Influence of the demixing of impurities on oxidation kinetics

Solid State Ionics 50 (1992) 87-97 North-Holland

Influence of the demixing of impurities on oxidation kinetics C. Petot, F. Armanet, H. Klimczyk

1 and G. Petot-Ervas

CNRS, University Paris XIII, Avenue J.B. Clement, 93430 Villetaneuse, France

Received 27 February I99 1;accepted for publication 25 September 199 1

This paper presents a general analysis of the effect of impurities on oxidation kinetics of alloys. From kinetic studies performed in the stability range of oxide solid solution it is shown that it is possible to follow a step in the complex mechanism of oxidation. This has allowed us to analyse the mass transport process in the oxidation layer independently of other transport processes occuring during the scale thickening. Such analysis has allowed us to explain the effect of impurities both on the shift velocity of the oxidation front in the material and on the kinetic demixing of the cations. It is shown that these effects are directly related to the relative diffusion coefficient values of the different cations in the oxide layer.

1. Introduction Oxidation is a complex mechanism which comprises different processes such as gas adsorption and surface reactions, mass transport through the thickening reaction product layer by point defects or other mechanisms and transfer across the corrosion product/substrate interface. In oxidation studies the emphasis is generally put on the whole process but any of the different stages may be rate controlling so the analysis of the results can prove difficult. Sometimes, the interpretation is simplified by the consideration of a representative system for each alloy which is corroded or oxidized in a similar manner [ I]. Cu-Be and Ni-Cr for example, are considered to be representative of different classes of alloys. In such approaches the basic processes still apply to closely related systems but they are only a prerequisite. Each alloy is in fact a different material whose transport properties are greatly influenced by thermodynamic factors (temperature, gas composition...) as well as by the microstructure and by the impurities present in the solid phases, for example. In a general way, oxidation is controlled ahead by thermodynamic considerations but the formation of oxide layers is governed essentially by kinetics. ’ On leave from the Institute of Metallurgy, Academy of Mining and Metallurgy, Cracow, Poland. Elsevier Science Publishers B.V.

The present study is not concerned with the initiation of the reaction between the substrate and the gaseous environment. We will consider only the stage when a thick continuous layer covers the surface of the substrate and separates the solid from the gas (thicknesses higher than 1 pm for T>500"C after Atkinson [ 1 ] ). Then oxidation is mainly governed by diffusion of the reactants through the reaction product layer. So this stage corresponds to a reactive diffusion process in which the driving force for transport of reactants is determined by the electrochemical potential gradient across the scale. While it has been recognized for many years that doping of corrosion layers is an important factor, few studies have been devoted to the complex interplay between species diffusion and thermodynamics on the growth of oxide solid solutions scales (doped materials). Furthermore, the level of impurities in technological materials is not negligible and their presence in the corrosion products cannot be avoided. Wagner [2 ] was the first to propose a model allowing to describe the parabolic kinetics of growth of an oxidation scale on a binary alloy and to relate the distribution of cations in the scale to their mobility. A computer solution of these equations has been done recently by Narita et al. [ 31. In their calculation the authors assume as Wagner [ 2 ] a parabolic growth of the oxide scale. They have determined the magnitude of the parabolic reaction kinetics and the metal

88

C. Petotet al. /Effect of impuritieson oxidationkinetics

concentration profiles in the scales formed on Co-Fe and Co-Ni alloys. The purpose of this paper is to analyse in a general case the behavior of cations under a chemical potential gradient as those observed in a corrosion layer and to understand the influence of dopants or impurities on the mass transport kinetics through the corrosion scales i.e. on the growth rate of these scales. In order to simplify the analysis we will first consider the influence of impurities on the advancement of the internal reaction front during the oxidation process of an oxide solid solution within its range of stability. We will examine both the thermodynamic and kinetic factors which govern the transport of matter under an oxygen potential gradient. As we shall see, these transport processes can be accompanied by a kinetic demixing of the impurities, followed in some cases by the precipitation of new phases. Then we shall consider the consequences of this kinetic demixing on the reaction rates. The results and predictions will be used to analyse observations performed in the corrosion of metals. This treatment concerns semiconductor oxides which are among the main compounds encountered in the high temperature oxidation of metals [4,5]. Of course, the same treatment can be applied to the formation of other corrosion products, such as sulfides or carbides.

