Determination of surface exchange and diffusion coefficient in mixed conductors using EMF measurements

Solid State Ionics 199–200 (2011) 25–31

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Solid State Ionics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / s s i

Determination of surface exchange and diffusion coefficient in mixed conductors using EMF measurements☆ J. Rutman 1, I. Riess ⁎ Physics Department, Technion, Haifa, 32000, Israel

a r t i c l e

i n f o

Article history: Received 7 July 2010 Received in revised form 14 April 2011 Accepted 25 April 2011 Available online 28 May 2011 Keywords: Surface reaction coefficient Chemical diffusion coefficient Incorporation/excorporation MIEC Experimental methods on MIEC

a b s t r a c t We discuss a new technique for determining the chemical diffusion coefficient, Dchem, as well as the coefficient Kchem of surface chemical exchange, in mixed ionic electronic conductors (MIECs). The method is based on EMF measurements following the response to chemical step changes. Expressions for the dependence of VOC(t), the open circuit voltage (EMF), on time after chemical step are developed. The interpretation of Dchem and Kchem depends on the defect model of the MIEC and the surface reaction process. The analytic solution for VOC(t) assumes constant Dchem and Kchem. However, the solution can be applied to cases with non-constant Dchem and Kchem provided the composition changes are done in small steps. The method is demonstrated by applying it to LSM (La0.8Sr0.2MnO3 − x) as the MIEC. © 2011 Elsevier B.V. All rights reserved.

1. Introduction The rate of uptake and loss of neutral components in mixed ionic electronic conductors (MIECs) is determined by the surface chemical exchange coefficient Kchem and bulk diffusion coefficient Dchem. Many methods have been applied to determine Dchem[1]. Among those are electrochemical methods where time-dependent EMF measurements are combined with electrochemical titration, [2] introduced by Weppner and Huggins [3,4]. Following the current response to potential steps is intensively used for deriving the chemical diffusion coefficient [5]. This method is sometimes combined with ac impedance measurements [6–9]. Alternatively the oxygen partial pressure P(O2) is abruptly changed and bulk properties, e.g. conductivity [10–12] or weight [13], are followed. From the time dependence Dchem is determined. Periodic changes in P(O2) are also used [14]. Constant P(O2) gradients allow determining Dchem from the permeation flux [15]. In many cases, though not all, those methods are used, for determining the chemical diffusion coefficient assuming that the surface reaction is fast. This situation changes for thin layer samples where limitation by surface reaction can become dominant. However, in the latter samples, extensive properties, such as weight or conductance, become small and difficult to follow. The surface exchange rate being considered in the present work is between a phase and a MIEC. This is presented by example of oxygen

☆ Presented at ISSFIT 9, June 1–5, 2010, Riga, Latvia. ⁎ Corresponding author. E-mail address: [email protected] (I. Riess). 1 Present address: Shilon Zuckerstein & Co. Azrieli Center 1, Round Tower, 19th Floor, Israel. 0167-2738/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2011.04.013

exchange between a gas phase and an oxide. The relevant surface exchange coefficient is also given, for instance, by those methods which follow changes in the bulk properties upon changes in the gas phase. However, the surface exchange coefficient that is derived from electrochemical titration measurements is the one between a solid electrolyte, serving as an ion pump, and a MIEC. While it is a chemical rate constant, Kchem, since the ion transfer must be accompanied by an electronic (electron/hole) transfer to avoid charging, the Kchem measured is that for exchange between a MIEC and a SE (solid electrolyte), not MIEC and gas. The former process may have in common with the latter one only the elementary step of ion incorporation into the MIEC. However, even this need not be the same step since the MIEC surface in contact with the second phase (say gas) and the surface of the MIEC in contact with a SE are not expected to be identical. In this work a novel experimental method is presented that combines time dependent EMF measurement with step changes in the chemical potential of a phase in contact with the tested MIEC. We refer specifically to changes in oxygen partial pressure, P(O2), in a gas phase. The method is first presented followed by the theory required to derive Dchem and Kchem from the experiments. The method is demonstrated experimentally by applying it to LSM (La0.8Sr0.2MnO3 − x). 2. The method The method for determining Kchem and Dchem for exchange between a material source/sink, say oxygen in the gas phase, and a MIEC, say a MIEC oxide, is based on the following. The oxygen uptake is followed via the change in the oxygen chemical potential in the MIEC at the interface contacting a solid electrolyte on the opposite side from the gas phase, as

