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An improved analysis on kinetics of electrochemical vapor deposition
Solid State Ionica 73 (1994) 255-263
ELSEWER
An improved analysis on kinetics of electrochemical vapor deposition Jonghee Han, Y.-S. Lin * Department of Chemical Engineering,
University of Cincinnati, Cincinnati, OH 4.5221-0171, USA
Received 17 March 1994;accepted for publication 28 July 1994
An improved method is presented to model the process of electrochemical vapor deposition (EVD) of solid oxide films on porous substrates. This method considers various reaction and mass transfer steps, dopant composition in the EVD film and the EVD reactor configuration. This model allows analysis of the effect of various parameters on the dopant composition in the deposited film as well as the film growth rate of the EVD process. If the surface oxidation reactions are at equilibrium, the dopant composition in the film is the same as the equilibrium value, which depends on the precursors concentration in the vapor phase and the reaction temperature. If the surface oxidation reaction step is the rate-limiting step, the dopant composition in the film is determined by the permeation parameters in the surface oxidation reaction step. In general cases, the dopant composition may vary along the film growing direction. The calculated results can explain the reported experimental data of EVD of yttria-doped zirconia films, and provide a better insight into the EVD process. Keywords:Ceramic electrolyte and membrane; Dopant concentration; Film growth kinetics; Oxygen permeation
1. Introduction Electrochemical vapor deposition (EVD) is a very promising technique for fabricating thin gas-tight solid oxide films on porous substrates for application in solid oxide fuel cells [ 1,2 ] and dense membrane composites [ 3 1. In the EVD process for growing solid
oxide films, a porous substrate separates the reactor into two parts, of which one is the metal source (e.g. a mixture of ZrC& and YC&) chamber and the other is the oxygen source (e.g. 0,) chamber. Initially, the two reactants inter-diffuse into the substrate pores and react to form the corresponding solid oxide product on the pore wall. As the reaction proceeds continuously, the deposited solid oxide grows and finally the * To whom all correspondence should be addressed 0167-2738/94/$07.00
substrate pores are plugged. After this step, no further direct reaction occurs between the two reactants. If the deposited solid oxide is an oxygen ionic conducting material with some electronic conductivity, the oxygen source reactant can diffuse through the oxide film and react with the metal source reactant leading to continuous growth of the oxide film. As such an EVD prooess is very difficult to be monitored experimentally, a theoretical model on the film growth kinetics is very important for understanding and controlling the process. In the previous studies, most researchers analyzed this film growth process as the Wagner scaling process [ 4,5 1. Therefore, their results showed that the film growth rate followed a parabolic rate law. De Haart et al. [ 61 reported a detailed analysis on this film growing process based on a model considering four mass transport steps in se-
0 1994 Elsevier Science B.V. All rights reserved
XSD10167-2738(94)00154-5
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J. Han, Y.-S. Lin /Solid State Ionics 73 (1994)255-263
ries originally proposed by Lin et al. [ 3 ] : ( 1) oxygen reactant diffusion in the substrate pores; (2 ) surface oxygen reduction reaction; (3) bulk electrochemical transport of oxygen ions in the EVD film; (4) surface reaction for formation oxide film. However, this model employed the empirical equations without physical significance for surface reactions because it is difficult, if not impossible, to integrate the surface reaction equations with the bulk diffusion equation using the Wagner approach. Furthermore, most of the previous theoretical studies considered essentially the EVD film as of a single component material. Recently, Lin et al. [ 71 developed a theoretical approach which allows integrating surface reaction equations with the bulk diffusion equation. This approach has been employed to derive equations for oxygen permeation through mixed conducting oxide membranes. It can be also used to model the EVD process. The electrochemical properties of the EVD film depend largely on the composition of the dopant (e.g. Y,O,) in the EVD film (e.g. ZrO*) because the composition of the dopant is directly related to the ionic conductivity of the EVD film. In the EVD process for growing zirconia-yttria films, zirconia is doped by generating a mixture of YC19and ZrC& vapor of controlled concentration in the chloride chamber. Thus, understanding the relationship between the yttrium content in the vapor phase and that in the deposited film is very important in controlling the proper amount of doping oxide in the EVD film. The only theoretical study on the dopant composition in the EVD film is reported by Sasaki et al. [ 8 1. However, their model neglects kinetics of surface reaction and oxygen permeation, and therefore cannot explain the variation of the dopant composition along the EVD film thickness reported by Dietrich [ 9 1. The main objective of this paper is to report an improved method for the analysis of the EVD process. This method considers various mass transfer and reaction steps, the dopant composition variation and the EVD reactor configuration. The surface reaction steps are modeled using a recently developed approach to give parameters with physical meanings. The analysis results are presented to examine the effects of experimental conditions and parameters on the dopant composition. Such analysis could provide a better insight into the EVD process, especially on
the control of the dopant composition. EVD of yttria-doped zirconia is considered in the analysis for the purpose of illustrating the method.
2. Model development The most common material fabricated by the EVD process is yttria-stabilized zirconia (YSZ). YSZ film is deposited on a porous substrate by introducing a mixture of YC& and ZrC& vapor as metal source reactants. As oxygen source reactant, oxygen mixed with steam is used. Fig. 1 shows the cross sectional view of the porous substrate separating the mixture of YC13and ZrC14 vapor and the mixture of oxygen and steam. L, r and H indicate the thickness and the average pore radius of the substrate and the EVD film thickness which is a function of the deposition time, respectively. Pb, , Po2cIj and PA, represent the partial pressures of oxygen in the oxygen chamber, the inner end of the substrate pore and the chloride chamber, respectively. PozcIIjand Po2~,II~indicate the oxygen partial pressures at the oxygen/film interface and the film/chloride interface, respectively. In the EVD process, the oxygen source reactant (oxygen molecule) first diffuses into the substrate pores. At the oxygen/film interface oxygen molecules are reduced to oxygen ions. Then these oxygen ions migrate through the EVD film toward the film/metal chloride interface (electrons move in the opposite direction) and react with YC13or ZrC& vapor to form YSZ on the film/metal chloride interface. Therefore, this EVD process can be determined by four mass transfer steps in series: ( 1) oxygen reactant diffusion in the substrate pores; (2 ) surface oxygen reduction reaction; (3) bulk electrochemical transport of oxygen ions in the EVD film; (4) surface oxidation re-
SUESTRATE
Fig. 1. Cross-sectional
PORE
view of EVD film growing process.
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J. Han, Y.-S. Lin /Solid State Ionics 73 (1994) 255-263
action for the formation of oxide film. Since the fluxes in film growth processes such as this EVD process are usually very small, a quasi-steady state can be assumed to simplify the mathematics of this model. In the oxygen pore diffusion step, the flux of oxygen molecules can be expressed with the steady state diffusion equation [ lo] as: Jo2 =S(&,
-Po*(1))
(la) Jo2 =a, (G/:cl, -~~~~u))
with (j=
Do LRT’
tion in YSZ exposed to an atmosphere of 1 atm oxygen partial pressure. If the surface charge transfer reaction is assumed to be the rate limiting step in the surface reaction (A), the flux of oxygen molecule for the surface reaction can be obtained from the mass action law combined with the Einstein relation and other relations (Eqs. (2)and(3))as[7]: (4a)
with
(lb)
where Joz is the flux of oxygen molecule; 6 is the permeation parameter in this step and Do is effective diffusivity of oxygen molecules in the pore; R and T indicate the gas constant and the reaction temperature, respectively. At the oxygen/film interface, a surface reaction occurs. This reaction can generally be expressed as:
(Y,=k;C$
(4b)
where (Y,is the permeation parameter in this step. In the step of bulk electrochemical transport of oxygen in the EVD film, the oxygen vacancies migrate from the film/metal chloride interface to the oxygen/film interface and electron-holes move in the opposite direction. This electrochemical transport process can be expressed as: V&III) +Vb’cu, 9
(B)
h;u, -+h;u,j .
