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Apurv Dash, [Koji Morita](https://orcid.org/0000-0001-6040-7054), Luca Balice, Robert Mücke, Olivier Guillon

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[Creep and Superplasticity of Gadolinium‐Doped Ceria Ceramics under AC Electric Current](https://mdr.nims.go.jp/datasets/88564d9c-b893-49f0-9115-9983cabc3155)

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Creep and Superplasticity of Gadolinium-Doped Ceria Ceramics under AC Electric CurrentCreep and Superplasticity of Gadolinium-Doped CeriaCeramics under AC Electric CurrentApurv Dash,* Koji Morita, Luca Balice, Robert Mücke, and Olivier Guillon1. IntroductionThe inherent brittleness of ceramics both at room and hightemperature (>1000 °C) has limited its applications and abilityto be shaped by hot deformation like metals.[1] Due to smallachievable strains, its effect for shaping technology is restricted,for example, the flattening of cambered multilayer compounds.[2]The Maximum achievable strain rates are 10�5–10�4 s�1 formost oxides.[3] In order to enable deformation-based shaping,much larger strain rates yielding considerable strains arerequired. During research on superplasticceramics, various oxide ceramics like3mol% Y2O3-stabilized tetragonalZrO2 polycrystals (3Y-TZP),[4,5] Al2O3-tZrO2-MgAl2O4 tri-phasic material,[3]Ca10(PO4)6(OH)2 hydroxyapatite,[6] fine-grained Al2O3,[7] and nonoxide ceramicslike Si3N4/SiC[8] composites were foundto allow much higher strains and strainrates than usual. Strain rates up to 0.01to 1 s�1 with strains of 3–25 wereobserved.[3,9] The superplastic behavior ofceramics is achieved by grain refinement,a higher grain boundary area ensures grainboundary sliding (GBS), which is one of themajor plastic deformation mechanismsof ceramics.[10] However, the temperaturesrequired for carrying out plastic deforma-tion are still very high (typically >1500 °C)with very low permissible rate of deforma-tion to avoid failure except a few high-strain-rate materials.[3] Thisfurther limits the economic prospects of superplasticity of sub-micrometer grained ceramics.[11] Furthermore, the fabrication ofsubmicrometer grained ceramics requires a nanometric primaryparticle size distribution (<100 nm) as the starting materialwhich further increases the cost and difficulty of the process.It is known since the 1960s that electrical fields can affect thecreep behavior on materials like MgO.[12] For 3Y-TZP, it wasfound that high field strengths (E= 1 kV cm�1) lower the flowstress and thus the viscosity in tensile creep experiments[13]and retard the typical accelerated grain growth and cavitationformation during high-strain-rate creep of ceramics.[14,15]Conrad et al. performed tensile experiments on MgO atE= 220 V cm�1 and showed that the flow stress reduced by halfwith the application of the electrical field.[16] The flow stressrecovered reversibly when the field was switched off. Similarbehavior was found for 3Y-TZP and Al2O3.[13,17] Yoshida et al.applied 120 V cm�1 on 3Y-TZP samples and achieved a strainof 1.35 using a strain rate of 0.001 s�1 at 1000 °C.[18] All theseexperiments were carried out under tensile loading and underDC fields, which result potentially in single-side reduction ofthe oxide material when used in field-assisted sintering.Electric field processing of ceramics peaked interest afterCologna et al. introduced the concept of flash sintering, thatis, sintering in a matter of seconds.[19] It was believed that theinteraction of electric field with oxide ceramics results in boththermal and athermal effects,[20] the thermal effect being Jouleheating and the athermal effects presumably being generationof defects and its concentration along the grain boundary,respectively.[21] The application of electric field resulted inA. Dash, L. Balice, R. Mücke, O. GuillonForschungszentrum Jülich GmbHInstitute of Energy and Climate Research (IEK)52425 Jülich, GermanyE-mail: a.dash@fz-juelich.deA. DashDepartment of Energy Conversion and StorageTechnical University of Denmark (DTU)Building 301, Anker Engelunds Vej, DK-2800 Lyngby, DenmarkK. MoritaResearch Center for Functional MaterialsNational Institute for Materials Science1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, JapanThe ORCID identification number(s) for the author(s) of this articlecan be found under https://doi.org/10.1002/adem.202300057.