Electronic Transport in 8 Mole Percent Y203-Zr02
Jong-Hee Park*
Materials and Components Technology Division, Argonne National Laboratory, Argonne, Illinois 60439
Robert N. Blumenthal
Department of Mechanical Engineering, Marquette University, Milwaukee, Wisconsin 53233
ABSTRACT
B y m e a n s o f a g a s - t i g h t e l e c t r o c h e m i c a l cell, o x y g e n p e r m e a t i o n m e a s u r e m e n t s h a v e b e e n p e r f o r m e d o n t h e o x y g e n
i o n c o n d u c t o r 8 m o l e p e r c e n t (m/o) y t t r i a - s t a b i l i z e d zirconia, as a f u n c t i o n of T (800~176
a n d Po2 (0.21-10-17 atm). I o n i c
c o n d u c t i v i t y w a s m e a s u r e d b y t h e c o n v e n t i o n a l f o u r - p r o b e m e t h o d . T h e f o l l o w i n g e m p i r i c a l e q u a t i o n s w e r e d e r i v e d for
t h e ion, e l e c t r o n , a n d h o l e c o n d u c t i v i t i e s , i n o h m -1 c m -1
~ion = 1.63 • 102 e x p ( - 0 . 7 9 eV/kT)
~ = 1.31 • 107 e x p ( - 3 . 8 8 eV/kT) Po2 1/4
~h = 2.35 X 102 e x p (--1.67 eV/kT)po2 +114
T h e e l e c t r o n i c diffusivity, D, a n d m o b i l i t y , ~, for h o l e s a n d e l e c t r o n s w e r e d e t e r m i n e d b y n o n s t e a d y - s t a t e o x y g e n p e r m e ation measurements. A gas-switching method was employed. Results indicate that the holes and electrons move by a therm a l l y a c t i v a t e d h o p p i n g - t y p e m e c h a n i s m . T h e e q u a t i o n s for D a n d ~ are as follows
For holes
Dh = 0.23 e x p ( - 1 . 1 5 eV/kT)
txh = 0.85 e x p ( - 1 . 0 5 eV/kT)
For electrons
De = 2.30 • 102 e x p ( - 2 . 0 0 eV/kT)
~e = 8.02 • 102 e x p ( - 1 . 8 9 eV/kT)
T h e e l e c t r o n i c s e m i c o n d u c t i n g p r o p e r t i e s o b e y B o l t z m a n n - t y p e statistics at t e m p e r a t u r e s i n v e s t i g a t e d . A n a n a l y s i s w a s
carried out by combining results from electronic transport and solid-state coulometric titration measurements under the
a s s u m p t i o n o f t r a p p i n g of e l e c t r o n s a n d h o l e s o n t h e a p p r o p r i a t e s u b l a t t i c e s . T h e r e s u l t s i n d i c a t e t h a t t h e t r a n s p o r t of
e l e c t r o n s a n d h o l e s is d u e to a t h e r m a l e x c i t a t i o n p r o c e s s a n d t h a t e l e c t r o n s a n d h o l e s are t r a p p e d o n t h e a p p r o p r i a t e s u b lattices.
P u r e ZrO2 h a s t h r e e w e l l - d e f i n e d p o l y m o r p h s , n a m e l y ,
the monoclinic, tetragonal, and cubic structures. The
m o n o c l i n i c p h a s e is s t a b l e u p to a b o u t ll00~
w h e r e it
t r a n s f o r m s o v e r a 100~ t e m p e r a t u r e r a n g e to t h e tetrag o n a l p h a s e ; at 2370~ t h e c o m p o u n d a d o p t s t h e c u b i c
fluorite s t r u c t u r e (Fig. 1), i n w h i c h e i g h t o x y g e n i o n s are
l o c a t e d o n a s i m p l e c u b i c s t r u c t u r e i n s i d e t h e face-cent e r e d c u b i c s t r u c t u r e of z i r c o n i u m ions. W h e n a m e t a l
o x i d e w i t h a l o w e r - v a l e n c e c a t i o n is i n c o r p o r a t e d i n t o
c u b i c ZrO2, t h e r e s u l t is a s t a b l e c u b i c fluorite s t r u c t u r e
p h a s e , r e f e r r e d to as s t a b i l i z e d zirconia. T h e m o s t c o m m o n
s t a b i l i z i n g o x i d e s are c a l c i u m a n d y t t r i u m oxides. T h e
s u b s t i t u t i o n of t h e s e l o w e r - v a l e n c e c a t i o n s (+2 or +3) o n
t h e Z r § s u b l a t t i c e sites c r e a t e s o x y g e n v a c a n c i e s (1). Acc o r d i n g to M o b i u s (2), t h e i o n i c r a d i i of Ca § a n d y+a, 1.10
a n d 1.068, r e s p e c t i v e l y , are l a r g e r t h a n t h a t of t h e Z r § ion.
T h e lattice c o n s t a n t of t h e ZrO2-Y203 s y s t e m c h a n g e s line a r l y w i t h t h e c o n c e n t r a t i o n of Y2Oa o v e r t h e r a n g e of u p to
35 m o l e p e r c e n t (m/o) Y203 (3), i n d i c a t i n g t h a t Y2Oa c a n
f o r m a solid s o l u t i o n w i t h ZrO2 in t h i s range. G a r v i e (4) h a s
reviewed previous work on the structure of pure ZrQ and
stabilized zirconia systems.
S t a b i l i z e d z i r c o n i a h a s b e e n utilized e x t e n s i v e l y i n scientific a p p l i c a t i o n s s u c h as h i g h - t e m p e r a t u r e p r o b e s for
m e a s u r i n g a n d c o n t r o l l i n g o x y g e n p o t e n t i a l , a n d as a b a s e
m a t e r i a l in h i g h - t e m p e r a t u r e fuel cells. V e r y r e c e n t l y , it
h a s b e c o m e i m p o r t a n t as a c o a t i n g m a t e r i a l to r e s i s t h o t
c o r r o s i o n . Also, it is well k n o w n to b e a n i o n i c c o n d u c t o r
o v e r a w i d e r a n g e of o x y g e n p a r t i a l p r e s s u r e s at e l e v a t e d
t e m p e r a t u r e s . T h i s ionic c o n d u c t i o n o c c u r s via t h e vac a n c y m e c h a n i s m , as K i n g e r y et al. (5) h a v e v e r i f i e d b y
c o m p a r i n g ionic c o n d u c t i v i t y a n d 180 t r a c e r d i f f u s i o n
m e a s u r e m e n t s . A c c o r d i n g to h i g h - t e m p e r a t u r e s o l i d - s t a t e
eoulometric titration studies on yttria-stabilized zirconia
*Electrochemical Society Active Member.
(YSZ), t h e c o n c e n t r a t i o n s of e l e c t r o n s (5) a n d h o l e s are
c o n s i d e r a b l e c o m p a r e d to t h o s e i n o t h e r m e t a l oxides. (6)
S e v e r a l d i f f e r e n t t e c h n i q u e s h a v e b e e n u s e d to d e t e r m i n e
e l e c t r o n i c c o n d u c t i v i t i e s . V e s t a n d T a l l e n (7) a n d Patt e r s o n et aI. (8) a p p l i e d a p o l a r i z a t i o n m e t h o d , a n d H e y n e
a n d B e e k m a n s (9) m e a s u r e d t h e p e r m e a b i l i t y o f o x y g e n .
B u r k e et al. (10) a n d W e p p n e r (11) a p p l i e d t h e v o l t a g e rel a x a t i o n t e c h n i q u e . M a n y s t u d i e s h a v e b e e n m a d e of elect r o n i c t r a n s p o r t i n stabilized zirconia; h o w e v e r , m o s t inv e s t i g a t i o n s h a v e b e e n p e r f o r m e d in t h e p-type, high-Po2
r e g i m e , w i t h o n l y l i m i t e d s t u d i e s r e p o r t e d in t h e n - t y p e reA
A
.J
W
W
Oxygen Ion
9
Zirconium or Yttrium Ion
Fig. 1. Cubic fluorite crystal structure of stabilized zirconium dioxide
J. Electrochem. Soc., Vol. 136, No. 10, October 1989 9 The Electrochemical Society, Inc.
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g i o n (12, 13). In order to obtain c o m p l e t e i n f o r m a t i o n on
t h e t r a n s p o r t properties, it is n e c e s s a r y to c o m b i n e the results for b o t h the n-type and p-type regions.
H e y n e and B e e k m a n s (9) m e a s u r e d the c h e m i c a l diffusivity D in the p-type, high-Po2 region for 15 m/o CaO-ZrO2
by u s i n g the gas-switching m e t h o d (14). W e p p n e r (15) det e r m i n e d the hole and electron mobilities ~h and a, for 10
m/o yttria-stabilized zirconia (YSZ) by u s i n g a voltage relaxation t e c h n i q u e ; f r o m the result, he calculated a gap
e n e r g y of 4.1 eV. Recently, h o w e v e r , P a r k and B l u m e n t h a l
(16) o b t a i n e d an optical gap e n e r g y of 2.7-2.8 eV in Y S Z at
t e m p e r a t u r e s from 800 ~ to 1000~ D i s c r e p a n c i e s of this
t y p e w e r e d i s c u s s e d by Tuller (17), w h o p r o p o s e d that if
the mobilities are a strong f u n c t i o n of t e m p e r a t u r e , t h e gap
e n e r g y should be calculated by subtracting the m i g r a t i o n
e n e r g y f r o m the activation e n e r g y that is o b t a i n e d from
conductivity measurements.
