrasives, and protective coatings, due to its high mechanical strength, excellent chemical inertness, wear resistance, and high working temperature [1] [2] [3] . For example, Qian et al. coated alumina on graphene nanosheets to make composites with high thermal conductivity [4] . Based on the research from Gestel et al., an alumina layer was added into titanium dioxide membrane to help it survive in strong acid and alkali due to its excellent chemical stability [5] . Chakravarty et al. used alumina as necessary materials and doped with magnesia to obtain high hardness fracture toughness property [6] . McElwain et al. utilized alumina as the reinforcement to improve the wear resistance of PTFE (polytetrafluoroethylene) by fabricating nanocomposites [7] . However, the relatively low electrical conductivity at room temperature limits its broader application in electronic devices [2] .
Fabricating composites is a standard method to improve the properties of a pure substance [8] . By introducing conductive materials such as multi-walled carbon nanotubes into a nonconductive ceramic matrix, ceramics matrix composites have been fabricated to improve the electrical properties. For example, Ahmad et al. used multi-walled CNTs (MWCNTs) as the reinforcement to enhance the electrical conductivity and dielectric properties of alumina. With 1.74 vol.% MWCNT, electrical conductivity increased eleven orders of magnitude (from 10 -12 to 10 -1 S/m), and the dielectric increased around 500 times [9] . Flahaut et al. synthesized CNT/Fe/alumina nanocomposites to improve the electrical conductivity of alumina [10] .
Conventional methods for processing of ceramics composites include powder processing, colloidal processing, sol-gel processing, powder derived ceramics, and spark plasma sintering (SPS) [11] . For example, Dusza et al. used the powder processing method to manufacture CNT/zirconia composites at a pressure of 41 MPa [12] . An et al. produced CNT/silicon
Ceramic materials such as alumina are widely used in diverse engineering applications including electric insulators, catalysts, filters, abrasives, and protective coatings, due to its high mechanical strength, excellent chemical inertness, wear resistance, and high working temperature [1] [2] [3] . For example, Qian et al. coated alumina on graphene nanosheets to make composites with high thermal conductivity [4] . Based on the research from Gestel et al., an alumina layer was added into titanium dioxide membrane to help it survive in strong acid and alkali due to its excellent chemical stability [5] . Chakravarty et al. used alumina as necessary materials and doped with magnesia to obtain high hardness fracture toughness property [6] . McElwain et al. utilized alumina as the reinforcement to improve the wear resistance of PTFE (polytetrafluoroethylene) by fabricating nanocomposites [7] . However, the relatively low electrical conductivity at room temperature limits its broader application in electronic devices [2] .
Fabricating composites is a standard method to improve the properties of a pure substance [8] . By introducing conductive materials such as multi-walled carbon nanotubes into a nonconductive ceramic matrix, ceramics matrix composites have been fabricated to improve the electrical properties. For example, Ahmad et al. used multi-walled CNTs (MWCNTs) as the reinforcement to enhance the electrical conductivity and dielectric properties of alumina. With 1.74 vol.% MWCNT, electrical conductivity increased eleven orders of magnitude (from 10 -12 to 10 -1 S/m), and the dielectric increased around 500 times [9] . Flahaut et al. synthesized CNT/Fe/alumina nanocomposites to improve the electrical conductivity of alumina [10] .
Conventional methods for processing of ceramics composites include powder processing, colloidal processing, sol-gel processing, powder derived ceramics, and spark plasma sintering (SPS) [11] . For example, Dusza et al. used the powder processing method to manufacture CNT/zirconia composites at a pressure of 41 MPa [12] . An et al. produced CNT/silicon 48th SME North American Manufacturing Research Conference, NAMRC 48 (Cancelled due to COVID- 19) carbonitride (SiCN) composites by polymer derived ceramics method to improve mechanical properties [13] . Inam et al. fabricated CNT/alumina composites by cold pressing for green bodies, followed by SPS to sinter samples [14] . While traditional methods are capable of rapid manufacturing ceramic composites in large batches, they are not capable of manufacturing complex 3D parts with free design.