© 2023 The Authors. Advanced Engineering Materials published by Wiley-VCH GmbH. This is an open access article under the terms of the CreativeCommons Attribution License, which permits use, distribution andreproduction in any medium, provided the original work is properly cited.DOI: 10.1002/adem.202300057Shaping of dense ceramics is difficult due to their inherent brittleness.Nanograined ceramics like tetragonal zirconia (TZP) can be superplasticallydeformed and shaped at high temperatures owing to grain boundary sliding(GBS). Herein, the enhanced plasticity of gadolinium-doped ceria (GDC)ceramics under mild and strong AC electric current in terms of steady state creeprate under both compressive and tensile loading is demonstrated. A currentdensity of 25 and 200 mAmm�2 is used for the creep deformation. The creep rateincreases by up to two orders of magnitude under electric current. The stressexponent remains unchanged for creep experiments at 1200 °C with and withoutelectric current, suggesting a GBS mechanism of plastic deformation in bothcases. The field-enhanced creep rate is attributed to the interaction of space–charge layer and the electric field resulting in enhanced GBS. A higher currentdensity results in enhanced ductility of GDC even when the Joule heating effect iscompensated by reducing the furnace temperature.RESEARCH ARTICLEwww.aem-journal.comAdv. Eng. Mater. 2023, 25, 2300057 2300057 (1 of 7) © 2023 The Authors. Advanced Engineering Materials published by Wiley-VCH GmbHmailto:a.dash@fz-juelich.dehttps://doi.org/10.1002/adem.202300057http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/http://www.aem-journal.comenhanced mass flow and hence the same can be used to induceplastic deformation of ceramics at moderately high temperatures(<1000 °C), which are the typical temperatures of flash sinteringfor oxide ceramics.[22]In our previous works we found that all sintering parameters(viscosity, viscous Poisson ratio, sintering stress, bulk, and shearviscosity) of ceria were modified even under moderate AC elec-trical fields in the order of 10 V cm�1.[23,24] As sintering is gov-erned by grain boundary diffusion which also is a majormechanism for creep in ceramics, it can be expected that thesemoderate electrical fields also change the creep behavior of ceria.Because of its relevance for membrane, fuel cells, and electrolysiscells, we used submicrometer 10mol% gadolinia-doped ceria(GDC10) in this work. In the past, it was shown that tensileand compressive loading leads to a symmetric mechanical sinter-ing behavior (sintering and creep are both controlled mainly bygrain boundary diffusion in this case).[25] Therefore, the fieldeffect was also studied for tensile and compressive stresses inthis work. Many ceramics show asymmetric creep behavior,which is generally attributed to preferential damage undertension, cavitation, or the existence of glassy phases on the grainboundaries.[26–29] The strain development over time was mea-sured at constant stresses with and without electrical field.Considering the window of secondary creep and differentstresses, the creep stress exponent was calculated to understandthe underlying creep mechanism and the influence of electriccurrent on the same.The influence of electric field or current on the mechanicalproperties of oxide ceramics is ultimately due to the powerdissipation and hence we have referred to the term “power”or “current” at many instances in the present work. The effectof Joule heating was found to be minor or compensated,suggesting athermal effects of electric current.2. Results and DiscussionsFigure 1a–d shows the typical creep curves of GDC ceramics with(red curve) and without (black curve) electric power under differ-ent compressive loading conditions of 20–40MPa at a furnace0 2000 4000 6000 8000 10000 12000 140000.0000.0050.0100.0150.0200.0250.0300.035No electrical power25 mA/mm2%,niartSTime, sGDC101200 °C25 MPaAC, 50 Hz0 2000 4000 6000 8000 10000 12000 140000.0000.0050.0100.0150.0200.0250.0300.035No electrical power25 mA/mm2Strain, %Time, sGDC101200 °C40 MPaAC, 50 Hz0 2000 4000 6000 8000 10000 12000 140000.0000.0050.0100.0150.0200.0250.0300.035No electrical power25 mA/mm2Strain, %Time, sGDC101200 °C30 MPaAC, 50 Hz0 2000 4000 6000 8000 10000 12000 140000.0000.0050.0100.0150.0200.0250.0300.035No electrical power25 mA/mm2Strain, %Time, sGDC101200 °C20 MPaAC, 50 Hz(a) (b)(c) (d)Figure 1. Steady state creep curves under compression of gadolinium-doped ceria under electric field of �6 V cm�1 and current density of 25 mAmm�2at an isothermal period at 1200 °C a), 10MPa, b), 20MPa, c), 30 Mpa, d), 40MPa.www.advancedsciencenews.com www.aem-journal.comAdv. Eng. Mater. 