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J. Rutman, I. Riess / Solid State Ionics 199–200 (2011) 25–31

shown, schematically, in Fig. 1. These changes are followed by EMF measurements on a solid electrochemical cell in which the MIEC under test serves as one electrode. We shall later (in Section 5) demonstrate the method by using the cell: gas,LSM|YSZ|Pt,air in which the SE is YSZ (yttria-stabilized zirconia), the electrode is porous Pt/air and the sample under test is LSM. For simplicity we discuss from here on the method, mostly, in terms of this example though it is not limited to it, of course. The material under investigation, LSM, is exposed to a sudden change in the oxygen concentration in the gas phase. The change in time of the voltage measured between the Pt/air electrode and the LSM is analyzed. The voltage depends on the chemical potential of oxygen at the LSM/YSZ interface. It therefore provides information on the rate of oxygen uptake (loss) in the LSM layer, from which the surface chemical exchange coefficient, Kchem, and chemical diffusion coefficient, Dchem, in the LSM can be determined. The method can easily cope with thin layers as it does not depend on extensive, bulk properties such as conductance or weight. It has thus the advantage that it can determine both the surface reaction coefficient Kchem when it is made to be the rate determining step by using thin layers, as well as the diffusion coefficient in thick layers. 3. Theory 3.1. General The magnitude of the voltage developed at any given time reflects the electrochemical potential difference between the holes at the LSM/YSZ and Pt/YSZ contacts:

V=


•
• μ˜ h Pt;air −μ˜ h LSM;YSZ q

ð1Þ

where μ˜ ðh• ÞLSM;YSZ is the hole electrochemical potential in the LSM at the LSM/YSZ interface, μ˜ ðh• ÞPt;air that at the Pt electrode, and q is the elementary charge. (We use the Kröger-Vink notation of point defects). Under open circuit conditions no overpotential appears between the contacts as the total as well as the partial ionic and electronic currents vanish. Thus for open circuit V = Δμ˜ ðh• Þ/q reflects also the difference in the oxygen chemical potential in the reference gas (air) and in the LSM near the LSM/YSZ interface [1].

VOC

0  1 = 2 1 1 0  P O P O 2;ref 2;ref k T k T C A = B lnB = B ln@  @  1 = 2 A 4q 2q P O2;bulk P O2;bulk

ð2Þ

where VOC is the open circuit voltage, kB the Boltzmann constant, T the temperature, P(O2, ref) the oxygen partial pressure on the Pt/air side of the cell and P(O2, bulk) is an oxygen partial pressure with which the LSM bulk near the LSM/YSZ interface can be in equilibrium. P(O2, bulk) changes when the gas composition just outside the surface of the LSM is changed. When P(O2,gas) is raised, oxygen crosses the solid/gas interface and then diffuses into the bulk LSM, affecting the oxygen chemical potential at the LSM/YSZ interface. Similarly, if P (O2,gas) is lowered oxygen diffuses out of the oxide into the gas phase, lowering the μ(O2) at the LSM/YSZ interface. To a good approximation all the oxygen entering (or leaving) the LSM remains in (or leaves) the LSM alone. It can be assumed that changes in the YSZ stoichiometry are negligible even if the volume of YSZ is a few orders of magnitude higher than that of the LSM. The reason is that the oxygen chemical diffusion coefficient in YSZ is significantly lower than that in LSM and only a small fraction of the already-small oxygen concentration change possible in YSZ, can occur during the measurement. In view of this Eq. (2) will be used also for the open circuit voltage measured under non steady state conditions as the ionic current in the YSZ can be neglected.

V

Environment the composition of which can be changed step wise, e.g. O 2 in the gas

MIEC

SE

E



phase.

Fig. 1. Schematic of the experimental setup of the present method for determining Kchem and Dchem in a dense mixed ionic electronic conductor (MIEC) layer which exchanges material with a contacting phase. SE – solid electrolyte, E – electrode with a fixed chemical potential, δ– the thickness of the MIEC. An example: oxygen from the gas phase is exchanged with a MIEC oxide. The SE conducts oxygen ions and E is exposed to a fixed oxygen chemical potential.