(C)
(A)
where k’, and k’_, indicate the forward and backward reaction rate constants for reaction (A), respectively. The Kriiger-Vink notation [ 111 is used in eq. (A) and for other electrochemical reaction processes in this paper. With this notation, V g, 00x and h’ indicate oxygen vacancy, lattice oxygen and electron-hole, respectively. If the EVD film is an ionic conducting material with small electronic conductivity contributed primarily by the electron-holes, the electron-hole concentration is correlated to the imaginary partial pressure of oxygen in the solid as [ 7 ] :
(2) where, C,,, Cv and [0,X ] indicate electron hole, oxygen vacancy and lattice oxygen concentration, respectively. In most ionic conductors, the concentration of the oxygen vacancy is much larger than that of the electron-holes. Therefore, the oxygen vacancy concentration can be assumed as constant: C”(i) = C8,
(3)
where, CO, indicates the oxygen vacancy concentra-
The flux of oxygen molecule in this step can be represented as [ 7 ] : (5a)
‘-
-- RTo;: 4F2
(5b)
where /I is the permeation parameter in this step; F is the Faraday constant and a: is the electron-hole conductivity of YSZ exposed to an atmosphere having 1 atm oxygen partial pressure. At the film/metal chloride interface, the lattice oxygen in the EVD film reacts with the metal chlorides and forms the metal oxide film. As different metal chlorides react with oxygen, this film growth reaction can be expressed as two separate reactions: kkl 2YC& + 300” + 6h’ e 2Y0,,5 + 3Cl2 + 3V; , (D) P-RI kkz ZrCl, + 200” + 4h ’ d Zr02 + 2C12+ 2V; kLm
,
(El
J. Han, Y.-S. Lin /Solid State Ionics 73 (1994) 255-263
258
where kk, and k’_-R1indicate the forward and the backward reaction rate constants for reaction (D) and k& and k’_,, for reaction (E). Making analogy to the mass action law, the following two equations are assumed for the separated oxygen fluxes:
-kl-RI(Y,X)2Pb*CZr(lII), J 42
=kk,[W
l*hc~$&m)
-kL2Y2(1
-W%&III~
the standard Gibbs free energy data for reactions (F) and (G) [ 161. By substituting Eqs. (9), ( IO) and (2) into Eqs. ( 6 ) and ( 7 ) , the oxygen fluxes for each reaction ( reactions (D) and (E)) can be expressed in terms of the oxygen partial pressures as:
(11)
(6)
(12)
(7)
,
where J4, and J42 are fluxes of oxygen molecule (0,) consumed in reactions ( D ) and (E ) , respectively and X is the atomic fraction of yttrium in the solid EVD film. yi and y2 represent activity coefficients of yttria and zirconia respectively. If there is no other oxygen consumption, the total oxygen flux (oxygen consumption rate) in this step equals the sum of the oxygen molecule fluxes for reactions ( D ) and ( E ) :
with 3
CO” v P2 YCl3= dl
cFPL
9
(13)
C@P v ZrCla= ah2 CTPZrcl4 9
(14)
2
a42 --kk,
( > -$
I
In this approach, the EVD process is considered as four mass transfer steps in series. Considering the EVD process as one overall process can give useful relations, The overall reactions occurring in the EVD process can be expressed as:
where 13~~and (~42are the permeation parameters for this step. Here the activity coefficients are canceled out because the difference between the activity coefficients of the equilibrium state and non-equilibrium state is assumed to be very small. Neglecting diffusion of yttrium in the EVD film, the yttrium (YO,.,) composition in the solid EVD film equals:
302+4YC13P4Y0i.s
x=jJ,,/($J41
Jo2= 34, +J42
.
(8)
+6 C12,
(F)
O2 + ZrC1, *ZrO, + 2 Cl2 .
(G)
Comparing reactions (F) and (G) with reactions (A), (D) and (E), the relations between these reactions can be easily found as (F) = 2 (D) + 6 (A) and (G) = (E) + 2 (A). Using these relations, the reaction equilibrium constants of reactions (F) and (G) can be expressed as: K
(Y~-w4f%, =’ = P;;:P&,
Ke2 = Y”z(1 -XC)Pcl* p;;,pzm4
=(~$Lg,
= ($-)‘(+-)
(9)
5
(10)
where Xc is the equilibrium dopant composition in the solid EVD film and ph is the equilibrium oxygen partial pressure in the chloride chamber. K,, and K,, are the equilibrium constants for the reactions (F) and (G), respectively, which can be calculated from
+J42)
.
(15)
Eqs. (l), (4), (5), (11) and (12) represent the oxygen fluxes in four steps connected in series. The relation correlating the EVD film growth rate to the oxygen flux can be simply obtained from mass balance as: 1 dH
Jo2= --2 V,,, dt
(16)
where V, = XV,,,., + ( 1- X)Vz,+. Since variation of Xalong the film growing direction is small, V, can be assumed to be the average molar volume of YSZ in the EVD film. t is the deposition time. Eqs. (1) (4),(5),(g), (ll), (12) (15)and (16) are seven nonlinear algebraic equations and one differential equation describing the EVD process. Simultaneous solution of these eight equations would give the time dependence of PozcIj, p 02ClI)9 PO2(III)> Jo2, J4,, J42, X and H. Of particular interest to this workis H=f(t), X=f (t) or X=f(H). To solve the
259
J. Han. Y.-S. Lin /Solid State Ionics 73 (I 994) 255-263
equations, values of parameters, 8, 8, aI, a41, a42, P&, P& and Xc should be given. Values of 8, /3 and Pb, are readily available. Theoretically, crI, cy4]and ~~42 are a function of variable Xbecause these parameters depend on C$ which is directly related to the dopant composition X. In this work, a dopant composition averaged across the film thickness, x* is assumed for or,, (~4~and (~42. Xc can be calculated from the reaction equilibrium Eqs. (9) and (10). Combining Eqs. (9) and (10) to . . ehmmate Pcl, and P& gives:
(YPXC) 4 {r;(l
---Ke, f%,
-xc)}’
-
K%
Grc,,
.
