Diffusion studies in oxides scales grown on alumina-and chromia-forming alloys

Seripta Materialia, Vol. 37, No. 5, pp. 651-660, 1997 Elsevier Science Ltd Copyright © 1997 Acta Metallurgica Inc. Printed in the USA. All rights reserved 1359-6462/97 S17.00 + .00

Pergamon

PII S1359-6462(97)00167-X

D I F F U S I O N S T U D I E S IN O X I D E S S C A L E S G R O W N O N ALUMINA-AND CHROMIA-FORMING ALLOYS A.M. Huntz, J. Balmain, S.C. Tsa'f, K. Messaoudi, M.K. Loudjani, B. Lesage and J. Li* M6tallurgie Structurale, CNRS URA 1107, Brit. 413, Universit6 de Paris-Sud, 91405 Orsay, France. *Institue of Corrosion and Protection of Metals, Academia Sinica, 110015 Shenyang, P.R.China (Received February 5, 1997) (Accepted April 2, 1997) Introduction

Sabioni [1] and Le Gall [2] showed that, in both chromia and alumina cases, the self-diffusion coefficients obtained in the literature for bulk materials could notaccount for the oxidation rate constants of such oxides. Thus, new diffusion experiments were performed in chromia [3-5] and alumina [6-9] single crystals and polycrystals, but these more recent results could not again account for the oxidation constants, as shown in Figure 1. Indeed, in the case of both oxides, the oxidation rate constants, calculated using Wagner's theory [10], were smaller than the experimental ones (Fig. 1, 1%being defined by: X2x = 1%t + cte). But, the temperature range of diffusion tests and of oxidation experiments is not the same. Later, TsaY [11,12] and other authors [13-17] performed, either on bulk materials or on oxide scales, diffusion experiments at lower temperatures than previously, i.e. in the temperature range of oxidation experiments. But, again, the comparison with 1%did not appear as satisfactory. Thus, Tsa'f, in chromia scales, analyzed the penetration profiles by intoducing two modifications of the classical analysis of the penetration curve [ 11,12]: °

2.

The first part of the penetration profiles was related to an effective diffusion composed of both bulk (Db) and grain boundary (Dgb) diffusion. Classically only bulk diffusion was considered. Secondly, the roughness of the scale's surface, which is important but uniform, was used to estimate the fraction "f" of sites associated with grain boundaries. This fraction appears in the expression of the effective diffusion coefficient [18], Deff= (1 - f) Db + f Dsb. In the case of smooth surfaces (diffusion in single or polycrystals of bulk oxides), "f" is classically given by f = 38 / ~ , where • is the average grain size of the studied material and 8 is the grain boundary width. In the case of a rough surface, (typically the roughness of an oxide scale surface Ra is of the order of 1 p.m), fr is given by: fr= ~

+ 4 Ra)

651

(1)

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DIFFUSION STUDIES 1N OXIDES SCALES

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1

10 -I

kc(eXp)

A l 2 0 3 ~

......................... ii ~.

!

......................

i ¢q

kc(e~P) il

..................

e x

2

3]

1 0 -1

1 0 "1

1 0 -1 4 1 0 "l

~t

................................................ !

~..i:..: ............ i................:..~..i

,[ kc(CMC)AI203

~

6.5

8

i

.......................~..........................

-I

lif t 7

7.5

8.5

9

9.5

1/T*104 (K" 1) Figure 1. Experimental and calculated kc values for Cr203 and AI203 scales. Calculations were made using Eq.7 [10] and D values from [1-9]. Experimental kc values are from [11, 12, 15].

With these two modifications, Tsa'f obtained a satisfying approach of the diffusion in chromia scales: as shown in Figure 2, there is agreement between calculated oxidation constants on the basis of his diffusion coefficients (using Wagner's theory, see eqs.7-8), and the experimental ones: So, in the following, only the results obtained by such an analysis will be considered. It can be noticed that if Graham's results [13] are analyzed as suggested by TsaI, then results similar to those of TsaY are obtained [11,12]. However, applying the same methodology for self-diffusion studies in alumina scales formed on [~ NiAI, Balmain [15] found diffusion coefficients which could not account for the oxidation rate: they were too small (as shown in Fig. 3). It was suggested that a part of this discrepancy could be due to the fact that diffusion coefficients were determined on the outer part of the scale, i.e., at high oxygen pressure, while the parabolic rate constants are relevant of the whole scale thickness. But, it was observed D °

---

Dcr

900°C

10-1o with Y 1 0 -11

-

with Y

m m .