We next develop the expression for the time dependence of the open circuit voltage after a step change in the oxygen partial pressure in the gas phase. At first diffusion limitation is considered, next surface exchange limitation and then the combined case. The calculation depends on the specific defect model and rate determining step in the gas/MIEC reaction. We consider a MIEC with holes, h •, and oxygen vacancies VO•• as point defects. Two defect models are considered, one with a relative low vacancy concentration  ••   •  VO bb h ≡p

ð3Þ

where [] denotes the concentration. This defect model corresponds to LSM [16] and is discussed in detail. In the second model the vacancy concentration is relatively high,  ••  VO NNp

ð4Þ

which corresponds to Ba0.5Sr0.5Co0.8Fe0.2O3 − x (BSCFO) [16]. 3.2. Diffusion limited composition changes In this section we assume that the response of P(O2, bulk) at the LSM/YSZ interface to a change in the gas composition is limited by diffusion and not by oxygen incorporation/excorporation at the gas/LSM interface. This limitation is later removed. Oxygen chemical diffusion in the LSM bulk is via ambipolar motion of oxygen vacancies and holes. The chemical diffusion coefficient is fixed by the vacancy diffusion, since the hole conductivity is high. (The ambipolar diffusion is limited by the slower diffusing species.) In LSM, [VO••]bbp, the chemical diffusion coefficient of the oxygen, Dchem (O) is given by the component diffusion coefficient of the oxygen vacancy D(VO••), [17] ••

Dchem ðOÞ = DðVO Þ

ð5Þ

D(VO••) is considered to be independent of [VO••]. We note that, on the other hand, in BSCFO, [VO••] NN p, [17]  
••  VO•• Dchem ðOÞ = D VO p

ð6Þ

Coming back to the LSM case, [VO••] bb p, the continuity equation for a one-dimensional configuration is,  ••  ∂ VO ∂JðVO•• Þ ¼ ∂x ∂t

ð7Þ

J. Rutman, I. Riess / Solid State Ionics 199–200 (2011) 25–31

where J denotes flux. Differentiating Eq. (7), assuming that D(VO••) is a constant, one arrives at a diffusion equation    
••  ∂2 VO•• ∂ VO•• ¼ D VO ∂t ∂x2

ð8Þ

Let x=0 denote the LSM/YSZ interface position and x=−δ denote the gas/LSM interface position. The LSM sample is subjected to a step function in the oxygen concentration. The oxygen concentration just under the LSM surface at x=−δ immediately reaches its equilibrium value (as the surface reaction is assumed, in the present section, not to be impeded),  ••   ••  VO x¼d ¼ VO final ; t N 0

ð9Þ

where [VO••] final is the final (equilibrium) oxygen vacancies concentration in the sample as fixed by equilibrium with the gas phase. For a finite sample of thickness δ with vanishing current at x = 0 and exposed to a step function in concentration at x = −δ, one may use an analytic solution for a finite layer of double thickness 2δ (−δ b x b δ) exposed on both sides to the same concentration change. The center point (or plane) x = 0 satisfies the condition of no flux due to symmetry. Hence one can use the solution for the latter sample to yield the concentration c(t) at x = 0 for the sample in our case. The solution is given in Crank [18]. The relevant oxygen concentration at the LSM/YSZ interface (x = 0), [VO••] = [VO••]x = 0, at time t is,  ••   ••  n V  VO initial 4 ∞ ð−1Þ −Dð2n +  •• O  ••  e = 1− ∑ π n = 1 2n + 1 VO final  VO initial

1Þ2 π2 t = 4δ2

ð10Þ

where [VO••]final = [VO••]x = 0 at long time, [VO••]initial = [VO••]x= 0 at t = 0 and D = Dchem(O) = D(VO••) (Eq. (5)). [VO••] is related to the local oxygen partial pressure. The relation is derived from the reaction between an atom from the gas phase with an oxygen vacancy, introducing an oxygen ion and two holes into the MIEC, 1 •• X • O + VO = OO + 2h 2 2

ð11Þ

Under equilibrium, 1 = 2  ••  VO

P ðO2 Þ

2

= K ðT Þp

ð12Þ

where K(T) −1 is the reaction constant. For the type of MIEC considered here, pNN [VO••]. Further, in LSM the high hole concentration is determined by the fixed concentration of Sr 2+ ions substituting for La 3+ ions. Eq. (12) for fixed p yields,  ••  0 −1 = 2 VO = K P ðO2 Þ

ð13Þ

where K′ = K(T)p 2. Inserting Eq. (13) into Eq. (2) yields,  ••  ! VO kB T   ln VOC ðtÞ ¼ 2q VO•• ref