2023, 25, 2300057 2300057 (2 of 7) © 2023 The Authors. Advanced Engineering Materials published by Wiley-VCH GmbH 15272648, 2023, 18, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202300057 by National Institute For, Wiley Online Library on [05/11/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.aem-journal.comhttps://onlinelibrary.wiley.com/action/rightsLink?doi=10.1002%2Fadem.202300057&mode=temperature of 1200 °C. The current density was set to25mAmm�2 and the electric field self-adjusted to 6.9 V cm�1,resulting in a very low electric power dissipation of17.25mWmm�3. The low electric power was used to investigatethe effect on creep without triggering Joule heating. A derivativeof the creep curve yielded the time window with constant creeprate and the regions are highlighted with a bold red segment inFigure 1. As compressive creep proceeds, the cross section of thecylinder increases as the height reduces and hence hardeningtakes place. The creep experiments were interrupted once asteady state was reached. The steady state creep rate was mea-sured from the lowest values of the derivative of the strain versustime. Ameagre electric power of 17.25mWmm�3 resulted in theincrease of creep rate by nearly two times. Figure 2a–c shows thecreep curves of GDC ceramics under tensile loading. A lowertensile stress was used (10–20MPa) as ceramics are weak undertensile loading, and this would risk the failure of dog bone sam-ples before testing. The current density was set to 25mAmm�2and the electric field self-adjusted to 20 V cm�1, resulting in apower dissipation of 50mWmm�3. The compression tests wereperformed on cylindrical samples where the platinum electrodewas a surface in contact with the flat ends of the cylinder whereastension tests were performed on a dog bone-shaped samplewhere the platinum electrode was a point in contact with thehole made at each end of the dog bone. Moreover, the surfacearea-to-volume ratios for cylindrical and dog bone-shapedsamples are very different. We believe that the aforementionedvariables like contact resistances and surface area-to-volume ratioare key to the total resistance offered by the sample which in turnreflects the net electric field across the sample. The sample is in astate of redox equilibrium with the ambient oxygen, and increas-ing surface area-to-volume ratio would drive equilibrium forwardand vice versa. The electric field across the ceramic can beassumed to be sample shape dependent. Table 1 shows a sum-mary of the creep rates in both tensile and compressive modes at0 and 25mAmm�2.Figure 1 and 2 are shown with similar strain window in they-axis and increasing time window on x-axis as creep is a time-dependent phenomenon. Strain rate under comparable condi-tions is always higher for the tensile loading due to samplegeometry. The difference is larger than the amount which canbe expected from the change in the cross-sectional area duringmechanical testing. We observed an intrinsic asymmetric creepbehavior common to many ceramics. We can exclude thecommon reasons for this asymmetry (damage, cavitation, glassyphases).The application of low electric power resulted in negligibleJoule heating and an increase in the creep rate at a furnace tem-perature of 1200 °C. The furnace temperature was lowered to1100 °C and a higher current density of 200mAmm�2 wasapplied to induce a Joule heating of around 100 K to have a sam-ple temperature of 1200 °C. A precalibration was done to obtainthe corresponding current density for a required increase in tem-perature of GDC ceramic. Figure 3 shows the creep curves ofGDC ceramics at a furnace temperature of 1100 °C and a sampletemperature of 1200 °C. A higher current density resulted inenhanced plasticity of the GDC ceramics. This result is in linewith the study of Sasaki et al. for 3Y-TZP.