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Impurity diffusion in NiO grain boundaries
J. Phys. C&m. Solids Vol. 47, No. 3, pp. 315-323, Printed in Great Britain.
IMPURITY
1986
DImSION
~22-3#9?/S6 $3.00 + .@I 0 1986 Persrunon Prm Ltd.
IN NiO GRAIN
BOUNDARIES
A. ATKINSON ~~~R.I.TAYLoR Materials Development Division, Building 552, AERE HaNveIl, Dideot, Oxon OX1 I ORA, U.K.
Abstract--The di~sion of ‘3vCeand S’Cr in polyc~~line NiO has been studied in the tem~mtu~ range 600-l 100°C in oxygen at a pressure of I atm. These impu~ti~ were chosen because of their different effective charges and segregation behaviour and because of their reievauce to the oxidation of metals at elevated temperature. The solubility of Ce in the NiO lattice is neghgibie, but Ce is soluble at NiO grain boundaries and diskrcations. ~~n~uently Ce tracer only diEused along these pathways and the resulting profiles were analysed s~ai~tfo~ard~y to give grain boundary and dislocation diffusion coefficients. The lattice solubility of Cr, on the other hand, is not negligible and Cr also segregates strongly to NiO grain boundaries. A procedure for analysing penetration profiles of such an impurity has been developed in which parameters describing segregation and gram boundary diffusion are deduced self-consistently. When combined with previous measurements of Ni and Co diffusion it is found that grain boundary coetlicients decrease in the order Co, Ni, Cr, Ce as is also found for Iattice dithrsion (except for Ce, which has negligible lattice
solubilityf. The implication of the results for the distribution of Cr and Ce in NiO films formed by metal oxidation is also discussed. ~e_~urd~: impu~ty scion, cerium.
nickel oxide, gram boundary dithrsion, grain boundary section,
The diffusion of material along grain boundaries is now known to control many processes involving transport in oxides such as creep, sintering and chemical reactions. For example it has been shown [I] that the growth of NiU films by thermal oxidation of Ni is controlled by the outward diffusion of Ni along grain boundaries in the NiO film. There is strong evidence that this type of behaviour is quite general and that grain boundary diffusion controls the growth of most corrosion-resistant oxide films. When an oxide film grows on an elementaf metal substrate, diffusion of only oxygen and the metal ion in the oxide need be considered. However, in nearly all cases of practical interest the oxide film grows on an ahoy (e.g. a stainless steel), or in the presence of additives deliberately introduced in the form of a surface treatment (e.g. a coating), In such cases the foreign elements influence the defect populations and transport properties of the host oxide in a way which depends on their distribution within the film. This dist~bution is controlled by the transport properties of the foreign dements within the film and this will also occur mainly by diffusion along grain boundaries. ft is therefore important to have some appreciation of how foreign ions diffuse in oxide boundaries as well as the constituent ions of the host oxide. Nickel oxide is suitable for such a study because it is a good model for oxides which form corrosion-resistant films on metals and because a substantial body of data and understanding already exists for this oxide. Data for diffusion of Ni in the NiO lattice are in good agreement 12, 31 and it has been established that dif-
chro~um,
fusion takes place by a vacancy mechanism [4]. Diffusion of 0 in the NiO lattice is not as well-understood and both oxygen vacancies and interstitials may be contributing [.S]. Data are also available for diffusion of Ni [6] and 0 [7] alang NiO gram boundaries. The experiments suggest that Ni grain boundary diffusion also takes place by a vacancy mechanism and this conclusion is supported by theoretical calculations of the properties of simple boundaries [S]. There have also been two earlier studies of impurity diffusion in NiO bounda~es. Chen and Petersen [9] measured the diffusion of Co and Cr radiotracers along grain boundaries in NiO bicrystals and large-grained polycrystalhne specimens. Atkinson and Taylor f to] measured Co radiotmcer diffusion along grain boundaries in finegrained polycrystalline NiO films. The two sets of data for Co diffusion are not in agreement, for reasons which are not clear. The objective of the work described here is to extend the me~uremen~ of grain boundary diffusion in finegrained polycrystalline NiO films to other ions of interest in oxidation processes, specifically Cr and Ce, The impu~ty ions Co’+, C#’ and Ce4’ cover a range of characteristics and most other impu~ties are likely to behave similarly to one or another from this group. Co is typical of an impurity which is completely soluble in the oxide lattice and does not segregate appreciably to grain boundaries. Ce has the extreme opposite behaviour in that its lattice solubility is negligible and it is only soluble at grain boundaries. The transport properties of this ion are relevant to understanding the way in which CeOz coatings reduce the rate of NiO growth on Ni. Cr is intermediate between these two extremes. It has slight lattice sohtbility and is known 315
316
A.ATKINSON andR.I.TAYLOR
to segregate appreciably to NiO grain boundaries. Its transport properties are relevant to the oxidation of Ni-Cr alloys. 2. THEORY
The theoretical model of a grain boundary which is normally used for analysing diffusion experiments considers it as a uniform slab, of width 6, (and perpendicular to the external surface) in which the diffusion coefficient, D’, is greater than that in the surrounding lattice, D. Diffusion from the external surface is a combination of fast diffusion along the boundary and slow diffusion sideways out of the boundary. The kinetics of the diffusion process are mainly dependent on two factors. The first is the boundary condition at the external surface; that is, whether the surface concentration is maintained constant or whether the total quantity of difIusant is maint~ned constant (in the limit this becomes the ‘thin film’ boundary condition). The second factor is the extent of lattice diffusion (characterised by (Dt)“‘) in comparison with other characteristic dimensions of the system such as 6 and grain size, g, We will use Harrison’s [ 1 l] terminology for the three types of kinetic regime which result from this second factor. Type A diffusion occurs in the limit of long times, when (&)‘I2 % g and the lattice and grain boundary diffusion processes are simply averaged out. None of the experiments reported here fall into this category. Type B diffusion occurs when most of the diffusant is in the lattice, but the concentration distributions from neighbou~ng grain boundaries do not interact. Type C diffusion occurs in the limit of short times when diffusion in the lattice is negligible and all the diffusant is retained in the boundary. The different surface boundary conditions were originally treated by Whipple [ 121 and Suzuoka [ 131 for the constant ~oneentmtion and thin-source cases respectively. In the present experiments we are in principle only concerned with the thin-source boundary condition and the solution for the average concentration of diffusant as a function of depth, as would be measured in a sectioning experiment. The original solution of Suzuoka for type B diffusion was modified by Atkinson and Taylor [6] to include the diffusant within the boundary and thereby cover both types B and C. The average concentration in the sectioning experiment may then be written in the form
C = K(~~~)-1’2[ex~-~z/4)
+ i (err + cu,)]
(1)
where 9 = y/(Df)L’2, y is the depth below the surface, Kis the concentration of diffisant per unit area initially on the surface and n = g/(4Dt)‘f2. The exponential term is the normal ~ont~bution from lattice diffusion in the absence of grain boundaries, cii describes the additional contribution from diffusant in the lattice associated with the grain boundary and ciii accounts for the diffusant within the boundary itself. Expressions
for C?irand cu,,,have been given for the case when the diffusant does not segregate at the boundary (that is, self-diffusion). LeClaire [ 141 has modified these expressions to account for segregation as is necessary when analysing results of impurity diffusion. Segregation is assumed to be characterised by a linear isotherm with segregation coefficient, s, equal to the concentration in the boundary divided by the concentration in the lattice. The resulting expressions for C?i,and C,,, are
X [F’/2exp(-X2)
- X erfcX] $
(2)
and
X erfcX :
.
(3)
The parameters in eqs (2) and (3) have the following definitions: 6
oc=201/2
/I=($ I)*
When eqns (2) and (3) are compared with the equivalent expressions in ref. [6] it is evident that the effect of segregation is simply to replace cxby so1.Thus the boundary behaves as if its width were increased by a factor equal to s and the transition from type R to type C diffusion occurs when s6 N 2(Dt)“‘. When analysing penetration profiles it is important to know whether the kinetics are type B or type C since asymptotic forms ofthe solutions are usually employed. In the case of type B diffusion the asymptotic solution predicts log cocy6f5 and the slope of such a plot gives p and, eventually, sD’6 if D is known [ 151:
The experiments of Co diffusion in NiO reported previously [lo] were analysed in this way. The asymp-
Impurity diffusion in NiO grain boundaries totic solution for type C diffusion predicts log ccc y2. The experiments of Ce diffusion described below have been analysed assuming type Cdiffusion, since the solubility of Ce in the NiO lattice is believed to be negligible. In the case of Cr diffusion, however, the analysis is not straightforward because of its intermediate behaviour. One does not know a priori whether diffusion is of type B or C for this impurity. In principle the different dependence of log e on y should enable a choice to be made, but in practice it is often found that because of experimental limitations the data fit either dependence equally well, or equally badly. This is particularly to be expected in the region of transition between type B and C where the asymptotic solutions am poor approximations in any case. We have therefore extended our earlier approach [6] to dealing with this transition region. This is based on estimating, from the full solutions, the error which is made by assuming that diffusion is either purely of type B or C when, in reality, it is not. The results for assuming type B diffusion have been reported previously [6]. Here we give the co~espon~ng analysis for type C diffusion. The asymptotic form of the solution in type C is ]6] (.s@“~C~~~ = 2(scu)3~2exp(-z2sLu/4)
(5)
or, in terms of measured quantities, i;=
2&K g(*D’t)“2 I
(6)
/
/
Fig. l._C&ulated curves for the laterally averaged concentration, C, of a diffusanf as a function of depth, y. The other parameters are defined in the text. Large values of scuare associated with strong segregation, low temperatures and short times. (Type C diffusion.)