ð14Þ

where,  1=2  ••  0 VO ref ¼K P O2;ref

where V(t) is short for VOC(t), Vinitial is VOC at t = 0, Vfinal is VOC after a long time so that a steady state has been reached (formally infinity) and β = 1/kBT . Eq. (16) holds for any process for which D is independent of [VO••]. The time dependence of the vacancy conentration near the interface between a MIEC with p NN [VO••] and YSZ after a step change in P(O2) in the gas phase (Eq. (10)) is presented in Fig. 2 (along with solutions for the case that surface impedance cannot be neglected). When P(O2) is reduced from P(O2)1 to P(O2)2 in the first step and then brought back to P(O2)1 in the a second step, [VO••]initial and [VO••]final are interchanged for the second step, but the expression ([VO••]-[VO••]initial)/([VO••]final-[VO••]initial) exhibits the same time dependence given by the right hand side of Eq. (10) (which depends only on two parameters D and δ). Thus, in Fig. 2 the time to reach 60% of the change in the concentration is 4500 s in both steps, as long as diffusion limitation takes place). The time dependence of the open circuit voltage, Eq. (16), for a step decrease in P(O2) is presented in Fig. 3. VOC(t) should be different for different intial conditions and thus also for the two steps (P(O2)1 b P(O2)2 and P(O2)1 N P(O2)2) mentioned above. This can be traced back to the time independent term in the argument of the ln funtion in Eq. (16) which depends on the initial P(O2) and hence on Vinitial . 3.3. Surface exchange limited flux Let us now consider the case where the gas/LSM oxygen exchange is the rate determining step. We first examine a model for the oxygen incorporation into LSM which yields a constant surface exchange coefficient Kchem and solve for V(t). We shall later cope with the question what to do when Kchem is not a constant. Further, the derivation will illustrate how to relate Kchem to the model parameters. The process considered commences with oxygen adsorption onto the LSM from the gas given by: 1 X 55 • O þV ↔Oad þ 2h 2 2;gas S

 1=2 h i h i X 55 2 P O2;gas VS ¼Kad Oad p

  V ðt Þ−Vinitial 1   ln 1 + e2qβðVfinal Vinitial Þ  1 ð16Þ = Vfinal −Vinitial 2qβ Vfinal −Vinitial  ! 4 ∞ ð−1Þn −Dð2n + 1Þ2 π2 t = 4δ2 e × 1− ∑ π n = 0 2n + 1

ð18Þ

−1 is the reaction constant. Assuming [VSX] and p to be large where Kad and thus largely unchanged by the adsorption of oxygen ions, Eq. (18) yields,

h

i  1=2 55 Oad ¼K2 P O2;gas

ð19Þ

where K2 includes all constant parameters. In the next step the adsorbed oxygen is incorporated into the oxide, 55

Inserting Eqs. (14) and (15) into Eq. (10) yields,

ð17Þ

\\ is where VSX is a surface vacancy (a site where oxygen can adsorb), Oad an adsorbed oxygen ion, and h • is an electron hole in the MIEC. This step (or series of elementary steps) is assumed to be close to equilibrium, i.e. not rate determining. Under equilibrium reaction (17) gives the mass action law,

••

X

Oad þVO j bulk →OO ð15Þ

27

ð20Þ

where VO••|bulk is an oxygen vacancy within the LSM bulk but near the surface. Reaction (20) is assumed to be slow i.e. rate determining. The net rate for Eq. (20) is given by the difference between forward and reverse reaction rates: →h jj i ••  ←h X i JO ¼ K Oad VO bulk  K OO

ð21Þ

→ ← where K, and K are the forward and reverse reaction rate constants, respectively.

28

J. Rutman, I. Riess / Solid State Ionics 199–200 (2011) 25–31

Fig. 2. Change in vacancy concentration in the MIEC at the MIEC/SE interface vs. time, after a step decrease by a factor 10 in P(O2) (Eq. (26) for K limited and Eq. (28) for the other cases). Time to reach 60% of the total change: 4500 s for diffusion (D) limitation and 30 s for surface exchange (K) limitation. L ≡ Kchemδ/Dchem, Kchem = 3.16 × 10−8 m/s, Dchem = 10−n m2/s, n = 13, 14, 15 and 16 as L increases, δ = 10−6 m.

[OOX] is the activity of OOX which is a constant in view of the large concentration of OOX. Eq. (21) is recast using Eq. (19) as,

(the flux of monatomic oxygen) is of interest (or Kchem = κ/2 if the flux of molecular oxygen is of interest),

   ••   •• JO ¼κ VO bulk  VO final

Kchem = κ = κ0 P ðO2 Þfinal

ð22Þ

where  1=2 1=2 κ¼κ0 P O2;gas = κ0 P ðO2 Þfinal

ð23Þ

→ ← X κ0 = K K2 and we replace K½OO  by κ [VO••]final using the fact that the current must vanish when the bulk vacancy concentration reaches its final value [VO••]final. The flux JO is expressed in terms of a difference in the oxygen vacancy concentration which is also the negative of the difference in the concentration of oxygen. Thus Kchem equals κ if JO

