Electronic Supplementary Information Proton Conductivity in Mixed-Conducting BSFZ Perovskite from Thermogravimetric Relaxation

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1 Electronic Suppleentary Material (ESI) for Physical Cheistry Cheical Physics. This journal is the wner Societies 014 Z ig / k Z / k phase / Electronic Suppleentary Inforation Proton Conductivity in Mixed-Conducting BSFZ Perovskite fro Therogravietric Relaxation aniel Poetzsch, Rotraut Merkle, Joachi Maier Max Planck Institute for Solid State Research, Heisenbergstrasse 1, Stuttgart, Gerany (1) Ipedance spectru of a BSFZ pellet equilibrated: 600 C in 1% dry T = 0 C C F r Z real / k frequency / Hz Fig. S1: Ipedance spectru of a BSFZ pellet easured at 0 C teperature. The pellet was equilibrated at 600 C in 1% and cooled to roo teperature in 1% within 10 in. The line represents the fit with the equivalent circuit described in the text. While a BSFZ pellet (thickness 0.1 c, area 0.16 c, Ag paste electrodes fired at 600 C) annealed in air at 600 C and cooled to 5 C within a few inutes shows an electronic conductivity which is in good agreeent with literature, 1 the bulk seicircle largely appears at frequencies higher than the easureent range (frequency of the highest point: = (RC) -1 ). Therefore, the pellet was annealed in 1% at 600 C (to decrease the p-type electronic conductivity) and easured at 0 C (decreasing the therally activated electronic conductivity 1 by decreasing T). Fig. S1 shows the ipedance spectru easured with a Novocontrol Alpha A ipedance analyzer. The spectru shows a single seicircle, the capacitance of which corresponds to a dielectric constant of r 75 which is in the range of typical bulk r values for perovskites. The seicircle was fitted with one resistance R and one constant phase eleent Q in parallel (shape paraeter p = 0.8; note that the stoichioetry within the pellet is slightly inhoogeneous owing to the cooling procedure) and a series connected L = H to account for the inductive effects of cables/wiring. The capacitance was calculated fro C = (R 1-p Q) 1/p. The absence of a low-frequency seicircle with high capacitance (typical grain boundary capacitances are > 1000 C bulk ) proves that the grain boundaries are not blocking for holes. In cases where perovskites such as slightly Fe-doped SrTi 3 exhibit blocking grain boundaries, this was found to be due to depletion of positive defects in space charge zones. 3-5 Thus, when no significant hole depletion is found for BSFZ, this indicates that also other positive defects such as H and V should not be blocked at the grain boundaries. 1

2 () Error bars The resolution of the Netzsch STA 449C therobalance is 1 icrogra. The baseline stability at elevated T and flowing gas (e.g. fro the initial segent in fig. ) is ± g over 8 h. Reproducibility of weights is ± g for several repetitions, and accuracy of absolute weights is better than relative to a calibrated lab balance. Thus, easured weight changes after ph, p steps are rounded to icrogra (rounding to tens of icrogra potentially induces artificial inaccuracy). Error bars are given for all extracted quantities. They correspond to three ties the standard deviation of the respective individual easureents (iodoetric titration for absolute, fro individual ph, p changes for ox and, diffusion coefficients fro four individual ph jups per teperature, error propagation fro ox and to defect concentrations, and fro and concentrations to proton conductivity). These error bars are larger than the error which corresponds to rounding values to 1 g. (3) Nuerical calculation of defect concentrations As entioned in the ain paper, and thus [H ] at given ph, p and T can be deterined fro the weight changes under the reasonable assuption that the activity coefficients iplicitly used in extracting ox fro isobars in dry p do not change upon water incorporation. To analyze the therodynaics the equilibrated states before and after ph change (e.g. state 1 and in Fig. 1 of the ain paper) are considered. For the sake of siplicity the following definitions are used: [H ] = c; [V ] = ; [h ] = p (S1) The concentration of the regular oxygen atos can be calculated by [ ] 3 c (S) The concentration of holes (forally corresponding to Fe 4+ oxidation state) can be calculated fro the electroneutrality condition: ' ' ' [Ba A]+[Sr A]+[Zn Fe ] c p (S3) p1. c ox can be calculated fro the values obtained by isobaric easureents in dry p (c = 0). (3 )(1. ) ox (S4) 1/ p Then, ox and are written for the two therodynaically equilibrated states of the saple with the corresponding concentrations at state 1 (index 1) and (index ). c1 p (3 c ) H,1 H, ox 1/ p 1 ox (3 c )(1. c ) p c (3 c ) (3 c )(1. c) 1/ p (S5)

