Nanomechanical Properties and Thermal Conductivity Estimation of

JOM

DOI: 10.1007/s11837-013-0601-8 2013 TMS

Nanomechanical Properties and Thermal Conductivity Estimation of Plasma-Sprayed, Solid-Oxide Fuel Cell Components: Ceria-Doped, Yttria-Stabilized Zirconia Electrolyte NEELIMA MAHATO,1 SAMIR SHARMA,1,2 ANUP KUMAR KESHRI,3 AMANDA SIMPSON,4 ARVIND AGARWAL,5 and KANTESH BALANI1,6 1.—High Temperature Fuel Cell Laboratory, Department of Materials Science and Engineering, Indian Institute of Technology, Kanpur, Kanpur 208016, India. 2.—Present address: Advanced Engineering, Ashok Leyland, Chennai 600103, India. 3.—Bharat Heavy Electrical Limited, Hyderabad, India. 4.—Hysitron Inc., 9625 West 76th Street, Minneapolis, MN 55344, USA. 5.—Mechanical and Materials Engineering, Florida International University, Miami, FL 33174, USA. 6.—e-mail: [email protected]

Solid-oxide fuel cell components were fabricated using an atmospheric plasma spraying method. Lanthanum strontium manganite (LSM), 8 mol% yttriastabilized zirconia (8YSZ), ceria (CeO2), and YSZ-NiO powders were used as feedstock materials for layered deposition of cathode, electrolyte, and anode, respectively, to make a complete cell. In this work, two types of electrolyte materials were investigated, viz., 8YSZ and the one containing 10 wt.% CeO2. Because a high densification is expected in the solid oxide electrolyte (as opposed to observed porosity of 27%), current work focuses only on the nanomechanical evaluation of the same. Scanning electron microscopy (SEM) images show the retention of nanocrystallinity in the plasma-sprayed deposits. Elemental analyses via energy-dispersive spectroscopy revealed chemically distinct identities of the cell components ruling out diffusion or reaction at the boundaries. Porosity values vary between 29.0% and 35.4% in anode and 42.9–48.4% in cathode, indicating appreciable achievement for high performance of electrode materials. The addition of 10 wt.% ceria to 8YSZ has shown enhancement in the elastic modulus and hardness of the electrolyte material by 18.4 GPa and 1.6 GPa, respectively. Theoretical estimation of thermal conductivity of the plasma-sprayed materials has been found to be in the order of 2.27–4.45 W/mK.

INTRODUCTION Solid-oxide fuel cells (SOFCs) are electrochemical devices consisting of solid ceramic cell components, viz., porous electrodes and a dense, gas-tight electrolyte in between. These devices convert chemical energy of the fuel gases into electricity with negligible pollution.1 Recent developments in SOFC technology focus on improved power output, lowering operational temperature (650–850C), enhancing the life of a fuel cell stack in terms of reliability and durability, and most importantly, reducing the cost of fabrication. Among the most commonly used SOFC materials, Ni/8-YSZ (8 mol% yttria-stabilized zirconia), 8YSZ (with and without dopants), and

lanthanum strontium manganite (LSM) are used as anode, electrolyte, and cathode, respectively. At the anode, the oxidation of fuel gases and production of electrons takes place by the virtue of its chemistry and microstructure. Ni (30–50 vol.%) dispersed in YSZ matrix assists in the conduction mechanism (electrical conductivity2 4 9 103), carries out electrocatalytic activity during the oxidation of fuel gases, and it offers low charge transfer resistance.3 In the microstructure, an amount of 40% porosity is desired to facilitate a fair supply of fuel gases, to remove reaction products, and to maintain triple-phase boundaries (TPBs) among the electrolyte, electrode, and gas phase.1 Besides these properties, phase stability in fuel environment as