1=2

ð24Þ

i.e. Kchem depends, in this reaction model, on the final P(O2) of the step. In particular if in two consecutive steps P(O2) is first reduced from P(O2)1 to P(O2)2 and in the second step it is increased again to P(O2)1 then the exchange rate in the second, oxidation, step should be governed by an exchange coefficient, higher than in the first step by a factor [P(O2)1/P(O2)2] 1/2. The flux JO across the surface can be related to the rate of change of the total oxygen content MO of the sample. The rate of change of the oxygen concentration is the opposite of the rate of change of the

Fig. 3. Open circuit voltage as function of time for a step decrease of a factor 10 in P(O2) (Eq. (27) for K limited and Eq. (30) for the other cases). L = Kchemδ/Dchem. Simulation done for T = 1000 K, P(O2)initial = P(O2)ref (Vinitial = 0), P(O2)final = 0.1P(O2)ref (Vfinal = 50 mV), Kchem = 3.16 × 10−8 m/s, Dchem = 10−n m2/s, n = 13, 14, 15 or 16 as L increases and δ = 10−6 m.

J. Rutman, I. Riess / Solid State Ionics 199–200 (2011) 25–31

29

vacancy concentration. This leads to a differential equation that may be solved to give the vacancy concentration as a function of time:

Kchemδ/Dchem bb 1 yields the surface exchange-limited cases. The voltage is calculated by inserting Eq. (14) into Eq. (28),

h i •• d VO;bulk 1 dMO =δ JO = A dt dt

  V ðt Þ−Vinitial 1   ln 1 + e2βqðVfinal −Vinitial Þ −1 ð30Þ = Vfinal −Vinitial 2βq Vfinal −Vinitial !! 2 2 ∞ 2Le−βn Dt = δ  × 1− ∑
2 2 n = 1 βn + L + L cos βn

ð25Þ

where δ is the length of the sample and A its cross-sectional area, and we have used the fact that the bulk concentration of VO·· is roughly •• uniform and equal to [VO, bulk] calculated at x ~ 0, in view of the fast vacancy diffusion assumed. Combining Eq. (22) with Eq. (25) and solving the differential equation yields the time dependence of •• [VO, bulk], h

i   ••   VO•• initial VO;bulk κ    ¼ 1  eδt   VO•• final  VO•• initial

3.5. Other defect models ð26Þ

The open circuit voltage, V(t), is obtained by inserting Eq. (14) into Eq. (26),     V ðt ÞVinitial 1 2βqðVfinal Vinitiall Þ κt ln 1þ e ¼ 1 1  e δ Vfinal −Vinitial 2qβðVfinal −Vinitial Þ ð27Þ Eq. (27) holds for κ which is independent of [VO••]. The time dependence of the vacancy concentration in the bulk, Eq. (26), is demonstrated in Fig. 2 (K limited case). For the factor 10 decrease in P(O2,gas), κ = 3.16 x 10 –8 m/s, δ = 10 –6 m and temperature T of 1000 K the time it takes to reach 60% of the change is 30 s. Repeating the calculation for an increase back to the initial P(O2) value (not shown) it takes only 9 s to reach 60% of the total change. The shorter time is expected according to Eq. (24). The time dependence of the open circuit voltage, Eq. (27) is presented in Fig. 3 (K limited case). The oxidation step (not shown) is, again, faster than the reduction one. The higher rate of oxidation is due to a higher concentration of oxygen vacancies in the initial reduced state which accelerates the surface reaction, (Eq. (21). When lowering the P(O2,gas) from a high initial value, the initial concentration of vacancies VO•• is low, causing a low initial exchange rate. This is in accordance with observations on LSM, where Kchem increases on reduction [12]. 3.4. Combined case – both diffusion and surface exchange affecting the stoichiometry change rate For the case of impeded surface exchange (Eq. (22)) in combination with diffusion (Eq. (8)) into a finite medium, a solution is found in [18] assuming a uniform initial vacancy concentration [VO••]initial and a no-flux boundary condition at the LSM|YSZ interface x = 0,  ••   ••  −β2 Dt = δ2 ∞ V  VO initial 2Le n  •• O  ••   = 1− ∑
2 2 VO final  VO initial n = 1 βn + L + L cos βn

ð28Þ

where D = Dchem and βn are the nonzero roots of the equation, βn tanβn ¼L ;

L≡

Kchem δ Dchem

The voltage of Eq. (30) is demonstrated in Fig. 3. The limits are obtained for Kchemδ/Dchem NN 1, Kchemδ/Dchem bb 1, as mentioned before. Eq. (30) holds for D and κ which are independent of [VO••].