317
The full solution (computed for a large value of s/?) is shown plotted in Fig. 1 and compared with eqn (6) for values of sol ranging from 0.1 to 10. As expected, the full solution approaches eqn (6) as scu increases. In actual experiments the average concentration in the grain boundary ‘tail’ of the penetration profile rarely falls by more than one or two orders of magnitude and therefore the region of Fig. 1 which is of relevance to experiments is that in which ~j~/(D’t) f 10. From the average slope of each curve in this region we have estimated the apparent vaIue of D’ which would be deduced by assuming the diffusion to be purely type C. The results are summarised in Fig. 2 together with the previous analysis assuming type B diffusion. The curves demonstrate that assuming type B diffusion leads to an increasingly serious underestimation ofsD’S as S(Yincreases beyond 0.1. Similarly, assuming type C diffusion leads to an increasingly serious under-estimation of D’ as sa: decreases below 10. These curves will be used later to analyse the data for Cr diffusion in NiO. 3. EXPE~ME~S Each polycrystalline NiO specimen (18 mm X 18 mm surface area) was fabricated by complete oxidation of a high purity Ni foil 25 pm in thickness supported on a sintered NiO substrate in oxygen at 1 1OO’C as described in previous studies of Ni, 0 and Co diffusion [6, 7, IO]. The resulting structure has a high density outer NiO layer approximately 20 pm thick in which the grain size is approximately 10 pm_ The specimens were annealed under the conditions of the intended diffusion anneal and then radiotracer was deposited directly onto the surface of the dense layer. The specimen surface was not polished because this is known to introduce dislocation structures which are difficult to anneal out. The tracers, ‘39Ceand “Cr, were obtained as chloride (from Amersham International plc) and transferred to the surface of the NiO specimens by vacuum evaporation. Only the central area (approximately 1 cm2) of the surface was coated in order to avoid surface diffusion over the specimen edges. The specimens were then given a diffusion anneal at the appropriate temperature in a stream of oxygen at a pressure of 1 atm (0.1 MPa). After the diffusion anneal the depth dist~bution of tracer in the specimen was determined by radiofrequency sputter-sectioning as described previously [2, 61. The i3’Ce tracer decays by K-capture to i3$La with a half-Iife of 140 days and the 5’Cr, also by Kcapture, to 5’V with a half-life of 27.8 days. The resulting X-ray emissions were counted using a gas-filled proportional counter with a Be window. 4. RESULTS 4.1 57Co dz~us~on The results of these experiments have already been reported [IO] and are only summa&d here. All the
Type0
1
a
_ut
A. ATKINSON andR.1. TAYLOR
318
NiO is about 8 eV. This is so large that the solubility of Ce in the NiO lattice in unlikely to be detected, even using radiotracers. Therefore the most likely cause of the surface ‘hold-up’ is low lattice solubility. Consequently the ‘tail’ region of the profile, at relatively large penetration depths has been analysed as type C diffusion along high angle boundaries using eqn (6) (that
TypdC
L! ;
P-= ob 22
2,
I”
01
00
I
I
I
r
'19Ce60 min at 9OO’C
Fig. 2. Calculated curves showing estimates of the errors which are generated by using the asymptotic solutions, for type B and type C diffusion, in the region of transition between them.
= 7 E
Of
i
2
5
experiments were analysed assuming type B diffusion to give the parameter SD’& An Arrhenius fit to the data gives (SD’&,
= 3.8 X IO-’ exp(-1.86
(eV)/kT)
cm3 s-l. (7)
Since s and 6 are not known for Co in NiO by other means, D’ cannot be extracted directly. However, it is unlikely that d is greatly different from that of Ni in NiO (0.7 nm) and strong segregation is not expected. We therefore make the approximations s = 1 and 6 = 1 nm to deduce that D’(Co) = 3.8 exp(which may be compared
1.86 (eV)/kT)
cm2 s-’
u
0
s” -1
_2
+c
Dislocations Dd I L x 10“
Y
$
cm2 5.’
-303
y*
I/ml
)*
*“1
(8)
with that of Ni [6]
D’(Ni) = 0.43 exp(-1.78
(eV)/kT)
cm* s-l.
(9)
4.2 ‘39Ce difusion Penetration profiles of ‘39Ce in polycrystalline NiO (e.g. Fig. 3a) show three regions. The first is a region of high concentration at the surface which is attributable to tracer that has not diffused into the specimen by a detectable amount during the diffusion anneal. Possible reasons for this ‘hold-up’ are: the solubility of Ce in NiO is very low; the diffusion coefficient of Ce in NiO is very small; the Ce is retained on the surface as CeCl, . Problems of ‘hold-up’ have been reported in some systems in which chloride tracers have not converted to oxide [ 161. This is not the cause of ‘hold-up’ in the present experiments since it is known that CeCl3 readily converts to Ce02 in air at temperatures above 550°C [17]. Ce ions are, however, expected to have very low solid solubility in the NiO lattice because of their high charge and large size (0.92 A). Tasker [ 181, using computer simulations, has estimated that the energy change in dissolving a Ce4+ ion from Ce02 into
1
y bml Fig. 3. Penetration profiles of ‘39Ce in polycrystalline NiO after diffusion for 60 min at 900°C in oxygen. (a) Plotted according to the expected solution for a thin tim (finite source) boundary condition. Separate contributions from grain boundaries and dislocations are indicated. (b) The grain boundary contribution plotted according to a constant surface concentration [c(O)] boundary condition.
319
fnpurity diffusion in NiO grain boundaries
is, ail the tracer is confined to the boundary iayer). Between these regions is another R&M which could either be the result of slower diffusion along other pathways in parallel with the grain boundaries (e.g. dislocations) or a diffusion coefficient in the high angle boundaries which is a strong function of Ce concentration (i.e. lower L)’ when Ce ccmcerrtratian is high). The region attributed to high angle ~~~d~es was analysed according to eqn (6) and the results are given in Table f along with details of the d~~~s~~n anneals and sectioning depths. The m-e-exponentid factor in eqn (6) cannot be evaIuated in the case af Ce because s tends to infinity. If no surface diffusion takes place and there is zero lattice salubility then the expected distribution is given by eqn (6) with s = 1. The contribution to the average concentration near the specimen surface which is associated with grain boundaries, c(Of/K, is expected to be in the range 3 X low5 to 2 X 10M4pm-' on this basis. This is roughly 3 orders of magnitude below the experimental! y observed values of e(O)/K (Table lb) and therefore Lateral diffusion must have taken place on, or very close to, the surface ff surface diffusion is so rapid t&at the ca~~ntm~on remains constant at the junction between the grain boundary and the surface the expected sofution is C=
T
erf@ y/(4D’t)‘la)
(10)
5
where 6, is the width of the surface ‘layer”. Fig. 3b shows the gmin boundary ‘tail’ of Fig. 3a platted according to equation (to) and values of D’ obtained in this way are given in Table t b, together with the ~offes~ndjng derived values of mean surface ~~~e~~a~an~ @(W K. According to eqn f IO), if S, = 6, NOVAK is expected to be -0.2 grn-‘. This is w&in an order of magnitude
of the measured values, but the fact that the measured values do change with annealing conditions indicates that surface diffusion is not infinitely fast. Since the uncertainty in II’ which results from the two interpretations is not great, we have chosen to adopt the values deduced from assuming a constant surface concentmtion as being prefeRed because of the better agreement with the observed surface concen~at~on. The resulting Arrhenius ~x~ress~o~ far Ce diffusion is
In order ta di&rentiate between the two possible causes of the intermediate region observed in the penetration profiles we carried out some experiments using tracer of much greater specific activity (Table la) so that the total Ce concentration, K, was much reduced. The intermediate region was still evident even with the high specific activity tracer (Fig. 4), which demonstrates that it is not due to a con~en~ation~e~ndent diffusion coe%cient. The int~~e~ate region was therefore attributed to division along d&cations and the d&location diffusion coefficients are also given in Table lb. The di#Gsion coe%cients for Ce along high a&e NiO boundaries and along dislocations are plotted in Arrhenius form ia Fig. 5. The actual concentration of diffusant in the grain boundary close to the external surface, C’(O), has &a been estimated and is listed in Table 1b. This represent8 a lower bound to Ehe ‘solubility’ of Ce in NiO bound* aries.
The Cr tracer ~~etmt~o~ prof&s are more di~c~~t b analyse because afthe uncertainty regarding whether
TabIe I. Diffusian of j3’Cein Ni0 grain boundaries and d&cations (a) Ditision (4,
Tracer specific activity (Ci g-‘)
(6, I.2 5.0 8.64 3.6
llO0 1100 fl(Kf ~
x x X X
79 1.t x IQ’ I.1 X I@ 280 123
10’ 103 $04 to3 103
180
7.2 X 10’
700
(b) Derived parameters
1100 1100 llclo
900 800 700
ll_l
anneals
1.2 5.0 8.64 3.6 3.6 7.2
x x x x x X
103 103 104 lo3 103 103
2 x IO-‘” ; ; KG $” 4 x 3 x 1w”‘S
2.4 x 1O-1’ 2.0 x 10-l’ 1.6 ;O-‘2 3.6 x fO_‘j 3.5 x f(IF
t AnaWed assuming a thin tifm tracer sowe. Z#ha&set aswning a cwstant surke concentration.
lato&m-‘) “~ 1.9 X 8.8 x 1.4 x 1.3 x 6.7 7.3 X
14P If19 $04 10” w 10”
Maximum penetration (pm) 4.1 ::f 2.1 f.r 0.4
320
A. 1
I-
.-
I
I
I.