In this paper, a gas-tight e l e c t r o c h e m i c a l oxygen-perm e a b l e cell has b e e n u s e d to obtain t h e m i n o r i t y conductivities, c h e m i c a l diffusion, and the s e m i c o n d u c t o r statistics
of 8 m/o Y20~-Zr02, Yoa48Zro.ss201.gas, for e l e v a t e d t e m p e r a tures h a v e b e e n d e m o n s t r a t e d .
A c c o r d i n g to H e y n e ' s m o d e l of a m b i p o l a r t r a n s p o r t (18),
mass t r a n s p o r t in ionic materials is controlled by the minority constituents; in yttria-stabilized zirconia (YSZ),
t h e s e are electrons and holes. W h e n steady-state m a s s flow
o c c u r s in a m e t a l o x i d e in the p r e s e n c e of a g r a d i e n t of oxy g e n c h e m i c a l potential, ~o2 the flux is g i v e n by
[la]
w h e r e ~t is the total c o n d u c t i v i t y of the s p e c i m e n ; ti and t~
are the ionic and electronic t r a n s f e r e n c e n u m b e r s , respectively; and F is t h e F a r a d a y constant. F o r the case of an
ionic conductor, i.e., t~ > 0.99, Eq. [la] m a y be written as
Ji = (~J4F) grad ~o2
~ = [e'] Iql ~
[2a]
~h = [h'] Iql ~h
[2b]
and
where, [e'] and [h'] are the c o n c e n t r a t i o n of electrons and
holes, ~ is mobility, and q is electronic charge for the electronic defects.
T h e defect reactions for Y S Z h a v e b e e n treated as b e i n g
controlled by the d o p i n g impurity, e.g.
[3]
w h e r e Y'Zr, Oo x, and Vo'" indicate y t t r i u m on t h e z i r c o n i u m
site w i t h a formal charge - 1 , n o r m a l o x y g e n on the o x y g e n
site, and a d o u b l y ionized o x y g e n vacancy, respectively.
We m a y write the following n o n s t o i c h i o m e t r i c defect reactions (8)
at low o x y g e n pressures
Oo ~ = 2e' + Vo-. + 1/2 O2(g)
'[4a]
at h i g h o x y g e n pressures
Vo" + 1/2 O2(g) = 2h- + Oo •
[4b]
B y a p p l y i n g the law of mass action to the low-Po2 nonstoic h i o m e t r i c defect reaction g i v e n in Eq. [4a], we obtain the
m a s s action c o n s t a n t
K = [Vo"]
[ e ' ] 2 P021/2
Analogously, in the h i g h Po2 region, application of electroneutrality gives 2[Vo--] + [h'] = [ Y z r ' ] . S i n c e 2[Vo"] > > [h']
and [Vo-'] is nearly constant, the Po2 d e p e n d e n c e of the hole
c o n d u c t i v i t y ~h is g i v e n by
[6b]
O"h ~ P o 2 +1/4
F r o m Eq. [2a] and [2b], the electronic c o n d u c t i v i t y ~e~is the
s u m of ae and ~h; since t h e s e values are d e p e n d e n t u p o n
Po2 as i n d i c a t e d in Eq. [6a] and [6b], respectively, we can express the i s o t h e r m a l electronic c o n d u c t i v i t y of t h e electrons as
[5]
w h e r e [Vo"] is the c o n c e n t r a t i o n of d o u b l y ionized vacancies on the o x y g e n sublattice. A p p l i c a t i o n of electroneu-
[7a]
and that of t h e holes as
~h(Po~) =
O'h(Po2 I)
[Po2/P02I] +1/4
[7b]
w h e r e Po2~ is the e q u i l i b r i u m o x y g e n partial p r e s s u r e for
t h e r e f e r e n c e side (I) of t h e s p e c i m e n at steady state. At
s t e a d y state, w i t h fixed po2 ~and Po2 values on b o t h sides of
a s p e c i m e n of t h i c k n e s s X, a c h e m i c a l potential g r a d i e n t
exists. The steady-state flux is d e r i v e d by integrating Eq.
[2a] and [2b] and inserting the Po2 d e p e n d e n c e of electronic
conductivity
J i X = ( R T / F ) [~h(po2I) {(Po2/Po2I) +114 - 1}
+ ~e(Po2~) {1 - (poJPo2 I) lJ4}] [8]
[lb]
i.e., the steady-state mass flux will be controlled by the
e l e c t r o n i c conductivity, (~ = ~ttel f r o m Eq. [lb]. Thus, the
mass flux is controlled by t h e m i n o r i t y c o n s t i t u e n t in the
m e t a l oxide.
On t h e a s s u m p t i o n that the mobilities do not d e p e n d
u p o n the carrier concentration, the c o n d u c t i v i t i e s v a r y
w i t h t h e c o n c e n t r a t i o n of electrons and holes then, the
electrical c o n d u c t i v i t y of electrons, ~ , and holes, ah
Y203 --->2Y'zr + 3 0 o ~ + Vo"
[6a]
O"e = P 0 2 -1/4
~e(Po2) = ~e(Po2 I) [Po2/Po2 I] 1/4
General Background
Ji = (~ttite/4F) grad 1~o2
trality at low Po2 gives 2[Vo..] = [YZr'] + [e']. H o w e v e r , in
Y S Z (in this study, [Yzr'] > > [e']), [Vo"] is nearly constant.
F r o m Eq. [5], we see that in the low Po2 region, [e'] = po2 -1/4.
T h e carrier c o n c e n t r a t i o n [ ]j, charge q, and m o b i l i t y u of
the c o m p o n e n t j are related by the c o n d u c t i v i t y equation,
~j = [ ]j q uj. A s s u m i n g the m o b i l i t y is n o t a f u n c t i o n of
c o m p o s i t i o n , the electron c o n d u c t i v i t y ~e in the low Po2 region s h o w s the s a m e Po2 d e p e n d e n c e as [e']
We n o w apply Eq. [8] to the two limiting cases, i.e., the lowPo2 region in w h i c h n-type b e h a v i o r p r e d o m i n a t e s and
p-type b e h a v i o r can be neglected, and the p r e d o m i n a n t l y
p-type region in w h i c h n-type b e h a v i o r can be neglected.
F o r low Po2 regions
(Po2/P02I)-l/4}]
[8a]
JihX = ( R T / F ) [~h(po2 I) {(po2/Po21) +114 - 1}]
[8b]
Ji~
= ( R T / F ) [~e(po2I) {1
-
and for h i g h Po2 regions
w h e r e Jie and Jib are the steady-state mass fluxes in regions
w h e r e the p r e d o m i n a n t b e h a v i o r of the m i n o r i t y constitu e n t s is n-type and p-type, respectively.
F i g u r e 2a is a s c h e m a t i c r e p r e s e n t a t i o n of an o x y g e n perm e a t i o n cell i n c o r p o r a t i n g a Y S Z specimen. Initially, t h e
s y s t e m is set up with the s a m e Po2 and h e n c e the s a m e oxyg e n c h e m i c a l potential inside and outside the cell, i.e.,
h~to2 = 0. In that e q u i l i b r i u m condition, no mass t r a n s p o r t
s h o u l d o c c u r t h r o u g h t h e specimen. W h e n a differential
(i.e., an o x y g e n c h e m i c a l potential difference) exists across
the s p e c i m e n , as s h o w n in Fig. 2b, o x y g e n will p e r m e a t e
through the specimen from the high Po2 to the low Po2 side.
This phenomenon
forms the basis of the well-known "time
lag" method for obtaining chemical diffusivity (9). According to Heyne (18), mass transport in metal oxide systems
requires local electroneutrality, which can be induced by
ambipolar transport. Therefore, when mass transport occurs in a metal oxide system at elevated temperatures, the
slowest-moving species determines the kinetics of the
whole process. As an example, Fig. 2c shows the n-type
ambipolar transport described by Eq. [ib], which involves
electrons and oxygen vacancies. In the p-type region,
holes and oxygen vacancies are involved in the transport
mechanism.
Experimental Method
Materials.--Sintered
"ZDY-2" disks of 8 m/o YSZ, 1/2 in.
in d i a m e t e r and 1/16 in. thick (12.7 • 1.5 ram), w e r e obt a i n e d f r o m Coors. The c h e m i c a l assay of the s p e c i m e n s
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J. Electrochem. Soc., Vol. 136, No. 10, O c t o b e r 1989 9 The Electrochemical Society, Inc.
I(/l llllli/l//
Z/llllll/llllllo
~
(B)
P y r e x seals. The entire stack, w i t h its cylindrical axis vertical, was placed in the furnace. B y m e a n s of t h r e e springs, a
force was a p p l i e d to t h e stack. A gas m i x t u r e of 3% 02 in A r
was passed t h r o u g h the s y s t e m d u r i n g firing at t e m p e r a t u r e of up to 1000~ D u r i n g heating, the P y r e x glass rings
m e l t e d and p r o v i d e d a gas-tight seal w h i c h was capable of
w i t h s t a n d i n g a m e c h a n i c a l p r e s s u r e difference of up to
0.35 atm at 950~ This limit was d e t e r m i n e d by continuously p u m p i n g o x y g e n t h r o u g h the electrolyte until the
cell failed. H o w e v e r , w h e n the o x y g e n was p u m p e d out,
the m a x i m u m p r e s s u r e difference that c o u l d be o b t a i n e d
was 0.03 atm b e c a u s e t h e initial gas m i x t u r e was 3% 02 in
Ar. No p r o b l e m in sealing was e x p e r i e n c e d d u r i n g p u m p ing out.