ð29Þ

where Kchem = κ. Eq. (28) is demonstrated in Fig. 2. The limit Kchemδ/Dchem NN 1 yields the diffusion-limited case and the limit

Other defect models lead to diffusion coefficients that may depend on concentration. An example was shown above for the case of BSCFO (Eq. (6)). The diffusion equation then has usually no analytical solution. Further, surface exchange processes with a rate determining step (rds) other than the one considered before (Eq. (20)) can lead to concentration dependent coefficients Kchem. We discuss first an example for the latter case and then comment on the possibility to measure concentration dependent Dchem and or Kchem with the present method. Let us consider a surface process in which the rds is, 5

5

X

•

O2;ad + VS →2Oad + h

ð31Þ

(rather the one in Eq. (20)). The elementary steps before and after this step are close to equilibrium. The flux is then determined by Eq. (31),  h → 5 ih X i ← h 5 i2 JO = 2 k O2;ad VS − k Oad p

ð32Þ \

with p and [VSX] being roughly constant. Thus the reaction that yields O2, ad, 5

X

•

O2 + VS ↔O2;ad + h

ð33Þ

(assumed to be close to equilibrium) gives the mass action law,  h i h i X 5 P O2;gas VS = K3 O2;ad p

ð34Þ

where K3−1 is a reaction constant. The reaction following the rate determining step is, 5

••

X

•

Oad + VO;bulk ↔OO + h

ð35Þ

for which the mass action law is, h

ih i h i 5 •• X Oad VO;bulk = K4 OO p

ð36Þ

where K4−1 is the reaction constant. [VSX], [OOX] and p are constant. Inserting Eqs. (34) and (36) into Eq. (32) yields, ←0  →0  k JO = k P O2;gas − h i2 •• VO;bulk

ð37Þ

→ → where various constants were absorbed into k 0 and k 0 . [VO••]final the final •• •• value of [VO, bulk] is fixed by P(O2,gas). When [VO, bulk] reaches the final value JO vanishes. Hence, 0

1

←0 B 1 1 C JO = k @ •• 2 − h i2 A •• VO final V O;bulk

ð38Þ

30

J. Rutman, I. Riess / Solid State Ionics 199–200 (2011) 25–31

•• which is not linear in the difference ([VO••]final −[VO, bulk]) and thus would introduce Kchem which depends on the vacancies concentration. One can still use concentration independent Dchem and Kchem if the experimental conditions induce only small concentration changes. This is achieved by using steps with small changes in P(O2). (Eq. (38) e.g. can then be linearized). In this case Dchem and Kchem can be considered constant during a single step but to change from step to step. Repeating the measurement for a series of steps, corresponding to different concentration of defects, allows determining the dependence of Dchem and Kchem on the relevant defect concentration (e.g. oxygen vacancies) and comparison with the model prediction.

4. Experimental and results Preliminary experimental results of Kchem aimed at demonstrating the method are presented. We assembled a simple cell that still allows applying two gases without using gas tight seals (see Fig. 4). Experiments were conducted on 1 μm thick, dense, polycrystalline, LSM layers. The LSM layers were applied by sputtering, from an LSM target, onto YSZ, single crystal, orientation (100), 0.5 mm thick. Counter electrodes were porous Pt made from Pt paste (Engelhardt 6082). The Pt and LSM electrodes are not put directly opposite each other, but rather about 1 cm apart, in order to reduce cross talk (i.e. mixing of the gases at the two electrodes). A Pt wire is wrapped around the YSZ and contacts the porous Pt electrode by Pt paste. The LSM is contacted by another Pt wire that is pressed against the LSM by means of a spring-loaded alumina tube. (In a MIEC with high electronic conductivity the position of the lead on the MIEC is of little concern as the voltage drop in the MIEC can be neglected). This tube also serves to convey different gases directly onto the LSM layer. The alumina tube fills most of the relevant compartment volume thus minimizing the dead volume there. The control gas flushing the LSM exits, mainly, through a slot in the holder of the solid electrochemical cell. Air flushes continuously the remote Pt electrode. The open circuit voltage, VOC, is monitored. The arrangement is sensitive to thermal noise as a result of a temperature difference between the two electrodes generated by the gas flow and care must be taken to reduce this noise.