Mahato, Sharma, Keshri, Simpson, Agarwal, and Balani

well as high operational temperatures and a good match of thermal expansion coefficients between the other cell components is also essential to abolish cracks/fractures and failure. The electrons generated at the anode travel through an external load and reach the cathode to combine with oxygen in the air being pumped in during the operation and to produce oxide ions. A functionally sound cathode usually consists of three functional layers: electrochemically active layers with fine grain size and good interfacial bonding, diffusion layers with large open porosity (40%), and current-collecting layers with high electronic conductivity (89–103 S cm1).4 In both cases, anodes as well as cathodes, functionally graded or multilayered structures with variations in composition and microstructure, are judiciously tailored to enhance electrochemical and mechanical performance. The oxide ions produced at cathode traverse through electrolyte to reach anode. The electrolyte, thus, must be highly dense (>98% of the relative theoretical density), gas tight (gas leak rate 1 9 106 mbar l s1 cm2 or less),5 and as thin as possible (2.5 W/mK).16–18 Therefore, theoretical models are utilized to estimate the thermal conductivity of the coated layers considering the influence of pore geometries, dimensions, and alignment with respect to the operational heat flux. EXPERIMENTAL DETAILS Powder Feedstock, and Microstructural and Phase-Characterization of Materials Nano and spray-dried powders (plasma spray grade) of 8 mol% YSZ, NiO, LSM, and CeO2 were procured from Inframat Advanced Materials (Manchester, CT). The morphology and particulars of the powder feedstock and blend proportions used in plasma spray coating are shown in Figs. 1 and 2 and summarized in Table I. The average particle size was determined using laser particle size analyzer (Analysette 22; Fritsch GMBH, Idar-Oberstein, Germany). The microstructural characterization of initial materials as well as fabricated cell components were carried out using scanning electron microscopy (SEM; ZEISS EVO 50 operated at 5– 20 kV; Carl Zeiss, Oberkochen, Germany) with energy-dispersive spectroscopy (EDS) facility (INCA Penta FETx3; Oxford Instruments, Oxfordshire, UK) and shown in Fig. 2. Phase characterization was carried out using x-ray diffraction (XRD; 2000D

Two SOFCs were processed via atmospheric plasma spraying of the powder feedstock using SG 100 plasma gun (Praxair Surface Technologies, Indianapolis, IN). The three different layers, cathode, electrolyte, and anode, were plasma sprayed on AISI 1020 (mild steel substrate) with the dimensions 100 9 20 9 3 mm3. A layer of LSM followed with deposition of YSZ (SOFC 1: without CeO2, and SOFC 2: with 10 wt.% CeO2 electrolyte) as a middle layer, and YSZ-NiO as the top layer. The cells were cathode supported type. The parameters used in plasma spray coating are listed in Table II. Physical, Micromechanical, and Nanomechanical Properties of Processed LSM/YSZCeO2/YSZ-NiO Plasma Sprayed Coatings The coating porosity was determined by digital image analysis using ImageJ (National Institutes of Health, Bethesda, MD). A cross-sectional surface profile of the two unpolished (leveled on emery cloth without any polishing media) SOFC coatings was generated by dynamically focusing of a laser beam (infra-red light k = 780 nm) and evaluation of the objective position (profile) using three-dimensional laser surface profilometry (Model: PGK 120; MAHR, Go¨ttingen, Germany) with spatial and vertical resolution of 0.1 lm and 5 nm, respectively. Approximately 20 line profiles of length 400 lm were used (in each region of the coating) for evaluating the average surface roughness using MAHR Perthometer Concept image analyzing software. Bulk hardness was determined via Vicker’s macroindentation using BAREISS-V-Test (Bareiss Pru¨fgera¨tebau GmbH, Oberdischingen, Germany). The samples were first polished smoothly using micrometerrange diamond pastes, and indentation experiments were carried out at a load of 0.98 N (100 g). Five indentations were made on each sample with a dwell time of 10 s. The indent diagonals were measured from the optical micrographs, and hardness values were calculated using the equation: P HV ¼ 1:854 2 d 2 and d is the average diagonal length where d ¼ d1 þd 2 in mm, Hv is the Vickers hardness, and P is the applied load (in Newton). Nanomechanical properties were investigated via nanoindentation using Hysitron TI900 Triboindenter equipped with a

–

–

LSM (La0.8Sr0.2MnO3) (cathode)

YSZ-CeO2 (10: 1) blend (electrolyte SOFC 2)

40–60 (YSZ) 20–50 (NiO)

50–80

CeO2 (nanopowder)

50 vol/% Ni/50 vol.% YSZ, after reduction (NiO to Ni)

40–60

8 mol% YSZ (agglomerated)

Compositions

Average particle size of nano powders (nm)

Table I. Specifications of the initial powder feedstock material

30–60

40–50

30–40

50–80

50–175

Particle size of spray-dried powders (lm)