(17)
A reactor configuration model is needed to evaluate PYCI~ and Pz,Q, which appear in Eqs. ( 13 ) , ( 14) and ( 17), and P&. The metal chloride chamber of the EVD reactor can be considered as a flow system, as shown in Fig. 2. As the EVD is operated at high temperature and low pressure, gases in the metal chloride chamber are well mixed and the CSTR reactor model [ 12 ] can be applied to the EVD reactor. The mass balance on YC13, ZrC14 and Cl2 in the metal chloride chamber is given: Qf’ya
RT
_
QPL RT
RT
epcl,
RT
RT
=s(2J,,+w4,)
3. Results and discussion
The EVD process for growing solid oxide film can bedescribedbyEqs. (l), (4), (5), (8), (ll), (12), ( 15 ) and ( 16 ) . For a given film thickness H, values 0fP02(I),
pOz(II),
POz(IlI)9
x9
502,
J4, ad
J42
were
found by solving the seven algebraic equations using subroutine SNSQE of tihaner et al. [ 131. The differential equation, Eq. ( 16)) coupled with the seven algebraic equations, was solved by the Euler method.
(18)
-4SJ419
QPzm. _ Qf-‘%a, _s
chamber and S indicates the surface area of the substrate. J4i and J42 are usually very small, SO Eqs. ( 18) and ( 19 ) become PyCLj%P&, , Pz~, BP&,, , where the superscript O indicates the partial pressures of metal chlorides entering the reaction zone. Once PYCls, Pzrc14and PCl, are known, p& can be calculated from Eqs. (9) and ( lo), which is usually very small ( < 10 - l’ atm for EVD of YSZ). Since practically the carrier gas contains 1Ov2 ppm of oxygen impurity, the contribution from the carrier gas will give P& z 10 - l I atm and this value is used in this work.
3. I. Surface oxidation reaction under equilibrium J
42 ,
,
(19)
(20)
where Q is inert gas flow rate in the metal source
Fig. 2. Schematic diagram of the metal source chamberof an EVD reactor reported in a Ref. [ 15 1.
If the EVD process is operated under conditions that the surface oxidation reaction step is at quasiequilibrium (with very large values of a41 and (~42), Eqs. ( 11) and ( 12) yield Po2CIIIJxP& and Xc X”. This means that the dopant composition is the same as the equilibrium value Xc, which can be found by solving Eq. ( 17 ). As indicated by Eqs. ( 13) and ( 14)) the fourth step (surface oxidation reactions) can be considered as quasi-equilibrium if the permeation parameters a$, and cyi2, and/or the chloride pressures are large. Values of cv& and ab2 depend mainly on the nature of the oxidation reactions, which are difficult to manipulate for a given system. The chloride pressures are, however, the experimentally controllable parameters. Obviously Eq. ( 17 ) shows that the equilibrium dopant composition Xc depends only on the temperature (through K,, and K,,) and chloride pressures in
260
J. Han, Y.-S. Lin /SolidState
the metal source chamber. To find X”, the activity coefficient rf and y$ should be given. Assuming a dilute solid solution for the deposited YSZ film, y5 (for ZIG,) can be considered as 1 and 74 (for Y01.5) approaches to a certain value, r;“, which is called Henry’s constant [ 141. The reaction equilibrium constants K,, and K,, for EVD of YSZ which are calculated from the Gibbs free energy data [ 16 1, are given in Table 1. For a total pressure (P&i 3+Gc14 = 1.89x 10e4 atm), calculation results of dopant (yttrium) composition X” versus yttrium chloride concentration in the vapor phase are given in Fig. 3 for different values of yp. The results given in Fig. 3 show that the equilibrium Table 1 Values of parameters and conditions for EVD of YSZ on porous a-alumina substrate used in calculations.
Temperature (T) Substrate thickness (L) Substrate area (S) Average molar volume OfYSZ (V,) pb, P& P Ycl3
&ICI4 DO or B &I 1 KczL
1000°C 2mm 113.99 mm2 20.7 ml/mol 10e3 atm IO-” atm 5.9X lo-‘atm 1.3x 10e4atm 0.12 cm2/s 5 X lo-’ mol/cm’ s atm’/r 1.6~10-“mol/cm~satm’~~ 2.126~10” 306474.67
Ionics 73 (1994) 255-263
dopant composition in the deposited film depends strongly on the concentration of the corresponding precursor in the vapor phase. Carolan and Michaels [4] found that the dopant (yttrium) compositions in the EVD YSZ film are essentially the same as the concentration of YC13in the vapor phase, as shown in Fig. 4. The results of the model calculation with y~=5.04~10-~, K,,=1.06~10’~ and K,,=6.72x lo4 are compared in Fig. 4. The model results agree reasonably well with the experimental data. De Haart et al. [ 15 ] also reported that the yttrium composition in the YSZ film is roughly the same as the chloride concentration in the vapor phase. The above calculations are based on the assumption that the surface oxidation reactions are under quasi-equilibrium. In this case, the dopant composition remains constant across the deposited film as Sasaki et al. reported [ 81. However, Dietrich et al. [9] found that the yttrium composition increases along the film growing direction in their EVD synthesized YSZ film (about 20 pm thick). Their results can be explained by the following two possibilities: First, the yttrium chloride vapor concentration increased during the EVD process; second, the surface oxidation reactions are not at equilibrium under the experimental conditions of Dietrich et al. Results of the theoretical analysis in such cases are presented next.
a Calculated from Gibbs free energy data [ 161.
0.4 xe
0.3 0.2
0.1 0 0
0.1
0.2 0.3 PYC13’(PYC13+PZ~C14)
0.4
0.5
Fig 3. Variation of equilibrium dopant (yttria) composition with corresponding concentration in vapor phase.
Fig. 4. Comparison of equilibrium dopant composition with experimental data reported in Ref. [4].
J. Han. Y.-S. Lin /SolidState
3.2. Surface oxidationreactionsnot under equilibrium
1.2
When the surface oxidation reactions are very slow compared to the other mass transfer steps, the surface oxidation reaction step can be considered as a rate limiting step (small a!4I and (~42). In this case, the mass transfer resistances of the first three steps can be assumed infinitely small and Pb, x POI(IIIj.In this case, the yttrium composition in the EVD film is not a function of the film thickness, because the resistance of this step is not a function of the EVD film thickness. Thus, the yttrium composition, in this case, can be calculated from Eqs. ( 11) and ( 12) combined with Eq. ( 15 ). Since oxygen partial pressure at the film/chloride interface is much larger than the oxygen partial pressure in the chloride chamber, the second terms in the brackets in Eqs. ( 11) and ( 12) can be neglected. Introducing a new parameter proportional to the ratio of rate parameters, a& and CY&:
0.8
.
a:,
1
1
261
Ionics 73 (1994) 255-263
1.0
,^a.
x
0.6 0.4 0.2 0.0 0.0
0.2
0.4
0.6
0.8
1.0
PYC13/(PYC13+pZrC14) Fig. 5. Variation of dopant (yttria) composition with corresponding concentration in vapor phase when surface reaction is rate-limiting. 0.45
- - -
ci&m7 a’&oElo
0.40
~
.r \
0.35 :
rius).m a’~.1.cm
1
-
-
dU4_
x_c
X
d &oEl? --_
--__
-----_.
0.30
__---
_---_.--
the yttria composition in the EVD film can be expressed simply by:
0.25
/ T
.