X
|
|
~62
I
P()2
I
o
(c)
2e' + vo + 1/2 O2(g)
9
o~) ~ 2e' + vo + 1/2 O2(g)
ox
v~
)
2e'
,ub2
,u~2
0
2869
X
Fig. 2. (A) Schematic figure of a permeation cell. (B) When the
chemical potential of oxygen is higher outside the cell than inside, oxygen permeation occurs from the outside to the inside by means of an
ambipolar mechanism. (C) In the n-type nonstoichiometric region, ambipolar diffusion of both electrons and ionized oxygen vacancies.
s h o w e d CaO, A1203, and SiO2 i m p u r i t y levels of less t h a n
1% each.
Construction of electrochemical ceiL--The gas-tight elect r o c h e m i c a l cell is s h o w n s c h e m a t i c a l l y in Fig. 3. It contains two identical Y S Z disks. T h e disk at the top serves as
a p e r m e a t i o n s p e c i m e n and o x y g e n sensor. T h e disk at the
b o t t o m is u s e d p r i m a r i l y as an o x y g e n p u m p . T h e wall of
t h e cell consists of three 1/2 in. od high-purity a l u m i n a
(no. 998A, McDanel) rings w h i c h are separated f r o m e a c h
o t h e r and f r o m the Y S Z disks by a P y r e x glass seal (no.
7740, s o f t e n i n g t e m p e r a t u r e 820~ Coming). The a l u m i n a
rings also p r o v i d e electrical insulation at h i g h t e m p e r a tures. P l a t i n u m electrodes w e r e m a d e by p a i n t i n g b o t h
Y S Z disks w i t h p l a t i n u m paste (no. 6926, unfluxed, Engelhard) on the o u t e r flat face and on that part of the i n n e r flat
face w h i c h w o u l d be w i t h i n t h e id of t h e a l u m i n a rings.
T h e p l a t i n u m electrodes w e r e h e a t e d in air to a b o u t 980~
and h e l d o v e r n i g h t to c o n d i t i o n them. P l a t i n u m wires 5
rail in d i a m e t e r w e r e u s e d as electrical leads t h r o u g h the
Measuring assembly.--Figure 4 s h o w s the m e a s u r i n g assembly. The l o w e r portion of the a s s e m b l y is e n c a s e d in a
quartz tube. C e r a m i c c e m e n t (no. 1, S a u e r e i s e n C e m e n t
C o m p a n y ) was u s e d to attach a brass O-ring fixture to t h e
o u t e r m o s t a l u m i n a tube, and a p o r t i o n of the cylindrical
wall n e a r the flat b o t t o m of that t u b e was cut a w a y so that
t h e e l e c t r o c h e m i c a l cell c o u l d be easily inserted. A springl o a d e d i n n e r a l u m i n a t u b e was placed in c o n t a c t w i t h t h e
e l e c t r o c h e m i c a l cell stack in order to facilitate sealing. A
Pt-13% R h / P t t h e r m o c o u p l e w i r e was i n s e r t e d into t h e
i n n e r a l u m i n a tube. The e l e c t r o c h e m i c a l cell o p e r a t e d in
t h e t e m p e r a t u r e r a n g e f r o m 800 ~ to 1050~ in a K a n t h a l
w i r e furnace. O v e r the 38 m m l o n g region in the vicinity of
t h e e l e c t r o c h e m i c a l cell, t h e furnace t e m p e r a t u r e was constant to w i t h i n I~ To r e d u c e electrical pickup, t h e measu r i n g a s s e m b l y was s u r r o u n d e d by a g r o u n d e d I n c o n e l
t u b e in the furnace. B e f o r e t h e m e a s u r e m e n t , t h e integrity
of the seals was c h e c k e d by s w i t c h i n g the gas f r o m 3% 02
in A r to p u r e oxygen. If t h e r e w e r e a leak in the seal, it
w o u l d be easily d e t e c t e d by a c h a n g e in the e m f of t h e cell.
T h e cell v o l u m e V was d e t e r m i n e d f r o m the ideal gas law.
Cell v o l u m e s as l o n g as t h e m e a s u r e d b y c o u l o m e t r i c titration w e r e r e a s o n a b l e and t h e e m f values w e r e c o n s t a n t
after s w i t c h i n g t h e gas, the cell was c o n s i d e r e d to be gastight.
Oxygen permeation measurement.--A steady-state flux
in t h e gas-tight e l e c t r o c h e m i c a l cell (Fig. 3) was o b t a i n e d
Pt-13%Rh/Pt
~.- Thermncoupla Leads
Gas Inlet
Spring Loaded
(120 Degree each 3
Parts)
"t
iz,
~
I/
I
0
!
EMF
Gas Outlet <
I Porous Platinum
'
Electrodes
," ~ ........
L_
.~sz .....
.
T,
t
~
9~
"?gZ
'
Brass Head Parts
: ~ :',- ~YSZ Disk
Inner 1/2 inch Dia. Alumina Tube
Alumina
Rings
\ m I
Pyrex
Glass
Seals
~
YSZDisk
,/
1--
-"~f
--
- -
E---Outer Quartz Tube
-Cell Guider (AluminaCup)
i
]
Platinum Lead Wires
Platinum Wire
(5 mil dia.)
t
~
I
/
(5 milY
I
1/2 inch
Ceil supporting
AluminaTube
....... o e
YSZ Specimen
with Porous Pt Electrode
2 inch Dla.AluminaTube. Cut
t
Pyrex Glass Sealing Parts
YSZ Pumping Electrolyte
/
Fig. 3. Cross-sectional side view of gas-tight electrochemical cell
used for oxygen flux measurements.
Fig. 4. Measuring assembly for the permeation measurements
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2870
J. Electrochem. Soc., Vol. 136, No. 10, October 1989 9 The Electrochemical Society, Inc.
b y fixing t h e c u r r e n t s u p p l i e d to t h e b o t t o m Y S Z disk.
W h e n t h e e m f of t h e t o p Y S Z d i s k r e a c h e d a c o n s t a n t
value, s t e a d y s t a t e w a s a t t a i n e d , i.e., t h e flux of t h e o x y g e n
p e r m e a t i o n t h r o u g h t h e t o p d i s k w a s e q u a l to t h e flux of
the oxygen which had been pumped. In this situation, the
d e v i a t i o n f r o m s t o ~ c h i o m e t r y o n b o t h sides o f t h e Y S Z
s p e c i m e n is i n e q u i l i b r i u m w i t h t h e s u r r o u n d i n g gases.
M e a s u r e m e n t s w e r e p e r f o r m e d s e p a r a t e l y for h i g h Po2 regions, w h i c h are e s s e n t i a l l y p-type, a n d l o w Po2 r e g i o n s ,
w h i c h are e s s e n t i a l l y n-type. F o r t h e p - t y p e r e g i o n s , air
(0.21 a t m ) w a s u s e d as a r e f e r e n c e gas so t h a t t h e i n s i d e of
t h e cell r e m a i n e d w i t h i n t h e p - t y p e m e a s u r e m e n t r e g i m e .
I n t h e n - t y p e region, a 50% CO-50% C Q (Po2 = 10-14 - 10-2~
a t m ) gas m i x t u r e w a s u s e d as a n o u t s i d e r e f e r e n c e gas. I n
t h e n - t y p e region, t h e i n s i d e o f t h e cell r e m a i n e d i n t h e
n-type regime, since the measurements were performed
under outgassing conditions.
For non-steady-state oxygen permeation measurements,
t h e " t i m e lag" m e t h o d as d e s c r i b e d p r e v i o u s l y (9, 13, 14)
w a s e m p l o y e d . Initially, t h e Po2 i n t h e p e r m e a t i o n cell w a s
set e q u a l to t h a t o u t s i d e t h e cell for a s u f f i c i e n t l y l o n g t i m e
to e n s u r e t h a t t h e o x y g e n c h e m i c a l p o t e n t i a l s i n s i d e a n d
o u t s i d e t h e cell w e r e t h e same. T h i s c o n d i t i o n w a s
a c h i e v e d b y m e a n s of p u m p i n g c o n t r o l or s h o r t c i r c u i t i n g .
S w i t c h i n g t h e o u t s i d e (reference) gas to o n e w i t h a m u c h
h i g h e r o x y g e n p a r t i a l p r e s s u r e (e.g., 1.0 a t m , w i t h a n i n s i d e
Po2 o f 10 -16 a t m ) i n i t i a t e s t h e n o n s t e a d y - s t a t e c o n d i t i o n .
O n e t h e n r e c o r d s t h e c h a n g e in e m f or Po2 w i t h t i m e (13).
A f t e r a g i v e n t i m e period, t h e c h a n g e in Po2 w i t h t i m e becomes constant, indicating a pseudo-steady-state condition. I n o t h e r w o r d s , t h e a m o u n t of o x y g e n t h a t h a s diff u s e d i n t o t h e cell t h r o u g h t h e s p e c i m e n b e c o m e s
c o n s t a n t . A t t h i s time, t h e Po2 in t h e cell is still a n o r d e r of
m a g n i t u d e s m a l l e r t h a n t h e r e f e r e n c e - g a s Po2 of 1.0 atm.
W h e n t h i s is true, w e h a v e m e t t h e b o u n d a r y c o n d i t i o n req u i r e m e n t as d i s c u s s e d i n t h e t h e o r e t i c a l a n a l y s i s for
F i c k ' s s e c o n d law. T h e c h e m i c a l d i f f u s i v i t y c a n b e obt a i n e d f r o m a p l o t of Po2 vs. t i m e (14). T h i s e x p e r i m e n t c a n
b e r e p e a t e d to o b t a i n t h e c h e m i c a l d i f f u s i v i t i e s o f t h e elect r o n s a n d h o l e s at v a r i o u s t e m p e r a t u r e s . F r o m a n a n a l y s i s
of a n A r r h e n i u s plot, t h e a c t i v a t i o n e n e r g y for c h e m i c a l
d i f f u s i o n a n d t h e m o b i l i t i e s of t h e e l e c t r o n i c s p e c i e s c a n
be obtained.