I
I
I
ATKINSON and R. I. TAYLOR
I
s = exp(0.46 (eV)/kT)
,
‘39Ce at llooOc
Cl-
+ 50.103 s 8~6X10L s x Corrected for grain boundary diffusion
l
+ +
= 7 E P
4
Y -1 I”
--__
D
--. ‘1,
;--+._+ .,
5
-;
-.
D’=2~5x10-‘1 m2 s-’ -+. ‘+.. ‘+. .. “+. Dd=1 6 x 1cFcm* s-1 _. 4X
li I jo
e
1
t
‘. ‘.,’
t
2
,
3
/
/
L 5 Y (w-n)
I
6
L
7
I
8
Fig. 4. Penetration profiles of Ce in polycrystalline NiO after diffusion for different times at 1100°C. The data points marked as X have been obtained by subtracting the grain boundary cont~butions (dashed curve) to leave that associated with dislocations (solid curves).
diffusion is of type B or C. The profiles themselves show the three regions, in common with Ni, Co and Ce tracers, which are attributed to lattice, dislocation and high angle grain boundary diffusion. In experiments at 800, 1000 and 1100°C the lattice portion of the tracer penetration profile was sufficiently well-developed to extract lattice diffusion coefficients for Cr in NiO. These are plotted in Fig. 5 compared with an extrapolation of the single crystal measurements of Chen d af. [ 191 which are described by D(Cr) = 8.6 X 10e3 exp(-2.93
(eV)/kT)
(13)
which gives the observed segregation coefficient at 1170°C. This activation energy is similar in magnitude to the internal energy change (0.17-0.53 eV) estimated theoretically for A13+ segregation to NiO grain boundaries [8] and is therefore reasonable. The values of D and s from equations ( 12) and (13) have been used to estimate the product SN (~suming 6 = 1 nm) for each diffusion anneal and these are listed in Table 2(a). The estimates indicate that the experiments at 600 and 7OO’C are expected to be well into the region of type C diffusion (scu > IO), but that the others are likely to be in the transition region with 0.1 < SCY< 10. The difhculty in attempting to distinguish between type B and type C diffusion from only the tracer penetration profile is illustrated in Fig. 6. The penetration profile, following diffusion for 30 min at 900°C is plotted as log,,(C/K) against depth, y, in Fig. 6(a). The grain boundary contribution on this plot is apparently of type B since the penetration profile shows a linear ‘tail’ (more strictly, a very slight downward curvature is expected from the y 6’5dependence). The same data are plotted in Fig. 6(b) as log,,(~/lK) against $. The grain boundary contribution now appears to be of type C since a linear ‘tail’ is also observed on this plot. It must be concluded that as a result of other extraneous factors (lattice diffusion, dislocation diffusion, residual porosity, experimental scatter, etc.) it is not possible to distinguish between type B and type C diffusion on the basis of the penetration profiles.
T (*Cl
-8
1100 / 1000 1 900 / 800
0
600 I
700
500 /
cm2 s-’ (12)
in the temperature range 1192-1642°C. The present m~surements are in acceptable agreement with the extrapolation and therefore eqn ( 12) was assumed to represent lattice diffusion of Cr over the entire temperature range of interest; that is, down to 6OO’C. This agreement also shows that there was no ‘hold-up’ due to sluggish conversion of 5’CrC13 to 5*Cr203 at 800°C. Chromium is known to segregate quite strongly to NiO grain boundaries. Notis et al. [20] studied Cr segregation to grain boundaries in hot-pressed polycrystalline NiO doped with 2 X 10e3 cation fraction of Cr. Using scanning transmission electron microscopy they deduced that, if the boundary was 1 nm wide, the Cr concentration in the boundary was 40 times that in the lattice at 1170°C. in order to estimate segregation at other temperatures we have crudely assumed
-16-
_,8_
-206
Y Denotes Cr lottrce ‘, dtffusion measured 1 in the present study ‘,
71
81
9I
10 I
\
11 I
\
NI tiatticei \
\
\\cr (latt Ice1 12 I 13 1 1LI
I
1O’I T ( K-‘I
Fig. 5. Arrhenius plot summa~sing the diffusion coefficients for cations in the NiO lattice and in grain boundaries (and dislocations in the case of Ce).
321
Impurity diffusion in NiO grain boundaries Table 2. Diffusion of 5’Cr in NiO grain boundaries (a) Diffusion
anneals
&)
(W (estimated) (cm)
(b)
1100 1000 900 800 700 600 600
1.2 4.2 1.8 5.76 1.58 7.56 6.05
x X X X X X X
103 IO3 10’ lo4 lo5 IO4 IO5
1.4 9.8 2.1 3.0 9.9 9.0 2.6
x x x x x x x
s (estimated)
10-S 10m6 10-6 lo-6 lo-’ lo-* lo-’
SLY (estimated)
Tracer specific activity (Ci g-l)
0.18 0.34 2.3 2.4 12.2 250 87
61 200 330 310 170 120 280
49 66 95 150 240 450 450
K (atoms cm-*) 6.4 1.7 4.0 7.2 2.0 2.6 4.3
X x x X x X x
10” 10’4 10” 10” lOI 10” 10’2
(b) Derived parameters m (G
(SW,, (cm’ s-l)
ct
(SD’@, (cm3 s-l)
D:pp (cm2 s-l)
&-U, (cm2 s-‘)
s 53
1100
1.2
x IO3
1.4 x lo-l5
1.5 x lO-‘5
6.6 x lo-”
2.8 x lo-”
1000 900 800 700 600 600
4.2 1.8 5.76 1.58 7.56 6.05
x x x X X X
1.1 4.2 8.6 4.0 5.3 5.2
1.3 x IO-l6 1.8 X IO-l6 3.8 X lo-” -
8.1 1.0 1.8 1.7 2.6 1.0
2.3 1.2 2.2 1.7 2.6 1.0
lo3 lo3 10“ 10’ lo4 10’
x X x X X X
lo-l6 lo-” 1O-‘8 IO-l9 1O-2o 1O-2o
x X X x x x
lo-l2 IO-” lo-” 10-13 lo-” lo-”
We therefore interpreted all the profiles initially both as type B (giving SD’S) and as type C (giving D’). These apparent estimates are given in Table 2(b). For those experiments having estimated values of so < 10 (that is, at temperatures greater than or equal to 800°C) the apparent values of SD’& deduced by assuming type B diffusion, were corrected to pure type B using Fig. 2. The corrected estimates of sD’6 are listed in Table 2. A complementary procedure was then used to correct the estimates of D’, which had been derived assuming type C diffusion, and these are also listed in Table 2. From the corrected estimates of sD’6 and D’, deduced from the penetration profiles, we can deduce a value of s (again assuming 6 = 1 nm). These are given in Table 2(b) and are seen to be in reasonable agreement with the initial estimates of s, from eqn (13) on which the correction procedure was based. It is therefore concluded that this interpretation of the penetration profiles is self-consistent. The final best estimates of D’ were obtained by combining the results of both type B diffusion [s given by eqn (13)] and type C and are shown plotted in Fig. 5. In principle it is possible to distinguish between pure type B and type C diffusion by carrying out diffusion anneals of different duration. This was done at 600°C where type C diffusion was expected. The results of this time dependence, shown in Table 2(b), are in better agreement with type B rather than the expected type C diffusion. The diffusion coefficients, assuming type C diffusion, differ by a factor of 2.6 which is much larger than the errors expected from sectioning and analysis of the profiles. Nevertheless, these experiments cannot be of type B because this would require s +$ 2; that is no segregation of Cr to the boundary, which is contrary to both theoretical predictions [8] and experimental observations [20]. We therefore conclude that
x X X x X x
lo-” lo-” lo-l2 lo-‘) lo-” lo-”
56 150 170
(best ezimate) (cm2 SK’)
(PL
c’(O) cation fraction
3.1 x lo-‘O 3.2 1.6 2.4 1.7 2.6 1.0
x x X x x x
-
IO-” lo-” IO-l2 lo-l3 lo-l3 lo-l3
0.016 0.034 0.034 0.077 0.066 0.032
2.5 1.2 2.2 1.4 1.6 1.3
x x x x x x
lO-3 lo-’ lo-4 lo-) lo-’ 1o-4
some other source of error in these experiments (e.g. incomplete oxidation of the CrC13 tracer at this low temperature) makes it unreliable to distinguish between type B and C diffusion from time dependence alone (as has also been shown to be the case for depth dependence). The grain boundary diffusion coefficients of Cr, unlike the other diffusion coefficients, do not exhibit Arrhenius behaviour. In particular, the two determinations at 6OO”C, discussed in the preceding paragraph, are approximately one order of magnitude greater than would be expected from an extrapolation of the data at higher temperatures. A possible explanation for this is that at 600°C the ‘iCr tracer concentration (or that of the 51V daughter) was no longer negligible in comparison with the intrinsic defect concentration in the boundary and was itself doping the boundary significantly. The maximum tracer concentration in the boundary, C’(O), is given in Table 2(b). If doping by the tracer was significant then the intrinsic defect concentration in the boundary must be of the order 10m410m3of boundary sites, which is a reasonable value. The Arrhenius expression for Cr grain boundary diffusion in the temperature range 700-l 100°C is D’(Cr) = 6.5 X 10-3exp(-2.0
(eV)/kT)
cm3 s-‘. (14)
5. DISCUSSION The present data for “Cr diffusion may be compared directly with the earlier measurements of Chen and Peterson [9]. Chen and Peterson found the activation energy for grain boundary diffusion to be approximately equal to that of lattice diffusion [2.93 eV, eqn (12)] whereas the present results give an activation energy which is only 70% of that for lattice diffusion.