Along with extensive research in 3D printing of polymers and metals, additive manufacturing (AM) has increasingly drawn attention in forming ceramics. The ability to fabricate ceramic components with arbitrary 3D design has been extremely challenging for conventional ceramic forming processes. AM processes including stereolithography, twophoton polymerization, selective laser sintering, binder jetting, robocasting, direct ink writing, and fused deposition modeling have been reported for fabricating 3D ceramics. For example, zirconia-alumina composites were made via stereolithography (SLA) method by Wu et al. to improve the mechanical properties [15] . Two-photon polymerization (TPP), developed by Strickler et al., is a specific SLA method to build models within micro or nanoscale [16] . Selective laser sintering (SLS) was used as a powder-based 3D printing method to fabricate alumina [17] , silicon carbide [18] , and zirconia [19] ceramics. Gaytan et al. manufactured a barium titanate piezoelectric sensor by the binder jetting method [20] . Robocasting and direct ink writing are both liquid based ME3DP method, and they have been applied to build calcium phosphate [21] , and silica [22] scaffold structures. Fused deposition modeling, a solid-based ME3DP method, was used to create silica and titanium dioxide composites by Onagoruwa et al. [23] . Among these 3D printing processes, material extrusion 3D printing (ME3DP) is a versatile and cost-effective method to form a 3D model by extruding viscous slurry layer by layer. Pure alumina slurry was extruded to form models by the ME3DP process from the research of Rueschhoff et al. [24] . Crucible-shape samples were fabricated by extruding alumina/copper composites demonstrated from research from Melcher et al. [25] . Despite extensive work focused on ME3DP of alumina and alumina composites, little research has been done on the carbon material/alumina composites built by the ME3DP method for conductive alumina-based composites.
In this work, we fabricated conductive CNT reinforced alumina matrix composites by the ME3DP method and thermal treatments. Inks for ME3DP were designed with controlled rheological properties, allowing excellent printability. Different CNT amounts (0-10 weight percentage) were loaded into alumina to study the electrical properties of composites sintered at temperatures ranging from 900 to 1400 °C. We performed electrical measurements to investigate the percolation threshold and electrical conductivities with different CNT ratios and sintering temperatures.
Aluminum oxide (Al2O3, A-16 SG, powder, 0.4 μm average particle size, 8.8 m 2 /g surface area, ALMATIS), multi-walled carbon nanotubes (MWCNTs, powder, >94%, 50-85 nm diameter, 1.7 g/ml density, Graphene Supermarket), polyvinylpyrrolidone (PVP, powder, average molecular weight~55,000 g/mol, Sigma Aldrich) were used for ink preparation.
The schematic of the process is shown in Figure 1 (a). The homogenous viscous ink was obtained by mixing MWCNTs, alumina, and PVP by ball milling. It was then loaded into a syringe to print ceramic green bodies with a homemade ME3DP printer. Final sintered CNT/alumina composite parts are achieved after a two-step thermal treatment.
First, two solid-state components, CNTs, and alumina, were mixed at different weight ratios. CNT with 0 wt%, 3 wt%, 5 wt%, 7 wt%, and 10 wt% of the total mass of CNTs and alumina was prepared by stir mixing. Deionized water was then added at 45-100 wt% of the total weight of CNTs and alumina to acquire a suitable viscosity for ME3DP. PVP was added as the binder at 5 wt% of the total mass of CNTs and alumina to prevent samples from cracking during the drying process. Then the mixture material and zirconia balls were loaded into a stainless-steel jar for a planetary ball mill (PM 200, Retsch) for 3 h at 400 rpm to obtain well-dispersed ink. 
To ensure the moldability and printability of the ink, we performed rotational rheological measurements by using a hybrid rheometer (DISCOVERY HR-2, TA Instruments) to measure the viscosity at steady shear mode with a shear rate from 0.01 s -1 to 100 s -1 . A 40 mm diameter parallel plate was adopted as a rotational accessory with a gap of 1 mm.
Inks were loaded into a 10 mL syringe with a 600 μm diameter nozzle. A homemade 3D printer redesigned from a commercial 3D printer (CR-10S, Creality), shown in Figure  1(b) , was used for ME3DP. The digital 3D model for 3D printing was designed as a cylinder, with 15 mm diameter and 2 mm height, by a 3D modeling software (SOLIDWORKS) and converted to GCODE for the 3D printer by a slicer software (Ultimaker Cura). The layer height was 0.4 mm, and the nozzle writing speed was 3 mm/s. The printed sample shown in Figure  1 (c) is a CNT/alumina composite green body that is ready for thermal treatment.
The green body was dried at room temperature for 2 days before thermal treatments. The green body was fired at 700 °C for 6 h at a heating rate of 3 °C/min in an argon atmosphere to remove the PVP binder. Green bodies after the removal of the binder are called as-debinded samples. The samples were then sintered at temperatures ranging from 900 to 1400 °C for 10 h at a heating rate of 5 °C/min in flow argon environment. Samples achieved after the sintering process are called assintered samples. 