(22)
The variation of dopant composition with the concentration of YC13in the vapor phase is presented in Fig. 5. The result given in Fig. 5 shows that the dopant composition in the EVD film under present conditions is determined by the ratio of the permeation rate constants, ,J .and the concentration of YC19 in the vapor phase, not by the equilibrium dopant composition, Xe (Xc = 0.3, the results in Fig. 5 ) . In more practical situations, the resistance in the EVD film increases as the film grows thicker. Mass transfer resistances in the pore diffusion and surface reduction reaction steps might be as large as that of the surface oxidation reaction step. In this case, there is no rate-limiting step, at least at the beginning of the EVD process. In this general case, the dopant composition profiles were obtained by simultaneous solution of the seven algebraic and one differential equations. Fig. 6 shows some calculated yttrium composition profiles along the film growing direc-
’
.%J’
....‘....‘....‘....‘...~
oal
1 X= 1+~(pzrcl,lp:cl~)
/f
0
10
xl
a
20
40
50
Thickness (pm)
Fig. 6. Calculated dopant (yttrium) composition along film growing direction when there is no rate-limiting step. ((~5, in mol/ cm2 s atm-7/2, (Y&in mol/cm* s atmW2).
tions for the general cases. The values of other parameters used are the same as in Table 1. As shown in Fig. 6, the yttrium composition, depending on its initial value, may increase, decrease, or remain constant along the film growing direction. The dopant composition approaches the equilibrium values (Xc= 0.3 in this case) as the film grows thicker. This is because, for thicker films, the bulk electrochemical transport becomes the rate-limiting step so the surface oxidation reactions are at quasi-equilibrium. The initial dopant composition depends on several parameters, primarily ai and ai,. This initial value canbefoundbysolvingEqs.(1),(4),(8),(12)and (15). The comparison of the calculation results with the experimental data of Dietrich et al. [ 9 ] is presented
J. Han, Y.-S. Lin /SolidState
262
in Fig. 7. It is possible to explain qualitatively the experimental data of Dietrich et al. [ 91 as follows. The EVD experiments of Dietrich et al. might not have performed under the conditions that the surface oxidation reaction step was at quasi-equilibrium. The initial yttrium composition is very likely smaller than the equilibrium yttrium composition because in EVD of YSZ a&, (for reaction (D)) is smaller than a& (for reaction ( E ) ) , which is a reasonable assumption as oxidation rate for yttrium chloride is expected to be lower than that of zirconium chloride. This could explain the experimental observation that the yttrium composition increases along the film growing direction. The present model also allows calculation of the EVD film thickness as a function of deposition time. Fig. 8 shows an example of the result of such calculations. The parameter values employed in these cal0.80
0
Experimental [91
0.18
0.10 0
4
8 12 Thickness (pm )
16
20
Fig. 7. Comparison of dopant composition with experimental data reported in Ref. [ 91.
- - G @.E17 d4=1.E7 a’4’1m1 -._-(I’
a’ &.ElS 41=1.E20 d&E10
0
5
lo
15
xl
Deposition Time (lx)
Fig. 8. EVD film thickness versus deposition time. (cr& in mol/ cm2 s atm-‘12, a& in mol/cm' s atmm2).
Ionics 73 (1994) 255-263
culations are the same as those listed in Table 1, but with different values of ai, and a&. The calculated film thickness versus deposition time is essentially linear at the beginning of the EVD process. This is because the electrochemical transport in the bulk oxide is not rate-limiting when the film thickness is small. The film growth rate decreases with increasing time because the oxygen permeation resistance in the EVD film increases with increasing the film thickness.
4. Conclusions The EVD process can be analyzed with an improved method which considers the various reaction and mass transfer steps, the dopant composition in the film and the EVD reactor configuration. The surface reaction steps were modeled by a recently developed approach, resulting in equations containing parameters with physical meanings. The model could be used to analyze the effects of various parameters on the dopant composition in the deposited film as well as on the film growth rate of the EVD process. If the surface oxidation reactions are at quasi-equilibrium, the dopant composition in the film is the same as the equilibrium value, which depends on the precursor concentration in vapor phase and the EVD temperature. If the surface oxidation reaction step is the rate-limiting step, the dopant composition in the film is determined by the permeation parameters for the surface oxidation reactions. In general cases, the dopant composition may vary along the film growing direction. The reported experimental data of EVD of yttria-doped zirconia film could be explained using the results of the theoretical analysis. The reactor configuration and carrier gas flow rates may also affect the kinetics and dopant composition in the film of the EVD process. Conditions with high chloride partial pressures, achieved by raising the chloride sublimation temperatures in the feed and lowering the substrate surface area to flow rate ratio, favor quasi-equilibrium of the surface oxidation reactions. The oxygen partial pressure in the chloride chamber can be predicted from the equilibrium relation and reactor performance equation. It is often determined by the oxygen impurity level in the carrier gas.
J. Han, Y.-S. Lin /Solid State Ionics 73 (1994) 255-263
Acknowledgement This work was supported by NSF under grant (CTS-9209518).
References [ 1 ] A.O. Isenberg, in: Electrode Materials and Processes for Energy Conversion and Storage, PV 77-6, eds. J.D.E. McIntyre, S. Srinivasan and F.G. Will, (The Electrochem. Sot. Softbound Proc. Series, Princeton NJ, 1977) p. 572. [2] J. Schoonman, J.P. Dekker and J.W. Broers, Solid State Ionics46 (1991) 299. [3]Y.S.Lin,L.G.J. deHaart, K.J.deVriesandA.J.Burggraaf, J. Electrochem. Sot. 137 ( 1990) 3960. [4] M.F. Carolan and J.N. Michaels, Solid State Ionics 37 (1990) 189. [ 51U.B. Pal and S.C. Singhal, J. Electrochem. Sot. 137 ( 1990) 2937. [6] L.G.J. de Haart, Y.S. Lin, K.J. de Vries and A.J. Burggraaf, Solid State Ionics 47 ( 199 1) 33 1.
263
[7] Y.S. Lin, W. Wang and J. Han, AIChE J. 40 ( 1994) 786. [S] H. Sasaki, C. Yakawa, S. Otoshi, M. Suzuki and M. Ippommatsu, J. Appl. Phys. 74 (1993) 4608. [ 9 ] G. Dietrich, H. Hermeking, A. Koch, W.J.C. Mllller and W. Schafer, Entwicklung und Bettieb von Dtlnnschichtzllen fur die Hochtemperaturelektrolyse ( 1984). [ lo] J. Crank, The Mathematics of Diffusion (Oxford University Press, London, 1975) 44. [ 111 F.A. Kroger and V.J. Vink, in: Solid State Physics, eds. F. Seitz and D. Tumbull, Vol. 3 (Academic Press, New York, 1956) pp. 307-435. [ 1210. Levenspiel, Chemical Reaction Engineering (Wiley, New York, 1972) p. 101. [ 13 ] D. Kahaner, C. Moler and S. Nash, Numerical Methods and Software (Prentice Hall, Englewood Cliffs, NJ, 1989) p. 258. [ 141 R.T. DeHoff, Thermodynamics in Material Science (McGraw-Hill, New York, 1993) p. 193. [15]L.G.J.deHaart,Y.S.Lin,K.J.deVriesandA.J.Burggraaf, J. Europ. Ceram. Sot. 8 ( 199 1) 59. [ 16 ] I. Barin, Thermochemical Data of Pure Substances, (Verlag Chemie, Weinheim, 1989).