322
A. ATKINSON and
“Cr 30 min,
I
++
--k+
L.2x10-‘7cm35.’
_;_jsD’610pp.
-+-_i -2
9OO’C
“\ ----+\
~
-----I
.L__ 0
1
2 Y @ml
2__i
5’Cr 30 min, 9OO~C
R. I. TAYLOR
the speculation that grain boundaries prepared in different ways may have very different properties. In earlier diffusion studies of Ni and Co, using samples prepared by oxidation of Ni (as in the present experiments), grain boundary diffisivity was found to depend on oxygen activity in a similar way to that established for lattice diffusion. This is good evidence to support the view that the boundaries in specimens prepared by oxidation of Ni are chara~te~stic of the pure oxide. Conversely, Chen and Peterson found SD% for Co to be independent of oxygen activity in their specimens. This could well indicate that other impu~ties were controlling the diffusion properties of their boundaries. Recent studies [Z 1] of NiO bicrystals and large-grained polycrystals have shown that it is extremely dificult to avoid impurity effects in such specimens. Arrhenius parameters for cation diffusion in ND grain boundaries derived from the present experiments are summarised in Table 3. Aiso shown in Table 3 are the corresponding parameters for diffusion in the lattice. Although the diffusion coefficients are in the order @Co) > D(Ni) > D(Cr) for both lattice and grain boundary diffusion the same correlation is not exactly repeated in the Arrhenius parameters. However, it is well-known that Arrhenius fits to data over a fairly narrow temperature range can give misleading results. Therefore the actual diffusion coefficients are likely to have more significance than the Arrhenius parameters. The diffusion of impurities in simple lattices can be analyzed in terms of the energetics and jump rates of point defects 1221.In anfic or bee lattice (constant aO) when diffusion takes place by a vacancy mechanism the result is D*(impurity)
NiO after diffusion for 30 min at 900°C in oxygen. (a) Plotted assuming type B diffusion. (b) Plotted assuming type C diffusion.
Fig. 6. Penetration profile of Cr in ~lyc~s~lli~e
Chen and Peterson’s measurements of sD'6are 1.7 X lo-l4 cm3 s-’ at 9OO’C (cf. 2.3 X 1O-‘6 cm3 s-’ in this study) and 2 X 10Vi3cm3 s-’ at 1lOO'C(cf. 1.5 X lo-” cm3 s-’ in this study), which are approximately two orders of magnitude greater than in the present measurements. This discrepancy is very similar to that noted previously for Co diffusion [101and reinforces
= a$fi
V]exp(-Ai”i,/kT).
(15)
In this expression AH, is the energy of association between the impurity ion and the vacancy (negative for an attractive interaction), w is the frequency of impurity-vacancy interchange jumps, [ VJ the fraction of vacant sites and f the correlation factor (in general a complex function of all the jump frequencies in the nei~bourh~ of the impu~ty). The activation energy for impurity diffusion has contributions from w, [ P’j, A& and the temperature dependence off: It is evident that analysis of lattice diffusion itself requires independent knowledge of several parameters. In extending this approach to grain boundary diffusion additional unce~inties are introduced because of the non-uniformity and low symmetry of the sites involved in the jump process. Nevertheless, the same qualitative features may be expected. In the case of Cr and Ce in NiO, the impurity-vacancy interaction will be attractive (because they have opposite effective charges) and this will tend to lower the activation energy with respect to Ni diffusion. Furthermore, the temperature dependence offis known to make only a small contribution to the activation energy for lattice diffusion [23]. Since the activation energies for Cr and Ce grain boundary diffusion are slightly greater than for Ni grain boundary
323
Impurity diffusion in NiO grain boundaries Table 3. Arrhenius parameters for diffusion in NiO D = A exp(-Q/kT) Lattice
Grain boundaries
Species Ni
cot Cr Ce
A’ (cm2 s--I)
Q’ (eV per atom)
0.43 3.8 6.5 x lo-’ 6.3 x lO-4
1.78 1.86 2.0 2.0
A (cm’ s--I) 2.2 x 1om2 9.1 x 10-j 8.6 x 10-3 -
Q (eV per atom) 2.56 2.35 2.93 -
t In the case of Co diffusion, segregation has been assumed negligible.
diffusion it must be concluded that the impurityvacancy jump for these ions has a considerably greater activation energy than the nickel-vacancy jump. Duffy and Tasker [24] have estimated that in a symmetrical NiO tilt boundary (about [OOl] direction and with (3 10) boundary plane) the activation energy for a nickelvacancy jump is 1.86 eV, whereas for a cerium-vacancy jump the activation energy is 3 eV. Thus, there is some qualitative agreement between the experimental results and theoretical estimates. The magnitudes of the grain boundary diffusion coefficients for Cr and Ce are much lower than for Ni and therefore it is to be expected that these impurities should be relatively immobile in NiO films which are growing by thermal oxidation of Ni. (However, this may not be true if the impurity also reduces the rate of film growth, as is the case with Ce.) The parabolic rate constant (d.X?/dt, where X is the film thickness) for the growth of NiO on Ni pre-coated with Ce02 [2.5] is approximately an order of magnitude greater than the coefficient for Ce diffusion along NiO grain boundaries. Thus at the outer surface of the growing film X/ 1.6. It is known from mi(4D’t) ‘t2 is approximately crostructural observations [25] that most of the Ce remains as Ce02 particles in a well-defined layer near the Ni/oxide interface. Therefore at a point midway between this layer and the oxide/gas interface the concentration of Ce in a grain boundary is expected to be about 30% of its maximum value (near the base of the film) and, near the oxide/gas interface, only 3% of its maximum value. This prediction is in qualitative agreement with the distribution of Ce observed in such films by secondary ion mass spectroscopy [25].
proximately, a self-consistent analysis is possible which resolves the ambiguity. The grain boundary coefficients in NiO are in the order D’(Co) > D’(Ni) > D’(Cr) > D’(Ce). For the first three elements, this is the same order found for their lattice diffusion coefficients (lattice diffusion of Ce is not detectable because of its very low solubility). This reinforces earlier observations of a general correlation between lattice, dislocation and grain boundary diffusion in NiO. The activation energy for an interchange jump, in a grain boundary, between a Ni vacancy and a Ce or Cr impurity is greater than for the interchange between a vacancy and Co or Ni. The expected distribution of Ce in NiO films grown on CeOz-coated Ni is in qualitative accord with that observed experimentally. Acknowledgements-The authors are grateful to A. T. Chadwick, A. D. LeClaire, D. M. DuEy and P. W. Tasker for useful discussions and permission to refer to unpublished work. REFERENCES 1. Atkinson, A., Taylor, R. I. and Hughes, A. E., Phil. Mug. A 45, 823 (1982). 2. Atkinson, A. and Taylor, R. I., Phil. Mug. A 39, 581
(1979). 3. Volpe, M. L. and Reddy, J., J. Chem. Phys. 53, 1117
( 1970). 4. Volpe, M. L., Peterson, N. L. and Reddy, J., Whys. Rev. 83, 1417 (1971). 5. Dubois, C., Monty, C. and Philibert, J., SolidState Ionics 12, 75 (1984). 6. Atkinson, A. and Taylor, R. I., Philos. Mug. A 43, 979 (1981). 7. Atkinson, A., Pummerv. F. C. W. and Montv. C.. in Transport in Nonstoichiometric Compounds (Edited by G. Simkovich and V. S. Stubican), p. 359. Plenum Press, New York (1985). 8. Duffy, D. M. and Tasker, P. W., J. Phys. (Paris) Colloque C4 46, C4-185 (1985). 9. Chen, W. K. and Peterson,
N. L., J. Am. Ceram. Sot. 63,
566 ( 1980). 10. Atkinson,
A. and Taylor,
R. I., Philos. Msg. A 45, 583
(1982). 11. 12. 13. 14. 15. 16.
Harrison, L. G., Trans. Faraday Sot. 57, 1191 (1961). Whipple, R. T. P., Phil. Mug. 45, 1225 (1954). Suzuoka, T., J. Phys. Sot. Japan, 19,839 (1964). L&l&e, A. D., Private communication. LeClaire, A. D., Br. J Appl. Phys. 14, 351 (1963). Rothman, S. J. in Diffusion in Crystalline Solids (Edited
by G. E. Murch and A. S. Nowick), p. 1. Academic Press, New York (1984). 17. Wendlandt, W. W., J. Inorg. Nucl. Chem. 5, 118 (1957). 18. Tasker, P. W., UK Atomic Energy Authority Report
AERE-M3292 (1983). W. K., Peterson, N. L. and Robinson, L. C., J. Phys. Chem. Solids 34,705 (1973). 20. Notis, M. R., Bender, B. and Williams, D. B., In Grain Boundary Phenomena in Electronic Ceramics (Edited by 19. Chen,
6. CONCLUSIONS The analysis of tracer penetration profiles is straightforward for diffusants which either do not segregate to grain boundaries (in this study Ni and Co) or do not dissolve in the lattice (in this study Ce). When a diffusant has appreciable lattice solubility and significant boundary segregation (in this study Cr) analysis of the profile can be ambiguous. It has been demonstrated that if the segregation coefficient is known ap-
L. M. Levinson and D. C. Hill), p. 91. Am. Ceram. Sot., Columbus (1981). 21. Atkinson, A., Moon, D. P. and Taylor, R. I., UKAtomic 22. 23. 24. 25.
Energy Authority Report AERE-RI1580 (1985). Lidiard, A. B., Handbuch der Physik 20, 246 (1957). Peterson, N. L., So/id State Zonics 12, 201 (1984). Duffy, D. M. and Tasker, P. W., Private communication. Chadwick, A. T. and Taylor, R. I., Solid State Ionics 12, 343 (1984).