1 0 -12 . - D g b 10-13 10.14 m m .

t~ 10"Is

Deff

\

/ without Y

10 "16

10-17

Db----" Diffusion in Cr203 scale

Calc. k

Exp. k c

Figure 2. Comparison at 900°C of Do and Dc, (full and dashed lines) [11,12], and o f calculated and experimental k~ for chromia scales formed on Ni-30Cr without or with yttrium.

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DIFFUSION STUDIES IN OXIDES SCALES

A 1203 on NiAI ll00°C

Dcr..

D°~

653

D°----~ A 1203/FeCrAI-1200°C with Y with Y

1 0 "12

....

1 0 q3-

---I7 ___.g

¢q

m

10a3

r

fq

""

1 0 qs-

Der r

1 0 qL

[~

1 fin

10q4

D'rt

1 0 q6-

O

with Y

Dgb

with Y

Derr

b~,;- -b:" D-b- "

L

O

1 0 4s

Derf

with Y

1 0 "16

10"17

Db

10"19with Y k c a l c

"----Db"

Calc. k c

kcex p

Figure 3. Comparison ofD ° (full lines) and D° (i.e. cation, dashed lines) in alumina scales formed on ~ NiAI, at 1100°C 115] and of calculated and experimental oxidation constants kc for alumina scales without or with Y-doping.

Exp. k c

Figure 4. Comparison of diffusion coefficients of oxygen (full lines) in alumina scales formed on "Z" FeCrAI alloy, at 1200°C with calculated and experimental oxidation constants k¢ for alumina scales without or with Y-doping. (FeCrAI). Since it is well known that the microstructure of alumina scales can vary widely according to the nature of thesubstrate, alloys of various origins were studied.

that agreement between calculated and experimental ko values in case of A1203 scales would need greater diffusion coefficients (Figs. 1 and 3). Even if the defect type and mobility near the inner interface (i.e. at low oxygen pressure) are different from those at the outer interface, they could not account for the discrepancy, as the parabolic growth rate is controlled by the "slowest diffusion step of the fastest chain" [19]. Considering that the k~ values determined by Balmain are close to Dgb values instead of being close to (f Dgb), this author suggested that the lack of compactness of the scale could be a reason for the discrepancy between calculated and experimental 1~ values [15]. The objective of this paper is to explain these discrepancies. Thus, diffusion studies are performed on chromia (yttrium diffusion) and alumina scales (oxygen and yttrium diffusion), and simultaneously (1) I v (counts/s) and (2) in Iv/(Iv+ Ic~) 3 10s[ 0

2 l0 s i

-5

[-........ .......'

(2) . . . . "". . . .

"--.

-1o

-6.S

L

-6.9

~

~'%

D

= 8 . 2 1 0 "s3 cm~/s

9.5

(1) -7

(2)

-7.1

before diffusion

,Dh,=' 310"~cm2'/s' 0 10 ° . 0

. 2

. 10 "s

. 4

10 "s

9

.10

(l) Iy ILj

-8.5

(2)

(2) In Iv/(Iv+ It,) after diffusion in CrzO~/scale at 900°C

1 l0 s

in (Iv/ Iv+ lcr) = (1) f (x2) and (2) f (x6/s) -6.7

6

10 "s

8

-15 10 "s

x (cm) Figure 5. Yttrium SIMS profiles:0) Initial yttrium film just afterdeposition on a chromia scale on a Hi-30Cr alloy, and (2) In of Y concentration, after diffusion at 900°C for 2h, showing that the penetration profile is made of two parts.

-7.2 2 10 .6

4 10"~

(1) xZl06 (cm 2)

6 10 .6

' ' '~"

-10.5

8 10 "~

10 "s

(2) x ~/s(cm "Is)

Figure 6. Analysis of the yttrium penetration profile of Figme 5 (curve 2): yttrium concentration as a function of(l) x 2 (determination of Db) and of (2) x615 (determination of Dgb).