3 All unknowns are colored in red. As we have five unknowns but only four equations a fifth condition is necessary. This equation coes fro the final ass change after changing ph or p which is n [( c c ) M ( ) M ] (S6) 1, BSFZ 1 H or 1 with n BSFZ ol of BSFZ and M olar weight of H, and. This eans that the absolute proton concentration is obtained fro the fit under the supposition that the increase of [H ] follows the ph -dependence as given by the defect odel based on ox and (assuing that changes in the activity coefficients are negligible). The resulting set of five equations with five unknowns can be solved nuerically using MatLab (fsolve function): function F = ccdd(x,k) MH = 1; %Set either to 1 (H) or () a = k(1)/1000; ah1 = k()/1000; ah = k(3)/1000; ox = k(4); nbsfz = k(5); %ol d = k(6); %g c1 = x(1); c = x(); d1 = x(3); d = x(4); = x(5); F = [(c1^)/(ah1*d1*(3-d1-c1))-; (c^)/(ah*d*(3-d-c))-; ((3-d1-c1)*(1.-*d1-c1)^)/(sqrt(a)*d1)-ox; ((3-d-c)*(1.-*d-c)^)/(sqrt(a)*d)-ox; (nbsfz*((c-c1)*mh+(d1-d)*16))-d]; end The first jup at 400 C in Fig. 1 of the ain paper is given as an exaple: 0.06 g; p 5.70 bar; p 9.83 bar; 1, H,1 H, ox.71; n 17.9 ol BSFZ The set of equations is solved with resulting in fsolve(@(x)ccdd(x,[10;5.70;9.83;.71;17.9;0.06]), [0.005;0.01;0.5;0.498;0.1]); c ; c ; ; ; Although this is not the only solution (note that the set of eq. (S5) is nonlinear), other solutions obtained by changing the start paraeters are eaningless as they are either outside physically reasonable values (uch higher than in dry atosphere, c uch higher than obtained values fro arl-fischer titration, negative values) or the condition 1 is not fulfilled. Hence, the solution above is the only reasonable one. An exaple of error propagation for the fraction of protons incorporated by redox reaction is given here: c 1, c, 1,, and redox fraction z = (c -c 1 )-( 1 - ) are calculated for 3

4 = 06 g and ox =.71 as above, and copared with results for larger or saller by 5 g (realistic estiate) or 10 g (pessiistic estiate): /g c 1 c 1 z While c 1, c, 1, values vary in the fourth digit after decial point, the redox fraction which is the difference of (c -c 1 ) and ( 1 - ) varies only in the fifth digit. This exaple shows that the finding of a sall but nonzero redox fraction is robust against the realistically estiated uncertainty of 5 icrogra and even a pessiistic estiate of 10 icrogra in the input weight change (cf. also hole concentration change in fig. 6 which - including its error range - always reains in the negative). (4) Effects of proton trapping The attractive interaction of protonic carriers with other defects can (forally) be described by a trapping reaction with trap T according to [(HT)] H T (H T) with T (S7) [H ][T] (the driving force for this reaction can be any defect interaction, e.g. electrostatic (in case of a negatively charged trap such as an acceptor dopant) but also of other origin (cf. ref. 6 ) - thus it is not necessarily a charged trap). This trapping reaction will affect the hydrogen uptake reactions (eq. (1) and (3)) as well as the cheical diffusion coefficients and. In a recent publication, significant proton trapping was observed in the proton-conducting perovskite BaZr 0.8 Y over an extended teperature range fro the cobination of therogravietry, ac ipedance and nuclear agnetic resonance, and an association enthalpy of -9 kj/ol deterined. 7 Thus, soe association between protons and other defects ay well appear also in the present BSFZ saples. (4a) Effect on water / hydrogen uptake, exeplified for reaction (1) For siplicity let us assue that water uptake occurs exclusively by reaction (1) (this assuption is realistic for BSFZ under the conditions applied here as Fig. 5 shows - the aount of hydrogen uptake at expense of holes according to reaction (3) is uch saller than by ion of [V ]). Let us further assue that the concentration of free traps is constant (i.e. the al proton concentration sall copared to the trap concentration, again supported by the low proton content of BSFZ) and also the concentration changes of regular oxide ions and V are negligible relative to the proton concentration changes (while this is fulfilled for ph changes at a given teperature, a teperature change will lead to oderate variations (cf. fig. ) which in the full defect odel is accounted for by reaction ()). Please note that H H 4