ELSEWER
An improved analysis on kinetics of electrochemical vapor deposition Jonghee Han, Y.-S. Lin * Department of Chemical Engineering,
University of Cincinnati, Cincinnati, OH 4.5221-0171, USA
Received 17 March 1994;accepted for publication 28 July 1994
An improved method is presented to model the process of electrochemical vapor deposition (EVD) of solid oxide films on porous substrates. This method considers various reaction and mass transfer steps, dopant composition in the EVD film and the EVD reactor configuration. This model allows analysis of the effect of various parameters on the dopant composition in the deposited film as well as the film growth rate of the EVD process. If the surface oxidation reactions are at equilibrium, the dopant composition in the film is the same as the equilibrium value, which depends on the precursors concentration in the vapor phase and the reaction temperature. If the surface oxidation reaction step is the rate-limiting step, the dopant composition in the film is determined by the permeation parameters in the surface oxidation reaction step. In general cases, the dopant composition may vary along the film growing direction. The calculated results can explain the reported experimental data of EVD of yttria-doped zirconia films, and provide a better insight into the EVD process. Keywords:Ceramic electrolyte and membrane; Dopant concentration; Film growth kinetics; Oxygen permeation
1. Introduction Electrochemical vapor deposition (EVD) is a very promising technique for fabricating thin gas-tight solid oxide films on porous substrates for application in solid oxide fuel cells [ 1,2 ] and dense membrane composites [ 3 1. In the EVD process for growing solid
oxide films, a porous substrate separates the reactor into two parts, of which one is the metal source (e.g. a mixture of ZrC& and YC&) chamber and the other is the oxygen source (e.g. 0,) chamber. Initially, the two reactants inter-diffuse into the substrate pores and react to form the corresponding solid oxide product on the pore wall. As the reaction proceeds continuously, the deposited solid oxide grows and finally the * To whom all correspondence should be addressed 0167-2738/94/$07.00
substrate pores are plugged. After this step, no further direct reaction occurs between the two reactants. If the deposited solid oxide is an oxygen ionic conducting material with some electronic conductivity, the oxygen source reactant can diffuse through the oxide film and react with the metal source reactant leading to continuous growth of the oxide film. As such an EVD prooess is very difficult to be monitored experimentally, a theoretical model on the film growth kinetics is very important for understanding and controlling the process. In the previous studies, most researchers analyzed this film growth process as the Wagner scaling process [ 4,5 1. Therefore, their results showed that the film growth rate followed a parabolic rate law. De Haart et al. [ 61 reported a detailed analysis on this film growing process based on a model considering four mass transport steps in se-
0 1994 Elsevier Science B.V. All rights reserved
XSD10167-2738(94)00154-5
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J. Han, Y.-S. Lin /Solid State Ionics 73 (1994)255-263
ries originally proposed by Lin et al. [ 3 ] : ( 1) oxygen reactant diffusion in the substrate pores; (2 ) surface oxygen reduction reaction; (3) bulk electrochemical transport of oxygen ions in the EVD film; (4) surface reaction for formation oxide film. However, this model employed the empirical equations without physical significance for surface reactions because it is difficult, if not impossible, to integrate the surface reaction equations with the bulk diffusion equation using the Wagner approach. Furthermore, most of the previous theoretical studies considered essentially the EVD film as of a single component material. Recently, Lin et al. [ 71 developed a theoretical approach which allows integrating surface reaction equations with the bulk diffusion equation. This approach has been employed to derive equations for oxygen permeation through mixed conducting oxide membranes. It can be also used to model the EVD process. The electrochemical properties of the EVD film depend largely on the composition of the dopant (e.g. Y,O,) in the EVD film (e.g. ZrO*) because the composition of the dopant is directly related to the ionic conductivity of the EVD film. In the EVD process for growing zirconia-yttria films, zirconia is doped by generating a mixture of YC19and ZrC& vapor of controlled concentration in the chloride chamber. Thus, understanding the relationship between the yttrium content in the vapor phase and that in the deposited film is very important in controlling the proper amount of doping oxide in the EVD film. The only theoretical study on the dopant composition in the EVD film is reported by Sasaki et al. [ 8 1. However, their model neglects kinetics of surface reaction and oxygen permeation, and therefore cannot explain the variation of the dopant composition along the EVD film thickness reported by Dietrich [ 9 1. The main objective of this paper is to report an improved method for the analysis of the EVD process. This method considers various mass transfer and reaction steps, the dopant composition variation and the EVD reactor configuration. The surface reaction steps are modeled using a recently developed approach to give parameters with physical meanings. The analysis results are presented to examine the effects of experimental conditions and parameters on the dopant composition. Such analysis could provide a better insight into the EVD process, especially on
the control of the dopant composition. EVD of yttria-doped zirconia is considered in the analysis for the purpose of illustrating the method.
2. Model development The most common material fabricated by the EVD process is yttria-stabilized zirconia (YSZ). YSZ film is deposited on a porous substrate by introducing a mixture of YC& and ZrC& vapor as metal source reactants. As oxygen source reactant, oxygen mixed with steam is used. Fig. 1 shows the cross sectional view of the porous substrate separating the mixture of YC13and ZrC14 vapor and the mixture of oxygen and steam. L, r and H indicate the thickness and the average pore radius of the substrate and the EVD film thickness which is a function of the deposition time, respectively. Pb, , Po2cIj and PA, represent the partial pressures of oxygen in the oxygen chamber, the inner end of the substrate pore and the chloride chamber, respectively. PozcIIjand Po2~,II~indicate the oxygen partial pressures at the oxygen/film interface and the film/chloride interface, respectively. In the EVD process, the oxygen source reactant (oxygen molecule) first diffuses into the substrate pores. At the oxygen/film interface oxygen molecules are reduced to oxygen ions. Then these oxygen ions migrate through the EVD film toward the film/metal chloride interface (electrons move in the opposite direction) and react with YC13or ZrC& vapor to form YSZ on the film/metal chloride interface. Therefore, this EVD process can be determined by four mass transfer steps in series: ( 1) oxygen reactant diffusion in the substrate pores; (2 ) surface oxygen reduction reaction; (3) bulk electrochemical transport of oxygen ions in the EVD film; (4) surface oxidation re-
SUESTRATE
Fig. 1. Cross-sectional
PORE
view of EVD film growing process.
257
J. Han, Y.-S. Lin /Solid State Ionics 73 (1994) 255-263
action for the formation of oxide film. Since the fluxes in film growth processes such as this EVD process are usually very small, a quasi-steady state can be assumed to simplify the mathematics of this model. In the oxygen pore diffusion step, the flux of oxygen molecules can be expressed with the steady state diffusion equation [ lo] as: Jo2 =S(&,
-Po*(1))
(la) Jo2 =a, (G/:cl, -~~~~u))
with (j=
Do LRT’
tion in YSZ exposed to an atmosphere of 1 atm oxygen partial pressure. If the surface charge transfer reaction is assumed to be the rate limiting step in the surface reaction (A), the flux of oxygen molecule for the surface reaction can be obtained from the mass action law combined with the Einstein relation and other relations (Eqs. (2)and(3))as[7]: (4a)
with
(lb)
where Joz is the flux of oxygen molecule; 6 is the permeation parameter in this step and Do is effective diffusivity of oxygen molecules in the pore; R and T indicate the gas constant and the reaction temperature, respectively. At the oxygen/film interface, a surface reaction occurs. This reaction can generally be expressed as:
(Y,=k;C$
(4b)
where (Y,is the permeation parameter in this step. In the step of bulk electrochemical transport of oxygen in the EVD film, the oxygen vacancies migrate from the film/metal chloride interface to the oxygen/film interface and electron-holes move in the opposite direction. This electrochemical transport process can be expressed as: V&III) +Vb’cu, 9
(B)
h;u, -+h;u,j .