Results and Discussion
Ionic c o n d u c t i v i t y . - - M e a s u r e m e n t s in air a n d in a 50%
CO-50% CO2 gas m i x t u r e s h o w e d n o d i f f e r e n c e i n t h e t o t a l
c o n d u c t i v i t y f r o m t h a t i n p u r e o x y g e n . Also, t h e ac (1592
Hz) a n d d c c o n d u c t i v i t i e s w e r e t h e s a m e . F r o m t h e r e s u l t s
of t h e f o u r - p r o b e m e a s u r e m e n t s o f electrical c o n d u c t i v i t y ,
w e m a y c o n c l u d e t h a t O ' t o t : O'io n in t h e Po2 r e g i o n i n v e s t i gated, s i n c e n o Po2 d e p e n d e n c e w a s o b s e r v e d . U s i n g t h e
empirical equation
mo~(T) = o-io~~ e x p (-QioJkT)
we obtain
o-ion(T) = 1.63 • 102 e x p (-0.79 eV/kT)
( o h m lcm-1)
[9]
w h e r e k is B o l t z m a n n ' s c o n s t a n t , 8.614 • 10 -~ eV/K. T h i s
gives a n i o n i c c o n d u c t i v i t y of 3.14 • 10 -2 o h m - l c m -1 at
800~ a n d 1.20 • 10 -1 o h m i c m ' a t 1000~
Steady-state electrochemical transport m e a s u r e m e n t s . T h e v a l u e s ofo-~ a n d o-h w e r e d e t e r m i n e d f r o m t h e r e s u l t s of
t h e s t e a d y - s t a t e m e a s u r e m e n t s c a r r i e d o u t in b o t h t h e
n - t y p e a n d p - t y p e r e g i m e s . T h e fixed c u r r e n t a n d e m f at
s t e a d y s t a t e w e r e u s e d i n c o n j u n c t i o n w i t h Eq. [8a] a n d [8b]
to c a l c u l a t e O-e a n d o-h, r e s p e c t i v e l y .
D e t e r m i n a t i o n o-~.--ln t h e low Po~ region, t h e e l e c t r o n
c o n d u c t i v i t y Se' v a r i e s l i n e a r l y w i t h po2 -1/4 (Eq. [6a]). F i g u r e
3a s h o w s p l o t s of log o-~vs. log Po2 for s e v e r a l t e m p e r a t u r e s .
A c c o r d i n g to Eq. [8a], u n d e r c o n d i t i o n s o f s t e a d y - s t a t e
flux, o n e o b t a i n s t h e Po2 b y m e a s u r i n g t h e e m f (po2~ is alr e a d y d e t e r m i n e d b y t h e e q u i l i b r i u m Po2 of 50% CO-50%
CO~). O n e c a n t h e n c a l c u l a t e o-~ at po2 I. I n g e n e r a t i n g Fig. 5,
o-e(Po2) w a s d e t e r m i n e d f r o m Eq. [7a]. F r o m t h e o-e data, t h e
e m p i r i c a l e q u a t i o n c a n b e e x p r e s s e d as
o-e(T, Po2) = O'e~ e x p ( - Q J k T ) p o 2 -114
[10]
A l e a s t s q u a r e s fit of t h e d a t a to Eq. [10] allows u s to determ i n e t h e p a r a m e t e r s o-e~ a n d Qe
o-e(T, Po2) = 1.31 x 107 e x p ( - 3 . 8 8 e V / k T ) Po2 114
[11]
T h e c a l c u l a t e d a c t i v a t i o n e n e r g y for e l e c t r o n c o n d u c t i o n ,
Qe is 3.88 eV. F i g u r e 6 is a p l o t o f log o-e a n d log o-h vs. 1/T(K)
for Po2 v a l u e s o f 10 -17 a t m (n-type b e h a v i o r ) a n d 1 a t m
(p-type behavior). T h e d a t a for n - t y p e b e h a v i o r w e r e determ i n e d f r o m t h e i n t e r c e p t at 10 17 a t m for e a c h i s o t h e r m
s h o w n i n Fig. 5a. I n T a b l e I, t h e c a l c u l a t e d p r e - e x p o n e n t i a l
t e r m a n d a c t i v a t i o n e n e r g y of Eq. [11] are c o m p a r e d w i t h
t h o s e of H e y n e a n d B e e k m a n s (9) a n d W e p p n e r (11).
[ H e y n e a n d B e e k m a n s ' v a l u e s for o-e~ a n d Qe w e r e indirectly calculated from an equation derived by Schmalzried
(19).]
D e t e r m i n a t i o n o f o-h.--According to t h e p r o p o s e d d e f e c t
r e a c t i o n for t h e h i g h Po region, t h e h o l e c o n d u c t i v i t y o-h
v a r i e s l i n e a r l y w i t h po= +~4. F i g u r e 5b s h o w s p l o t s of log o-h
vs. log Po2 for s e v e r a l d i f f e r e n t t e m p e r a t u r e s . To d e t e r m i n e
o-h (Po2), a n a p p r o a c h s i m i l a r to t h a t for o-e w a s used. F r o m a
l e a s t s q u a r e s fit of t h e d a t a to t h e e m p i r i c a l e q u a t i o n for
h o l e c o n d u c t i v i t y , o-h(T, Po2) = o-h~ e x p (-Qh/kT) po2 +1/4 o n e
obtains
o-h(T, Po2) = 2.35 x 102 e x p (-1.67/kT) po2 +1/4 9 ( o h m - l c m 1)
[12]
F o r Po2 = 1 a t m , t h i s gives c a l c u l a t e d v a l u e s of 5.84 x 10 -5
o h m - l c m -1 at 1000~ a n d 1.60 x 10 -~ o h m ~cm-' at 900~
T h e c a l c u l a t e d a c t i v a t i o n e n e r g y for h o l e c o n d u c t i o n , Qh,
is 1.67 eV. T h e s e r e s u l t s are c o m p a r e d w i t h t h o s e of H e y n e
a n d B e e k m a n s (9) a n d W e p p n e r (11) i n T a b l e II.
T h e v a l u e s of o-~o~,o-~, a n d o-h are s h o w n t o g e t h e r in Fig. 7.
It is ciear t h a t t h e n-p t r a n s i t i o n p o i n t s s h i f t to l o w e r Po2
v a l u e s as t h e t e m p e r a t u r e d e c r e a s e s .
Steady-state measurement across p- a n d n-type r e g i o n s . These studies were performed by means of steady-state
oxygen permeation measurements in which the p-type
and n-type regions were separated by establishing approp r i a t e c o n d i t i o n s (see Eq. [Sa] a n d [8b]. We also t e s t e d t h e
t w o r e g i o n s w i t h o u t s e p a r a t i o n for t h e 950~ i s o t h e r m ; Fig.
8 s h o w s t h e d a t a p o i n t s (circles) a n d t h e fit f r o m t h e separate runs discussed previously.
Determination of diffusivity and mobility.--The chemical d i f f u s i v i t y a n d e l e c t r o n i c m o b i l i t i e s w e r e d e t e r m i n e d
by using nonsteady-state oxygen permeation measurem e n t s . B o t h p- a n d n - t y p e r e g i o n s w e r e i n v e s t i g a t e d .
Holes (high-po2 r e g i o n ) . - - N o n s t e a d y - s t a t e o x y g e n perm e a t i o n in t h e h i g h Po2 r e g i o n w a s a n a l y z e d b y p l o t t i n g
po2 +1~4vs. t i m e to d e t e r m i n e t h e t i m e lag, ~. F i g u r e 9 s h o w s
t h e p l o t s for (A) e m f vs. t i m e ; w h i c h is s i m i l a r m e t h o d w i t h
K i t a z a w a a n d C o b l e (20), (B) Po2 +'/4 vs. t i m e ; w h i c h w a s
c o n s i d e r e d t h e h o l e c a r r i e r c o n c e n t r a t i o n , i.e., [h'] = po2 +1/4,
a n d (C) Po2 vs. time. A c c o r d i n g to B a r r e r ' s a n a l y s i s for t h e
t i m e lag m e t h o d (14)
[13]
v = X2/6D
w h e r e X is t h e s p e c i m e n t h i c k n e s s . I n t h e i r a n a l y s e s ,
H e y n e a n d B e e k m a n s (18) a n d S m i t h et al. (13) u s e d a Po2
vs. t i m e plot, a n d K i t a z a w a a n d C o b l e (20) m a d e u s e of a n
e m f vs. t i m e plot, to d e t e r m i n e t h e t i m e lag v. I n t h e prese n t s t u d y , a plot ofpo~ +~4 vs. t i m e w a s e m p l o y e d . F r o m t h e
analysis, t h e e m p i r i c a l e q u a t i o n for h o l e c o n d u c t i v i t y i n
8 m / o Y~O3-ZrO2 c a n b e r e p r e s e n t e d as
Table I. Comparison of pre-exponential terms (o-e~ and activation
energies (Qe) for electron conduction
Heyne and
This work,
Beekmans (9) Weppner (11)
Eq. [11]
ae~
i)
Qe(eV)
(re (ohm -I cm ') at 900~
and Po2 = I0 17atm
3.7 • 106
3.7
8.26 x lO-6
--
4.1
4.8 x 10-6
1 . 3 1 x I0v
3.88
4.93 x 10-6
Downloaded on 2016-09-18 to IP 130.203.136.75 address. Redistribution subject to ECS terms of use (see ecsdl.org/site/terms_use) unless CC License in place (see abstract).
J. Electrochem. Soc., Vol. 136, No. 10, October 1989 9 The Electrochemical Society, Inc.
-4.1
-3.0
.
