Modelling and Prediction of Deformation During Sintering of a Metal Foam Based SOFC (EVOLVE)

Transcription

1 Modelling and Prediction of Deformation During Sintering of a Metal Foam Baed SOFC (EVOLVE) M. Xu, D. Maon, D. Ryckelynck, A. Chenaud and A. Thorel Centre de Matériaux, Mine-PariTech PSL, UMR CNRS 7633, BP 87, Evry Cedex, France Stacking of cell in a SOFC tack require that each element be perfectly flat and deprived, a much a poible, of internal tree while maintaining their electrochemical capabilitie. The EVOLVE concept introduce a metal foam baed anode in which the foam play the role of current collector, ga diffuer and thermo-mechanical deformation buffer. Owing to the different mechanical behaviour of the anode component, the deformation during intering cannot be intuitively anticipated. Therefore, the global deformation of the cell wa modelled and imulated by Finite Element conidering a phenomenological approach of the aniotropic intering. The thermo-mechanical parameter of each component were determined experimentally by dilatometry and three-point bending tet operated under condition identical to thoe of the intering. Reult provide relevant indication on component compoition and morphology, and on the intering condition for producing flat and tackable cell. Introduction Solid Oxide Fuel Cell (SOFC) i one of the mot attractive energy converion ytem for tationary application owing to it efficiency (80% net in cogeneration) and fuel flexibility (hydrocarbon, CO, bio-fuel, ). Although the feaibility and potentiality of SOFC have already been demontrated for age, their repeated delaying large-cale commercialization till prove the exitence of cientific and technological challenge which are imperative to olve. The main limitation of SOFC that retrict their bringing to market remain the fat-acting deterioration of material through redox cycling at the operating temperature, particularly on the anode ide. In thi day and age, three main configuration of planar SOFC have been experimented either at the laboratory or indutrial cale. The electrolyte-upported cell (ESC) preent the advantage of being olid and adaptable depite it very low level of performance. Nowaday, the high power output of the anode-upported cell (ASC) make thi configuration the mot mature deign (1,2), neverthele it life pan remain trongly limited owing to mechanical and chemical degradation mechanim promoted at high temperature by the preence of nickel particle (3-,4,5,6,7). Even if the operating temperature i reduced, coking and ulphur poioning become the main ource of performance degradation through redox cycle. The metal-upported cell (MSC) bring ignificant advantage in term of mechanical tability and robutne under tranient condition (8), however it power denity remain low compared to the ASC (9).

2 The originality of the EVOLVE concept reide in the implementation of an innovative architectured current collector, on the anode ide, baed on material that can withtand mechanical and chemical tree. The current collector i contituted of a NiCrAl foam impregnated with La 0.1 Sr 0.9 TiO 3+ (LST), that alo play the role of ga diffuer a well a mechanical upport (Figure 1) for the following equence: the anode (LST or LST + GDC10), the electrolyte (YSZ), the diffuion barrier (GDC10) and the cathode (LSCF48). Thi configuration combine all attractive feature of an ESC, i.e. the robutne and flexibility, with the advantage of an ASC, the electrical power upplied, along with the electrochemical tability under redox cycle of a MSC. Therefore, uch architecture repreent a trategy to improve performance, reliability and durability of SOFC, along with their tolerance regarding ulphur. Figure 1. Schematic view of the layer configuration in the anode upported SOFC. The connected phere repreent the keleton of the metal foam. A predictive thermo-mechanical model that i able to decribe the global deformation of thi cell during intering i propoed. The numerical imulation wa carried out conidering a phenomenological approach of the aniotropic intering. Thi theoretical tudy aimed at reducing the trial-error experimental approach for optimizing the intering cycle, guide the choice of material and cell dimenion for producing flat and tackable cell. Fabrication of the Anode-architectured Cell Experimental ection A equence of procee i implemented in order to fabricate a complete anodearchitectured cell. The current collector i made from a NiCrAl foam impregnated with a LST powder that i further cold rolled to decreae it thickne and poroity down to µm and 15% to 20%, repectively. The 50 µm LST (or GDC10-LST) functional anode i then depoited by creen printing or bar coating. Initial poroitie of 45% are uually meaured from SEM image recorded on microtructure of layer fabricated with uch procee. The mooth urface of the anode i afterward covered with a µm thick YSZ electrolyte layer uing an electron-beam phyical vapor depoition technique achieved at 600 C. Thi latter i repeated for the coating of the 2-5 µm thick GDC10 diffuion barrier. The advantage of thi technic i that fully dene material (relative denity in the range 95-99%) can be directly depoited at 600 C without any additional pot thermal treatment. The final LSCF48 cathode layer with a thickne varying from 30 to 50 µm i then coated by creen printing; the initial layer poroity i