White powder of molecular weight 121.75 g/mol, BET specific surface area 15–40 m2/g. Density of the initial nanopowder is 6.1 g/cm3 Yellow powder of molecular weight 172.12 g/mol and BET specific surface area of 11–17 m2/g, density 7.65 g/cm3 Agglomerated composite 8 mol% YSZ nanopowder and black nickel oxide nanopowder with 0.5 wt.% PVA binder added. Porosity 87% Particles are spherical made from small particles and the surface is uneven, with high amount of porosity 73% Particles are mostly spherical and made of smaller particles agglomeration and contain porosity 85%

Remarks

Nanomechanical Properties and Thermal Conductivity Estimation of Plasma-Sprayed, Solid-Oxide Fuel Cell Components: Ceria-Doped, Yttria-Stabilized Zirconia Electrolyte


Table II. Plasma-spraying parameters Parameters Plasma power (kW) Current (amperes) Voltage (V) Stand-off distance (mm) Feed rate (g/min) Primary gas, argon (slm or standard liters per minute) Secondary gas, helium (slm) Carrier gas, argon (slm)

Value 24–32 kW 600–800 40 100 Variable 32 60 30

three-sided Berkovich diamond indenter (Hysitron, Minneapolis, MN). The load–displacement data were analyzed utilizing the Oliver and Pharr19 method (depth-sensing indentation). RESULTS AND DISCUSSION Characterization of Phase and Microstructure of the Fabricated Cell The SEM of the cross-sectioned samples shows four distinct regions (Fig. 3) with different contrasts corresponding to anode, electrolyte, cathode, and substrate. The layers are flat and the boundaries are uniform after deposition, and there occurred no bending/deformation of either the substrate or SOFC component layers and layers show good adhesion. This indicates that the plasma spray coating conditions and parameters were well adjusted. Microstructures show the presence of a bimodal type of grain structure in all the three cell component layers, i.e., fully melted (FM) surface and partially melted (PM) surface. This is because of poor thermal conductivity of the material, which renders the surface particles fully melted and resolidified, whereas the particle core partially melts and sinters in a solid state. Image analyses of the layered deposits show the sufficient amount of porosity (or low densification) in SOFC 1 and SOFC 2 (Tables III and IV), which is necessary to supply air/oxygen at reaction sites (triple phase boundary). Pores are created by three different mechanisms. Macropores are developed due to the presence of nonmelted or partially melted particles; micropores and submacropores are formed due to the entrapment of gas between the splat layers and by reduction of NiO in anode by the fuel gas (volume shrinkage, and can also form by graphite burn-off in case when graphite is present in the initial feed stock) during working of SOFC during operation. The reduction of NiO to Ni in the coating also has a significant effect on the conductivity behavior of the coating. The conductivity changes from that of ceramic insulator to metallic conductor. Pore formers or precursors, such as Na2CO3, could also be added to generate/enhance porosity.20 Submicronsize pores are distributed throughout the coating.

Fig. 3. Scanning electron micrographs of the cross section of the two plasma spray coated (a) SOFC 1 and (b) SOFC 2, with components.

An increase in the number of these tiny pores enhances the amount of TPB. The porosity of SOFC anode must be 40% for developing better function in terms of electrical conductivity. Porosity is an important factor for improving anode fabrication,

YSZ-NiO (anode) YSZ-10 CeO2 (electrolyte) LSM (cathode)

57.1

73.4

64.6

SOFC 1 Anode (NiO-8YSZ) Electrolyte (8YSZ) Cathode (LSM) SOFC 2 Anode (NiO-8YSZ) Electrolyte (8YSZ + 10 wt.% CeO2) Cathode (LSM)

SOFC components

74 57 50 82 88 91 81 53 67 67 71

0.29 0.32 0.41

f1 (cylindrical)

6.3 ± 0.7

7.8 ± 0.9

10.1 ± 1.0

7.4 ± 0.9 5.6 ± 0.7

9.3 ± 1.0

35.4 26.6 42.9

05 25 20 16 05 05 30 13 12 20 17

0.32 0.57 0.58

± ± ± ± ± ± ± ± ± ± ±

Bulk hardness (GPa)

29.0 19.9 48.4

Total porosity (%)

Table IV. Estimation of thermal conductivity

SOFC 2

80.1 51.6

YSZ (electrolyte) LSM (cathode)

fi fi fi fi fi fi fi fi fi fi fi

Crystallite size (nm)