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the microstructure o f the scale is observed. An attempt will be made to relate the discrepancies between the diffusion coefficients and the oxidation rate constants (1~) to the scale morphologies (and not only to the grain size as made by [16]). It would also be interesting to take into account the effect of impurities. Indeed, the two considered oxides are very stoichiometric, particularly alumina [20], and small amounts of impurities, at the ppm level, can alter the behavior of these oxides. Besides, this effect is a reason for the dispersal of the literature data in both oxidation and diffusion domains. But, at this date, even if STEM results have been obtained, literature data on impurity segregation in chromia and alumina oxide scales are insufficient to give clear ideas on these phenomena.

Experimental Procedure and Materials Cr203 scales were formed on a Ni-30Cr alloy manufactured by CECM (France) [l 1,12,17]. Alumina scales were formed on ~ NiAI and on three FeCrAI alloys of various origins: alloy "A" is a high purity laboratory alloy, provided by ENSM Saint Etienne. Alloy "F" is MA 956, provided by INCO Limited and alloy "Z" was provided by Imphy S.A. and contains Zr as a doping element. The NiAI ingot was prepared by arc melting under argon at CEN Saclay. Yttrium ion implantation (in NiCr and NiAI) was performed at an energy of 150 keV with a dose of 10 ~6at/cm 2 (CSNSM, Orsay). Oxide scales were grown at 900°C in order to develop chromia and at 1100°C in order to develop alumina for durations long enough to form a continuous scale with thickness above 1.5 ~un. It was verified that, in all cases, for such oxidation durations, the oxidation process is diffusion-controlled. It means that diffusion experiments were not performed, neither on thin scales (the kinetics of which could be controlled by a reaction at the interface), nor on thick scales with microcracks. Moreover, it was also verified, for several oxidation times, that the diffusion coefficient does not depend on the oxidation duration [11, 21]. The average grain size cb in the oxide scales was determined by SEM observations of the surface. Oxygen diffusion experiments were carried out by changing the environmental gas during oxidation from 160 to lSo (at pO2 = 0. latm) without intermediate cooling. Before yttrium deposition, the scale was grown on the alloys and the cooling was performed at a controlled rate (below 2°C/min) in order to avoid the formation of damages in the scale [ 11 ]. Then, a drop of an yttrium chloride solution was deposited on the outer surface of the scale and a stabilisation annealing was carried out at 300°C in air for 1 hour in order to form yttrium oxide [17]. It was verified that the thickness of the yttrium film was -- 15 nm (see further on). The diffusion treatments were made at 900°C for chromia scales, and at 1100°C or 1200°C for alumina scales. For all experiments, the tracer concentration profiles were measured by SIMS (Secondary Ion Mass Spectrometry) [ 11,12,17]. The sputtering rate was determined by measuring the crater depth so that the sputtering time can be transformed into deepness. The ratios I v / I v + Icr and I~80 / (I~gO + I160) have been used to calculate the diffusion coefficients. It was confirmed that the diffusion of yttrium in the Cr203 scale occurs in a B regime [22], i. e.: ~i < (Dbt) ~n << cb. So, the first part of the penetration profiles makes it possible to determine effective diffusion coefficients according to Fick's solution for thin films in the case of Ydiffusion (eq.2) and for constant surface concentration in the case of O-diffusion (eq.3): C(x) = M(~D~. t) 1/2 exp(-x2 / 4D~f. t)

(2)

(C(x~ - Cs) / (Co - Cs) = erf(x / 2 D~D-~a~.t )

(3)

and

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DIFFUSION STUDIES 1N OXIDES SCALES

655

From the second part of the profiles which is related to grain boundary diffusion, Dsb can be determined by equation (4) proposed by Whipple-Le Claire: (4)

Dgb ~ = 0.661 (-Pgb)"5/3(4Db ] 0 I/2

Psb is the slope of the curve lnC -- f(x6/5), plotted for the second part of the experimental profiles. Taking ~5= 107cm and combining above eqns. of Deft and (4) yields (1-fr)Db + (1.332 X 107) fr (-Pgb)5/3 t '/2 (Db) 1/2 -Derr : 0