2. Basic equations During the oxidation of a metallic alloy A-B, an oxide solid solution of the corresponding cations may be formed. The ratio of the number of moles of A and B in the oxidation scale is controlled in part by the chemical potential of the species in the alloy and in the scale, inasmuch the less noble metal oxidizes preferentially. In fact, the composition of the oxide layer depends both on the concentration of the less noble metal in the alloy, the oxygen activity in the ambient gas and on the oxide growth rate. Consequently, in order to avoid the kinetic factors of the substrate we have considered the simple case of an oxide solid solution (AO-BOy) exposed at high temperature to an oxygen potential gradient within its range of stability. Furthermore, the diffusion problem has been solved when no additional phase

is formed during the transport process. We have also assumed that the reaction rate is exclusively controlled by bulk diffusion, which seems to be the case [ 1 ] at temperatures higher than 0.6T, (where T,,, is the melting temperature of the oxide). Nevertheless, the conclusions can be extended to lower temperatures when grain boundary diffusion prevails. Finally, we have assumed that the oxygen sublattice is immobile with respect to the laboratory reference frame and that the prevailing point defects are cationic vacancies. This situation is encountered in the main corrosion products, such as the transition metal oxides. Let us consider the transport processes occurring in the oxide solid solution (AO-BOy) under an oxygen potential gradient. The basic features have been described previously [6]. Therefore, only the main ideas will be recalled in the following. According to our assumptions, only a flux of cations A’+ and of solute cations B”+ (with a = 2~) appears in the material. If these fluxes move independently they can be expressed in the oxygen sublattice reference frame by the following relations [ 5-101: J ,,+=-~,(D,/RT)(l-m)(6~~~+/~x),

(1)

J pa+= -cM(DBIRT)m(srl,+lsx),

(2)

where cMis the overall concentration (in mol crne3 ) of cation sites in the lattice (with cM= c, in the present case), m the mole fraction of B, D, and DB the diffusion coefftcients of A and B in the solid solution and n, the electrochemical potential of the cations A’+ and Ba+ related to the chemical potential (p,) by the relation: rl~=P’i+~i~@

9

(3)

with z, the electrical charge of species i, F the Faraday constant and 9 the internal electrical potential. Furthermore, these cationic fluxes are coupled with the flux of vacancies (Jv) by the condition: Jv+

1 Jc=O,

(4)

the shift velocity of the oxidation front (v) is given by the following expression: v= -Jv V,,

(5)

where V, is the molar volume of the oxide, and the shift velocity of the oxidation front in a pure oxide

a9

C. Petot et al. /Effect of impurities on oxidation kinetics

A0 is given by the relation [ 5,6 1: u= +DA( 6Lnuo/Gx)

.

(6)

When assuming site conservation in the cationic sublattice and taking into account the electroneutrality condition and the local chemical equilibrium between the different components and defect species, it has been possible to express the different fluxes as a function of the oxygen potential gradient in the oxide solid solution [ 6-8 ] : J,,+ =cMDA( &n/6x+

(1 -m)6

J,,+ = -c,DB(6m/6x-my6

Lnuo/Sx)

Lnao/Gx) ,

,

1121.

(7) (8)

where 6m/6x is the impurity concentration gradient across the sample. If one neglects the small changes of volume due to the impurity and vacancy concentration variation, it is then possible to express the shift velocity of the oxidation front in the oxide solid solution (eqs. (4) and (5)) as a function of the oxygen potential gradient: v= +(yDB-DA)(m13Ln&/Gx-am/ax) -D,(l-y)6m/6x+D,6Lnao/6x.

the side of the lower oxygen partial pressures. The experimental and calculated cation distribution profiles, in (Co, Mg)O solid solutions exposed to oxygen potential gradients [ 9- 111, illustrate particularly well these composition changes under non equilibrium conditions. If the oxygen potential gradient is maintained, the increase concentration of impurities can lead to the precipitation of new phases, as it has been observed for Ni2Si04, for example