3 about 45%. At lat, the whole multilayered tructure i intered at 1100 C for 5 hour in air. Dilatometry Tet The aniotropic hrinkage curve for each component of the cell wa deduced from dilatometry data of correponding material. The unidirectional variation of the dimenion of ample, i.e. expanion and hrinkage, were ucceively recorded a a function of the temperature uing a differential horizontal dilatometer DIL 402 CD from NETZSCH. Thi apparatu i equipped with two high reolution inductive enor (digital reolution of 1.25 nm) connected with an alumina puhrod that enable to apply continuouly a preure on the ample during meaurement. Data collection wa carried out in tatic air, between 35 C and 1570 C with a heating rate of 5 C min -1 while a tatic load of MPa (45 cn applied on a urface of 28.3 mm 2 ) wa continuouly applied. The thermal expanion of the ample holder wa ytematically ubtracted from the raw data applying the DIN calibration correction and uing alumina calibration tandard. The data were recorded and analyed uing the Netzch-Proteu oftware (v 6.1.0). Three-point Bending Tet The three-point bending tet were carried out in tatic air uing a vertical multi-unit SETARAM TMA-92 thermo-mechanical analyer equipped with a dedicated ample holder contituted of a flange upporting two alumina triangle-haped edge paced 8 mm. A contant load of 45 cn i continuouly applied during meaurement by mean of an ended-edge upporting haft having a knife-haped ection. The alumina haft i connected to a linear variable differential tranducer (LVDT) which record the vertical deflection of the middle line of the pecimen. The diplacement range wa fixed to ± 2.0 mm with a linearity of 0.3% and the vertical deflexion wa meaured with a reolution of 0.1 μm. Beam-haped ample of 10 mm long by 3 mm wide by 500 μm thick were ued to neglect hear tree. Vertical deflexion data were collected between 35 C and 1570 C with a heating rate of 5 C min -1 and the maximal temperature wa maintained for 5 hour. The data were collected and proceed uing the CALISTO v oftware. Modelling of the Deformation Model and Numerical Simulation In order to predict the deformation of the cell during heating, a phenomenological approach of the intering wa conidered. The procedure conit in following the total deformation of the cell over time during the heat treatment. Thi deformation occur according to four ucceive procee: two reverible phenomena, i.e. (i) the elatic deformation ( e ) and (ii) the thermal dilatation ( th ), followed by two imultaneou phenomena, i.e. (iii) a vicoplatic deformation ( vp ) related to the creep and (iv) a hrinkage ( ) aociated to intering. The global behaviour law of the deformation kinetic can be expreed by: total e th vp [1]