We used scanning electron microscope (SEM, Quanta 200F, FEI) to study the dispersion of CNTs in the alumina matrix and microstructure of nanocomposites Thermogravimetric (TG) and differential thermal analysis (DTA) were performed by SDT Q600 (TA Instruments) from room temperature to 1400 °C at a heating rate of 10 °C/min in flowing argon. X-ray diffraction (XRD, D2 PHASER, BRUKER) with CuKα (λ = 0.154 nm) radiation was used to analyze the phase composition of samples.
We use a multimeter (2831E, BK Precision) to measure the electrical conductivities of the CNT/alumina composite samples at room temperature. Copper foils were glued to both the top and bottom surfaces of cylindrical samples by conductive silver paste (Sigma-Aldrich) to decrease the influence of contact resistances. The electrical conductivity could be calculated with sample dimensions by the formula as follows:
where is the electrical conductivity; ℎ is the height of the sample; is the resistance; is the area of top/bottom surface.
Inks used for ME3DP needed to have suitable viscosity for both moldability and printability. Rheological properties were measured to investigate viscosities of inks with 0-10 wt% CNTs, and 45-100 wt% water, shown in Figure 2 (a). The viscosity of each sample decreased as the shear rate increased, showing shear thinning property, which is preferable for ME3DP. The ink was in a static state without shear stress applied because the molecule chains of PVP wrap around CNT and alumina nanoparticles and twisted together. However, the weak bonding between PVP molecule chains and nanoparticles was impaired and separated as a shear force was applied to the ink during the extrusion process. Therefore, the viscosity of ink decreased, allowing the ink to start flowing. After the ink exiting the nozzle, the shear force vanished, resulting in the entanglement of molecule chains, and the increase of viscosity for the formation of the sample. Although the ink with a low amount of water, such as the ink with 3 wt% CNT-45 wt% water, can be extruded from the nozzle and form a model, the high viscosity ink inhibited continuously extruding and resulted in a rough surface as shown in Figure 2(b) . The printing quality improved with the increasing amount of water in ink with 3 wt% CNT-65 wt% water, shown in Figure 2(c) . Nevertheless, the ink became too dilute to hold 3D shapes with more water added. As shown in Figure 2(d) , it was effortless to extrude 3 wt% CNT-100 wt% water sample, but we observed evident collapse from the cross-sectional view. The height of the printed sample was 1.5 mm, demonstrating a 25% shrinkage compared to the designed sample. Furthermore, the shrinkage of the sample induced the arched-shape deformation. One separated layer was assumed to shrink uniformly, but a transverse surface tension applied by the additional layer resulted in the bend of the bottom layer. In summary, we found an advisable range of water loaded could from 45 wt% and to 100 wt% in 3% CNT samples. For samples of other CNT contents (0 wt%, 5 wt%, 7 wt%, and 10 wt%), We found that the amount of CNT slightly affected the viscosity. Considering samples with 0-10 wt% CNT and fixed 65 wt% water amount, the viscosity changed little shown in Figure 2(a) , and all samples could be high-quality printed with similar morphology.
The printability of the ink was also affected by parameters of 3D printing, such as printing speed, nozzle size, and layer height. First, the printing speed would affect the continuity of extrusion. The high viscosity of CNT/alumina composites inhibited the continuous extrusion at high printing speed (10 mm/s). Otherwise, the evaporation of water in ink at low printing speed (1 mm/s) induced the blocking in the nozzle and non-continuous printing. As for the nozzle size, the large nozzle (>800 μm) decreased the number of printing paths, which decreased the quality of printing. Abreast alumina particles in the inks were likely to block the small nozzle (<200 μm) and ceased the printing. Layer height was another key parameter for extrusion printing. With exceeded layer height (>0.6 mm), the ink dropped, rather than laid on the building plate, resulting in low-quality printing. However, the nozzle would immerse into former layers with a small layer height during printing, resulting in the coarse surface or blocking of the nozzle.
The TG/DTA was conducted to identify the substances and thermal behavior of the composites, shown in Figure 3 . The 0.5 wt% weight loss below 150 °C was due to the removal of residual water. The decomposition of PVP accounted for the drastic weight loss between 350 °C and 450 °C. The weight loss in this process was less than the mass of PVP in the composites, indicating the elements of PVP were not entirely removed in the anoxic oxygen environment. The weight of the composites declined slowly between 450 °C to 1100 °C due to the volatilization. Above 1100 °C, the weight decreased discernibly, and an apparent exothermic peak was observed based on the DTA curve. It suggested that some CNTs were oxidized in this process. Although the oxygen partial pressure was low in the flowing argon, oxidation of carbon material occurred at high temperature [26] .