_
(a)
.
.
.
i
1 1024 ~: 1
/
i
2 io17
I
9
3 1011
I
I
4
|
.
i
5 950
9 .~
.
6
916
7
8
900
865
" ',, ~',,"'J.,
"' ",.~,,"-
"-
E
.
989
o
'E
-5.(
o
l
/
|
ale
o
-I
~=
O
E
cO
O
T (~
1 1019.5
2 1013.9
3 976.0
4 950.6
5 973.0
6 925.0
7 902.0
I
J
.i
-4.0
(b)
2871
-6.0
-5.0
-7.0
Ai
-6.0
I
-21
-20
I
-19
I
i
I
I
I
-18
-17
-16
-15
-14
I
-13
-14
-12
log Poe (atm)
Dh(T) = 0.23 e x p ( - 1 . 1 5 eV/kT) (cm2/s)
vs.
[14]
T h e c a l c u l a t e d h o l e d i f f u s i v i t y is 6.39 • 10 -~ cm2/s at
1000~ a n d 9.04 • 10 -7 cm2/s at 800~ T h e c a l c u l a t e d mig r a t i o n e n e r g y for h o l e diffusion, Em.h, is 1.15 eV. T h e h o l e
T (~
1000
950
900
850
-4.0
-4
-2
0
log Po2 for 8 m/o yttria-stabilized zirconia at different temperatures
d i f f u s i v i t y of H e y n e a n d B e e k m a n s ' (9) c a l c i u m - s t a b i l i z e d
z i r c o n i a (CSZ) w a s 8.7 • 10 -6 cm2/s at 1000~ a n d 7.1 • 10 -7
cm2/s at 800~ w i t h a m i g r a t i o n e n e r g y for h o l e d i f f u s i o n
o f 1.24 eV. W e p p n e r (12) o b t a i n e d a h o l e d i f f u s i v i t y at
900~ of 1.5 • 10 ~ cm2/s f r o m v o l t a g e r e l a x a t i o n m e a s u r e m e n t s . B y u s i n g t h e N e r n s t - E i n s t e i n relation, t h e h o l e m o bility c a n b e e x p r e s s e d as
bth(T) = 0.85 e x p ( - 1 . 0 5 eV/kT) (cm2/V 9 s)
[15]
Electrons (low-po2 region).--Similarly, t h e t i m e lag
m e t h o d w a s a p p l i e d to t h e n o n s t e a d y - s t a t e p e r m e a t i o n i n
t h e l o w Po2 r e g i o n b y p l o t t i n g Po2 1/4vs. t i m e (Fig. 11). A f t e r
the gas was switched, the monitored emf did not reach the
e x p e c t e d values. M o r e t h a n 10 r a i n w a s r e q u i r e d to r e a c h
t h e t h e r m o d y n a m i c v a l u e in emf, as is s h o w n in Fig. 11.
N e v e r t h e l e s s , Po2 -1/4 v a l u e s m e a s u r e d a f t e r 30 m i n s h o w e d
a l i n e a r i n c r e a s e w i t h time. B y e x t r a p o l a t i o n f r o m t h e
s t r a i g h t - l i n e p o r t i o n , t h e a p p a r e n t c a l c u l a t e d e l e c t r o n diff u s i v i t y at 1028~ w a s 2.5 x 10 -8 cm2/s. A c c o r d i n g to S m i t h
et al. (13), t h e v a l u e in C S Z at t h i s t e m p e r a t u r e w a s 8 • 10 -8
cm2/s. I n o r d e r to c o n f i r m t h e e l e c t r o n diffusivity, t h e deviation from stoichiometry obtained from a high-temperat u r e s o l i d - s t a t e c o u l o m e t r i c t i t r a t i o n (6) h a s b e e n e m ployed.
% (p02 = 1 atrn)
Q, = 1.67 eV
E
-6
T h i s e x p r e s s i o n yields a h o l e m o b i l i t y of 5.82 • 10 5
cm2/V - s at 1000~ a n d 9.74 • 10 -6 cm2/V 9s at 800~ T h e
c a l c u l a t e d m i g r a t i o n e n e r g y , Eh, is 1.05 eV. F i g u r e 10
s h o w s t h e h o l e d i f f u s i v i t y a n d m o b i l i t y vs. 1/T(K). A c c o r d i n g to W e p p n e r (21), t h e m o b i l i t y at 900~ is 1.5 • 10 -4
cm2/V . s. H o w e v e r , for t h e s e l o w m o b i l i t y values, cond u c t i o n o c c u r s b y a t h e r m a l l y a c t i v a t e d p r o c e s s s u c h as
hopping.
Lines; least-squares fit
-4.5
-8
log P02 (atm)
Fig. 5. Log electron conductivity (a) and log hole conductivity (b)
1050
-10
o
"T
E
eo
_~-5.0
~e (P02= 10-17atm) /
Qe = 3.88 eV
-5.5
Table II. Comparison of pre-exponential terms (sh~ and activation
energies (Qh) for hole conduction
7.6
7.8
8.0
8.2
8.4
104/T (K)
8.6
8.8
Heyne and
This work,
Beekmans (9) Weppner (11) Eq. [12]
9.0
Fig. 6. Temperature dependence of electron conductivity (Po2 = 10 17
arm) and hole conductivity (Po2 = 1.0 arm) for 8 m/o yttrio-stabilized
zirconia.
%0 ( o h m - 1 c m - ' )
Qp(eV)
% ( o h m -1 c r n -1) a t 900~
a n d Po2 = 1.0 a t m
6.6 x 102
1.9
4.51 • 10 -6
-1.85
1.4 x 10 5
2.35 • 102
1.67
1.60 • 10 ~5
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J, Electrochem. Soc., V o l . 136, No. 10, O c t o b e r 1989 9 The Electrochemical Society, Inc.
2872
u
g
- 1
95ooc
2 |I
'
u
n
u
Ion (~on)
x 10 -4
E
qO0~
850~
u
u
1000~
,800~
o
12.
>:
-3
2
'~,
~ ~ 1 0 0 0 oC 4
Electron (ae) /
..,~,~'"
~.~o.
r~
0
-0
~r
,
E
......
1000oC
($e - ~h
--8
0
~
9
~
i
I
I
I
-2
-4
-6
-8
.
/
"
J
I
1%
-10
I
-12
I
-14
-16
0
10
20
Fig. 7. Electron, hole, and ion conductivities in yttria-stabilized zirconia, including data of Burke et al. (10) for 10 m/o yttria-stabilized
zirconia.
~~
n
-4.5
9
i
9
i
30
40
Time (min)
log P02 (atm)
i
u
u
i
Fig. 9. Typical plots used in the gas-switching method to determine
the diffusion coefficient in the p-type region. (A) EMF vs. time, (B)
po2+1/4 vs. time, and (C) Po2 vs. time.
"j
950
-4.2
"
I
n
900
I
9
9
II
850
"
"
'
|
800 ~
I
'
'
,I
i
P02 (ref) = Air
9
~'~ _4. 4
T = 950~
-5.0
~-4.E
--~
-5.5
Specimen
"~":- 4.~
Area, 0.55 cm 2
Thickness, 0.14 cm
-6.0
-5.0
Air
9
I
-16
I
,
I
-12
,
I
I
,
I
,
-8
log P02 (arm)
Fig. 8. Log of experimental steady-state current,
I
,
i
-4
-5.3
i vs.
Heyne and Beekmans (4)
log Po2
9
P~vS. Time
9
PO vs. Time
2
-5.5
Determination of carrier concentration.--By combining
the results of steady-state conductivity m e a s u r e m e n t s and
n o n s t e a d y - s t a t e d i f f u s i v i t y m e a s u r e m e n t s , o n e can o b t a i n
t h e carrier c o n c e n t r a t i o n s o f h o l e s (for h i g h Po2) a n d elect r o n s (for l o w Po2) f r o m Eq. [2a] a n d [2b]).
H o l e s . - - C o m b i n i n g t h e e m p i r i c a l e q u a t i o n for h o l e m o b i l ity, Eq. [15], w i t h t h a t for h o l e c o n d u c t i v i t y , Eq. [12], o n e
o b t a i n s t h e h o l e carrier c o n c e n t r a t i o n
[h'] = 1.72 x 1021 e x p (-0.62 e V / k T ) po2 +u4
[16]
A t Po~ = 1 atm, Eq. [16] yields a h o l e carrier c o n c e n t r a t i o n
o f 6.26 x 10Wcm 3 at 1000~ a n d 3.88 x 10Wcm 3 at 900~
F i g u r e 12 s h o w s a c o m p a r i s o n b e t w e e n s e v e r a l p r e v i o u s l y
r e p o r t e d v a l u e s for h o l e carrier c o n c e n t r a t i o n a n d t h e
p r e s e n t r e s u l t s for Po~ = 1.0, 4 x 10 -2, a n d 10 .8 atm. T h e
v a l u e o f x in Y0.148Zr0.84201.92~+= w a s c a l c u l a t e d f r o m t h e h o l e
c o n c e n t r a t i o n b y u s i n g t h e r e l a t i o n s h i p x = [h']ao'~/4, w h e r e
ao = 5.138A (22)
x = 5.84 x 10 2 e x p (-0.62 e V / k T )
[17]
T h u s at Po2 = 1 atm, x = 2.12 x 10 -4 at 1000~ a n d x = 1.32
x 10 -4 at 900~ W e p p n e r (15) r e p o r t e d a h o l e c o n c e n t r a t i o n
E
o
~:~- 5.7
//' 9
'~
This Study
o
"e,~,~. 11sev
"
~
-5.9
,
8.0
.
.
.
8,2
.