[30] This plastic behaviorcannot be attributed to Joule heating as previous experimentsdone at 1200 °C did not result in the same level of plasticity.All the three stages of creep can be seen in Figure 3 marked withI, II, and III. The first stage is characterized by initial rapidincrease in strain, followed by the second stage II, which isthe steady-state creep regime where the strain increases linearlywith time. In the final stage III, the strain increases rapidly with0 2000 4000 6000 8000 10000 12000 14000 160000.00.51.01.52.0Strain, %Time, s1200 °CTensile creep of GDC0 2000 4000 6000 8000 10000 120000.00.51.01.52.0Strain, %Time, s1200 °C0 2000 4000 6000 80000.00.51.01.52.0Strain, %Time, s1200 °CTensile creep of GDC(a) (b) (c)Figure 2. Steady-state creep curves under tension of gadolinium-doped ceria under electric field of�20 V cm�1 and current density of 25 mAmm�2 at anisothermal period at a) 1200 °C, b) 10MPa, c) 15MPa, 20MPa.Table 1. Summary of creep rates in tensile and compressive mode.Tensile creepCreep strain rateLoad [MPa] 0 mAmm�2 25 mAmm�210 2.31E�05 9.30E�0515 4.09E�05 1.20E�0420 9.69E�05 1.26E�04Compressive creep20 5.83E�07 1.10E�0630 1.30E�06 2.52E�0640 1.91E�06 4.38E�0625 1.30E�06 1.95E�0635 1.94E�06 2.89E�0650 4.34E�06 7.35E�06www.advancedsciencenews.com www.aem-journal.comAdv. Eng. Mater. 2023, 25, 2300057 2300057 (3 of 7) © 2023 The Authors. Advanced Engineering Materials published by Wiley-VCH GmbH 15272648, 2023, 18, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202300057 by National Institute For, Wiley Online Library on [05/11/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.aem-journal.comhttps://onlinelibrary.wiley.com/action/rightsLink?doi=10.1002%2Fadem.202300057&mode=time. The total strain with 200mAmm�2 is much higher (40 %)as compared to that of 25mAmm�2 (<2%).Figure 4a,b shows the log–log plot of creep strain rate versusthe applied stress for compressive and tensile creep experiments,respectively. The application of 25mAmm�2 results in the dou-bling of the creep rate but slope of the curve depicting the stressexponent remained the same with the applied electric current.The same is true for tensile creep as well, even the injectionof a higher current density of 200mAmm�2 resulted in the samestress exponent of �2. For the fine-grained materials as in thepresent material, the deformation behavior characterized by astress exponent of n= 2 has generally been attributed toGBS.[14,31–34] For the deformation of GDC, it would be reason-able to interpret that the flow behavior with n= 2 takes placepredominantly by GBS, irrespective of the current/fieldcondition, as reported by groups.[33–35] In order to deformcontinuously by the GBS process, the stress concentrationscaused around the multiple grain junctions by GBS should beaccommodated by diffusional processes along lattice or grainboundary[31,36] and/or by plastically through dislocation-relatedprocesses.[32,37] It has recently been reported that cation diffusiv-ity is likely to be accelerated under the electric current/field.[33–35]This suggests that under electric current/field, the enhanced dif-fusivity can not only trigger the diffusion-related accommodationprocess but also the dislocation-related accommodation processby accelerating the recovery rate of dislocations. It is thereforedifficult to provide a comprehensive understanding of thepredominant rate-controlling mechanisms under the electriccurrent/field. The recent work by D. Liu et al. stateddislocation-related accommodation process as the rate-controlling mechanism under electric current/field based onthe transmission electron microscopy (TEM) characterization.[32]If this is the case of the present study, the deformation of GDCcan also be ascribed to GBS mechanism, in which the rate ofdeformation is rate controlled by the dislocation-related pro-cesses. Whether the creep mechanism is different below theapplied stress of 5MPa was not studied in the present workas that of Liu et al.[32] The creep rate increases on average by afactor of �70 with the applied current density of 200mAmm�2:The maximum steady-state strain rate was 9� 10�3 s�1 with fieldcompared to 9� 10�5 s�1 without field at 20MPa. The former isclose to the values reported for superplastic ceramics.[11,14,18]This shows the potential of application of the electrical field.If the current density was higher or the grain size was smaller,even full superplasticity can be expected for GDC.