YSZ NiO 107.9 ± 8.8 YSZ 211.8 ± 13.5 LSM MnO 162.9 ± 10.8 YSZ NiO 84.4 ± 9.8 YSZ CeO2 215.9 ± 14.6 LSM MnO

174.6 ± 8.8

% Th. Thickness density (lm)

71.0

Cell component

SOFC 1 YSZ-NiO (anode)

Cells

0.24 0.20 0.14

0.13 0.17 0.13

0.47 0.48 0.45

0.55 0.27 0.29

Plasticity index

Coefficient of friction

5.05 3.77 9.60

5.05 3.50 9.60

k0 (W/mK)

2.54 2.65 3.42

2.27 2.84 4.45

k (W/mK)

29.9 ± 1.0 0.69 ± 0.01 0.121 ± 0.008

34.5 ± 0.8 0.66 ± 0.01 0.106 ± 0.008

32.1 ± 1.8 0.71 ± 0.02 0.095 ± 0.002

38.2 ± 3.1 0.68 ± 0.03 0.102 ± 0.007 31.2 ± 3.7 0.69 ± 0.02 0.128 ± 0.002

31 ± 1.3 0.70 ± 0.02 0.103 ± 0.004

hc (nm)

f3 (spheroid)

16.8 ± 0.7

13.5 ± 0.5

15.0 ± 0.8

11.9 ± 1.4 15.5 ± 2.4

15.8 ± 0.9

H (GPa) Nanoindentation

f2 (lamellar)

176.7 ± 6.0

157.4 ± 2.7

197.4 ± 7.6

139.0 ± 9.3 188.3 ± 15.4

205.6 ± 6.7

Er (GPa)

Table III. Microstructural and mechanical properties of the plasma-sprayed SOFC component coatings



but at the same time, it affects the bonding strength of the coating and leads to poor contacts between the phases, and therefore, poor electrical conductivity. SOFC components fabricated by plasma spray coating exhibit lower relative theoretical density (73–84%) compared to those processed by sintering methods, e.g., spark plasma sintering (94–98%) technique employed by our group for similar materials and composition.21 It must be mentioned here that air plasma spraying is not ideal for the deposition of electrolyte, as an ideal SOFC would require a very dense (near to complete theoretical density) electrolyte. In actual application, vacuum plasma spraying may be utilized for the deposition of electrolyte. Current work focuses only on the nanomechanical performance and estimates the theoretical thermal conductivity of the air plasma processed composite layers in SOFC. Spray-dried agglomerates of 8 mol% YSZ seem perfectly spherical, and the presence of YSZ can be identified by two major characteristic peaks at 30.11, 50.18 and 59.65, while the CeO2 characteristic peak matches well at 28.56, 47.51, and 56.38. The major characterization peaks for NiO and LSM are 37.28, 43.32, 62.9, and 32.52, 46.83, and 58.15, respectively. No other peaks were found in the XRD pattern for the initial powders. The XRD patterns confirm that zirconia was in fully stabilized form. No peak shifts of the major peaks of YSZ and CeO2 phase have been detected. The XRD results reveal the presence of nanocrystallites of different phases (in size range of 40– 80 nm). Nanocrystalline YSZ electrolytes have been reported to exhibit enhanced electrical conductivity of 2–3 orders of magnitude higher as compared to microcrystalline specimen.22 Magnified images of the pores show densely sprayed splats and many globular structures that are remnants of unmolten or partially molten powder particles embedded at the floor of the pores (Fig. 4). Anode and cathode materials are the same for both the SOFCs (Fig. 4a–d), whereas only electrolyte is different. In SOFC 1 (Fig. 4e, f), electrolyte is 8YSZ, whereas in SOFC 2 (Fig. 4g, h), electrolyte is 10 wt.% CeO2 reinforced 8YSZ. The addition of ceria in 8YSZ does not exhibit any apparent change in the microstructure and proportion of partially and fully melted regions. Only a few pores/micropores at the floor of the pore are visible, and the surface elicits a compact appearance ruling out any preexisting cracks. Interfacial bonding between cathode and electrolyte layer shows a discontinuous layer in SOFC 1, whereas electrolyte coating of SOFC 2 is completely intact with cathode material showing good adhesion (Fig. 3). The absence of the discontinuity in SOFC 2 suggests that the addition of CeO2 improves adhesion with the cathode. It is also possible that the loss of material could have occurred at the interface during cross sectioning and polishing of the deposited layers. The densification of the electrolyte layers, as indicated earlier,