4 The vicoplatic deformation i driven by a thermally activated creep deformation Norton law; the intering hrinkage, alo a thermally activated proce, expree the denification of the material. Elatic and thermal deformation were not taken into account a they contribute by an inignificant margin compared with irreverible ( vp and ) procee. The model integrate morphological (initial f o and final f poroitie) and mechanical characteritic of each contituent layer, a well a the cell dimenion (Figure 2a). In the preent cae, the improvement of the model application wa achieved by conidering the real mechanical behaviour of each material that wa deduced from dilatometric and creep tet. Thee latter were operated in the ame heat and atmophere condition a the real intering. In addition, the aniotropic intering wa conidered and i detailed herein below. For the modelling, the thickne of each layer of the cell wa fixed (Table I), while cell diameter of 10 mm, 20 mm, and 40 mm were implemented. The numerical imulation wa carried out integrating the functional anode material either a ingle phae or compoite (Table I). TABLE I. Thickne of each layer implemented in the thermo-mechanical model. Deignation Compoition Initial thickne Initial poroity Current collector NiCrAl-LST 600 µm 15% Anode LST (or LST-GDC10) 50 µm 45% Electrolyte YSZ 15 µm 1% Diffuion barrier GDC10 2 µm 1% Cathode LSCF48 30 µm 45% Cell - t cell = 697 µm - For ymmetry reaon, only a ection of the cell wa mehed; a quadratic element (c2d8) without model reduction wa ued and applied to the cell element of diameter Ø cell /2 (Figure 2a and b). The mehing wa refined cloe to the layer interface. The numerical imulation were performed in 2D uing the Z-et finite element code, implemented in the Zebulon oftware and developed by MINES-PariTech (10). Figure 2. (a) Longitudinal ection of a 2D-aymmetrical element extracted from the cylindrical cell and (b) it correponding mehing. One layer correpond to one grey level. For the calculation, only the horizontal diplacement (U 1 ) of the node on the left ide of the cell element wa blocked a if the cell wa ubjected to free intering. The initial poroity of each contituting layer of the cell (Table I) wa et o that it i imilar to that obtained by the correponding haping proce. However, the realitic condition of intering hould be that one blocking the creep of the cell put on a ubtrate.

5 Modelling of the Aniotropic Shrinkage During Sintering Experimentally, the ample for dilatometry tet are cylindrical with a diameter of 6 mm. Given that preure and temperature field impoed to the ample are uniformly ditributed on their urface, the meh geometry and dimenion will not impact reult obtained from the imulation. A a matter of fact, the numerical geometry of the ample can be implified uing a 3D mehing of a linear cubic element (Figure 3a). For the calculation, the three diplacement U 1 (along x), U 2 (along y) and U 3 (along z) of the (0,0,0) origin point were blocked. In addition, the diplacement U 3 of the (0,0,1) point wa blocked in order to avoid rotation of the element. Figure 3. Geometrical element ued to model (a) the technical hrinkage and (b) the 3- point bending tet. An aniotropy model of the intering wa conidered to imulate the material behaviour (11). The deformation kinetic of intering depend on temperature and poroity of the ample. It can be expreed by a two-order tenor: f,t x f,t 0 0 y 0 f,t 0 z 0 0 f,t [2] The intering being thermally activated, the kinetic deformation of intering in each direction can be written: β Q x, y,z f,t Ao f f exp [3] RT A o i the pre-exponential factor, f and f the time-dependent and final poroitie, repectively, β a contant that depend on the material, Q the intering activation energy, and R the ideal ga contant. By introducing aniotropy coefficient for the intering to decribe the component of the deformation in the direction perpendicular to the cylinder axi, i.e. y, the kinetic of deformation along x and z can be expreed a a function of y f,t and K 1 and K 2 repectively: x f,t K 1 y f,t f,t K f,t with K 1 = K 2 in the cae of a cylinder-haped ample. z [4] 2 y [5]

6 Modelling of the 3-point Bending Tet In order to imulate the vertical deflexion of the rod-haped ample ubmitted to 3- point bending tet that will lead to the identification of creep kinetic parameter, a 3D mehing a illutrated in Figure 3b wa ued. Since a force of 45 cn i uniformly applied on a rectangular urface (3 mm length and 2 mm width) of the top urface of the element, the charge can be converted to a uniform preure field. For the calculation, the diplacement U 1 and U 2 of the bottom left egment a well a the diplacement U 2 of the right bottom egment of the 3D element were blocked. Beide, the U 3 diplacement of the (0,0,0) origin wa blocked. The vicou flowing i uppoed to be linearly dependent of the tre in accordance with a creep aociated with a high temperature diffuion proce. Neverthele, the kinetic of deformation alo depend on the material poroity. So the kinetic of creep deformation i written a: vp f,t 1 Mσ f : [6] η t,t Where η(t,t) repreent the vicoity of the material according to the Arrheniu law: η t,t 1 Q exp vp 1- f K RT o o [7] Q c i the creep activation energy, R the ideal ga contant and T the temperature. The tenor M f of order 4 wa introduced to model the effect of the poroity on the kinetic of deformation. The creep i aumed to be iotropic, therefore M f C f J F f I M f can be written: 3 [8] 2 With C(f) and F(f) two coefficient that depend on the poroity defined a: F Cf f Otherwie, the tenor of order 4, i.e. I and J are expreed by: I : J : n c 1 C o f [9] n F F o f [10] tr I [11] 1 tr I [12] 3 For NiCrAl foam, only the creep phenomenon occur o that it deformation during intering can be decribed according to a Norton-Hoff vicoplatic model given by:

7 vp f,t n Qvp n ko exp KT RT [13] The creep activation energy Q vp i the ame a the intering activation energy Q auming that both phenomena are controlled by elf-diffuion. Dilatometric Meaurement and Modelling Reult and Dicuion The longitudinal hrinkage ( l ) of all material contituting the cell wa meaured on compacted powder, in the form of cylinder, a a function of the temperature. Tet were carried out in tatic air under a load of 45 cn. The reult i diplayed in Figure 4a for the YSZ electrolyte material. In the low temperature region (< 1000 C), the compacted powder expand which reult in an increae of the ample length. From 1000 C, the intering take place and the ample dratically hrink up to 1400 C and then it dimenion remain unchanged. During cooling, the contraction make poible the determination of the thermal expanion coefficient (TEC) of the ample. The technical curve wa built by extracting the reverible thermal deformation th (equation 14) from the dilatometric data dil. The reultant curve (Figure 4a) obtained i only compried of the irreverible procee, i.e. the intering and vicoplatic deformation that occur almot imultaneouly. The ample length i reduced by 24% a illutrated by the evolution of the hrinkage curve recorded between room temperature (RT) and 1570 C. The hrinkage curve how that the ample length doe not evolve from RT to 600 C. tech t,t t,t TEC 100(T T ) [14] dil T i (= 35 C) i the temperature from which dilatometric data were recorded. tech and dil are the technical and dilatometric hrinkage, repectively. i Figure 4. (a) Dilatometric (unbroken line) and technical hrinkage (dahed line) curve; the inet repreent the meaurement configuration in the ample-holder of the dilatometer; (b) evolution of the experimental (open quare) and imulated (light grey unbroken line) poroity of the YSZ material a a function of the temperature.

8 TEC i the thermal expanion coefficient deduced from the lope of the linear portion of the dilatometric curve (Figure 4a) recorded during the cooling tep. The evolution of the material poroity a a function of the temperature, diplayed in Figure 4b, wa then calculated uing the theoretical approach reported by K. Maca et al. (12). The mechanical parameter A o, β and Q of the intering behaviour law were refined for each material by fitting the experimental curve diplaying the poroity a a function of the temperature. In order to do thi, all parameter were adjuted until both the imulated and experimental curve match. Figure 4b illutrate an example of uch a refinement achieved on the YSZ electrolyte material and leading to a perfect agreement between experimental and imulated curve. The morphological parameter f o and f are data meaured on the ample before and after intering, repectively, and aniotropy factor (K 1 = K 2 ) are deduced from the total hrinkage l (inet in Figure 4a) along the cylinder axi. The ame procedure wa followed for the other material. The experimental and imulated curve are compared in Figure 5a and refined parameter are gathered in Table II. Figure 5. Evolution of (a) the poroity and (b) the deflexion of the ample veru the temperature. Symbol and unbroken light grey line are ued for experimental data and imulation, repectively. Apart from material containing the LST phae, a very good agreement between experimental and imulated data i noticed. Indeed, L. Amaral et al. reported a two-tep denification proce in nontoichiometric LST ceramic (13). TABLE II. Refined mechanical parameter and final poroitie for all material of the anode-architectured cell. Parameter GDC10 YSZ LSCF48 LST GDC10- GDC10- NiCrAl LSCF48 LST A o / K o β f /% K 1 (= K 2 ) α exp / 10 6 K η o /MPa Q/kJ mol C o n c F o