8.4
" 8.6
8.8 " 9.0
104/T (K)
9.2
' 9.4
Fig. 10. Temperature dependence of (A) hole mobility and (B) hole
diffusion coefficient, as determined by the time lag method.
o f 6.3 x 10Wcm 3 at 900~ a n d Po2 = 1 a t m (Fig. 12, c u r v e D),
w h i c h c o r r e s p o n d s to a n x v a l u e o f 2.1 x 10 -~.
E l e c t r o n s . - - A n e l e c t r o n diffusivity, De, o f 3.7 x 10 -6 cm2/s
(at 1028.5~ w a s o b t a i n e d b y u s i n g t h e t i m e lag m e t h o d .
T h e m o b i l i t y c a l c u l a t e d f r o m t h e d i f f u s i v i t y is 3.3 x 10 ~
cm2/V - s. F r o m t h e s t e a d y - s t a t e e x p e r i m e n t a l results, Eq.
[11] a n d mobility, w e can o b t a i n t h e e l e c t r o n c o n c e n t r a tion; at Po2 = 10-14 a t m a n d 1028.5~ is [e'] = 7.34 x 1018/cm 3
(or x = 1.24 x 10-4). B y c o m p a r i s o n , at this t e m p e r a t u r e
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J. Electrochem. Soc., Vol. 136, No. 10, October 1989 9 The Electrochemical Society, Inc.
1050
1000 T (~
-4.0
X
9.5 x 10".
A
950
920
Solid State Coutometric Titration ref (6) -
"~
.OO
2873
~
(P~= 10"14arm)
"~H
T =1028.5~
.
~= 3.98 eV
Switching Method
90% CO2-CO + 500/0 CO2-CO
_4.,=
g
.~ 9.0 x 102 "
-
Eo
~-5.c
8.5
x
-5.5
9
x
2.00eV
Time Lag
oJ~
8.0
,~=
Method
102
-6.C
0.0
0.5
1.0
Time (hr)
I
2.0
1.5
I
1200
I 9
1000900
800
I I
I
,
i
8.2
8.4
l
T h e e l e c t r o n c a r r i e r c o n c e n t r a t i o n for Y S Z , c a l c u l a t e d
f r o m [e'] = (8X/ao3), is [e'] = 1 . 0 4 • 1023 e x p ( - 1 . 9 9 e V / k T )
po2 -'/4. T h u s , at Po2 = 10-i4 arm, [e'] = 4.31 x 10Wcm 3 at
1000~ a n d 9.18 x 1017/cm 3 at 900~ F o l l o w i n g t h e calculat i o n of t h e e l e c t r o n c a r r i e r c o n c e n t r a t i o n , t h e e l e c t r o n diff u s i v i t y a n d m o b i l i t y are c a l c u l a t e d . F i g u r e 13 s h o w s log x
(6), log ~e, a n d log De vs. 1/T(K) for t h e n - t y p e region. F i g u r e
14 c o m p a r e s t h e c h e m i c a l d i f f u s i v i t y d a t a f r o m t h i s s t u d y
w i t h p r e v i o u s l y r e p o r t e d data. B y c o m b i n i n g t h e steadystate measurements and the present data on electron and
hole mobilities, we can calculate the carrier concentrations
of t h e e l e c t r o n s a n d holes. T h e r e s u l t s o f t h e s e c a l c u l a t i o n s
are s h o w n i n Fig. 15. T h e c o n c e n t r a t i o n s of h o l e s a n d elect r o n s are c o m p a r a b l e w i t h t h o s e of o t h e r c o n v e n t i o n a l
m e t a l o x i d e s y s t e m s (24) s u c h as CeO2 x (25) a n d NiO,+=
(26) in t h i s t e m p e r a t u r e a n d Po2 region, b u t t h e m o b i l i t i e s
19
P
E
~
o.
~ * ' 4 x 10 -2 atm
.9
17
8
I
8.0
700~
A
">
,
Fig. 13. Temperature dependence of (A) deviation from stoichiometry, x; (B)-electron mobility; and (C) diffusivity in the n-type region of
8 m/o yttria-stabilized zirconia.
2o
16 5
I
7.8
104/T (~
Fig. 11. Po2-1/4 VS. time in n-type region
1500
,
7.6
;
10
I
104/T (K)
Fig. 12. Temperature dependence of hole concentration in yttriastabilized zirconia and comparison with previously reported values.
A = Smith et al., Po2 = 10-6 atm (13), B = Heyne and Beekmans, air/
CSZ/vacuum (9), C = Kitazawa and Cable, Po2 = 10 3.5 atm (20),-this study.
1200
I
x ( T , Po2) = 1.75 e x p ( - 1 . 9 9 eV/kT) po2 -'/4
I 9
T (~
900
I
--~
~-
a n d Po2- E q u a t i o n [7] gives [e'] = 1.37 x 10'9/cm 3 (or x = 2.32
x 10 %
S i n c e t h e n o n s t e a d y - s t a t e m e a s u r e m e n t s i n t h e l o w Po2
r e g i o n w e r e n o t precise, t h e r e s u l t s o f h i g h - t e m p e r a t u r e
s o l i d - s t a t e c o u l o m e t r i c t i t r a t i o n m e a s u r e m e n t s o n 8 m/o
Y203-ZrO2 (6) w e r e also u s e d to d e t e r m i n e t h e e l e c t r o n carrier c o n c e n t r a t i o n . I n t h e f o r m u l a Y0.,48Zr0.8520, 926 =, x w a s
r e p r e s e n t e d as (6)
1000
__!
~ ~
IZL~ ,I~i~%"~ ~
800
9
700
I
A
B
C
D
E
9
9
a-6
O
I
Smithe~al.(13)
" ,
Heyne and Beekmans (9)
Kitazawa and Cable (20)
Palguev et al. (23)
Weppner (12)
This Study (hole)
This Study (electron)
E
-7
[18]
T h i s y i e l d s x v a l u e s at 1000~ o f 2.31 x 10 -8 at Po2 = 1 a t m ,
a n d 79 x 10 .5 at 10 ,4 atm. A t 900~ t h e v a l u e s are 4.92
• 10 -9 a n d 1.56 • 10 -~, r e s p e c t i v e l y . F i g u r e 12 ( c u r v e A)
s h o w s t h e r e s u l t s of t h e s o l i d - s t a t e c o u l o m e t r i c t i t r a t i o n
(6).
6
7
8
9
104/T (K)
10
11
Fig. 14. Comparison of temperature dependence of diffusion coefficient in yttria-stabilized zirconia with previously reported values.
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2874
d. Electrochem. Soc., Vol. 136, No. 10, October 1989 9 The ElectrochemicalSociety,Inc.
2O
o
~9
~'~
."
~
-_
[h'l
[20a]
~h = ~h~ e x p ( - E h / k T )
[20b]
w h e r e ~e~ a n d ~h~ are t h e p r o p e r p r e - e x p o n e n t i a l cons t a n t s , a n d Ee a n d Eh r e p r e s e n t t h e e l e c t r o n a n d h o l e migration energies.
B y c o m b i n i n g Eq. [19a] w i t h [20a] a n d Eq. [19b] w i t h
[20b], a n d i n s e r t i n g t h e r e s u l t s into Eq. [2a] a n d [2b], w e obtain t h e f o l l o w i n g r e l a t i o n s
o
o
~ = ~~ exp (-QJkT)po2
o
--
~e = ~e~ e x p ( - E e / k T )
and
16
lt4
[21a]
and
15
I
I
i
I
I
I
-16 -14 -12 -10 -8 -6
logp%(atm)
Fig. 15. Concentration of electrons and hales
temperatures in yttria-stabilized zirconia.
-4
I
-2
~h = ~h~ e x p ( - Q h / k T ) po2 +1/4
0
w h e r e t h e p r e - e x p o n e n t i a l t e r m s are
~ ~ = [e'o]~ ~ Iql
[22a]
(Th~ = [h'o] b~h~
[225]
log po~ at different
vs.
and
o f e l e c t r o n s a n d h o l e s are m u c h l o w e r in our s p e c i m e n .
T h e ionic t r a n s f e r e n c e n u m b e r , t~o~,is g r e a t e r t h a n 0.99 a n d
t h e m a t e r i a l h a s a h i g h e r ionic c o n d u c t i v i t y . C o n s e q u e n t l y , t h e e l e c t r o n i c t r a n s f e r e n c e n u m b e r , t~, o f 0.01, as
w e l l as t h e e l e c t r o n i c c o n d u c t i v i t i e s , are s i g n i f i c a n t l y
l o w e r t h a n in o t h e r m e t a l o x i d e s . F o r m a t e r i a l s e x h i b i t i n g
h i g h ionic c o n d u c t i o n , s u c h as Y S Z a n d CSZ, e l e c t r o n i c
conduction may be suppressed. The trapping of mobile
e l e c t r o n i c carriers ( e l e c t r o n s a n d holes) on lattice sites
m a y a c c o u n t for g o o d e l e c t r o l y t e b e h a v i o r . This p o s s i b i l i t y
has been investigated and the results show that such low
c o n d u c t i v i t i e s are n o t l i m i t e d b y t h e carrier c o n c e n t r a t i o n ,
as in o t h e r m e t a l o x i d e s y s t e m s w h i c h h a v e h i g h e l e c t r o n i c
conductivities.
W h e n t h e m o b i l e e l e c t r o n i c s p e c i e s are t r a p p e d o n t h e
lattice sites, u s e f u l B o l t z m a n n statistics for m o b i l e elect r o n s a n d h o l e s m a y b e applicable.