can be enhanced via utilization of other deposition techniques (such as vacuum plasma spraying) to achieve enhanced solid-oxide fuel cell performance. EDS and elemental mapping of the coated cell component layers (for SOFC 1 and SOFC 2 in Figs. 5, 6, respectively) reveal chemically distinct identities of the cell components with clean boundaries ruling out diffusion or reactions at the boundaries. The interface between the layers is thin and continuous for both SOFC 1 (Fig. 5a) and SOFC 2 (Fig. 6a). So after efficiently sustaining the thermal shocks during the processing, an essential requirement of SOFC is, therefore, met here. Additionally, the net chemical analysis of each layers of SOFC 1 (Fig. 5b1/2/3) and SOFC 2 (Fig. 6b1/2/3) indicates an absence of any diffusion between the layers during deposition. Because all components are basically oxides, the distribution of oxygen (Figs. 5c1, 6c1) is uniform throughout with somewhat greater concentration in the middle electrolyte layer, which looks darker due to its greater density. Cathode, electrolyte, and anode regions exhibit uniform distribution of Mn, Ni, Zr, La, and Y (Fig. 5c2/3/4/5/6) in SOFC 1 and that of Mn, Ni, Zr, La, Ce, and Y (Fig. 6c2/3/4/5/6/7) in SOFC 2. Distribution of yttrium and zirconium is observed in both anode and electrolyte regions (Figs. 5c4/6 in SOFC 1 and 6c4/7 in SOFC 2). The appearance of cerium in the electrolyte part of SOFC 2 (Fig. 6c6) is diffused and not distinct, which might be due to low concentration (10 wt.%), but it is well detected in the point EDS shown in Fig. 6b2. In the SEM image of SOFC cross section (Fig. 5a), a discontinuity is also observed (also see Fig. 4a/c). It is possible that discontinuity might have occurred during cutting/ polishing of the sample prior to imaging or even earlier during processing due to the difference in thermal conductivity, which is explained in the last section. Such a crack is not present in the microstructure of SOFC 2 (Fig. 6a). The latter shows better adhesion of the component layers, which helps in improving the life of the cell and enhances its performance. The presence of major characteristic peaks in the coated layers validates the presence of undisturbed YSZ (Fig. 7). But the CeO2 peaks are missing, which indicates that CeO2 is forming a solid solution with YSZ and goes into the YSZ matrix. The major characterization peaks of YSZ have been shifted from its standard position, which may arise due to the stress developed in the YSZ lattice. This peak shifts also indicate the formation of CeO2-YSZ solid solution. The XRD results show the presence of some different phases, i.e., MnO2 in LSM cathode, which shows the decomposition of perovskite phases (Fig. 7). This is not desirable because it reduces the catalytic property of the cathode in SOFC for the reduction of oxygen. Peak broadening observed in the coated samples relative to the initial powder suggested that particle size reduces during plasma spray deposition. This is


Fig. 4. Scanning electron micrographs of different coating layer interfaces of SOFC 1, viz., cathode–substrate interlayer and pore interior at high magnification (a, b); electrolyte–cathode interface and pore interior (c, d); anode–electrolyte interface and pore interior (e, f); electrolyte–cathode interface and pore interior of SOFC 2 (g, h). Addition of ceria to 8YSZ in the electrolyte of SOFC 2 does not seem to have imparted any apparent change in the microstructure and proportion of PM and FM regions.

supposed to help improve the performance of the cell. The XRD pattern of anode coating shows the main composition NiO and YSZ, and a small

amount of metallic Ni is formed by the reduction of NiO during spraying. The phase composition analysis reveals that nanocrystallinity was achieved


Fig. 5. (a) SEM image, and EDS maps of (b1) anode, (b2) electrolyte, and (b3) cathode, and elemental mapping with (c1) O, (c2) Mn, (c3) Ni, (c4) Zr, (c5) La, and (c6) Y in plasma-sprayed SOFC 1 coating. Elemental mapping shows uniform distribution of elements in the respective layers (anode, electrolyte, and cathode) as well as sharp and clean boundaries ruling out any possibility of reaction between the component materials at the interface.