(C)
(A)
where k’, and k’_, indicate the forward and backward reaction rate constants for reaction (A), respectively. The Kriiger-Vink notation [ 111 is used in eq. (A) and for other electrochemical reaction processes in this paper. With this notation, V g, 00x and h’ indicate oxygen vacancy, lattice oxygen and electron-hole, respectively. If the EVD film is an ionic conducting material with small electronic conductivity contributed primarily by the electron-holes, the electron-hole concentration is correlated to the imaginary partial pressure of oxygen in the solid as [ 7 ] :
(2) where, C,,, Cv and [0,X ] indicate electron hole, oxygen vacancy and lattice oxygen concentration, respectively. In most ionic conductors, the concentration of the oxygen vacancy is much larger than that of the electron-holes. Therefore, the oxygen vacancy concentration can be assumed as constant: C”(i) = C8,
(3)
where, CO, indicates the oxygen vacancy concentra-
The flux of oxygen molecule in this step can be represented as [ 7 ] : (5a)
‘-
-- RTo;: 4F2
(5b)
where /I is the permeation parameter in this step; F is the Faraday constant and a: is the electron-hole conductivity of YSZ exposed to an atmosphere having 1 atm oxygen partial pressure. At the film/metal chloride interface, the lattice oxygen in the EVD film reacts with the metal chlorides and forms the metal oxide film. As different metal chlorides react with oxygen, this film growth reaction can be expressed as two separate reactions: kkl 2YC& + 300” + 6h’ e 2Y0,,5 + 3Cl2 + 3V; , (D) P-RI kkz ZrCl, + 200” + 4h ’ d Zr02 + 2C12+ 2V; kLm
,
(El
J. Han, Y.-S. Lin /Solid State Ionics 73 (1994) 255-263
258
where kk, and k’_-R1indicate the forward and the backward reaction rate constants for reaction (D) and k& and k’_,, for reaction (E). Making analogy to the mass action law, the following two equations are assumed for the separated oxygen fluxes:
-kl-RI(Y,X)2Pb*CZr(lII), J 42
=kk,[W
l*hc~$&m)
-kL2Y2(1
-W%&III~
the standard Gibbs free energy data for reactions (F) and (G) [ 161. By substituting Eqs. (9), ( IO) and (2) into Eqs. ( 6 ) and ( 7 ) , the oxygen fluxes for each reaction ( reactions (D) and (E)) can be expressed in terms of the oxygen partial pressures as:
(11)
(6)
(12)
(7)
,
where J4, and J42 are fluxes of oxygen molecule (0,) consumed in reactions ( D ) and (E ) , respectively and X is the atomic fraction of yttrium in the solid EVD film. yi and y2 represent activity coefficients of yttria and zirconia respectively. If there is no other oxygen consumption, the total oxygen flux (oxygen consumption rate) in this step equals the sum of the oxygen molecule fluxes for reactions ( D ) and ( E ) :
with 3
CO” v P2 YCl3= dl
cFPL
9
(13)
C@P v ZrCla= ah2 CTPZrcl4 9
(14)
2
a42 --kk,
( > -$
I
In this approach, the EVD process is considered as four mass transfer steps in series. Considering the EVD process as one overall process can give useful relations, The overall reactions occurring in the EVD process can be expressed as:
where 13~~and (~42are the permeation parameters for this step. Here the activity coefficients are canceled out because the difference between the activity coefficients of the equilibrium state and non-equilibrium state is assumed to be very small. Neglecting diffusion of yttrium in the EVD film, the yttrium (YO,.,) composition in the solid EVD film equals:
302+4YC13P4Y0i.s
x=jJ,,/($J41
Jo2= 34, +J42
.
(8)
+6 C12,
(F)
O2 + ZrC1, *ZrO, + 2 Cl2 .
(G)
Comparing reactions (F) and (G) with reactions (A), (D) and (E), the relations between these reactions can be easily found as (F) = 2 (D) + 6 (A) and (G) = (E) + 2 (A). Using these relations, the reaction equilibrium constants of reactions (F) and (G) can be expressed as: K
(Y~-w4f%, =’ = P;;:P&,
Ke2 = Y”z(1 -XC)Pcl* p;;,pzm4
=(~$Lg,
= ($-)‘(+-)
(9)
5
(10)
where Xc is the equilibrium dopant composition in the solid EVD film and ph is the equilibrium oxygen partial pressure in the chloride chamber. K,, and K,, are the equilibrium constants for the reactions (F) and (G), respectively, which can be calculated from
+J42)
.
(15)
Eqs. (l), (4), (5), (11) and (12) represent the oxygen fluxes in four steps connected in series. The relation correlating the EVD film growth rate to the oxygen flux can be simply obtained from mass balance as: 1 dH
Jo2= --2 V,,, dt
(16)
where V, = XV,,,., + ( 1- X)Vz,+. Since variation of Xalong the film growing direction is small, V, can be assumed to be the average molar volume of YSZ in the EVD film. t is the deposition time. Eqs. (1) (4),(5),(g), (ll), (12) (15)and (16) are seven nonlinear algebraic equations and one differential equation describing the EVD process. Simultaneous solution of these eight equations would give the time dependence of PozcIj, p 02ClI)9 PO2(III)> Jo2, J4,, J42, X and H. Of particular interest to this workis H=f(t), X=f (t) or X=f(H). To solve the
259
J. Han. Y.-S. Lin /Solid State Ionics 73 (I 994) 255-263
equations, values of parameters, 8, 8, aI, a41, a42, P&, P& and Xc should be given. Values of 8, /3 and Pb, are readily available. Theoretically, crI, cy4]and ~~42 are a function of variable Xbecause these parameters depend on C$ which is directly related to the dopant composition X. In this work, a dopant composition averaged across the film thickness, x* is assumed for or,, (~4~and (~42. Xc can be calculated from the reaction equilibrium Eqs. (9) and (10). Combining Eqs. (9) and (10) to . . ehmmate Pcl, and P& gives:
(YPXC) 4 {r;(l
---Ke, f%,
-xc)}’
-
K%
Grc,,
.