[14,30] Thestress exponent remained unchanged close to 2, suggestingno modification of the rate-controlling mechanism. The interac-tion of electric current with the oxide ceramic may have resultedin the change of the grain boundary structure, that is, local reduc-tion along the grain boundary resulting in a high concentrationof oxygen vacancies. The accelerated mass flow may also be dueto the reduction of grain boundary mobility. The theory of graingrowth retardation during electric field-assisted deformation of3Y-TZP has been well presented by Yang et al.[15] but in the0 2000 4000 6000 8000 10000010203040Strain, %Time, s 10 MPa 15 MPa 20 MPa1100 °CCurrent density: 200 mA/mm2Tensile creep of GDCIIIIIII IIIIIIIIFigure 3. Creep curves of gadolinium-doped ceria under a current densityof 200mAmm�2 at an isothermal furnace temperature of 1100 °C under atensile loading of 10MPa, 15MPa, and 20MPa.(a) (b)1.30 1.39 1.48 1.56 1.65 1.7420 25 30 37 45 55-6.3-6.1-5.9-5.6-5.4-5.2-5.05.0×10-78.3×10-71.4×10-62.3×10-63.7×10-66.1×10-61.0×10-5Creep strain rate, s-1Applied stress, MPa no electric current 25 mA/mm2gol,)etarni artsp eerc( gol(s-1)Compressive creepStress exponent = 1.95 ± 0.140.87 0.96 1.04 1.13 1.22 1.30 1.397 9 11 13 16 20 25-5.2-4.8-4.3-3.9-3.5-3.0-2.6-2.2-1.76.1×10-61.7×10-54.5×10-51.2×10-43.4×10-49.1×10-42.5×10-36.7×10-31.8×10-2Creep strain rate, s-1Applied stress, MPa no electric current  25 mA/mm2 200 mA/mm2gol,)etarniartspeerc(gol(s-1)Tensile creepStress exponent = 1.86 ± 0.32Figure 4. a) Log–log plot of min. creep strain rate as a function of applied compressive stress; b) joule heating of sample as observed with the increase ofelectric power density in GDC at an isothermal temperature of 1200 °C.www.advancedsciencenews.com www.aem-journal.comAdv. Eng. Mater. 2023, 25, 2300057 2300057 (4 of 7) © 2023 The Authors. Advanced Engineering Materials published by Wiley-VCH GmbH 15272648, 2023, 18, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202300057 by National Institute For, Wiley Online Library on [05/11/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.aem-journal.comhttps://onlinelibrary.wiley.com/action/rightsLink?doi=10.1002%2Fadem.202300057&mode=present work, the use of electric current did not affect the micro-structure, as shown in Figure 5. On the contrary, there was amoderate grain growth observed with an increase of current den-sity. The enhanced mass flow might be due to the local grainboundary degradation.[38] However, the use of AC current mighthave limited the extent of local grain boundary reduction. Thereversal of the polarity might lead to a reoxidation of the grainboundary. Previous studies on the electric field-assisted creepand superplasticity were conducted in DC electric field. Thismight result in a permanently reduced material after deforma-tion, ascribing to the nature of DC current. The present workuses AC electric power, always keeping the system symmetricand lowering the probability of permanent reduction or forma-tion of defects which cannot be annealed by heat treatment in air.Figure 5 shows the postcreep microstructure of GDCceramics deformed under 1) 200mAmm�2, 2) 25mAmm�2,and 3) without any electric power, deformed under 15MPa oftensile stress. The microstructure of the sample was investigatedboth near the electrodes and the core; it was observed that themicrostructure is homogeneous. It is noteworthy that a verylow degree of cavitation was observed even at a strain level of40%, suggesting that the GBS is accommodating in nature.With the application of a higher current density, there was aslight grain growth observed (0.62� 0.04 μm). This increasein grain size might be due to dynamic grain growth due to grainboundary diffusion accelerated by damage accumulation.[39] Theincrease in grain size due to the Joule heating can be ruled out asthe temperature was only 1200 °C; in addition, if there was anincrease in temperature, then it would not have increased beyond1350 °C which was the sintering temperature of the ceramic. Theapplied current density cannot result in an increase of tempera-ture over 1350 °C, leading to grain growth. Hence, the graingrowth can be ascribed to either current effect or defect accumu-lation. The grain growth was also symmetric and homogeneousacross the gauge length. The application of AC current has beenassumed as responsible for enhancing the grain growth withoutan increase in the sample temperature.