after plasma spraying and all the peaks associated with prime YSZ powder are apparent in the fabricated cell. This signifies that the main phase and chemical compositions are retaining their respective individual identities and no undesirable second phase is observed. Mechanical Properties of Solid-Oxide Fuel Cells The hardness of different coating layers was measured by Vickers indentation method on cross sections of the cells. An applied load of 100 g was taken toward the lower end to avoid the cracking at

the edges of the indent utilizing all the energy to deform the material. The results of bulk hardness and nanoindentation are summarized in Table III. A minimal improvement is observed in the mechanical properties of the SOFC2 as most of the error values are overlapping. This slight improvement cannot directly be correlated with the densification of the different layers. In case of electrolyte, it is observed that CeO2 addition decreases the densification by 8.4%, whereas the hardness increases from 7.41 to 7.79 GPa. A similar trend is observed with anode that shows an enhancement of 9%. However, in case of cathode of SOFC 2, with an increase in densification, hardness enhances by


Fig. 6. (a) SEM image and EDS maps of (b1) anode, (b2) electrolyte, and (b3) cathode, and elemental mapping with (c1) O, (c2) Mn, (c3) Ni, (c4) Zr, (c5) La, and (c6) Ce, and (c7) Y in plasma sprayed SOFC 2 coating. Elemental mapping shows uniform distribution of elements in the respective layers (anode, electrolyte, and cathode) as well as sharp and clean boundaries ruling out any possibility of reaction between the component materials at the interface.


Fig. 7. Phase characterization of the two plasma-sprayed SOFC coatings.

12%. A higher hardness value implies good coating quality in SOFC 2. Coatings prepared from spraydried powders have been reported to exhibit greater hardness values than those made of blended powders.10 This is attributed to the larger size of the spray-dried powder compared with the blended powders. Therefore, the transfer of heat flux is also greater. On the other hand, in case of blended powders, owing to low dwell time, higher particle size, irregular morphology, and density difference among the phases, the heat flux cannot penetrate the core, causing a large deviation in hardness measurement in the resultant coating.10 In the case of spray-dried powders, the deviation is less. The addition of 10 wt.% ceria to 8YSZ enhances the modulus and hardness of the electrolyte material by 18.4 GPa and 1.6 GPa, respectively. SOFC 2 shows a smooth transition in the reduced modulus values. This reduces the probability of failure of the cell at the operating temperature. SOFC 1 shows a drastic variation in the elastic modulus values for the anode, electrolyte, and cathode part. The hardness values obtained from nanoindentation experiments are 1.6–2.7 times higher than bulk. One plausible reason is the difference between the two techniques. Vickers’ hardness elicits the resistance to plastic deformation in the bulk of the plasma coated layers, i.e., splats. The splat length and thickness range from 12.6 lm to 36.9 lm and 4.2 lm to 7.6 lm, respectively. Thus, the area impacted under Vickers’ indenter covers multiple splats on the surface. A single splat layer as well as successive layers may contain fully melted, partially melted, or sintered regions, which have different hardness values. Moreover, there are currently many pores of different geometries that tend to lower the hardness of the material. On the other hand, the Berkovich indenter impacting a nanoregion on the splat meets the nanocrystallites present in the splat (as