(5)

which makes Db calculation possible. Dgb can be obtained from equation (4). The fr values were calculated (eq. 1) on the basis of determinations of • and of the surface roughness Ra by profilometry. The choice of lnm for ~5in chromia and alumina scales is arbitrarily done in all the literature. 5 can vary with temperature and segregation, especially segregation of aliovalent elements which can induce charge effects. But, at this date, there are no available literature results on these variations. TEM and especially HREM images on aluminas [23, 24] seem to indicate that, except when an amorphous phase is present, there is no geometric width of the grain boundaries. Results and Discussion

Due to the disagreement of theoretical and experimental values of oxygen diffusion in alumina scales developed on 13NiA1 alloy (see Fig. 3), oxygen diffusion in alumina scales was studied for other alloys (FeCrAI). Since it is well known that the microstructure of alumina scales can vary widely according to the nature of the substrate, alloys of various origins were studied. Results o f the FeCrAI "Z" alloy, given in Figure 4, are similar to those found for alumina scales developed on 13NiAI: small values of calculated 1~ compared to the experimental ones and Dgb values close to experimental 1~ values. The second alloy tested was the high purity "A" FeCrAI. Similar observations as for the "Z" alloy were made. Again, Dgb values are close to experimental k¢ values. Yttrium diffusion was studied in both chromia and alumina scales. Such diffusion coefficients are of interest due to the important role of yttrium for the high temperature environmental resistance of such 13 12

1.5 l0 s (l) In Iv before diffusion

11

1 lO s

(I)~o

(2)

9

5 104

8 7

i V(~bdiffusion ~ ~ a f t e r __~tA19.0LG. . . . . . . 0 2 l0 "s 4 10-s X (cm)

11 6 1"0"s

Figure 7. YttriumSIMS profiles:(1) Initial yttriumfilmjust afterdeposition:yttriumhas penetratedup to 600nm in an alumina scale previouslyformedon a "A" FeCrAIalloy.(2) Yttriumprofileafterdiffusion2h at 1100°C.

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DIFFUSION STUDIES IN OXIDES SCALES

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(a)

(b)

(c) Figure 8. Morphology of the surface of the oxide scales formed on: (a) Ni-30Cr alloy (i.e. chromia scale), (b) [i NiAI, i.e. alumina scale, (c) "Z" FeCrAI alloy, i.e. alumina scale, (d) "A" FeCrAI alloy, i.e. alumina scale, (e) "F" FeCrAI alloy, i.e. alumina scale. (Figure continued.)

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DIFFUSION STUDIES IN OXIDES SCALES

657

(e) Figure 8. (continued).

scales [25,26]. For chromia scales, before the diffusion treatment (Fig. 5 curve(I)), there is a yttrium film of thickness - 15nm at the sample surface. It can be considered as a thin film compared to the further diffusion depth which reaches = 700nm (Fig. 5 curve (2)). From such a penetration profile, and as shown in Figure 6 (curves (1) and (2)), bulk and grain boundary diffusion coefficients o f Y in chromia scales can be determined with accuracy: at 900°C, it is found that Db = 3 10"~s cm2s"t and Dgb = 8.2 10"13 cm2s-k Both bulk and grain boundary diffusion coefficients of yttrium, are lower than those for oxygen and chromium diffusion in the same chromia scale [17]. The same experiment made on an alumina scale developed by oxidation at 1100°C of "A" alloy leads to surprising results, though the sample was cooled before the yttrium film deposition at a rate much smaller than that used for chromia scale. Figure 7, curve (1) corresponds to a profile after the film deposition, thus without any diffusion treatment, and reveals an yttrium penetration up to 600nm, a distance as important as the penetration after the diffusing treatment (Fig. 7,curve 2)....Diffusion coefficients cannot be calculated from such a penetration profile.

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TABLE 1 Diffusion Results at 1200°C in an Alumina Scale Formed on MA956 Oxygen Cation(chromium)

Db [cm2s- 1] 2.7 t0 -21 9.8 10-17

Deft [cm2s" 1] 2.310 -15 2.5 10-14

D8 b [cm2s- 1] 317 10-13 3.9 10-12

Detailed studies of the external scale morphology, Figs. 8, show that: - for chromia, (Fig. 8a), the scales are compact and homogeneous, while, - for alumina formed on I] NiAI or on "Z" and "A" FeCrAI alloys, Fig. 8b, c and d respectively, the scale is either quite buckled, heterogeneous or porous, possibly with a honeycomb structure.