(9)

According to eqs. (6) and (9), the effect of impurities, or dopants, on the oxidation kinetics depends both on the diffusion coefficient of the cations (A*+ and B”+ ) and on the impurity or dopant concentration but also on the kinetic demixing of the solute cations B”+(am/Sx) in the considered material. One may recall that the flux of vacancies which occurs in an oxide solid solution exposed to an oxygen potential gradient is directed toward the direction of the lower oxygen partial pressure side (eq. ( 10) ). This flux is of course accompanied by a flux of cations in the opposite direction (eq. (4) ). The exchange frequency between the vacancies and the cations is lower for the less mobile cations. Consequently, simultaneously with the shift of the oxidation front in the oxide solid solution, a cation redistribution can take place in the considered materials [ 6-101. If one neglects the correlation effects between the jumps of the cations A and B (i.e. if one assumes weak vacancy-cation binding energies), this leads to an initially homogeneous solution, to an enrichment of the less mobile cations at

3. Influence of the dynamic segregation of the imparities on the reaction kinetics 3.1. General approach When a homogeneous solid solution ( AO-BOy ), which is in thermodynamical equilibrium with the ambient atmosphere, is submitted at high temperature to an abrupt change of the oxygen partial pressure, a defect relaxation occurs in the material. To reach the new thermodynamical equilibrium the crystal incorporates or releases oxygen at its surface, depending on the oxygen partial pressure in the gaseous environment. In p-type semiconducting compounds, in which the prevailing defects are cationic vacancies, this surface reaction can be primarily described by the following equation:

with K= ([P’]

[h’]“)/P&*

,

(10)

where V’“’and h’ are a cationic vacancy a times ionized and an electron hole, respectively. The square brackets indicate molar concentrations. A vacancy concentration gradient is then set up between the surface and the bulk of the crystal (es. (10)). This leads to a vacancy flux (eqs. (4), (7), (8) ). According to eq. (9 ), the driving force of the rate of propagation of the new defect concentration into the crystal is given by the chemical potential gradient (6 In ao/Sx), related to the vacancy concentration gradient (eq. ( 10) ), through: ~ln~/6x=(1+a)61n[Va’]/&.

(11)

One can point out that in relaxation experiments

90

C. Petot et al. / Eflit of impurities on oxidation kinetics

diffusion takes place in the bulk until all concentration gradients are eliminated, while in corrosion scales the chemical potential gradient is decreased with the thickening of the scale (but is never eliminated). Nevertheless, in both cases the flux of vacancies (eq. (5) ) controls the rate of displacement of the reaction front in the oxide solid solution. Kinetic studies performed in the stability range of the oxide then allow the diffusion processes in the oxide to be followed independently of all other transport processes occuring during the corrosion scale thickening. Consequently, such studies allow analysis of a step in the complex mechanism of corrosion. Eq. (9) shows that the rate of displacement of the reaction front in the material is related to the relative diffusion coefficients values of the cations A2+ and B”+ and to their effective charge. This leads to different types of behaviour: if D,,=D,,, in the presence of homovalent cations no demixing occurs in the material and the reaction rate is the same as in the pure oxide (eq. (6) ), while the presence of alliovalent impurities increases or decreases the reaction rates (eq. (9 ) ) depending on the charge state of the cations (y higher or lower than 1): Jv = -cMvlDA((y- I )m+ 1)6Lnao/Gx.

(12)

if D,#DB, the reaction rate in the solid solution is always related to the charge on the impurity, but it also depends on the relative diffusion coefficient values of the cations (eq. (9)). As an example, we have considered the case where the charge on the solute cations (B”+ ) is higher than that of the cations of the host lattice (y=a/2> 1): If DA> yDs, an enrichment of B must be observed near the side of the lower oxygen partial pressures (i.e. near the metal/oxide interface in corrosion scales). The gradients 6m/6x and 6 LnaolGx have opposite signs. The presence of impurities leads then to a decrease in the reaction rates (eq. (9 ) ). If D, DP Eq. (9) can be written in the following form: Jv=-cM(DA+(yDs-DA)m) x6Lnao/6x+cM(DB-DA)6m/6x.