W h e n a Y S Z s p e c i m e n is in e q u i l i b r i u m w i t h o x y g e n at
e l e v a t e d t e m p e r a t u r e s , t h e o x y g e n is i n c o r p o r a t e d a c c o r d ing to t h e reaction, Eq. [4a] a n d [4b]
1 / 2 0 o ~ + 1/2 Vo'- = 1/4 Oe(g) + e',
T h e a c t i v a t i o n e n e r g i e s for t h e c o n d u c t i v i t i e s are
Q~ = AH~ ~ + E~
[23a]
Qh = AHh~ + Eh
[23b]
and
r e s p e c t i v e l y . T a b l e III s h o w s t h e m o d e l a n d e m p i r i c a l
equations that were obtained by combining the results on
electrical c o n d u c t i v i t i e s a n d m o b i l i t i e s o f m i n o r i t y c o n s t i t u e n t s for 8 m/o Y203-ZrO2.
The carrier concentrations were calculated by combining t h e e q u a t i o n s for c o n d u c t i v i t y a n d m o b i l i t y for e a c h
t y p e o f e l e c t r o n i c defect. F o r e l e c t r o n s
[e'] = a J g e q = ( ~ o / ~ o q ) e x p [ - ( Q e
- E~)/kT] Po2 -1/4
[26a]
a n d for h o l e s
[h'] = ffh/P.hq = (gh~176
e x p [-(Qh - Eh)/kT] po2 +1/4 [26b]
T h e p r o d u c t o f t h e t w o e l e c t r o n i c d e f e c t c o n c e n t r a t i o n s is
nile ~
[e'][h'] = (%(rh/p.~h)/q 2
at low Po~ (n-type region), or
2] e x p [-(Q~ + Q h - E~ - E h ) / k T ]
= [((re~176176176
1/2 Vo" + 1/4 O~(g) = 1 / 2 0 o • + h',
AHh~
[19a]
po~ - ~
[e'][h'] = N ~ v e x p ( - E r / k T )
n~ = ~
]
= ~/(NcN~) e x p ( - E f / k T )
w h e r e [e'o] a n d [h'o] d e n o t e t h e p r e - e x p o n e n t i a l c o n s t a n t s .
F r o m Eq. [2a] a n d [2b] a n d t h e a s s u m p t i o n t h a t t h e m o b i lities d o n o t d e p e n d u p o n c o n c e n t r a t i o n , w e a s s u m e t h e
expressions
[28]
B y c o m p a r i n g Eq. [27a] a n d [27b], w e get
Ef = Q~ + Qh - Ee - Eh
[19b]
§
[27b]
w h e r e Nc a n d N~ are t h e e f f e c t i v e d e n s i t y o f s t a t e s for elect r o n s a n d holes, r e s p e c t i v e l y , a n d Ef is t h e e l e c t r o n - h o l e
pair f o r m a t i o n e n e r g y . H e n c e t h e i n t r i n s i c carrier c o n c e n t r a t i o n is g i v e n b y
and
[h'] = [h'o] e x p ( - A H h ~
[27a]
which has the form
at h i g h Po~ (p-type region), w h e r e AH~~ a n d h H h ~ are t h e rea c t i o n e n t h a l p i e s o f t h e p r o p o s e d d e f e c t r e a c t i o n s at l o w
a n d h i g h Po~, r e s p e c t i v e l y . I f w e a s s u m e t h a t (i) e l e c t r o n s
a n d h o l e s e x h i b i t i d e a l - s o l u t i o n b e h a v i o r a n d (ii) t h e elect r o n a n d h o l e c o n c e n t r a t i o n s are n e g l i g i b l e c o m p a r e d w i t h
t h e d o p i n g a m o u n t of y t t r i u m [Y'zr], w e m a y e x p r e s s t h e
e l e c t r o n e u t r a ] i t y as [Y'z~] = 2 [ V o " ]. We t h e n o b t a i n t h e relations
[e'] = [e'o] e x p ( - A H ~ ~
[21b]
[29]
and
[30]
N~N~ = ((re~176176176
N o t e t h a t at Po2 = 1 atm, t h e i n d i v i d u a l e f f e c t i v e d e n s i t i e s
o f s t a t e are g i v e n b y
Table III. Mobilities and conductivities of minority constituents in 8 m/o Y203-Zr02
Model equations
~e = ~e~ exp ( - E e / k T )
~h = ~h~ exp (-Eh/kT)
ere = c%~ exp ( - Q J k T ) po2 -114
ah = ~h~ exp (-Qh/kT) po2§
Empirical equations
[20a]
[20b]
[21a]
[21b]
t~e = 8.02 • 102 exp (-1.89/kT)
~h = 0.85 exp (-1.05/kT)
(~e = 1.31 • 10 exp (-3.88/kT) Po2
Crh= 2.35 • 102 exp (-1.67/kT) Po2+1/4
[24]
[25]
[11]
[12]
Where ~ = mobility (cm2/V. s), E = migration energy (eV), k = Boltzmann constant, 8.614 • 10-5 eV/deg, ~ = conductivity (ohm -I cm-1),
Q = activation energy (eV}, and subscripts e and h designate electrons and holes, respectively.
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Soc., Vol. 136, No. 10, O c t o b e r 1989 9 The Electrochemical Society, Inc
J. E l e c t r o c h e m .
N~ = (%~176
for h o l e s
2875
[31a]
T (~
900
1000
and
9
N c = ((reO/p~e~ for e l e c t r o n s
[31b]
.
.i
I
"
.
I
800
.
9
..... f " ~ .
Lattice
NcNv = [16 y(1 - y)/ao 6] = ((~ o/~ Oq)((~ o/~ oq)
[33]
w h e r e q is t h e c h a r g e o f t h e e l e c t r o n a n d y is 0.148 for 8 m/o
Y~O~-ZrO~, i.e., Y0.~Zr0.8~20,9~6. It w a s a s s u m e d t h a t t h e
e l e c t r o n s are t r a p p e d o n t h e n o r m a l z i r c o n i u m site as
(Zrz~• - e')'. B e c a u s e t h e e l e c t r o n m o b i l i t y e x h i b i t e d t h e
b e h a v i o r o f a t h e r m a l l y a c t i v a t e d p r o c e s s , t h e h o l e s are
also c o n s i d e r e d to b e t r a p p e d o n a p p r o p r i a t e lattice sites.
H e r e it is a s s u m e d t h a t t h e h o l e is t r a p p e d at t h e y t t r i u m
i o n o n a z i r c o n i u m site, i.e., (Y'z~ - h')~ a l t h o u g h t h e r e are
s e v e r a l p o s s i b l e sites for h o l e t r a p p i n g in t h e lattice, only
o n e m a y p r e d o m i n a t e , i.e., t h e o n e w i t h t h e s t r o n g e s t b i n d i n g b e t w e e n h o l e s a n d sites. T a b l e IV s h o w s t h e e f f e c t i v e
d e n s i t y o f s t a t e s for h o l e s (N,) a n d for e l e c t r o n s (N~) for t h e
s p e c i m e n . T h e c a l c u l a t e d v a l u e s for t h e e x p e r i m e n t a l l y
o b t a i n e d e f f e c t i v e d e n s i t y of s t a t e s for h o l e s is 2.5 t i m e s
smaller than the values calculated from the lattice model.
The effective density of states for electrons is 3.9 times
larger than the values calculated from the lattice model.
T h e agreement between the experimental and theoretical
values is considered reasonable. T h e hopping of electrons
from one trapped site to another site occurs by thermal excitation. That is,the electron hops from one trapping zircon i u m site, (Zrz~~ - e')',to a neighboring normal zirconium
site, Zrz~K Similarly, a hole trapped by yttrium on a zircon i u m site,(Y'z~ - h')~ can hop to normal yttrium on a zircon i u m site,Y'z~. F r o m Eq. [2a] and [2b],[4a] and [4b],and [33],
w e can calculate the electron-hole pair formation energy,
i.e., E~ = 2.61 eV, b y a d d i n g t h e r e a c t i o n s
1/2Oo ~ = 1/4 O2(g) + 1/2Vo-- + e'
(AHe~ = 1.99 eV)
1/2 Vo'" + 1/4 02 (g) = 1 / 2 0 o ~
+
h"
(AH~~ = 0.62 eV)
nil =
e'
+ h"
o
Ef = 2.61 e V
w h e r e AHe~ = [Qe - Eel in Eq. [12] a n d [25] a n d AHh~ =
[Qh - Eh] in Eq. [11] a n d [24]. T h e p r o d u c t o f t h e e f f e c t i v e
d e n s i t y o f s t a t e s (N~N~) has a v a l u e o f 1.7 x 1044/cm 6 as calc u l a t e d f r o m t h e p r e - e x p o n e n t i a l t e r m s in t h e e m p i r i c a l
e q u a t i o n s , a n d a v a l u e o f 1.10 x 1044/cm 6 as c a l c u l a t e d f r o m
t h e lattice m o d e l (Table IV).
.
9
~
9
Ernpirica,Equation
16
,
9
9
,
I
9
,
9
.
I
.
1
(b)
[32b]
w h e r e w e a s s u m e t h e e l e c t r o n s to b e t r a p p e d on o n e o f t h e
f o u r p o s s i b l e n o r m a l z i r c o n i u m sites f o r m i n g a (Zrzr • - e')'
c o m p l e x . T h e p r o d u c t o f Eq. [32a] a n d [32b] is t h e f o l l o w i n g
equation
.
~"~
Model
[32a]
N~ = [4(1 - y)/ao 3] (cm -3)
I
= 1.30s eV
ao
in w h i c h w e a s s u m e t h a t t h e h o l e is t r a p p e d at t h e y t t r i u m
l o c a t i o n o n o n e o f t h e f o u r p o s s i b l e z i r c o n i u m sites in t h e
u n i t cell o f Zrl_yY~O2_y/2. T h i s gives a (Y'zr -- h') ~ c o m p l e x .