Quartz tube

YSZ

Porous Pt electrode LSM

Slot for exhaust gas

The cell is placed in a furnace, brought to the desired experimental temperature and the gas streams are switched on. After reaching steady state, the gas composition flowing over the LSM is suddenly changed, and the time evolution of the cell voltage is measured. The respond time of the gas flow system was ~1 s, much faster than the time it took for the LSM to change stoichiometry. Figs. 5–7 exhibit typical results at 773 and 883 K. The theoretical response under surface impedance limitation (“K limited”) is immediate while the response under diffusion limitation (“D limited”) exhibits a characteristic initial delay. The absence of a delay in the experimental results is in favor of the surface exchange limitation case, Eq. (27), which also provides a better fit along the whole curves. The combined case of both bulk diffusion and surface limitations, Eq. (30), does not yield a better fit than the surface limitation only. The accuracy in the experiments was limited, apparently by thermal noise and the fitted Kchem values had a scatter of a factor 2.5 about the average. The Kchem value seems to be in reasonable agreement with published results. la O' et al. [19] report Kchem determined by impedance measurements on LSM of the same composition for the temperature range 660–770 °C and P(O2) of 10 −4 and 10 −2 bar. Extrapolating the data to 600 °C (873 K) and correcting for P(O2) of 0.2 bar yields, Kchem = 2×10 −6cm/s. The extrapolation was done using the activation energy of 2.06 eV holing for P(O2) = 10−2bar. As the activation energy increases with P(O2) it is expected that Kchem at 600 °C is lower which should bring it within less than one order of magnitude difference with the values measured here: 1.2 × 10 −7 cm/s for oxidation and 0.53× 10−7 cm/s for reduction. The conclusion arrived here that the 1 μm layer exhibits surface limitation and not a diffusion one at T = 873 K (and below) is in agreement with the published data. Dchem is reported to be in the range 10−10 to 10−8 cm2/s at 873 K, for the same LSM composition [20]. Thus the ratio L = Kchemδ/Dchem bb 1 indicating that the rate determining step is the surface reaction one. This is further supported by the fact that if one tries to fit the data in Figs. 6 and 7 by Eq. (16) (ignoring the poor fit) assuming diffusion limitation, the value of the fitted Dchem is at least three orders of magnitude lower than the values reported in literature [20]. The detailed interpretation of Kchem depends on the rds of the surface reaction. Is Eq. (20) the right rds? The exchange rate increases with temperature as expected and is higher for oxidation. The fact that fitting with a constant Kchem when P(O2) changes by 1.6 orders of magnitude, yields rather good results supports the model considered. The fact that Kchem increases at 873 K less than predicted by Eq. (24) (by a factor of 2.3 rather than a factor 6.3 according to Eq.

Pt wires

Spring loaded ceramic rod

Bore for gas supply

V VOC Spring

Gas inlet

Air inlet

Fig. 4. Cell for following the open circuit voltage, VOC, on a solid galvanic cell (gas,LSM|YSZ|Pr,air) after a change in the gas composition at one (the LSM) electrode.

Fig. 5. Open circuit voltage change after decrease in the oxygen partial pressure from air by 1.6 orders of magnitude at 773 K. “D only” refers to Eq. (16). “K only” to Eq. (27). The use of Eq. (30) does not provide a better fit than the “K only” one. Time to 60% of total change: 125 s.

J. Rutman, I. Riess / Solid State Ionics 199–200 (2011) 25–31

31

T=873K

Fig. 6. Open circuit voltage change after decrease in the oxygen partial pressure from air by 1.6 ordes of magnitude at 873 K. “D only” refers to Eq. (16). “K only” to Eq. (27). The use of Eq. (30) does not provide a better fit than the “K only” one. Time to 60% of total change: 16 s.