(17)
A reactor configuration model is needed to evaluate PYCI~ and Pz,Q, which appear in Eqs. ( 13 ) , ( 14) and ( 17), and P&. The metal chloride chamber of the EVD reactor can be considered as a flow system, as shown in Fig. 2. As the EVD is operated at high temperature and low pressure, gases in the metal chloride chamber are well mixed and the CSTR reactor model [ 12 ] can be applied to the EVD reactor. The mass balance on YC13, ZrC14 and Cl2 in the metal chloride chamber is given: Qf’ya
RT
_
QPL RT
RT
epcl,
RT
RT
=s(2J,,+w4,)
3. Results and discussion
The EVD process for growing solid oxide film can bedescribedbyEqs. (l), (4), (5), (8), (ll), (12), ( 15 ) and ( 16 ) . For a given film thickness H, values 0fP02(I),
pOz(II),
POz(IlI)9
x9
502,
J4, ad
J42
were
found by solving the seven algebraic equations using subroutine SNSQE of tihaner et al. [ 131. The differential equation, Eq. ( 16)) coupled with the seven algebraic equations, was solved by the Euler method.
(18)
-4SJ419
QPzm. _ Qf-‘%a, _s
chamber and S indicates the surface area of the substrate. J4i and J42 are usually very small, SO Eqs. ( 18) and ( 19 ) become PyCLj%P&, , Pz~, BP&,, , where the superscript O indicates the partial pressures of metal chlorides entering the reaction zone. Once PYCls, Pzrc14and PCl, are known, p& can be calculated from Eqs. (9) and ( lo), which is usually very small ( < 10 - l’ atm for EVD of YSZ). Since practically the carrier gas contains 1Ov2 ppm of oxygen impurity, the contribution from the carrier gas will give P& z 10 - l I atm and this value is used in this work.
3. I. Surface oxidation reaction under equilibrium J
42 ,
,
(19)
(20)
where Q is inert gas flow rate in the metal source
Fig. 2. Schematic diagram of the metal source chamberof an EVD reactor reported in a Ref. [ 15 1.
If the EVD process is operated under conditions that the surface oxidation reaction step is at quasiequilibrium (with very large values of a41 and (~42), Eqs. ( 11) and ( 12) yield Po2CIIIJxP& and Xc X”. This means that the dopant composition is the same as the equilibrium value Xc, which can be found by solving Eq. ( 17 ). As indicated by Eqs. ( 13) and ( 14)) the fourth step (surface oxidation reactions) can be considered as quasi-equilibrium if the permeation parameters a$, and cyi2, and/or the chloride pressures are large. Values of cv& and ab2 depend mainly on the nature of the oxidation reactions, which are difficult to manipulate for a given system. The chloride pressures are, however, the experimentally controllable parameters. Obviously Eq. ( 17 ) shows that the equilibrium dopant composition Xc depends only on the temperature (through K,, and K,,) and chloride pressures in
260
J. Han, Y.-S. Lin /SolidState
the metal source chamber. To find X”, the activity coefficient rf and y$ should be given. Assuming a dilute solid solution for the deposited YSZ film, y5 (for ZIG,) can be considered as 1 and 74 (for Y01.5) approaches to a certain value, r;“, which is called Henry’s constant [ 141. The reaction equilibrium constants K,, and K,, for EVD of YSZ which are calculated from the Gibbs free energy data [ 16 1, are given in Table 1. For a total pressure (P&i 3+Gc14 = 1.89x 10e4 atm), calculation results of dopant (yttrium) composition X” versus yttrium chloride concentration in the vapor phase are given in Fig. 3 for different values of yp. The results given in Fig. 3 show that the equilibrium Table 1 Values of parameters and conditions for EVD of YSZ on porous a-alumina substrate used in calculations.
Temperature (T) Substrate thickness (L) Substrate area (S) Average molar volume OfYSZ (V,) pb, P& P Ycl3
&ICI4 DO or B &I 1 KczL
1000°C 2mm 113.99 mm2 20.7 ml/mol 10e3 atm IO-” atm 5.9X lo-‘atm 1.3x 10e4atm 0.12 cm2/s 5 X lo-’ mol/cm’ s atm’/r 1.6~10-“mol/cm~satm’~~ 2.126~10” 306474.67
Ionics 73 (1994) 255-263
dopant composition in the deposited film depends strongly on the concentration of the corresponding precursor in the vapor phase. Carolan and Michaels [4] found that the dopant (yttrium) compositions in the EVD YSZ film are essentially the same as the concentration of YC13in the vapor phase, as shown in Fig. 4. The results of the model calculation with y~=5.04~10-~, K,,=1.06~10’~ and K,,=6.72x lo4 are compared in Fig. 4. The model results agree reasonably well with the experimental data. De Haart et al. [ 15 ] also reported that the yttrium composition in the YSZ film is roughly the same as the chloride concentration in the vapor phase. The above calculations are based on the assumption that the surface oxidation reactions are under quasi-equilibrium. In this case, the dopant composition remains constant across the deposited film as Sasaki et al. reported [ 81. However, Dietrich et al. [9] found that the yttrium composition increases along the film growing direction in their EVD synthesized YSZ film (about 20 pm thick). Their results can be explained by the following two possibilities: First, the yttrium chloride vapor concentration increased during the EVD process; second, the surface oxidation reactions are not at equilibrium under the experimental conditions of Dietrich et al. Results of the theoretical analysis in such cases are presented next.
a Calculated from Gibbs free energy data [ 161.
0.4 xe
0.3 0.2
0.1 0 0
0.1
0.2 0.3 PYC13’(PYC13+PZ~C14)
0.4
0.5
Fig 3. Variation of equilibrium dopant (yttria) composition with corresponding concentration in vapor phase.
Fig. 4. Comparison of equilibrium dopant composition with experimental data reported in Ref. [4].
J. Han. Y.-S. Lin /SolidState
3.2. Surface oxidationreactionsnot under equilibrium
1.2
When the surface oxidation reactions are very slow compared to the other mass transfer steps, the surface oxidation reaction step can be considered as a rate limiting step (small a!4I and (~42). In this case, the mass transfer resistances of the first three steps can be assumed infinitely small and Pb, x POI(IIIj.In this case, the yttrium composition in the EVD film is not a function of the film thickness, because the resistance of this step is not a function of the EVD film thickness. Thus, the yttrium composition, in this case, can be calculated from Eqs. ( 11) and ( 12) combined with Eq. ( 15 ). Since oxygen partial pressure at the film/chloride interface is much larger than the oxygen partial pressure in the chloride chamber, the second terms in the brackets in Eqs. ( 11) and ( 12) can be neglected. Introducing a new parameter proportional to the ratio of rate parameters, a& and CY&:
0.8
.
a:,
1
1
261
Ionics 73 (1994) 255-263
1.0
,^a.
x
0.6 0.4 0.2 0.0 0.0
0.2
0.4
0.6
0.8
1.0
PYC13/(PYC13+pZrC14) Fig. 5. Variation of dopant (yttria) composition with corresponding concentration in vapor phase when surface reaction is rate-limiting. 0.45
- - -
ci&m7 a’&oElo
0.40
~
.r \
0.35 :
rius).m a’~.1.cm
1
-
-
dU4_
x_c
X
d &oEl? --_
--__
-----_.
0.30
__---
_---_.--
the yttria composition in the EVD film can be expressed simply by:
0.25
/ T
.