suggested by XRD results, Fig. 7), and hence, the measured hardness values are higher. Coefficient of friction measurements exhibit no apparent change on adding 10 wt.% CeO2 in YSZ electrolyte and show better adherence between the coated layers. Higher surface roughness is beneficial in the case of electrodes as it increases the reaction area and performance of the SOFC cell. On the other hand, surface roughness of the electrolyte should be low in order to reduce the leakage and improve the ionic conductivity. The average roughness determined for SOFC 1 is 99.8 ± 68.5 lm, 17.7 ± 9.3 lm, and 20.9 ± 8.5 lm, respectively, for cathode, electrolyte, and anode. Similarly, average roughness values were determined for SOFC 2 as 103.2 ± 73.9 lm, 5.6 ± 2.7 lm, and 31.4 ± 20.7 lm, respectively, for cathode, electrolyte, and anode. These observations suggest that the average roughness remains similar for the cathode, anode, and electrolyte regions, but it can also be observed that ceria addition has resulted in a smoother surface (with a lower standard deviation). Theoretical Estimation of Thermal Conductivity The SOFC cell fabricated by the atmospheric plasma spray method bears pores of more than one type. During the process, the spray-dried powders are exposed to plasma and get melted and sprayed with a momentum against a flat substrate. The spherical molten particles splat on the substrate and flatten to make a deposition. Numerous subsequent splats make a, overall coating of a certain defined thickness. After adhering to the surface, the temperature of the matrix tends to decrease and shrink a little. On such cooling splats when another big splat hits with a momentum, it either gets glued with the former or sits as a separate splat. However, strict binding among subsequent splats causes mechanical stress and may generate a discontinuity or delamination of layer as observed in Fig. 4c. Certain pores are observed to distribute randomly, whereas certain locations show lamellar porosity or even cylindrical morphology (cylindrical pores). Under operational conditions at an elevated temperature, these create nonhomogeneous temperature distributions and large internal stresses inside the cell component matrix, which may generate bigger cracks and material failure. Therefore, it is very important to consider the matching between the coefficient of thermal expansion and thermal conductivity between materials of the cell components. During thermal cycles, phase transition or corrosion phenomena of both metallic bound coat and the substrate must not occur. An increase in the temperature may also lead to a progressive destabilization of the coating material. To minimize the internal stress, the thermal diffusivity of the material has to be kept as low as possible.23 In plasma-sprayed coatings, it depends on the microstructural characteristics, viz., grain size, morphology, porosity, and phase


composition. The relation between thermal conductivity k and thermal diffusivity is given by kðT Þ ¼ aðT Þ Cp ðT Þ qB , where, a(T) is thermal diffusivity, Cp(T) is specific heat and qB is the bulk density of the coating.24 Both thermal conductivity and diffusivity decrease in a similar fashion with the increase in the content of lamellar and cylindrical pores oriented perpendicular the thermal flux, whereas in the case of randomly oriented cylinders and spheres, there lies little difference in the trend (Figs. 10 and 11 of Ref. 23). In plasma-sprayed coatings, besides grain size, morphology, porosity, phase composition, etc., thermal conductivity also depends on cell parameters. Stack design and operating conditions, such as cell geometry and operating voltage, influence temperature distribution in a very complicated way. To estimate thermal conductivity, the microstructural properties are taken into consideration, viz., percentage, type shape, and orientation of porosities. Inside the pores, there exists a radiative mode of thermal conduction, and hence, its contribution to the overall thermal conduction of the coated material is negligible. Since plasma-sprayed coating possesses more than one type of porosities, viz., spheroid (spherical, oblate, and prolate), lamellar, and cylindrical, all these are to be taken into consideration. Since it was very difficult to classify the porosities into different categories form the microstructural images, a stereological analysis of the binary images of real material cross sections was employed to calculate porosity. Among the different models available in the literature,16,23,25 the one incorporating an iterative approach to extend the already existing models for a material possessing single type of porosity (spherical or lamellar) to the materials containing many types of porosities (spherical, lamellar, and cylindrical) is taken in this article. This model is a hybrid between symmetrical (for spheroid pores) and asymmetrical (for lamellae and cylindrical pores) approaches. An approximation that most of the pores are aligned perpendicular to the heat flux is taken in this investigation. The expression giving the final thermal conductivity k of the plasma-sprayed coating with three types of porosities existing in the coating is16: k0 f2 f1 k ¼ fU W H ðf 3 Þ 6 ð1 ðf1 þ f3 ÞÞ ð1 f3 Þ f1 f2 þW U Hðf3 Þ ð1 ðf2 þ f3 ÞÞ ð1 f 3Þ f2 f3 þU Wðf1 Þ H ð1 ðf1 þ f3 ÞÞ 1 f1 f1 f3 þW H Uðf2 Þ ð1 ðf2 f3 ÞÞ ð1 f 2 Þ f3 f2 þH U Wðf1 Þ ð1 ðf1 þ f2 ÞÞ ð1 f1 Þ f3 f1 þH W Uðf2 Þg ð1 ðf1 þ f2 ÞÞ ð1 f 2 Þ