(24)) may be due to limited accuracy of the results. Alternatively, this may indicate that a different step for which Kchem is weakly dependent on [VO••] is rate determining. A modification of the experimental setup has also been examined. In this case the two electrodes are placed opposite each other on the solid electrolyte and they are exposed to the same gas stream. If the reference electrode is responding fast and the dense MIEC slowly then after a step in P(O2) the first electrode reaches quickly the final composition while the second lags behinds. A time dependent open circuit voltage is generated that, after the response time of the fast electrode, provides information on the second electrode. In our case the Pt electrode responded fast while the dense LSM, slowly. (The apparent response time of the fast electrode was 1 s, which, however, included also a delay in the gas flow after switching gases. Thus the actual respond time of the Pt electrode could have been much shorter). This arrangement may have a drawback if the characteristic initial delay in the diffusion limited response is masked by a delay in the response of the reference electrode, when it is not sufficiently fast responding. 5. Summary We have devised and analyzed a novel experimental method for measuring the surface chemical exchange coefficient, Kchem, and the chemical diffusion coefficient, Dchem, in a mixed ionic electronic conductors, MIECs. The method is based on following the chemical potential of the relevant species at one boundary of the MIEC being exposed to a sudden change in the chemical potential at the opposite boundary. The chemical potential changes are determined from open circuit voltage on a solid electrochemical cell in which a dense layer of the MIEC serves as one of the electrodes. The method depends on an intensive parameter (concentration) measured at an interface and not an extensive bulk one and can be applied to thin as well as thick MIEC layers. By increasing the MIEC thickness one can switch from surface impedance limitation to bulk diffusion limitation. Solutions for the time dependence of the voltage assuming surface exchange alone, diffusion alone and combined surface exchange and diffusion impedance are presented. Specific solutions depend on the bulk defect model and surface processes relevant to the MIEC. We

Fig. 7. Open circuit voltage change after increase in the oxygen partial pressure by 1.6 orders of magnitude to ambient pressure, at 873 K. “D only” refers to Eq. (16). “K only” to Eq. (27). The use of Eq. (30) does not provide a better fit than the “K only” one. Time to 60% of total change: 7 s.

have discussed this using the example of oxygen as the material being exchanged and an oxide as the MIEC. Analysis of the method applied to MIECs of the type of LSM (La0.8Sr0.2MnO3−δ) was presented. It was argued and shown that Kchem is higher on oxidation than on reduction. In this model Dchem and Kchem are constants. When they depend on the defect concentration the method should be applied using only small stoichiometric steps thus for each step Dchem and Kchem are approximately constant. The method was demonstrated by preliminary measurements on LSM as the MIEC. For the thin films used (1 μm thick) diffusion is fast at 773 and 873K and the rate is determined by the surface reaction. Two version of the experimental setup were described.

Acknowledgement This work was supported by ISF – Israel Science Foundation.

References [1] I. Riess, in: P.J. Gellings, H.J.M. Bouwmeester (Eds.), CRC Handbook of Solid State Electrochemistry, CRC press, Boca Raton New York, London, Tokyo, 1997, pp. 223–268. [2] W. Weppner, R.A. Huggins, J. Electrochem. Soc. 124 (1977) 1569. [3] W. Weppner, R.A. Huggins, Ann. Rev. Mater. Sci. 8 (1978) 269. [4] O. Porat, Z. Rosenstock, I. Shtreichman, I. Riess, Solid State Ionics 86–88 (1996) 1385. [5] C. Montella, Electrochim. Acta 51 (2006) 3102. [6] S.B. Tang, M.O. Lai, L. Lu, J. Alloys and Compounds 449 (2008) 300. [7] M.D. Levi, D. Aurbach, J. Phys. Chem. B 101 (1997) 4641. [8] A. Dell'Era, M. Pasquali, J. Solid State Electrochem. 13 (2009) 849. [9] J. Backholm, P. Georén, G.A. Niklasson, J. Appl. Phys. 103 (2008) 023702. [10] E. Bucher, A. Benisek, W. Sitte, Solid State Ionics 157 (2003) 39. [11] P. Ried, E. Bucher, W. Preis, W. Sitte, P. Holtappels, ECS Trans. 7 (2007) 1217. [12] I. Yasuda, M. Hishinuma, J. Solid State Chem. 123 (1996) 382. [13] L. Mikkelsen, E. Skou, J. Therm. Anal. Cal. 64 (2001) 873. [14] M. Burriel, C. Niedrig, W. Menesklou, S.F. Wagner, J. Santiso, E. Ivers-Tiffée, Solid State Ionics 181 (2010) 602. [15] W.K. Hong, G.M. Choi, J. Membr. Sci. 346 (2010) 353. [16] L. Wang, R. Merkle, J. Maier, ECS Trans. 25 (2009) 2497. [17] J. Maier, Physical Chemistry of Ionic Materials Ions and Electrons in Solids, John Wiley & Sons Ltd, London, 2004, pp. 300–305. [18] J. Crank, The Mathematics of Diffusion, 2nd edition, Oxford Sci. Publ, 1975, p. 47, Eq.(4.17) and page 60, Eqs. (4.50)-(4.52) applied at x=0. [19] G.J. la O', Y. Shao-Horn, J. Electrochem. Soc. 156 (2009) B816. [20] T. Bak, J. Nowotny, M. Rekas, C.C. Sorrell, E.R. Vance, Solid State Ionics 135 (2000) 557.