(22)
The variation of dopant composition with the concentration of YC13in the vapor phase is presented in Fig. 5. The result given in Fig. 5 shows that the dopant composition in the EVD film under present conditions is determined by the ratio of the permeation rate constants, ,J .and the concentration of YC19 in the vapor phase, not by the equilibrium dopant composition, Xe (Xc = 0.3, the results in Fig. 5 ) . In more practical situations, the resistance in the EVD film increases as the film grows thicker. Mass transfer resistances in the pore diffusion and surface reduction reaction steps might be as large as that of the surface oxidation reaction step. In this case, there is no rate-limiting step, at least at the beginning of the EVD process. In this general case, the dopant composition profiles were obtained by simultaneous solution of the seven algebraic and one differential equations. Fig. 6 shows some calculated yttrium composition profiles along the film growing direc-
’
.%J’
....‘....‘....‘....‘...~
oal
1 X= 1+~(pzrcl,lp:cl~)
/f
0
10
xl
a
20
40
50
Thickness (pm)
Fig. 6. Calculated dopant (yttrium) composition along film growing direction when there is no rate-limiting step. ((~5, in mol/ cm2 s atm-7/2, (Y&in mol/cm* s atmW2).
tions for the general cases. The values of other parameters used are the same as in Table 1. As shown in Fig. 6, the yttrium composition, depending on its initial value, may increase, decrease, or remain constant along the film growing direction. The dopant composition approaches the equilibrium values (Xc= 0.3 in this case) as the film grows thicker. This is because, for thicker films, the bulk electrochemical transport becomes the rate-limiting step so the surface oxidation reactions are at quasi-equilibrium. The initial dopant composition depends on several parameters, primarily ai and ai,. This initial value canbefoundbysolvingEqs.(1),(4),(8),(12)and (15). The comparison of the calculation results with the experimental data of Dietrich et al. [ 9 ] is presented
J. Han, Y.-S. Lin /SolidState
262
in Fig. 7. It is possible to explain qualitatively the experimental data of Dietrich et al. [ 91 as follows. The EVD experiments of Dietrich et al. might not have performed under the conditions that the surface oxidation reaction step was at quasi-equilibrium. The initial yttrium composition is very likely smaller than the equilibrium yttrium composition because in EVD of YSZ a&, (for reaction (D)) is smaller than a& (for reaction ( E ) ) , which is a reasonable assumption as oxidation rate for yttrium chloride is expected to be lower than that of zirconium chloride. This could explain the experimental observation that the yttrium composition increases along the film growing direction. The present model also allows calculation of the EVD film thickness as a function of deposition time. Fig. 8 shows an example of the result of such calculations. The parameter values employed in these cal0.80
0
Experimental [91
0.18
0.10 0
4
8 12 Thickness (pm )
16
20
Fig. 7. Comparison of dopant composition with experimental data reported in Ref. [ 91.
- - G @.E17 d4=1.E7 a’4’1m1 -._-(I’
a’ &.ElS 41=1.E20 d&E10
0
5
lo
15
xl
Deposition Time (lx)
Fig. 8. EVD film thickness versus deposition time. (cr& in mol/ cm2 s atm-‘12, a& in mol/cm' s atmm2).
Ionics 73 (1994) 255-263
culations are the same as those listed in Table 1, but with different values of ai, and a&. The calculated film thickness versus deposition time is essentially linear at the beginning of the EVD process. This is because the electrochemical transport in the bulk oxide is not rate-limiting when the film thickness is small. The film growth rate decreases with increasing time because the oxygen permeation resistance in the EVD film increases with increasing the film thickness.
4. Conclusions The EVD process can be analyzed with an improved method which considers the various reaction and mass transfer steps, the dopant composition in the film and the EVD reactor configuration. The surface reaction steps were modeled by a recently developed approach, resulting in equations containing parameters with physical meanings. The model could be used to analyze the effects of various parameters on the dopant composition in the deposited film as well as on the film growth rate of the EVD process. If the surface oxidation reactions are at quasi-equilibrium, the dopant composition in the film is the same as the equilibrium value, which depends on the precursor concentration in vapor phase and the EVD temperature. If the surface oxidation reaction step is the rate-limiting step, the dopant composition in the film is determined by the permeation parameters for the surface oxidation reactions. In general cases, the dopant composition may vary along the film growing direction. The reported experimental data of EVD of yttria-doped zirconia film could be explained using the results of the theoretical analysis. The reactor configuration and carrier gas flow rates may also affect the kinetics and dopant composition in the film of the EVD process. Conditions with high chloride partial pressures, achieved by raising the chloride sublimation temperatures in the feed and lowering the substrate surface area to flow rate ratio, favor quasi-equilibrium of the surface oxidation reactions. The oxygen partial pressure in the chloride chamber can be predicted from the equilibrium relation and reactor performance equation. It is often determined by the oxygen impurity level in the carrier gas.
J. Han, Y.-S. Lin /Solid State Ionics 73 (1994) 255-263
Acknowledgement This work was supported by NSF under grant (CTS-9209518).
References [ 1 ] A.O. Isenberg, in: Electrode Materials and Processes for Energy Conversion and Storage, PV 77-6, eds. J.D.E. McIntyre, S. Srinivasan and F.G. Will, (The Electrochem. Sot. Softbound Proc. Series, Princeton NJ, 1977) p. 572. [2] J. Schoonman, J.P. Dekker and J.W. Broers, Solid State Ionics46 (1991) 299. [3]Y.S.Lin,L.G.J. deHaart, K.J.deVriesandA.J.Burggraaf, J. Electrochem. Sot. 137 ( 1990) 3960. [4] M.F. Carolan and J.N. Michaels, Solid State Ionics 37 (1990) 189. [ 51U.B. Pal and S.C. Singhal, J. Electrochem. Sot. 137 ( 1990) 2937. [6] L.G.J. de Haart, Y.S. Lin, K.J. de Vries and A.J. Burggraaf, Solid State Ionics 47 ( 199 1) 33 1.
263
[7] Y.S. Lin, W. Wang and J. Han, AIChE J. 40 ( 1994) 786. [S] H. Sasaki, C. Yakawa, S. Otoshi, M. Suzuki and M. Ippommatsu, J. Appl. Phys. 74 (1993) 4608. [ 9 ] G. Dietrich, H. Hermeking, A. Koch, W.J.C. Mllller and W. Schafer, Entwicklung und Bettieb von Dtlnnschichtzllen fur die Hochtemperaturelektrolyse ( 1984). [ lo] J. Crank, The Mathematics of Diffusion (Oxford University Press, London, 1975) 44. [ 111 F.A. Kroger and V.J. Vink, in: Solid State Physics, eds. F. Seitz and D. Tumbull, Vol. 3 (Academic Press, New York, 1956) pp. 307-435. [ 1210. Levenspiel, Chemical Reaction Engineering (Wiley, New York, 1972) p. 101. [ 13 ] D. Kahaner, C. Moler and S. Nash, Numerical Methods and Software (Prentice Hall, Englewood Cliffs, NJ, 1989) p. 258. [ 141 R.T. DeHoff, Thermodynamics in Material Science (McGraw-Hill, New York, 1993) p. 193. [15]L.G.J.deHaart,Y.S.Lin,K.J.deVriesandA.J.Burggraaf, J. Europ. Ceram. Sot. 8 ( 199 1) 59. [ 16 ] I. Barin, Thermochemical Data of Pure Substances, (Verlag Chemie, Weinheim, 1989).