IMPURITY
1986
DImSION
~22-3#9?/S6 $3.00 + .@I 0 1986 Persrunon Prm Ltd.
IN NiO GRAIN
BOUNDARIES
A. ATKINSON ~~~R.I.TAYLoR Materials Development Division, Building 552, AERE HaNveIl, Dideot, Oxon OX1 I ORA, U.K.
Abstract--The di~sion of ‘3vCeand S’Cr in polyc~~line NiO has been studied in the tem~mtu~ range 600-l 100°C in oxygen at a pressure of I atm. These impu~ti~ were chosen because of their different effective charges and segregation behaviour and because of their reievauce to the oxidation of metals at elevated temperature. The solubility of Ce in the NiO lattice is neghgibie, but Ce is soluble at NiO grain boundaries and diskrcations. ~~n~uently Ce tracer only diEused along these pathways and the resulting profiles were analysed s~ai~tfo~ard~y to give grain boundary and dislocation diffusion coefficients. The lattice solubility of Cr, on the other hand, is not negligible and Cr also segregates strongly to NiO grain boundaries. A procedure for analysing penetration profiles of such an impurity has been developed in which parameters describing segregation and gram boundary diffusion are deduced self-consistently. When combined with previous measurements of Ni and Co diffusion it is found that grain boundary coetlicients decrease in the order Co, Ni, Cr, Ce as is also found for Iattice dithrsion (except for Ce, which has negligible lattice
solubilityf. The implication of the results for the distribution of Cr and Ce in NiO films formed by metal oxidation is also discussed. ~e_~urd~: impu~ty scion, cerium.
nickel oxide, gram boundary dithrsion, grain boundary section,
The diffusion of material along grain boundaries is now known to control many processes involving transport in oxides such as creep, sintering and chemical reactions. For example it has been shown [I] that the growth of NiU films by thermal oxidation of Ni is controlled by the outward diffusion of Ni along grain boundaries in the NiO film. There is strong evidence that this type of behaviour is quite general and that grain boundary diffusion controls the growth of most corrosion-resistant oxide films. When an oxide film grows on an elementaf metal substrate, diffusion of only oxygen and the metal ion in the oxide need be considered. However, in nearly all cases of practical interest the oxide film grows on an ahoy (e.g. a stainless steel), or in the presence of additives deliberately introduced in the form of a surface treatment (e.g. a coating), In such cases the foreign elements influence the defect populations and transport properties of the host oxide in a way which depends on their distribution within the film. This dist~bution is controlled by the transport properties of the foreign dements within the film and this will also occur mainly by diffusion along grain boundaries. ft is therefore important to have some appreciation of how foreign ions diffuse in oxide boundaries as well as the constituent ions of the host oxide. Nickel oxide is suitable for such a study because it is a good model for oxides which form corrosion-resistant films on metals and because a substantial body of data and understanding already exists for this oxide. Data for diffusion of Ni in the NiO lattice are in good agreement 12, 31 and it has been established that dif-
chro~um,
fusion takes place by a vacancy mechanism [4]. Diffusion of 0 in the NiO lattice is not as well-understood and both oxygen vacancies and interstitials may be contributing [.S]. Data are also available for diffusion of Ni [6] and 0 [7] alang NiO gram boundaries. The experiments suggest that Ni grain boundary diffusion also takes place by a vacancy mechanism and this conclusion is supported by theoretical calculations of the properties of simple boundaries [S]. There have also been two earlier studies of impurity diffusion in NiO bounda~es. Chen and Petersen [9] measured the diffusion of Co and Cr radiotracers along grain boundaries in NiO bicrystals and large-grained polycrystalhne specimens. Atkinson and Taylor f to] measured Co radiotmcer diffusion along grain boundaries in finegrained polycrystalline NiO films. The two sets of data for Co diffusion are not in agreement, for reasons which are not clear. The objective of the work described here is to extend the me~uremen~ of grain boundary diffusion in finegrained polycrystalline NiO films to other ions of interest in oxidation processes, specifically Cr and Ce, The impu~ty ions Co’+, C#’ and Ce4’ cover a range of characteristics and most other impu~ties are likely to behave similarly to one or another from this group. Co is typical of an impurity which is completely soluble in the oxide lattice and does not segregate appreciably to grain boundaries. Ce has the extreme opposite behaviour in that its lattice solubility is negligible and it is only soluble at grain boundaries. The transport properties of this ion are relevant to understanding the way in which CeOz coatings reduce the rate of NiO growth on Ni. Cr is intermediate between these two extremes. It has slight lattice sohtbility and is known 315
316
A.ATKINSON andR.I.TAYLOR
to segregate appreciably to NiO grain boundaries. Its transport properties are relevant to the oxidation of Ni-Cr alloys. 2. THEORY
The theoretical model of a grain boundary which is normally used for analysing diffusion experiments considers it as a uniform slab, of width 6, (and perpendicular to the external surface) in which the diffusion coefficient, D’, is greater than that in the surrounding lattice, D. Diffusion from the external surface is a combination of fast diffusion along the boundary and slow diffusion sideways out of the boundary. The kinetics of the diffusion process are mainly dependent on two factors. The first is the boundary condition at the external surface; that is, whether the surface concentration is maintained constant or whether the total quantity of difIusant is maint~ned constant (in the limit this becomes the ‘thin film’ boundary condition). The second factor is the extent of lattice diffusion (characterised by (Dt)“‘) in comparison with other characteristic dimensions of the system such as 6 and grain size, g, We will use Harrison’s [ 1 l] terminology for the three types of kinetic regime which result from this second factor. Type A diffusion occurs in the limit of long times, when (&)‘I2 % g and the lattice and grain boundary diffusion processes are simply averaged out. None of the experiments reported here fall into this category. Type B diffusion occurs when most of the diffusant is in the lattice, but the concentration distributions from neighbou~ng grain boundaries do not interact. Type C diffusion occurs in the limit of short times when diffusion in the lattice is negligible and all the diffusant is retained in the boundary. The different surface boundary conditions were originally treated by Whipple [ 121 and Suzuoka [ 131 for the constant ~oneentmtion and thin-source cases respectively. In the present experiments we are in principle only concerned with the thin-source boundary condition and the solution for the average concentration of diffusant as a function of depth, as would be measured in a sectioning experiment. The original solution of Suzuoka for type B diffusion was modified by Atkinson and Taylor [6] to include the diffusant within the boundary and thereby cover both types B and C. The average concentration in the sectioning experiment may then be written in the form
C = K(~~~)-1’2[ex~-~z/4)
+ i (err + cu,)]
(1)
where 9 = y/(Df)L’2, y is the depth below the surface, Kis the concentration of diffisant per unit area initially on the surface and n = g/(4Dt)‘f2. The exponential term is the normal ~ont~bution from lattice diffusion in the absence of grain boundaries, cii describes the additional contribution from diffusant in the lattice associated with the grain boundary and ciii accounts for the diffusant within the boundary itself. Expressions
for C?irand cu,,,have been given for the case when the diffusant does not segregate at the boundary (that is, self-diffusion). LeClaire [ 141 has modified these expressions to account for segregation as is necessary when analysing results of impurity diffusion. Segregation is assumed to be characterised by a linear isotherm with segregation coefficient, s, equal to the concentration in the boundary divided by the concentration in the lattice. The resulting expressions for C?i,and C,,, are
X [F’/2exp(-X2)
- X erfcX] $
(2)
and
X erfcX :
.
(3)
The parameters in eqs (2) and (3) have the following definitions: 6
oc=201/2
/I=($ I)*
When eqns (2) and (3) are compared with the equivalent expressions in ref. [6] it is evident that the effect of segregation is simply to replace cxby so1.Thus the boundary behaves as if its width were increased by a factor equal to s and the transition from type R to type C diffusion occurs when s6 N 2(Dt)“‘. When analysing penetration profiles it is important to know whether the kinetics are type B or type C since asymptotic forms ofthe solutions are usually employed. In the case of type B diffusion the asymptotic solution predicts log cocy6f5 and the slope of such a plot gives p and, eventually, sD’6 if D is known [ 151:
The experiments of Co diffusion in NiO reported previously [lo] were analysed in this way. The asymp-
Impurity diffusion in NiO grain boundaries totic solution for type C diffusion predicts log ccc y2. The experiments of Ce diffusion described below have been analysed assuming type Cdiffusion, since the solubility of Ce in the NiO lattice is believed to be negligible. In the case of Cr diffusion, however, the analysis is not straightforward because of its intermediate behaviour. One does not know a priori whether diffusion is of type B or C for this impurity. In principle the different dependence of log e on y should enable a choice to be made, but in practice it is often found that because of experimental limitations the data fit either dependence equally well, or equally badly. This is particularly to be expected in the region of transition between type B and C where the asymptotic solutions am poor approximations in any case. We have therefore extended our earlier approach [6] to dealing with this transition region. This is based on estimating, from the full solutions, the error which is made by assuming that diffusion is either purely of type B or C when, in reality, it is not. The results for assuming type B diffusion have been reported previously [6]. Here we give the co~espon~ng analysis for type C diffusion. The asymptotic form of the solution in type C is ]6] (.s@“~C~~~ = 2(scu)3~2exp(-z2sLu/4)
(5)
or, in terms of measured quantities, i;=
2&K g(*D’t)“2 I
(6)
/
/
Fig. l._C&ulated curves for the laterally averaged concentration, C, of a diffusanf as a function of depth, y. The other parameters are defined in the text. Large values of scuare associated with strong segregation, low temperatures and short times. (Type C diffusion.)