(13)

In this expression, the first and second terms always

have opposite signs. Consequently, the flux of vacancies is higher in the doped material than in the pure oxide when the reaction starts (sm/&x=O). Then the flux of vacancies decreases with increasing demixing of the impurities in the solid solution independently from the relative diffusion coefftcient values of the cations. A similar analysis could be done if y c 1. As we shall see these conclusions are in agreement with available experimental results. 3.2. Influence of chromium on the oxido-reduction kinetics of transition metal oxides within their range of stability In the following we shall analyse re-equilibration kinetics which are available for pure and chromiumdoped transition metal oxides. In such experiments thermogravimetry and electrical conductivity measurements have been carried out in order to monitor the rate of propagation of the reaction front into the crystal. As we have shown previously the shift velocity of the reaction front is directly related to the prevailing defects in the material (eqs. (9) and ( 11) ). So, we will first consider the defect structure in transition metal oxides on the basis of available experimental results for COO. 3.2.1. Influence of chromium doping on the defect structure and on the transport properties in Co0 One may recall that in eq. ( 10) the cationic vacancy (V”’ ) can be an isolated defect (simple defect model) or a vacancy in interaction with the surrounding atoms and/or defects. As has been suggested theoretically [ 13,141 this interaction can lead to defect aggregates or clusters. “a” is then the mean charge of the vacancy in the cluster. One may point out that these interactions may also be analysed on the basis of the Debye-Hlickel model. Nevertheless, from a thermodynamical point of view the two approaches are identical [ 151. From recent electrical conductivity measurements [ 16,171, on pure Co0 and Co0 doped with chromium or aluminium, it follows that the simple defect model generally used to interpret mass transport experiments is only valid at very low defect or impurity concentrations. The inadequacy of such a model is clearly shown in figs. 1(a and b) where results ob-

C. Petot et al. / E#ect of impurities on oxidation kinetics

-2

(4

...... pure Co0 -6

I;ppPO2 &:~

O

. , .2 ;

-1

.- 0

...... pure Co0 -8

-2

-4

-6

log PO2

.-I t

(atm.)

Fig. I. Electrical conductivity of cobalt oxide pure and doped with aluminium (a) or chromium (b) as a function of the oxygen partial pressure, refs. [ 16,171.

tained on pure Co0 and Co0 doped with chromium or aluminum. Indeed, for the higher doped sample andinthehigh (x A,=2.5x10-3,x~,=3.86~10-3) oxygen partial pressure range (Po, > lo-‘), the electrical conductivities of the doped materials are higher than that of the pure oxide. As we have shown previously, this dependence can be expected only if we take into account defect interactions. In our analysis

91

we have assumed that these interactions lead to defect aggregates as those suggested by theoretical considerations [ 13,141. As an example, we have reported in fig. 2 the various defect concentrations as a function of the oxygen partial pressure (a, = PA/:), for Co0 pure and doped with Al (x,,=O.6~ 10e3) or Cr (xc,= 1.04x 10e3). In this calculation [ 16,171 it is assumed that the interactions among defects lead to the 4: 1 clusters [ 13,141 formed by the tetrahedral aggregate of four vacancies with a cobalt (C”’ ) or a solute cation (To’) in an interstitial position. For aluminium or chromium concentrations higher than 10-3, these results show that clusters are the prevailing defects in Co0 [ 16,171 in the high PO2range. Finally, this analysis shows that the increase in trivalent impurity concentration does not necessarily lead to an increase in cationic vacancy concentration and consequently to an increase in the diffusion processes, as has generally been assumed in the literature. Unfortunately, diffusion studies in chromium or aluminum doped Co0 has not been reported until now, to our knowledge. (a) Influence of chromium on the oxidolreduction kinetics of wiistite