Similarly
.
(a)
T h e e f f e c t i v e d e n s i t i e s o f s t a t e s o f e l e c t r o n s a n d holes, Nr
a n d N~, in t h e fluorite c u b i c s t r u c t u r e c a n b e d e s c r i b e d in
t e r m s o f t h e p o s s i b l e t r a p p i n g sites a n d lattice p a r a m e t e r ,
Nv = [4y/ao 3] (cm -3)
I
8,
= 2.74eV
.~
4.42 eV
o. -10
o
-11
~
~
-1:
,
7
"*..
I
. . . .
8
I
9
*r, ,
I
10
104/T (K)
Fig. 16. Temperature dependence of (a) intrinsic carrier concentration and (b) oxygen partial pressure for ~ = ~h and [e'] = [h'], for 8
m/o Y203-ZrO2.
F i g u r e 16a s h o w s a p l o t o f ~ ]
vs. 1/T a n d Fig. 16b
s h o w s a p l o t o f log Po2 vs. 1/T for t h e v a l u e s o f ~e = ~h" a n d
[e'] = [h']. B e c a u s e t h e e l e c t r o n m o b i l i t y is l o w e r t h a n t h e
h o l e m o b i l i t y o v e r t h e r e g i o n o f i n t e r e s t , t h e ~e = ~h c u r v e
is l o w e r t h a n t h e [e'] = [ h ] curve. This i n d i c a t e s t h a t t h e
e l e c t r o n m i g r a t i o n e n e r g y , E~ is h i g h e r t h a n t h e h o l e mig r a t i o n e n e r g y , Eh.
C o m p a r i s o n o f optical a b s o r p t i o n d a t a w i t h the combined d a t a f r o m the above a n a l y s i s . - - T h e e l e c t r o n - h o l e
p a i r f o r m a t i o n e n e r g y o f 2.61 e V for t h e e x p e r i m e n t a l t e m p e r a t u r e r a n g e (850~176
a g r e e s r e a s o n a b l y well w i t h
t h e optical gap e n e r g y of 2.7-2.8 e V (16). A s l i g h t l y h i g h e r
optical g a p e n e r g y is e x p e c t e d a c c o r d i n g to t h e F r a n k C o n d o n p r i n c i p l e , w h i c h s t a t e s t h a t t h e optical gap e n e r g y
is n o t l o w e r t h a n t h e t h e r m a l g a p e n e r g y (27).
Acknowledgment
This w o r k w a s s u p p o r t e d b y t h e U.S. D e p a r t m e n t o f
E n e r g y , Office o f Basic E n e r g y S c i e n c e s , u n d e r C o n t r a c t
W-31-109-Eng-38.
M a n u s c r i p t s u b m i t t e d J u l y 21, 1988; r e v i s e d m a n u s c r i p t
r e c e i v e d M a r c h 5, 1989.
A r g o n n e N a t i o n a l L a b o r a t o r i e s assisted in m e e t i n g the
p u b l i c a t i o n costs o f this article.
REFERENCES
1. T. T a k a h a s h i , in " P h y s i c s o f E l e c t r o l y t e s , " J. Hladik,
Editor, p. 989, A c a d e m i c P r e s s (1972).
2. H. H. M o b i u s , Z. Chem., 4, 81 (1964).
Table IV. Comparison of the effective density of states calculated from the lattice model and from empirical equations for holes (N,) and
electrons (No) in an 8 m/o Y203-ZrO2 specimen ~
Effective density of states, Nv or Nr
Empirical equations
Lattice model
(Po2 = 1.0 atm)
Holes (Y'zr h') ~
Electrons (Zrzrx - e')'
NvN~
(NvNc)1/~
[4y/ao 3] = 4.36 • 1021/cm3
y)/ao 3] = 2.51 x 1022/cm3
i.i0 x 1044/era~
[4(1
1.05 • 1022/cm~
((rh~176
((~e~
= 1.72 • 1021/cm~
= 9.89 • 1022/cm3
1.71 X 1044/cm~
].31 • 1022/cm3
aThe following nonstoichiometric defect reactions were assumed: for low Po2 regions, 1/20o x = 1/4 02 (g) + Vo'" + e' [4a], for high Po2 regions, 1/2 Vo" + 1/2 02 (g) = 1/20o x + h" [4b].
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Sorensen, Editor, Chap. 6, Academic
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York (1982).
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The Molecular-Level Interpretation of Salt Uptake and Anion
Transport in Nation Membranes
Scott W. Capeci 1 and Peter N. Pintauro*
Department of Chemical Engineering, Tulane University, New Orleans, Louisiana 70118
Douglas N. Bennion*
Department of Chemical Engineering, Brigham Young University, Provo, Utah 84602
ABSTRACT
The idealized " c l u s t e r - n e t w o r k " structure for Nation | cation e x c h a n g e m e m b r a n e s has b e e n used to g e n e r a t e molecular-level m o d e l s for m e m b r a n e salt solubility and anion transport. E q u i l i b r i u m salt u p t a k e by Nation was f o u n d to be dep e n d e n t on the size and wall c h a r g e of t h e m e m b r a n e ' s i n v e r t e d micelle clusters. T h e a n i o n / m e m b r a n e binary interaction
t r a n s p o r t p a r a m e t e r was d e p e n d e n t on m e m b r a n e tortuosity and the electrostatic r e p u l s i o n forces in t h e n a r r o w pores
w h i c h i n t e r c o n n e c t the i n v e r t e d micelles. T h e salt solubility m o d e l p r e d i c t e d m e m b r a n e cation c o n c e n t r a t i o n s to w i t h i n
8% for e x t e r n a l NaC1 c o n c e n t r a t i o n s of 1.0-5.0M. The t r a n s p o r t analysis accurately p r e d i c t e d the c o n c e n t r a t i o n depende n c e of t h e C1 / m e m b r a n e binary interaction parameters.
Phenomenological transport models have been used
successfully to analyze mass transfer in reverse osmosis
(1-3) and ion e x c h a n g e m e m b r a n e s (4-6). T h e s e m o d e l s are
e m p i r i c a l in n a t u r e and v i e w t h e m e m b r a n e as a " b l a c k
b o x " t h r o u g h w h i c h solute and solvent move. On first inspection, the p h e n o m e n o l o g i c a l e q u a t i o n s a p p e a r to give
no insight into structure/function relationships for m e m b r a n e transport. This, however, is not entirely correct.
P h e n o m e n o l o g i c a l coefficients can be related m a t h e m a t i cally to t h e traditional transport p a r a m e t e r s of m e m b r a n e
conductivity, diffusion coefficient, and t r a n s f e r e n c e n u m ber (6). In s o m e cases t h e s e m a c r o s c o p i c p a r a m e t e r s h a v e
b e e n related to the m i c r o s t r u c t u r e of m e m b r a n e s , e.g., the
use of percolation t h e o r y to e x p l a i n the electrical conductivity of Nation m e m b r a n e s (7). In this p a p e r w e seek struct u r e / f u n c t i o n correlations for two p a r a m e t e r s w h i c h app e a r in the set of p h e n o m e n o l o g i c a l t r a n s p o r t e q u a t i o n s
for an ion e x c h a n g e m e m b r a n e . T h e s e p a r a m e t e r s are the
m e m b r a n e salt solubility and the p h e n o m e n o l o g i c a l transport p a r a m e t e r w h i c h describes a n i o n / m e m b r a n e interactions.
* Electrochemical Society Active Member.
Present address: Shell Oil Company, P.O. Box 10, Norco, Louisiana 70079.
2 Nation is a registered trademark of E.I. du Pont de Nemours &
Company for its perfluorinated sulfonic acid products.
In order to g e n e r a t e structure/function models, the mic r o s c o p i c structure of a m e m b r a n e m u s t be k n o w n , there
m u s t be sufficient e x p e r i m e n t a l m e m b r a n e transport and
solubility data to accurately characterize m e m b r a n e performance, and m o d e l s (either e m p i r i c a l or f u n d a m e n t a l in
nature) m u s t be p r o p o s e d to interrelate the data with
m e m b r a n e structure.
A particularly interesting m e m b r a n e to e x a m i n e from a
s t r u c t u r e / f u n c t i o n v i e w p o i n t is the Nation cation exc h a n g e m e m b r a n e s , m a n u f a c t u r e d b y E. I. du P o n t de
N e m o u r s & C o m p a n y . T h e s e perfluorosulfonic acid m e m branes h a v e b e e n u s e d f r e q u e n t l y in e x p e r i m e n t a l salt solubility and transport studies and their m i c r o s t r u c t u r e is
relatively well understood. Theories on the molecularlevel structure of Nation center a r o u n d t h e highly idealized " c l u s t e r - n e t w o r k " m o d e l p r o p o s e d by G i e r k e in 1977
(8). In his work, G i e r k e describes Nation as a series of ionic
clusters or i n v e r t e d micelles, i n t e r c o n n e c t e d by n a r r o w
pores. A s c h e m a t i c d i a g r a m of Nation's c l u s t e r - n e t w o r k
s t r u c t u r e is s h o w n in Fig. 1. When w a t e r enters into Nation, it is repelled from t h e h y d r o p h o b i c tetrafluor o e t h y l e n e b a c k b o n e and attracted to the sulfonate fixedcharge sites. I n order for a s!gnificant a m o u n t of w a t e r to
be a c c o m m o d a t e d into t h e m e m b r a n e , a large n u m b e r o f
ion-sites m u s t cluster t o g e t h e r and shield t h e w a t e r f r o m
t h e p o l y m e r b a c k b o n e . F i x e d - i o n clustering in w e t Nation
has b e e n indicated by a variety of physical m e a s u r e m e n t s ,
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