317
The full solution (computed for a large value of s/?) is shown plotted in Fig. 1 and compared with eqn (6) for values of sol ranging from 0.1 to 10. As expected, the full solution approaches eqn (6) as scu increases. In actual experiments the average concentration in the grain boundary ‘tail’ of the penetration profile rarely falls by more than one or two orders of magnitude and therefore the region of Fig. 1 which is of relevance to experiments is that in which ~j~/(D’t) f 10. From the average slope of each curve in this region we have estimated the apparent vaIue of D’ which would be deduced by assuming the diffusion to be purely type C. The results are summarised in Fig. 2 together with the previous analysis assuming type B diffusion. The curves demonstrate that assuming type B diffusion leads to an increasingly serious underestimation ofsD’S as S(Yincreases beyond 0.1. Similarly, assuming type C diffusion leads to an increasingly serious under-estimation of D’ as sa: decreases below 10. These curves will be used later to analyse the data for Cr diffusion in NiO. 3. EXPE~ME~S Each polycrystalline NiO specimen (18 mm X 18 mm surface area) was fabricated by complete oxidation of a high purity Ni foil 25 pm in thickness supported on a sintered NiO substrate in oxygen at 1 1OO’C as described in previous studies of Ni, 0 and Co diffusion [6, 7, IO]. The resulting structure has a high density outer NiO layer approximately 20 pm thick in which the grain size is approximately 10 pm_ The specimens were annealed under the conditions of the intended diffusion anneal and then radiotracer was deposited directly onto the surface of the dense layer. The specimen surface was not polished because this is known to introduce dislocation structures which are difficult to anneal out. The tracers, ‘39Ceand “Cr, were obtained as chloride (from Amersham International plc) and transferred to the surface of the NiO specimens by vacuum evaporation. Only the central area (approximately 1 cm2) of the surface was coated in order to avoid surface diffusion over the specimen edges. The specimens were then given a diffusion anneal at the appropriate temperature in a stream of oxygen at a pressure of 1 atm (0.1 MPa). After the diffusion anneal the depth dist~bution of tracer in the specimen was determined by radiofrequency sputter-sectioning as described previously [2, 61. The i3’Ce tracer decays by K-capture to i3$La with a half-Iife of 140 days and the 5’Cr, also by Kcapture, to 5’V with a half-life of 27.8 days. The resulting X-ray emissions were counted using a gas-filled proportional counter with a Be window. 4. RESULTS 4.1 57Co dz~us~on The results of these experiments have already been reported [IO] and are only summa&d here. All the
Type0
1
a
_ut
A. ATKINSON andR.1. TAYLOR
318
NiO is about 8 eV. This is so large that the solubility of Ce in the NiO lattice in unlikely to be detected, even using radiotracers. Therefore the most likely cause of the surface ‘hold-up’ is low lattice solubility. Consequently the ‘tail’ region of the profile, at relatively large penetration depths has been analysed as type C diffusion along high angle boundaries using eqn (6) (that
TypdC
L! ;
P-= ob 22
2,
I”
01
00
I
I
I
r
'19Ce60 min at 9OO’C
Fig. 2. Calculated curves showing estimates of the errors which are generated by using the asymptotic solutions, for type B and type C diffusion, in the region of transition between them.
= 7 E
Of
i
2
5
experiments were analysed assuming type B diffusion to give the parameter SD’& An Arrhenius fit to the data gives (SD’&,
= 3.8 X IO-’ exp(-1.86
(eV)/kT)
cm3 s-l. (7)
Since s and 6 are not known for Co in NiO by other means, D’ cannot be extracted directly. However, it is unlikely that d is greatly different from that of Ni in NiO (0.7 nm) and strong segregation is not expected. We therefore make the approximations s = 1 and 6 = 1 nm to deduce that D’(Co) = 3.8 exp(which may be compared
1.86 (eV)/kT)
cm2 s-’
u
0
s” -1
_2
+c
Dislocations Dd I L x 10“
Y
$
cm2 5.’
-303
y*
I/ml
)*
*“1
(8)
with that of Ni [6]
D’(Ni) = 0.43 exp(-1.78
(eV)/kT)
cm* s-l.
(9)
4.2 ‘39Ce difusion Penetration profiles of ‘39Ce in polycrystalline NiO (e.g. Fig. 3a) show three regions. The first is a region of high concentration at the surface which is attributable to tracer that has not diffused into the specimen by a detectable amount during the diffusion anneal. Possible reasons for this ‘hold-up’ are: the solubility of Ce in NiO is very low; the diffusion coefficient of Ce in NiO is very small; the Ce is retained on the surface as CeCl, . Problems of ‘hold-up’ have been reported in some systems in which chloride tracers have not converted to oxide [ 161. This is not the cause of ‘hold-up’ in the present experiments since it is known that CeCl3 readily converts to Ce02 in air at temperatures above 550°C [17]. Ce ions are, however, expected to have very low solid solubility in the NiO lattice because of their high charge and large size (0.92 A). Tasker [ 181, using computer simulations, has estimated that the energy change in dissolving a Ce4+ ion from Ce02 into
1
y bml Fig. 3. Penetration profiles of ‘39Ce in polycrystalline NiO after diffusion for 60 min at 900°C in oxygen. (a) Plotted according to the expected solution for a thin tim (finite source) boundary condition. Separate contributions from grain boundaries and dislocations are indicated. (b) The grain boundary contribution plotted according to a constant surface concentration [c(O)] boundary condition.
319
fnpurity diffusion in NiO grain boundaries
is, ail the tracer is confined to the boundary iayer). Between these regions is another R&M which could either be the result of slower diffusion along other pathways in parallel with the grain boundaries (e.g. dislocations) or a diffusion coefficient in the high angle boundaries which is a strong function of Ce concentration (i.e. lower L)’ when Ce ccmcerrtratian is high). The region attributed to high angle ~~~d~es was analysed according to eqn (6) and the results are given in Table f along with details of the d~~~s~~n anneals and sectioning depths. The m-e-exponentid factor in eqn (6) cannot be evaIuated in the case af Ce because s tends to infinity. If no surface diffusion takes place and there is zero lattice salubility then the expected distribution is given by eqn (6) with s = 1. The contribution to the average concentration near the specimen surface which is associated with grain boundaries, c(Of/K, is expected to be in the range 3 X low5 to 2 X 10M4pm-' on this basis. This is roughly 3 orders of magnitude below the experimental! y observed values of e(O)/K (Table lb) and therefore Lateral diffusion must have taken place on, or very close to, the surface ff surface diffusion is so rapid t&at the ca~~ntm~on remains constant at the junction between the grain boundary and the surface the expected sofution is C=
T
erf@ y/(4D’t)‘la)
(10)
5
where 6, is the width of the surface ‘layer”. Fig. 3b shows the gmin boundary ‘tail’ of Fig. 3a platted according to equation (to) and values of D’ obtained in this way are given in Table t b, together with the ~offes~ndjng derived values of mean surface ~~~e~~a~an~ @(W K. According to eqn f IO), if S, = 6, NOVAK is expected to be -0.2 grn-‘. This is w&in an order of magnitude
of the measured values, but the fact that the measured values do change with annealing conditions indicates that surface diffusion is not infinitely fast. Since the uncertainty in II’ which results from the two interpretations is not great, we have chosen to adopt the values deduced from assuming a constant surface concentmtion as being prefeRed because of the better agreement with the observed surface concen~at~on. The resulting Arrhenius ~x~ress~o~ far Ce diffusion is
In order ta di&rentiate between the two possible causes of the intermediate region observed in the penetration profiles we carried out some experiments using tracer of much greater specific activity (Table la) so that the total Ce concentration, K, was much reduced. The intermediate region was still evident even with the high specific activity tracer (Fig. 4), which demonstrates that it is not due to a con~en~ation~e~ndent diffusion coe%cient. The int~~e~ate region was therefore attributed to division along d&cations and the d&location diffusion coefficients are also given in Table lb. The di#Gsion coe%cients for Ce along high a&e NiO boundaries and along dislocations are plotted in Arrhenius form ia Fig. 5. The actual concentration of diffusant in the grain boundary close to the external surface, C’(O), has &a been estimated and is listed in Table 1b. This represent8 a lower bound to Ehe ‘solubility’ of Ce in NiO bound* aries.
The Cr tracer ~~etmt~o~ prof&s are more di~c~~t b analyse because afthe uncertainty regarding whether
TabIe I. Diffusian of j3’Cein Ni0 grain boundaries and d&cations (a) Ditision (4,
Tracer specific activity (Ci g-‘)
(6, I.2 5.0 8.64 3.6
llO0 1100 fl(Kf ~
x x X X
79 1.t x IQ’ I.1 X I@ 280 123
10’ 103 $04 to3 103
180
7.2 X 10’
700
(b) Derived parameters
1100 1100 llclo
900 800 700
ll_l
anneals
1.2 5.0 8.64 3.6 3.6 7.2
x x x x x X
103 103 104 lo3 103 103
2 x IO-‘” ; ; KG $” 4 x 3 x 1w”‘S
2.4 x 1O-1’ 2.0 x 10-l’ 1.6 ;O-‘2 3.6 x fO_‘j 3.5 x f(IF
t AnaWed assuming a thin tifm tracer sowe. Z#ha&set aswning a cwstant surke concentration.
lato&m-‘) “~ 1.9 X 8.8 x 1.4 x 1.3 x 6.7 7.3 X
14P If19 $04 10” w 10”
Maximum penetration (pm) 4.1 ::f 2.1 f.r 0.4
320
A. 1
I-
.-
I
I
I.