5 the key conclusions reain valid also without these assuptions, but the atheatical expressions becoe ore involved. Then we can write with redefined ass action constants ' [H ] (S8) p H ' [(H T)] T (S9) [H ] with [(H T)] denoting the concentration of trapped protons. The al proton concentration [H ] (conservative enseble) as easured fro TG aounts to ' ' T p [H ] [H ] [(H T)] (1 ) H (S10) Plotting an effective ion ass action constant '' [H ] (S11) '' ' ' (1 T) ph calculated fro easured [H ] versus reciprocal teperature will result in a slope deterined by H 0 = H 0 '' ' for the case of sall trapping ( ), and a steeper slope deterined by H 0 = H 0 + trap H 0 for the case of strong trapping '' ' ' ( (1 ) ). The decrease of the slope for the ion ass action constant in T Fig. 3 at the highest teperatures (where the relative iportance of the trapping reaction decreases) ay be caused by this effect. (4b) Effect on the cheical diffusion coefficient, exeplified for : H In the presence of the trapping reaction (S7), instead of eq. (4) the cheical diffusion coefficient for water has to read (cf. refs ) V H V H H (S1) 4F c H H V where is the su of the conductivity contributions fro free and H H (HT) trapped protons, chc 0.5( c c ) 0.5 c with c denoting the su V H (HT) H H of free and trapped protons, and. Thus H H V [H ] 4RT [H ] RT 4 c [H ] [H ] [H ] [H ] [V ] H H V H cv (S13) where an additional differential defect fraction H [H ]/ [H ] appears (eq. (S13) assues absence of trapping for V ). For obtaining the variation of free proton concentration with al proton concentration, the trapping ass action constant T (eq. (S7), with [T] = [(H T) ]+[T]) has to be inserted, yielding 5

6 1 1 [H ] [(H T)] T[T] H 1 1 [H ] [H ] (1 T[H ]) [T] T([T] [(H T)]) [T] For [T] [T] (i.e. trap concentration >> proton concentration) it follows that H 1 4RT RT c 1 [T] [H ] [V ] H T (S14) (S15) and thus H V H (S16) 4F 1 H V T[T] [H ] [V ] Assuing strong trapping (typically at low teperatures) [T] 1 T and inserting [T] [H ] [(H T)] this results in T The quantity H H V 4 1 H 4 F [(H H V T)] [V ] (S17) contains contributions fro the diffusivity of the trapped species itself which we can ignore (the trap is ost probably an iobile acceptor dopant), hence F [H ] H. Nonetheless it is convenient to relate to an effective H H H proton diffusivity that H. For strong trapping H [H ] [(H T)], hence it forally follows F [H ] F [(H H T)] H (S18) H Note that because of [H ] [H ] it follows that H [H ]/[H ] [H ]/[(H T)]. Inserting (S18) together with H H H H [H ] [(H T)] X and [V ] (1 X )[V ]( p H [V ] [V ] 0) into (S17) yields ( ph 0) ( ph 0) H X ( X ) H H V (1 X ) V (S19) which is isoorphic to eq. (4), with the proton diffusivity being now replaced by an effective diffusivity. H H lies between the diffusion coefficient of the oxygen vacancy V and the effective proton diffusivity H H H H, depending on the degree of ion. Yet, note that [H ]/[(H T)]. Thus in case of strong trapping, the activation energy of will be higher than the igration energy of the free protons. At high teperatures the effect of trapping decreases, and eq. (4) becoes relevant which contains only H (activation energy = free proton igration energy). This can be one reason for the decreasing slope in Fig. 9 with increasing teperature. 6

7 (4c) Effect on proton conductivity as calculated fro eq. (6): Inserting the effective proton diffusivity (with H H for low degrees of * ion) and the al proton concentration [H ] into the Nernst-Einstein equation (cf. eq. (S18)) results in an effective proton conductivity, which would be directly easured (if not covered by the higher electronic conductivity). This is valid irrespective of the trapping effect. The conductivity always originates fro the free protons (the acceptors acting as traps are iobile). For strong trapping the fraction of free protons is deterined by the trapping equilibriu eq. (S9) leading to an increased activation energy. For higher degrees of ion the protonic conductivity would be underestiated in the present analysis as the easured H H H H is lower than the effective proton diffusion coefficient. Nevertheless, when we argue whether this conductivity is high enough to enable the bulk path for the oxygen reduction reaction, we are on the safe side with eq. (S1) as we never overestiate the protonic conductivity. This is one reason for the greater-than-orequal-to sign in eq. (S1) and (6) in the ain paper. References H FH[H ] (S1) 1. B. Wei, Z. Lu, X. Q. Huang, M. L. Liu, N. Li and W. H. Su, J. Power Sources, 008, 176, J. Fleig, Solid State Ion., 00, 150, M. Vollan and R. Waser, J. A. Cera. Soc., 1994, 77, I. enk, J. Claus and J. Maier, J. Electroche. Soc., 1997, 144, R. A. e Souza, J. Fleig, J. Maier,. ienzle, Z. L. Zhang, W. Sigle and M. Rühle, J. A. Cera. Soc., 003, 86, reuer, W. Munch, M. Ise, T. He, A. Fuchs, U. Traub and J. Maier, Ber Bunsen Phys Che, 1997, 101, Y. Yaazaki, F. Blanc, Y. kuyaa, L. Buannic, J. C. Lucio-Vega, C. P. Grey and S. M. Haile, Nat. Mater., 013, 1, J. Maier, in Physical Cheistry of Ionic Materials: Ions and Electrons in Solids, Wiley, Chichester, 004, pp J. Maier, J. A. Cera. Soc., 1993, 76, J. Maier, J. A. Cera. Soc., 1993, 76,