Fig. 3 shows re-equilibration kinetic curves deduced from thermogravimetric measurements performed by Wagner et al. [ 181 on pure and chromium-doped wiistite samples (0.67 wt% Cr). The authors have previously checked that wiistite doped with 0.67 wtl Cr forms a complete solid solution. The results in fig. 3 correspond to the reduction of a wiistite sample from a 1.125 to a 1.050 O/Fe ratio. In fig. 4 we have reported the diffusion coefficient values of Cr and Fe as a function of the oxygen partial pressure [ 19 1, for a ratio O/Fe = 1.05. These data show that chromium diffuses more slowly than iron in wiistite. This set of results is consistent with our formal treatment (cf. 3.1.) and suggests an enrichment of chromium near the crystal surface during the reduction process. This conclusion has been confirmed by examinations of partially reduced wiistite samples [ 201. The partial reduction experiments were performed (in pure CO) on single crystals of wiistite previously annealed at 1386 K in a 50% CO/SO% CO, mixture. As an example, fig. 5 shows chromium segregation

C. Perot et al. / Elfirt of impurities on oxidation kinetics

92

I

(4

I

I

I

pure Co0

(b)

I

I

I

I

I

I

1

1

1200°C

2-

6

/

..’

8

-4

,i

,

1

-2 log PO2 calm.)

I

81

0

r’

1 -4

-2 log PO2 (atm.)

I

0

I

2-

loooOc

2

-

C&

.’

h,,’ ,

..

. V”

.S/‘. 14’ 4-

Y .I;’

4

; a ?

/v;,-’

/’

.I’

,.I

-

/

/‘

.I.‘.

1

-

./;‘, v’ ,..-

-0’

,:‘_..‘,

,g

I

/-I

,.

_-‘,.’ ,’

.:. .:’ :’

./‘.

:

A’

..

/’

/”

: :’

./‘.

/”

,.‘.

_:.

./’

./.”

C 4’ /...” ,:’

.:’ ..‘_ .J.” ./”

.. .

C 3’*/” /’

XQ = 3.86 10-J I)

L

I

1

-4

log PO2

(atm.)

1

1

-2 log

PO2

(atm.1

Fig. 2. Concentrations of the various defects as a function of PO, (a) in Co0 pureref. [ 171 and doped with (b) aluminum x,=0.6x calculated at 1200°C ref. [ 171 or (c) chromium xcr=3.86x lo-” calculated at 1000°C [ 161.

profiles near the metal/oxide interface and the morphology of the partially reduced chromium doped wtistite sample ( 1000 ppm in weight of chromium). The experiments have been done for reduction times between two and five hours. It is important to point out that the thickness of the iron scale does not seem to increase with reduction times. Once formed, the iron layer seems to prevent any direct exchange between wiistite and the gaseous environment. There-

I

1

IO-’

fore, the reduction of Fe0 occurs within its range of stability. This reduction is accompanied by outward diffusion of vacancies, which condense on voids at the metal/oxide interface and by an increase in chromium segregation experimentally observed. (b) Injluence of chromium on the oxidation kinetics of cobalt oxide

Fig. 6 shows re-equilibration kinetic data obtained

93

C. Petot et al. /Effit of immuitieson oxidationkinetics I

I

I

I

..

0.8 -

.

...

pure Fe0

_ - _-chromium

I

doped

wt %

1

J

1

1

2000

( 0.87

Fe0

4000

c

time (sec.)

Fig. 3. Re-equilibration kinetics of pure and doped iron monoxide, ref. [ 18 1.

I

I

I

M

this .

.

.

\

(a)

work

t

’

*\

‘,* . \\ \

-7

I

-*EPMA -_gsmls

-+-

h

rl

lw

-0-

Q

-o-

tmcelapcrI 5sFe)

\* ?

\‘=-

-l! -lO-

-llFeO*94

0

l

\

\%

I

7

8

9

104/T

(K)

I 5

I

f04

\

I T

,

(‘IQ

Fig. 4. (a) Diffusion coefficient values of Fe and Cr in wtistite single crystals, ref. [ 91; (b) Diffusion coefficient values of chromium and nickel (orcobalt) inNiOandCoO,ref. [21].