[18] The grain size of theceramic exposed to 25mAmm�2 remained unchanged as com-pared to the material deformed without electric current and theparent material with a grain size of 0.45 μm. A low current den-sity did not result in a significant defect concentration in thegrain boundary to induce grain growth but enough to enhancethe GBS phenomenon. This corresponds well to the same sinter-ing trajectories (grain size as function of density) measured dur-ing sintering with and without electric field of ceria.[23] Theporosity of crept samples under 200mAmm�2 wasmeasured to be 1.2% by image analysis as compared to 0.9%for creep under 25mAmm�2 and 0.7% for creep without electriccurrent. Pore coalescence might have appeared in the case of200mAmm�2 because of large strain and eventual formationof pores along the grain boundary.[40]The sample temperature was measured by inserting a thermo-couple into a drilled hole in the GDC ceramic for thecompression setup. Figure 6 shows the increase in the sampletemperature with increasing power density and current density.It is evident that at a current density of 25mAmm�2 only 5 K ofJoule heating was observed. Using a simple black body radiationmodelPel ¼ εAσðT4sample � T4furnaceÞ (1)with Pel as the dissipated electrical power, ε as emissivity�0.9), Athe sample area, σ the Stefan–Boltzmann constant, and T theabsolute temperate, the sample temperature increase(T sample � T furnace) was calculated to 21 and 11 K for the compres-sion and tension setup, respectively. These values overestimatethe temperature significantly as the mechanical contacts for themechanical testing conduct substantial heat. A full electrother-mal simulation similar to Cao et al.[23] yielded a temperatureincrease of 1–12 K depending on the position inside the3 μm 3 μm 3 μm(a) (b) (c)d = 0.62 ± 0.04 µm d = 0.45 ± 0.04 µm d = 0.45 ± 0.02 µm200 mA/mm2 25 mA/mm 2 0 mA/mm 2ε = 40 % ε = 1.7 % ε = 1.0 %Figure 5. Postcreep microstructure of gadolinium-doped ceria under tensile loading of 15MPa and current density of a) 200mAmm�2 at 1100 °C,b) 25mAmm�2 at 1200 °C, and c) 1200 °C without any electric field.0 5 10 15 20012345Power density (mW/mm3)051015202530Current density (mA/mm2 )1200 °CGDC10Figure 6. Joule heating of sample as observed with the increase of electricpower density in GDC at an isothermal temperature of 1200 °C.www.advancedsciencenews.com www.aem-journal.comAdv. Eng. Mater. 2023, 25, 2300057 2300057 (5 of 7) © 2023 The Authors. Advanced Engineering Materials published by Wiley-VCH GmbH 15272648, 2023, 18, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202300057 by National Institute For, Wiley Online Library on [05/11/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.aem-journal.comhttps://onlinelibrary.wiley.com/action/rightsLink?doi=10.1002%2Fadem.202300057&mode=specimen for the compression test. Therefore, an effectiveincrease of the sample temperature of around 5 K for thecompression mode is justified and an even small increase tookplace during the tension test at 25mAmm�2 due to the highersample surface-to-volume ratio.The constitutive equation that describes the creep behavior interms of temperature (T ), strain rate (ε:), applied stress (σ), andgrain size (d) is[3,11,18,35,41]ε: ¼ A ⋅ σn ⋅ d�p expð�Q=RTÞ (2)where A, n, p, Q, and R are the material constant, stress expo-nent, grain size exponent, creep activation energy, and universalgas constant, respectively. An increase in 5 K of the sample wouldnot result in the increase of creep rate by a factor of 2 as seen inthe present work. A similar deduction can be made for the creepexperiments done with a current density of 200mAmm�2: a sig-nificantly higher creep rate (70 times) cannot be explained byonly temperature rise and can be attributed to the interactionof electric power with oxide ceramic and its consequences onthe transient change of grain boundary defect chemistry.