I
I
I
ATKINSON and R. I. TAYLOR
I
s = exp(0.46 (eV)/kT)
,
‘39Ce at llooOc
Cl-
+ 50.103 s 8~6X10L s x Corrected for grain boundary diffusion
l
+ +
= 7 E P
4
Y -1 I”
--__
D
--. ‘1,
;--+._+ .,
5
-;
-.
D’=2~5x10-‘1 m2 s-’ -+. ‘+.. ‘+. .. “+. Dd=1 6 x 1cFcm* s-1 _. 4X
li I jo
e
1
t
‘. ‘.,’
t
2
,
3
/
/
L 5 Y (w-n)
I
6
L
7
I
8
Fig. 4. Penetration profiles of Ce in polycrystalline NiO after diffusion for different times at 1100°C. The data points marked as X have been obtained by subtracting the grain boundary cont~butions (dashed curve) to leave that associated with dislocations (solid curves).
diffusion is of type B or C. The profiles themselves show the three regions, in common with Ni, Co and Ce tracers, which are attributed to lattice, dislocation and high angle grain boundary diffusion. In experiments at 800, 1000 and 1100°C the lattice portion of the tracer penetration profile was sufficiently well-developed to extract lattice diffusion coefficients for Cr in NiO. These are plotted in Fig. 5 compared with an extrapolation of the single crystal measurements of Chen d af. [ 191 which are described by D(Cr) = 8.6 X 10e3 exp(-2.93
(eV)/kT)
(13)
which gives the observed segregation coefficient at 1170°C. This activation energy is similar in magnitude to the internal energy change (0.17-0.53 eV) estimated theoretically for A13+ segregation to NiO grain boundaries [8] and is therefore reasonable. The values of D and s from equations ( 12) and (13) have been used to estimate the product SN (~suming 6 = 1 nm) for each diffusion anneal and these are listed in Table 2(a). The estimates indicate that the experiments at 600 and 7OO’C are expected to be well into the region of type C diffusion (scu > IO), but that the others are likely to be in the transition region with 0.1 < SCY< 10. The difhculty in attempting to distinguish between type B and type C diffusion from only the tracer penetration profile is illustrated in Fig. 6. The penetration profile, following diffusion for 30 min at 900°C is plotted as log,,(C/K) against depth, y, in Fig. 6(a). The grain boundary contribution on this plot is apparently of type B since the penetration profile shows a linear ‘tail’ (more strictly, a very slight downward curvature is expected from the y 6’5dependence). The same data are plotted in Fig. 6(b) as log,,(~/lK) against $. The grain boundary contribution now appears to be of type C since a linear ‘tail’ is also observed on this plot. It must be concluded that as a result of other extraneous factors (lattice diffusion, dislocation diffusion, residual porosity, experimental scatter, etc.) it is not possible to distinguish between type B and type C diffusion on the basis of the penetration profiles.
T (*Cl
-8
1100 / 1000 1 900 / 800
0
600 I
700
500 /
cm2 s-’ (12)
in the temperature range 1192-1642°C. The present m~surements are in acceptable agreement with the extrapolation and therefore eqn ( 12) was assumed to represent lattice diffusion of Cr over the entire temperature range of interest; that is, down to 6OO’C. This agreement also shows that there was no ‘hold-up’ due to sluggish conversion of 5’CrC13 to 5*Cr203 at 800°C. Chromium is known to segregate quite strongly to NiO grain boundaries. Notis et al. [20] studied Cr segregation to grain boundaries in hot-pressed polycrystalline NiO doped with 2 X 10e3 cation fraction of Cr. Using scanning transmission electron microscopy they deduced that, if the boundary was 1 nm wide, the Cr concentration in the boundary was 40 times that in the lattice at 1170°C. in order to estimate segregation at other temperatures we have crudely assumed
-16-
_,8_
-206
Y Denotes Cr lottrce ‘, dtffusion measured 1 in the present study ‘,
71
81
9I
10 I
\
11 I
\
NI tiatticei \
\
\\cr (latt Ice1 12 I 13 1 1LI
I
1O’I T ( K-‘I
Fig. 5. Arrhenius plot summa~sing the diffusion coefficients for cations in the NiO lattice and in grain boundaries (and dislocations in the case of Ce).
321
Impurity diffusion in NiO grain boundaries Table 2. Diffusion of 5’Cr in NiO grain boundaries (a) Diffusion
anneals
&)
(W (estimated) (cm)
(b)
1100 1000 900 800 700 600 600
1.2 4.2 1.8 5.76 1.58 7.56 6.05
x X X X X X X
103 IO3 10’ lo4 lo5 IO4 IO5
1.4 9.8 2.1 3.0 9.9 9.0 2.6
x x x x x x x
s (estimated)
10-S 10m6 10-6 lo-6 lo-’ lo-* lo-’
SLY (estimated)
Tracer specific activity (Ci g-l)
0.18 0.34 2.3 2.4 12.2 250 87
61 200 330 310 170 120 280
49 66 95 150 240 450 450
K (atoms cm-*) 6.4 1.7 4.0 7.2 2.0 2.6 4.3
X x x X x X x
10” 10’4 10” 10” lOI 10” 10’2
(b) Derived parameters m (G
(SW,, (cm’ s-l)
ct
(SD’@, (cm3 s-l)
D:pp (cm2 s-l)
&-U, (cm2 s-‘)
s 53
1100
1.2
x IO3
1.4 x lo-l5
1.5 x lO-‘5
6.6 x lo-”
2.8 x lo-”
1000 900 800 700 600 600
4.2 1.8 5.76 1.58 7.56 6.05
x x x X X X
1.1 4.2 8.6 4.0 5.3 5.2
1.3 x IO-l6 1.8 X IO-l6 3.8 X lo-” -
8.1 1.0 1.8 1.7 2.6 1.0
2.3 1.2 2.2 1.7 2.6 1.0
lo3 lo3 10“ 10’ lo4 10’
x X x X X X
lo-l6 lo-” 1O-‘8 IO-l9 1O-2o 1O-2o
x X X x x x
lo-l2 IO-” lo-” 10-13 lo-” lo-”
We therefore interpreted all the profiles initially both as type B (giving SD’S) and as type C (giving D’). These apparent estimates are given in Table 2(b). For those experiments having estimated values of so < 10 (that is, at temperatures greater than or equal to 800°C) the apparent values of SD’& deduced by assuming type B diffusion, were corrected to pure type B using Fig. 2. The corrected estimates of sD’6 are listed in Table 2. A complementary procedure was then used to correct the estimates of D’, which had been derived assuming type C diffusion, and these are also listed in Table 2. From the corrected estimates of sD’6 and D’, deduced from the penetration profiles, we can deduce a value of s (again assuming 6 = 1 nm). These are given in Table 2(b) and are seen to be in reasonable agreement with the initial estimates of s, from eqn (13) on which the correction procedure was based. It is therefore concluded that this interpretation of the penetration profiles is self-consistent. The final best estimates of D’ were obtained by combining the results of both type B diffusion [s given by eqn (13)] and type C and are shown plotted in Fig. 5. In principle it is possible to distinguish between pure type B and type C diffusion by carrying out diffusion anneals of different duration. This was done at 600°C where type C diffusion was expected. The results of this time dependence, shown in Table 2(b), are in better agreement with type B rather than the expected type C diffusion. The diffusion coefficients, assuming type C diffusion, differ by a factor of 2.6 which is much larger than the errors expected from sectioning and analysis of the profiles. Nevertheless, these experiments cannot be of type B because this would require s +$ 2; that is no segregation of Cr to the boundary, which is contrary to both theoretical predictions [8] and experimental observations [20]. We therefore conclude that
x X X x X x
lo-” lo-” lo-l2 lo-‘) lo-” lo-”
56 150 170
(best ezimate) (cm2 SK’)
(PL
c’(O) cation fraction
3.1 x lo-‘O 3.2 1.6 2.4 1.7 2.6 1.0
x x X x x x
-
IO-” lo-” IO-l2 lo-l3 lo-l3 lo-l3
0.016 0.034 0.034 0.077 0.066 0.032
2.5 1.2 2.2 1.4 1.6 1.3
x x x x x x
lO-3 lo-’ lo-4 lo-) lo-’ 1o-4
some other source of error in these experiments (e.g. incomplete oxidation of the CrC13 tracer at this low temperature) makes it unreliable to distinguish between type B and C diffusion from time dependence alone (as has also been shown to be the case for depth dependence). The grain boundary diffusion coefficients of Cr, unlike the other diffusion coefficients, do not exhibit Arrhenius behaviour. In particular, the two determinations at 6OO”C, discussed in the preceding paragraph, are approximately one order of magnitude greater than would be expected from an extrapolation of the data at higher temperatures. A possible explanation for this is that at 600°C the ‘iCr tracer concentration (or that of the 51V daughter) was no longer negligible in comparison with the intrinsic defect concentration in the boundary and was itself doping the boundary significantly. The maximum tracer concentration in the boundary, C’(O), is given in Table 2(b). If doping by the tracer was significant then the intrinsic defect concentration in the boundary must be of the order 10m410m3of boundary sites, which is a reasonable value. The Arrhenius expression for Cr grain boundary diffusion in the temperature range 700-l 100°C is D’(Cr) = 6.5 X 10-3exp(-2.0
(eV)/kT)
cm3 s-‘. (14)
5. DISCUSSION The present data for “Cr diffusion may be compared directly with the earlier measurements of Chen and Peterson [9]. Chen and Peterson found the activation energy for grain boundary diffusion to be approximately equal to that of lattice diffusion [2.93 eV, eqn (12)] whereas the present results give an activation energy which is only 70% of that for lattice diffusion.
322
A. ATKINSON and
“Cr 30 min,
I
++
--k+
L.2x10-‘7cm35.’