94

C. Petot et al. /Effect of impurities on oxidation kinetics

:,,,;I

; partially reduced

( 2 h ) at 1385K 4.10s2

Fig. 5. Morphology of the iron layer formed on a partially reduced single crystal of wiistite doped with chromium ( 1000 ppm) and chromium segregation profile near the metal oxide interface.

in the range of stability of pure and chromium-doped cobaltous oxide, at 1373 K. The uniform distribution of chromium in the samples has been checked by ion probe micro-analysis before the experiments. Electrical conductivity measurements have been used to monitor the re-equilibration kinetics after an abrupt change in the equilibrium oxygen partial pressure. Such measurements allow a precise and direct evaluation of the relaxation process. Indeed, Co0 shows a small range of departure from stoichiometry ( < 10T2). The mobility (P) of the electronic holes then may be assumed to be constant within the range

of oxygen partial pressure corresponding to the relaxation experiments (fig. 6). Consequently, the electrical conductivity changes (Aa= (ep)Ap) during the re-equilibration process can be assumed to be directly related to the electron hole concentration changes (Ap). In the kinetics experiments the oxygen partial pressure was changed isothermally by admitting a new gas mixture in less than one minute. Then the electrical conductivity was measured as a function of time until the new equilibrium state was reached. The oxygen partial pressure was measured permanently near the sample with a zirconia elec-

95

C. Petot et al. / Efwt of impurities on oxidation kinetics 1.01

0.9 -

__Cr ,.

rtitim I

2

time 10m3(sec.)

fromoz1

I.2 .* I

1

I

1

doped NiO

@lat.

‘/

pure NiO

‘H/.

%)

/

/

&<,a

K

1

’

Fig. 6. Re-equilibration kinetics of pure and chromium doped cobalt oxide (reduction from oxygen to air).

trochemical gauge. Details of the experimental arrangement have been reported in previous papers [ 17-191. The results reported in fig. 6 show that chromium decreases the rate of re-equilibration and this effect is more pronounced when the chromium concentration is increased. These results then suggest that yDcr< DCO. This conclusion is in agreement with chromium and cobalt diffusion data reported by Peterson et al. [ 2 1 ] (fig. 4b) and with data concerning the repartition of chromium in Co0 under the influence of the chemical potential gradient. Indeed, an increase of the chromium concentration is observed near the metal/oxide interface of partially reduced samples (as previously mentioned for wtistite ). Furthermore, an enrichment of chromium has been observed near the surface of chromium-doped samples after quenching [ 22-241. This effect has been attributed to the outward diffusion of vacancies (reduction process) which occurs in the material during cooling [ 25 1. (c) Influence of chromium doping on the oxidoreduction kinetics of nickel oxide

Nickel oxide has been widely studied in the literature due to its fundamental and technological interest. As an example, fig. 7 shows the results obtained by Nowotny et al. [ 261 during the oxidation

0

1

tip?

1W3 (sec.)

3

Fig. 7. Re_equilibrium kinetics curves of pure and chromium doped nickel oxide, ref. [ 261 (oxidation from PO,= lo-* atm. to Po,=O.21 atm.)

of pure and chromium doped (0.1 atl Cr) single crystals of nickel oxide. The amount of chromium in the doped crystals is lower than its limit of solubility (close to l.OW at 12OO’C). As for Co0 and FeO, these results show that chromium decreases the oxidation/reduction kinetics of nickel oxide and this effect is more pronounced for the higher doped samples (0.62%). According to the diffusion data obtained by Peterson et al. [ 12 ] (fig. 4b) it follows that yDcr< DNi. In agreement with our formal treatment and with this set of data an enrichment of chromium has been observed near the metal/oxide interface of the corrosion layers (as we shall see in the following section) or near the surface of quenched samples [ 22,241. As for the quenched chromium-doped Co0 samples this enrichment has been attributed to the reduction processes (decrease of the vacancy concentration on the sample surface) occuring during cooling [ 251.