9 Three-point Bending Tet and Modelling The deflexion of each ample under contant load of 45 cn wa meaured a a function of the temperature (Figure 5b) A with dilatometric meaurement, dilatation effect were firt removed from the raw data prior to numerical imulation. Modelling of Deformation in Complete Cell The influence of the intering temperature wa invetigated on laboratory-cale cell with Ø cell = 10 mm. Layer thicknee a indicated in Table I were implemented in the model. An initial poroity of 15% wa et for the NiCrAl-LST current collector. Three calculation were carried out in order to imulate deformation in the cell after intering at 1100 C, 1200 C and 1300 C for 5 hour. For the imulation, a heating rate of 5 C min -1 wa implemented. A illutrated in Figure 6, a intering at either 1100 C or 1200 C ha a limited influence on the cell deformation. At higher temperature, e.g C (Figure 6c), the cell ignificantly bend a a direct conequence of the important hrinkage of the LSCF48 cathode material that reache it optimal intering temperature. Figure 6. Finite element modelling of the curvature of the complete cell during intering at (a) 1100 C, (b) 1200 C and (c) 1300 C. The grid arrangement (in red) ymbolize the initial mehing of the cell. In a econd time, the influence of cell diameter on the total deformation wa regarded. The calculation were carried out uing initial thickne and poroitie gathered in Table I and the intering wa operated at 1100 C for 5 hour with a heating rate of 5 C min -1. At uch a intering temperature, the Figure 7 how that the cell diameter ha an unimportant influence on the total deformation of the cell. Strong deformation will take place at a temperature from which the creep of material become ignificant, that i to ay 1200 C. Figure 7. Scale effect on the curvature of the cell at 1100 C for 5 hour.

10 Concluion A thermo-mechanical model wa developed in order to predict deformation during intering of a elf-upported current collector SOFC. Thi model wa fed with mechanical and morphological parameter deduced from dilatometric and creep tet. The numerical imulation were carried out auming that material are homogeneou media and implementing variou cell diameter and intering temperature a thee two parameter are likely to influence deformation of the multilayered tructure after thermal treatment. Finite element imulation demontrated that plane and tackable cell can be fabricated after intering at 1100 C for 5 hour if and only if the tarting powder are identical to thoe one ued for dilatometric and three-point bending tet. Indeed, interability of a pulverulent material depend on it granulometry while creep propertie are linked to the microtructure of the related dene bodie. Acknowledgment The reearch leading to thee reult ha received funding from the European Union Seventh Framework Programme (FP7/ ) for the Fuel Cell and Hydrogen Joint Technology Initiative under grant agreement N The author thank the CerPoTech company for upplying the powder. Reference 1. F. Han, A. Leonide, T. Van Getel, H.P. Buchkremer, in the 10 th European Fuel Cell Forum, Luzern, Switzerland (2010). 2. M. Lang, C. Wetner, R. Geieregger, B. bentlohner, R. Schwub, in the 10 th European Fuel Cell Forum, Luzern, Switzerland (2010). 3. P. Lohoontorn, D.J.L. Brett, N.P. Brandon, J. of Power Source, 183, (2008). 4. D.G. Ivey, E. Brightman, N. Brandon, J. of Power Source, 195, (2010). 5. L. Holzer, B. Iwanchitz, Th. Hocker, B. Münch, M. Pretat, D. Wiedenmann, U. Vogt, P. Holtappel, J. Sfeir, A. Mai, Th. Graule, J. of Power Source, 193(3), (2011). 6. S.D. Ebbeen and M. Mogenen, Electrochemical and Solid State Letter, 13, B106-B108 (2010). 7. T. Klemeno, M. Mogenen, J. Amer. Ceram. Soc., 90, (2007). 8. P. Bance, N.P. Brandon, B. Girvan, P. Holbeche, S.O Dea, B.C.H. Steele, J. Power Source, 131, (2004). 9. P. Szabo, J. Arnold, T. Franco, M. Gindrat, A. Refke, A. Zagt, A. Anar, ECS Tranaction, 25(2), (2009). 10. J. Beon and R. Fœrch, Rev. Eur. Elém. Fini, 7(5), (1998). 11. S. Sarbandi, Ph.D thei, Mine PariTech (2011). 12. K. Maca, V. Pouchly, A.R. Boccaccini, Science of Sintering, 40, (2008). 13. L. Amaral, A.M.R. Seno, P.M. Vilarinho, Mater. Re. Bull., 44, (2009).