_;_jsD’610pp.
-+-_i -2
9OO’C
“\ ----+\
~
-----I
.L__ 0
1
2 Y @ml
2__i
5’Cr 30 min, 9OO~C
R. I. TAYLOR
the speculation that grain boundaries prepared in different ways may have very different properties. In earlier diffusion studies of Ni and Co, using samples prepared by oxidation of Ni (as in the present experiments), grain boundary diffisivity was found to depend on oxygen activity in a similar way to that established for lattice diffusion. This is good evidence to support the view that the boundaries in specimens prepared by oxidation of Ni are chara~te~stic of the pure oxide. Conversely, Chen and Peterson found SD% for Co to be independent of oxygen activity in their specimens. This could well indicate that other impu~ties were controlling the diffusion properties of their boundaries. Recent studies [Z 1] of NiO bicrystals and large-grained polycrystals have shown that it is extremely dificult to avoid impurity effects in such specimens. Arrhenius parameters for cation diffusion in ND grain boundaries derived from the present experiments are summarised in Table 3. Aiso shown in Table 3 are the corresponding parameters for diffusion in the lattice. Although the diffusion coefficients are in the order @Co) > D(Ni) > D(Cr) for both lattice and grain boundary diffusion the same correlation is not exactly repeated in the Arrhenius parameters. However, it is well-known that Arrhenius fits to data over a fairly narrow temperature range can give misleading results. Therefore the actual diffusion coefficients are likely to have more significance than the Arrhenius parameters. The diffusion of impurities in simple lattices can be analyzed in terms of the energetics and jump rates of point defects 1221.In anfic or bee lattice (constant aO) when diffusion takes place by a vacancy mechanism the result is D*(impurity)
NiO after diffusion for 30 min at 900°C in oxygen. (a) Plotted assuming type B diffusion. (b) Plotted assuming type C diffusion.
Fig. 6. Penetration profile of Cr in ~lyc~s~lli~e
Chen and Peterson’s measurements of sD'6are 1.7 X lo-l4 cm3 s-’ at 9OO’C (cf. 2.3 X 1O-‘6 cm3 s-’ in this study) and 2 X 10Vi3cm3 s-’ at 1lOO'C(cf. 1.5 X lo-” cm3 s-’ in this study), which are approximately two orders of magnitude greater than in the present measurements. This discrepancy is very similar to that noted previously for Co diffusion [101and reinforces
= a$fi
V]exp(-Ai”i,/kT).
(15)
In this expression AH, is the energy of association between the impurity ion and the vacancy (negative for an attractive interaction), w is the frequency of impurity-vacancy interchange jumps, [ VJ the fraction of vacant sites and f the correlation factor (in general a complex function of all the jump frequencies in the nei~bourh~ of the impu~ty). The activation energy for impurity diffusion has contributions from w, [ P’j, A& and the temperature dependence off: It is evident that analysis of lattice diffusion itself requires independent knowledge of several parameters. In extending this approach to grain boundary diffusion additional unce~inties are introduced because of the non-uniformity and low symmetry of the sites involved in the jump process. Nevertheless, the same qualitative features may be expected. In the case of Cr and Ce in NiO, the impurity-vacancy interaction will be attractive (because they have opposite effective charges) and this will tend to lower the activation energy with respect to Ni diffusion. Furthermore, the temperature dependence offis known to make only a small contribution to the activation energy for lattice diffusion [23]. Since the activation energies for Cr and Ce grain boundary diffusion are slightly greater than for Ni grain boundary
323
Impurity diffusion in NiO grain boundaries Table 3. Arrhenius parameters for diffusion in NiO D = A exp(-Q/kT) Lattice
Grain boundaries
Species Ni
cot Cr Ce
A’ (cm2 s--I)
Q’ (eV per atom)
0.43 3.8 6.5 x lo-’ 6.3 x lO-4
1.78 1.86 2.0 2.0
A (cm’ s--I) 2.2 x 1om2 9.1 x 10-j 8.6 x 10-3 -
Q (eV per atom) 2.56 2.35 2.93 -
t In the case of Co diffusion, segregation has been assumed negligible.
diffusion it must be concluded that the impurityvacancy jump for these ions has a considerably greater activation energy than the nickel-vacancy jump. Duffy and Tasker [24] have estimated that in a symmetrical NiO tilt boundary (about [OOl] direction and with (3 10) boundary plane) the activation energy for a nickelvacancy jump is 1.86 eV, whereas for a cerium-vacancy jump the activation energy is 3 eV. Thus, there is some qualitative agreement between the experimental results and theoretical estimates. The magnitudes of the grain boundary diffusion coefficients for Cr and Ce are much lower than for Ni and therefore it is to be expected that these impurities should be relatively immobile in NiO films which are growing by thermal oxidation of Ni. (However, this may not be true if the impurity also reduces the rate of film growth, as is the case with Ce.) The parabolic rate constant (d.X?/dt, where X is the film thickness) for the growth of NiO on Ni pre-coated with Ce02 [2.5] is approximately an order of magnitude greater than the coefficient for Ce diffusion along NiO grain boundaries. Thus at the outer surface of the growing film X/ 1.6. It is known from mi(4D’t) ‘t2 is approximately crostructural observations [25] that most of the Ce remains as Ce02 particles in a well-defined layer near the Ni/oxide interface. Therefore at a point midway between this layer and the oxide/gas interface the concentration of Ce in a grain boundary is expected to be about 30% of its maximum value (near the base of the film) and, near the oxide/gas interface, only 3% of its maximum value. This prediction is in qualitative agreement with the distribution of Ce observed in such films by secondary ion mass spectroscopy [25].
proximately, a self-consistent analysis is possible which resolves the ambiguity. The grain boundary coefficients in NiO are in the order D’(Co) > D’(Ni) > D’(Cr) > D’(Ce). For the first three elements, this is the same order found for their lattice diffusion coefficients (lattice diffusion of Ce is not detectable because of its very low solubility). This reinforces earlier observations of a general correlation between lattice, dislocation and grain boundary diffusion in NiO. The activation energy for an interchange jump, in a grain boundary, between a Ni vacancy and a Ce or Cr impurity is greater than for the interchange between a vacancy and Co or Ni. The expected distribution of Ce in NiO films grown on CeOz-coated Ni is in qualitative accord with that observed experimentally. Acknowledgements-The authors are grateful to A. T. Chadwick, A. D. LeClaire, D. M. DuEy and P. W. Tasker for useful discussions and permission to refer to unpublished work. REFERENCES 1. Atkinson, A., Taylor, R. I. and Hughes, A. E., Phil. Mug. A 45, 823 (1982). 2. Atkinson, A. and Taylor, R. I., Phil. Mug. A 39, 581
(1979). 3. Volpe, M. L. and Reddy, J., J. Chem. Phys. 53, 1117
( 1970). 4. Volpe, M. L., Peterson, N. L. and Reddy, J., Whys. Rev. 83, 1417 (1971). 5. Dubois, C., Monty, C. and Philibert, J., SolidState Ionics 12, 75 (1984). 6. Atkinson, A. and Taylor, R. I., Philos. Mug. A 43, 979 (1981). 7. Atkinson, A., Pummerv. F. C. W. and Montv. C.. in Transport in Nonstoichiometric Compounds (Edited by G. Simkovich and V. S. Stubican), p. 359. Plenum Press, New York (1985). 8. Duffy, D. M. and Tasker, P. W., J. Phys. (Paris) Colloque C4 46, C4-185 (1985). 9. Chen, W. K. and Peterson,
N. L., J. Am. Ceram. Sot. 63,
566 ( 1980). 10. Atkinson,
A. and Taylor,
R. I., Philos. Msg. A 45, 583
(1982). 11. 12. 13. 14. 15. 16.
Harrison, L. G., Trans. Faraday Sot. 57, 1191 (1961). Whipple, R. T. P., Phil. Mug. 45, 1225 (1954). Suzuoka, T., J. Phys. Sot. Japan, 19,839 (1964). L&l&e, A. D., Private communication. LeClaire, A. D., Br. J Appl. Phys. 14, 351 (1963). Rothman, S. J. in Diffusion in Crystalline Solids (Edited
by G. E. Murch and A. S. Nowick), p. 1. Academic Press, New York (1984). 17. Wendlandt, W. W., J. Inorg. Nucl. Chem. 5, 118 (1957). 18. Tasker, P. W., UK Atomic Energy Authority Report
AERE-M3292 (1983). W. K., Peterson, N. L. and Robinson, L. C., J. Phys. Chem. Solids 34,705 (1973). 20. Notis, M. R., Bender, B. and Williams, D. B., In Grain Boundary Phenomena in Electronic Ceramics (Edited by 19. Chen,
6. CONCLUSIONS The analysis of tracer penetration profiles is straightforward for diffusants which either do not segregate to grain boundaries (in this study Ni and Co) or do not dissolve in the lattice (in this study Ce). When a diffusant has appreciable lattice solubility and significant boundary segregation (in this study Cr) analysis of the profile can be ambiguous. It has been demonstrated that if the segregation coefficient is known ap-
L. M. Levinson and D. C. Hill), p. 91. Am. Ceram. Sot., Columbus (1981). 21. Atkinson, A., Moon, D. P. and Taylor, R. I., UKAtomic 22. 23. 24. 25.
Energy Authority Report AERE-RI1580 (1985). Lidiard, A. B., Handbuch der Physik 20, 246 (1957). Peterson, N. L., So/id State Zonics 12, 201 (1984). Duffy, D. M. and Tasker, P. W., Private communication. Chadwick, A. T. and Taylor, R. I., Solid State Ionics 12, 343 (1984).