96

C. Petot et al. / Eflect of impurities on oxidation kinetics

3.3. Corrosion of Ni/Cr alloys

Extensive examinations of the NiO scales formed during the oxidation of Ni/Cr alloys have been performed by Ben Abderrazik [27] and by Stott et al. [28,29]. On the one hand, Ben Abderrazik has observed an increase of the chromium concentration near the metal/oxide interface, in agreement with our previous conclusions. On the other hand, Stott et al. [ 281 have examined in more detail the early stages of the oxidation of Ni/Cr alloys containing 20 wt% Cr. They have shown that a NiO layer develops at the surface of the alloy, while Cr203 forms as discrete precipitates in the subjacent alloy. These precipitates are subsequently incorporated into the thickening NiO scale. After a few hours they have observed that the oxidation rate decreases considerably due to the formation of a continuous layer of Cr203 at the alloy/oxide interface. This layer is much more protective than the nickel rich oxide scale and thickens at a lower rate. Its formation then explains the lowering of the oxidation rate experimentally observed. Furthermore, Stott et al. [28] have studied the corrosion of Ni/Cr alloys containing 1 to 5 wt% Cr. They have observed that the depth of penetration of the oxidation front in the alloy decreases with the increasing of chromium concentration (fig. 8). This observation is consistent with the oxidation/reduction kinetics results obtained by Nowotny et al. [ 261 (fig. 7)) who have observed a decrease of the reduction kinetics when the amount of chromium increases (cf. 3.2.1.(c)). The observations of Stott et al. may then be attributed to an increase in concentration of chromium in the nickel oxide scale when the amount of Cr increases in the alloy. This decreases the shift velocity of the oxidation front in the corrosion layer and consequently in the alloy. Let us remark that the oxygen potential gradient is continuously maintained through the oxide layer during corrosion and this leads to an increase in chromium segregation in the scale with time until the formation of a second phase. One can point out that Stott et al. [ 28,291 have observed the formation of discrete Crz03 precipitates in the subjacent alloys, which are subsequently incorporated into the thickening NiO scale when corrosion proceeds. Consequently, both the difference of mobilities of nickel and chromium in the nickel rich oxide scale and the

1

lh

1

I

I

I

.

Lo-

\

5h \

‘\ ‘\

\

l

‘\\,’‘*\\

\ --\

l

‘.

.N

-.._

-

- .,

---.-

HOO°C 1ono’c

10 h

.

;\ IO -

‘0

\

20 h \

l\

I

0

‘9, --•-

-_

-

_._

-.--__._

I

0.02

chromium

I

9ooQC 990°c

1

0.04

concentration

I

1

0.00

(wt )

Fig. 8. Depth of penetration of the oxidation front in a Ni/Cr alloy as a function of the chromium concentration, ref. [ 281.

incorporation into the thickening corrosion layer of the CrZO, precipitates present in the subjacent alloy, contribute to the formation of the CrZ03 layer at the alloy/oxide interface after a few hours of oxidation [28,29]. Remark: One can point out that the good consistency between our formal treatment and the different available experimental results (diffusion, kinetics, demixing) confirms that the correlation effects between the different fluxes can be neglected in the case of NiO, Co0 and Fe0 doped with chromium. This assumption is in agreement with an analysis of chromium diffusion data done by Peterson [ 2 1] from which it follows that modest impurity/vacancy binding energies must be expected in NiO as well as in Coo.

4. Conclusion From the expression of the flux of matter which appears in ptype semiconducting oxides exposed to an oxygen potential gradient it has been possible to predict the influence of impurities on the oxidation/

C. Petot et al. /EBpcrof impuritieson oxidationkinetics

reduction kinetics of oxides. According to the available experimental results in the stability range of oxide solid solutions we have shown that the formal treatment we have proposed allows explanation of both the enrichment of chromium near the metal/ oxide interface in corrosion layers and the decrease of depth of penetration of the internal oxidation front in the alloy when the chromium concentration increases. Furthermore, we have shown that the chromium kinetic demixing in the oxide scale contributes to the formation of a continuous layer of Cr203 experimentally observed at the metal/oxide interface of Ni/Cr alloys after a few hours of oxidation. Finally, it has been possible to show that kinetic studies performed in the stability range of oxide solid solutions allow the diffusion processes in corrosion layers to be followed independently from all other transport processes occuring during the scale thickening. Such studies then allow a step in the complex mechanism of alloy corrosion to be followed.