where W(f), U(f), and H(f) are the functions describing the effects of the three different types of porosities on the thermal conductivity of the matrix. W, H, and U can be defined in terms of morphology of the porosity; e.g., U(f) = (1 f)X, and 2 a cos2 a X ¼ 1cos 1F þ 2F . Here, F is the shape factor of the spheroid and a is the angle between the revolution axis of the spheroid and the nonperturbed heat flux. For sphere (a = c), F is 1/3, for oblate spheroids (c > a), it varies between 0 and 1/3. For prolate spheroids (a > c), it is between 1/3 and 1/2. In this article, X values are taken for spheroid, lamellar, and cylindrical pores as 3/2, 1, and 2, respectively, for orientation perpendicular to the heat flux.16 The thermal conductivity (k0) of crystalline and undoped matrix without porosity is taken from the literature and is calculated using rule of mixtures.26–30 Percentages of the types of porosities, viz., cylindrical, lamellar, and spheroid, are denoted as f1, f2, and f3, respectively. The results of the calculation have been tabulated (Table IV). The estimated thermal conductivities are found to be very low, influenced significantly by pores and cracks, and they seem to be favorable. The overall structural and mechanical properties of the plasma-sprayed coatings are basically dependent on the particle size distribution and material properties of the starting powders. Besides these spraying modes, coating parameters also play key role in achieving the overall desired properties of the fabricated coatings. It is, therefore, essential to perform a comparative and systematic study and analysis of the coating obtained with different structures using finer starting powders with the same chemical composition but with different physical and technical properties. This would bring clearer insight to achieve better adherence and anchorage between successive splats, different layers of the coating and control optimum porosity, better mechanical properties, and crack resistance at the same time. If suspension plasma spraying is incorporated to fabricate the electrolyte in combination with atmospheric plasma spraying employed to fabricate the two porous electrodes, then it would help achieving highly densified coating. Young’s modulus is expected to increase significantly provided that heat treatment is given to the coated layers. A considerably high porosity level (30–45%) of the coating creates a strong barrier against heat flux and protects the material from sintering and densification. The theoretical model for estimation of thermal conductivity used in this article considers porosity only and not the scattering effects by the sintered, semimolten, or partially molten agglomerated particles embedded in the coated microstructure (Fig. 4). Thus, it is very important to analyze the microstructures of the coated materials at various angles. There is scope for the development of thermomechanical models of the fabricated coating layers and simulation of their behavior at various temperatures. This, in turn, requires reliable values for the thermal


and mechanical properties of the materials at different elevated temperatures. CONCLUSIONS The plasma-sprayed coating layers of the two types of SOFCs show distinct identities in terms of elemental distribution, phase, and microstructure signifying the attainment of optimal processing parameters. The processed SOFCs have been shown to retain the nanocrystallinity and well exhibit appreciable hardness values of the coated layers. Addition of 10 wt.% ceria to 8-YSZ in SOFC 2 marginally enhanced the hardness and exhibited a smooth transition in the reduced elastic modulus. Apparently, no change is observed in the roughness or coefficient of friction after the addition of 10 wt.% CeO2 in YSZ electrolyte. SOFC 2 also exhibited good adherence between the coated layers compared with that of SOFC 1. Besides this, the addition of ceria in SOFC 2 electrolyte is also bound to enhance the oxide ion conductivity, i.e., electrolyte efficiency. Although air plasma spraying is not an optimal technique for deposition of dense electrolyte, this work has analyzed the nanomechanical behavior of deposited SOFC composite layers. Bulk hardness values are lower (5.6–10 GPa) compared with the hardness values obtained from nanoindentation results (139–205 GPa), indicating a contribution of randomly scattered pores in the coating. Thermal conductivity estimations ranged between 2.27 W/mK and 4.45 W/mK, which are lower when compared with their bulk counterparts (3.5–9.6 W/ mK). The thermal conductivity values for SOFC 2 are comparatively lower than SOFC 1, suggesting higher resistance to thermal damage during operation. A quantitative estimation of the thermal conductivity of the coated layers using pore geometries (viz., spheroid, cylindrical and lamellar), along with inclusion of total porosity content, renders a realistic contribution of the pore types on thermal conductivity. ACKNOWLEDGEMENTS K.B. acknowledges funding from Department of Science and Technology, Ministry of Human Resource Development, Government of India, and CARE grant, Indian Institute of Technology Kanpur, India. REFERENCES 1. R. Hui, Z. Wang, O. Kesler, L. Rose, J. Jankovic, S. Yick, R. Maric, and D. Ghosha, J. Power Sourc. 170, 308 (2007).

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