The dispersion of reinforcement affects the performance of the composites in most cases. Herein, the dispersion of CNT in the alumina matrix was a crucial criterion to evaluate the electrical conductivity of the composites because the degree of CNT aggregation determined its connectivity. The crosssectional SEM images of samples with different CNT loading were shown in Figure 4 . The tube-shaped fiber highlighted by yellow arrows represented CNTs, and other bulks represented alumina particles. All green body, as-debinded, and as-sintered samples showed good dispersion of CNT in the alumina matrix because no recognizable aggregations of CNTs were observed. Focusing on as-debinded samples with various weight percent of CNTs, shown in Figure 4 (a-d), the increasing amount of CNT in the SEM images corresponded to the increase of CNT contents in the inks. As shown in Figure 4(a, b) , the gaps between alumina crystals became larger with CNT loaded, and the infilled CNTs changed the microstructure of alumina. Figure 4 (b-d) showed that CNTs kept dispersing uniformly in the alumina matrix with the increasing CNT ratio. As shown in Figure 4 (d-f), comparing green bodies, as-debinded, and assintered samples with 10 wt% CNT, we found that the dispersion of CNT was stable no matter if the composites were burned or not. The particle size of alumina became more homogeneous when the composites were heat-treated with higher temperature and longer duration.
The phase compositions of green bodies, as-debinded, and as-sintered samples with 0-10 wt% CNT loading were shown in Figure 5 by XRD patterns. The positions of peaks indicated that the α-alumina phase and the infill of CNTs did not affect the phase composition. No peaks observed other than alumina, indicating no phase change or reactions occurred during debinding and sintering processes. Comparing the XRD of green body and sintered sample at the same CNT ratio, the peaks of sintered samples were narrower than the green body, revealing the larger crystallite size formed after the thermal treatment because the average crystallite size was in inverse proportion to the full width at half maximum (FWHM) according to Scherrer Equation [27] . Since the diameter of CNT in our experiments was 50-85 nm, which was extremely smaller than the particle size of alumina, the average particle size of composites kept decreasing as CNT ratio increased. The XRD results confirmed peaks became broader as more CNTs were reinforced into alumina at the same thermal treatment condition.
Pure alumina was nonconductive at room temperature, but the electrical conductivity of CNT reinforced alumina composites increased significantly, as the loading of CNT increased, shown in Figure 6(a) . The conductivity demonstrated a sharp increment at 3 wt% CNT compared to pure alumina, increased slowly from 3 wt% to 7 wt% CNT ratios, and kept stable from 7 wt% to 10 wt% CNT ratios. The results indicated the percolation theory of nanocomposites. At a low CNT ratio, CNTs were disconnected and no electrical paths formed between the top and bottom surface electrodes. The conductive pathways emerged as the increase of CNTs, resulting in a drastic increase in electrical conductivity. More paths generated between electrodes as more CNTs were loaded gradually, enhancing the electrical conductivity. It reached the maximum when the CNT loaded to the percolation threshold.
The conductivities of as-debinded samples were higher than that of the green bodies. The crystallite size of alumina became larger after thermal treatment, promoting the CNT attachment to the alumina particles and better connection after debinding process. The conductivity of the CNT/alumina composite improved because more electrical pathways generated based on CNT connection. However, as shown in Figure 6 (a), the conductivities dropped after thermally treated at higher temperatures during sintering processes. The mechanism of solid-state sintering accounted for the decrease in conductivity [28] . Particle spheres contacted due to the surface diffusion at a high temperature and induced the formation of grain boundaries. The pore volume in the composites shrunk in this diffusion process, destroying the CNT network in the microstructure. The decrease of electrical pathways in the composites caused the reduction of conductivity According to Figure 6 (b), the decline of conductivity of 5 wt% CNT samples corresponded to the suggestion based on the mechanism of solid-state sintering.
Furthermore, we measured the conductivities of printed samples and cast samples, shown in Figure 6 (b). We concluded that the conductivity of printed samples was considerably higher than cast samples and more ordered. Compared to the cast samples, 3D printed samples had advantages such as fewer voids and a more uniform structure.
In summary, we successfully fabricated conductive CNT/alumina composites by the ME3DP method. The electrical conductivity of the composites reached high conductivity (10 -1 S/m), with more than 7 wt% CNT infilled. The percolation threshold of CNTs in alumina was 3 wt% for a conductive CNT/alumina composite. We demonstrated that the ME3DP was an effective method to manufacture CNT reinforced ceramic matrix composites. The electrical conductivities of 3D printed samples were found better than the casted samples. Further study would focus on decreasing the consumption of carbon at high sintering temperature.