References [ 1 ] A. Atkinson, Modem Phys. 57 ( 1987) 437. [2] C. Wagner, Corms. Sci. 9 (1969) 91.

[ 31 T. Narita, K. Nishida and W.W. Smeltzer, J. Electrochem. Sot., Solid State Sci. Techn. 129 (1982) 209.

[ 41 J. Benard, L’Gxydation des Metaux (Gauthier Villars, Paris, 1962).

[ 5 ] P. Kofstad,

HQh Temperature Corrosion (Elsevier, Amsterdam, 1988). [6] G. Petot-Ervas and C. Petot, J. Phys. Chem. Solids 5 1 (1990) 901. [ 71 G. Petot-Ervas and C. Petot, Science of Ceramics 14, ed. D. Taylor (Institute of Ceramics, University of Kent, Canterbury, UK, 1987) p. 527. [S] G. Petot-Ervas, in: Surfaces and Interfaces of Ceramic Materials, eds. L.C. Dufour, C. Monty and G. Petot-Ervas (Kluwer, Dordrecht, 1989) p. 337.

97

[ 91 H. Schmalxried and W. Laqua, Oxid. Met. 15 ( 1981) 339.

[ lo] H. Schmalzried, React. Solids 1 ( 1985) 119. [ 111 D. Monceau, G. Petot-Ervas and C. Petot, Solid State Ionics 45 (1991) 231.

[12 1J. Wolfenstine, D. Dimos and D.L. Wohlstedt, J. Am. Ceram. Soc.68 (1985) 117. [13‘IS.M. Tomlinson, C.R.A. Catlow and J.H. Harding, in: Transport in Nonstoichiometric Compounds, eds. G. Simkowitch and V.S. Stubican (Plenum Press, New York, 1985) p. 539. [14,I A.B. Anderson, R.W. Grimes and A.H. Heuer, in: Transport in Nonstoichiometric Compounds, eds. G. Simkowitch and V.S. Stub&n (Plenum Press, New York, 1985 ) p. 527. [ 151 R. Farhi and G. Petot-Ervas, J. Phys. C 37 (1976) 438. [ 161 F. Gesmundo, F. Viani, G. Petot-Ervas, C. Petot and V. Buscaglia, Adv. Ceram. 23 (1987) 83. [ 171 G. Petot-Ervas, C. Petot, F. Gesmundo and C. Clayss, J, Phys. Chem. Solids 5 1 ( 1990) 27. [IS] R.L. Levin and J.B. Wagner, Trans. Met. Sot. AIME 233 (1965) 159. [ 191 G. Petot-Ervas, H. Klimnyk, C. Monty, J. Janowski and C. Petot, in: Nonstoichiometric Compounds, eds. J. Nowotny and W. Weppner (Kluwer, Dordrecht, 1989) p. 4 11. [20] H. Klimczyk, G. Petot-Ervas, C. Monty, St. Jasienska and C. Petot, X-ray Optics and Microanalysis ( 1990) p. 690. [21] N.L. Peterson, Solid StateIonics 12 (1985) 201. [ 221 W. Hirschwald, I. Sikora and F. Stolze, Surface Interface Anal. 7 (1985) 155. [23] I. Sikora, F. Stolze and W. Hirschwald, Surface Interface Anal. 10 (1987) 424. [24] W. Hirschwald, I. Sikora, F. Stolze and J. Oblakowski, Surface Interface Anal. 14 (1989) 477. [25] G. Petot-Ervas and C. Petot, J. Eur. Ceram. Sot. 6 (1990) 323. [26] J. Nowotny, J. Oblakowski and A. Sadowski, Bull. Acad. Polon. Sci. 33 ( 1985) 100. [27] G. Ben Abderraxik, Thesis (University Paris XI, 1986). [28] F.H. Stott, G.C. Wood, D.P. Whittle, B.D. Bastow and Y. Shida, Solid State Ionics 12 (1984) p. 365. [29] F.H. Stott, J.S. Punni, G.C. Wood and G. Deamaley, in: Transport in Nonstoichiometric Compounds, eds. G. Simkowitch and V.S. Stubican (Plenum Press, New York, 1985) p. 463.