[38]3. ConclusionThe creep behavior of gadolinium-doped ceria ceramics wasstudied under both compressive and tensile loading at 1200 °Cwith and without the application of electric power. The resultsshow that a higher current density (200mAmm�2) results inan enhanced mass flow (70 times increased creep rate) ascompared to 25mAmm�2 (2 times increased creep rate). Themaximum tensile strain rate was found to be 9� 10�3 s�1 forthe higher current density. The application of electric powerdid not result in the change of the rate-controlling factor.Analysis of the postcreep microstructure revealed that a highercurrent density resulted in moderate cavitation, leading to porecoalescence. The present work showcases that ceria ceramics alsoexhibit electroplasticity as compared to zirconia- and alumina-based ceramics, which were reported in the past. Especiallythe use of AC current opens a plethora of new research avenuesfor the study of electroplasticity of ceria and other ceramics.4. Experimental SectionCommercial gadolinium-doped cerium oxide ceramics (Gd0.10Ce0.90O1.95,Fuel Cell Materials, USA) was used as received. The powders were uniaxiallypressed into disks (Ø 30mm height: 4mm), cylinders (Ø 20mm, height:10mm) at 50MPa, followed by isostatic pressing (EPSI, Belgium) at300MPa. The pressed pellet was carefully placed in a resistance-heatedfurnace (Nabertherm, Germany) with a heating ramp of 5 Kmin�1 with adwell time of 150min. at 1350 °C to have a relative density above 98%and a grain size below 0.5 μm.The sintered ceramic was 98.5% dense with a grain size of 0.45 μm.The sintered blocks were machined using diamond tools to obtain cylin-ders (Ø 4mm, height: 9 mm) and dog-bone (gauge length: 15mm,cross-section: 3 mm� 2mm)-shaped specimen. The cylindrical anddog-bone-shaped specimen were subjected to compressive and tensioncreep experiments, respectively. Compressive strain was applied by acustom-made sinter forging device[42] equipped with a resistance-heatedfurnace for heating the sample, a mechanical testing machine (Instron5565, Norwood, USA) for applying mechanical load, AC power source(ACS-2200, HBS Electronic GmbH, Brühl, Germany) for applying electricbias, and a laser scanner (Model 162-100, Beta Laser Mike, Dayton, USA)to measure the strain of the sample excluding any thermal expansion ofthe alumina setup for transmitting the load. Platinum plate electrode andwire electrode were used for compression and tension creep, respectively.The sample was painted with platinum paste on both ends to create inti-mate contact between the ceramic and the electrode. All creep experi-ments were done under an AC frequency of 50 Hz. The electric currentwas increased at a rate of 100mAmm�2 min. After the preset current den-sity was reached, the electric field self-adjusted to a certain value to main-tain the current density. All the log data from each unit of the setup wasrecorded using a custom-made LabVIEW program. Tensile strain wasapplied in a similar setup in which the gauge area of dog-bone sampleswas clamped in SiC jigs and the displacement was measured by crossheaddisplacement. The creep investigation was done at 1200 °C in the stressrange of 10–50MPa. Postcreep microstructural investigations (SEM, ZeissUltra55, Carl Zeiss, Oberkochen, Germany) were done by grinding andpolishing in subsequently finer diamond suspensions and thermal etchingat 1100 °C for 30 min.AcknowledgementsThe authors acknowledge funding from the German Science Foundation(DFG), under priority program “Fields Matter” SPP 1959, under thegrant no. GU 933/9-2. Dr. Doris Sebold is acknowledged for her helpin microscopy of crept samples.Open Access funding enabled and organized by Projekt DEAL.Conflict of InterestThe authors declare no conflict of interest.Data Availability StatementThe data that support the findings of this study are available from thecorresponding author upon reasonable request.Keywordsceria ceramics, creep, electric current, electro plasticity, grain boundarysliding, plastic deformationReceived: January 12, 2023Revised: July 14, 2023Published online: August 8, 2023[1] W. D. Kingery, H. K. Bowen, D. R. Uhlmann, Introduction To Ceramics,John Wiley & Sons, Hoboken 1976.[2] R. Mücke, N. H. Menzler, H. P. Buchkremer, D. Stöver, J. Am. Ceram.Soc. 2009, 92, S95.[3] B.-N. Kim, K. Hiraga, K. Morita, Y. Sakka, Nature 2001, 413, 288.[4] F. Wakai, S. Sakaguchi, Y. Matsuno, Adv. Ceram. Mater 1986, 1,259.[5] K. Kajihara, Y. Yoshizawa, T. Sakuma, Acta Metall. Mater. 1995, 43,1235.[6] F. Wakai, Y. Kodama, S. Sakaguchi, T. Nonami, J. Am. 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See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.aem-journal.comhttps://onlinelibrary.wiley.com/action/rightsLink?doi=10.1002%2Fadem.202300057&mode= Creep and Superplasticity of Gadolinium-Doped Ceria Ceramics under AC Electric Current 1. Introduction 2. Results and Discussions 3. Conclusion 4. Experimental Section