Thus, it seems that the quality of the diffusion coefficient determination in scales depends on the compactness of the scale rather than on its nature. If the scale is not compact and/or contains porosity, short-circuits between buckled zones or between grains, microcracks .... then the diffusing species rapidly reach the inner interface of the scale via these short-circuits and the oxidation rate is controlled by this fast diffusion along the short-circuits. In order to verify this idea, two other experiments were made. One concerns a diffusion experiment in an alumina scale which looks very compact and homogeneous, Figure Be, formed on MA956 FeCrAI alloy ("F" alloy). In this case, results agree with those obtained on chromia scales, and values of anionic and cationic selfdiffusion coefficients are given in Table 1. Cationic diffusion was simulated by chromium diffusion as Cr is isovalent with AI, and it was shown that in alumina Dcr = DA! [27]. Then, the oxidation constant was calculated according to Wagner's theory, i.e. using the following equation: Ppo ext

b

k~(calc.) = JPo,:' [D~'i°"+aD¢~i°"] dln(p°')

(6)

(b) (a)

Figure 9. SIMS ionic image on the cross section of: (a) Ni-30Cr oxidized 165h in 1602, then 5h in 1802 at 900°C and, (b) 13NiAl oxidized at 1100°C 24h in ~602, then lh in ISO2.

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DIFFUSION STUDIES IN OXIDES SCALES

659

for an oxide MaOb, with pO ~xt and pO ~nt the oxygen pressure at the outer and inner interfaces of the scale, respectively, taken as the equilibrium pressures. This relation leads to: l~ -- 6D0°f+8 D taro. ~ff

(7)

if it is assumed that diffusion depends on the oxygen pressure, that the prevailing defects in alumina, in the oxygen pressure range of the diffusion experiments, are the aluminium vacancies (V 'Al) and/or the oxygen interstitials (O '~') and that these two defects are present simultaneously in equal quantities. In the case of this system, A1203 on MA956, there is agreement between the calculated and the experimental oxidation constants as kc (calc.)= 2 10-~3cm2s"l and 1%(exp.) = 5 10"13cm2s-~. A remark can be made in connection with the diffusion results given in Table 1. They are slightly different from those determined by Clemens et al.[16] in an alumina scale formed on the same alloy, but these differences are largely related to the interpretations. They made the assumption that oxygen diffusion was preponderant for the scale growth while our results (Table 1) shows that cationic diffusion predominates. Thus, as they calculate D Ob from k~, this diffusion coefficient is overestimated as well as D o. The second experiment consists in ionic imaging of the cross section of two previously oxidized samples (Fig. 9). The ~80-image of a chromia scale formed on NiCr (Fig. 9a) shows that ~aO is concentrated in the scale, while, the lSO-image of an alumina scale formed on NiA1 (Fig. 9b) shows that ~SO has diffused more than 100lxm into the substrate, which indicates that quasi-instantaneously, there is a sheet of ~So at the inner interface of the scale. This sheet feeds the diffusion in the substrate. So, though many microstructural studies have been made on both chromia and alumina scales [28], it is difficult to draw general conclusions. This isprobably due to the fact that the structure of the scale can vary according to the substrate type. For instance, duplex scales can be observed with small grains at the outer side and large columnar grains at the inner side, or inversely...The grain size evolves with the oxidation time, as shown by Clemens et al. [16]....So, the question remains open: are the rapid diffusion paths in oxide scales grain boundaries or something else, such as microcracks or voids? It seems that according to the microstructure both cases can occur. If the scale is not very compact, then surface diffusion paths justify the growth rate, and the bulk and grain boundary diffusion coefficient determined in the outer part of the scale do not account for the growth rate. Conclusion

This work allowed us to show that an analysis of diffusion in scales is possible, provided that: 1. 2. 3.

the roughness of the scale surface is taken into account, the first part of the penetration profiles is considered as due to effective diffusion, i.e. bulk and grain boundary diffusion, the scale is compact and homogeneous.

Any type of fast short-circuits such as porosities, microcracks, etc...make the diffusion analysis impossible. Therefore every diffusion study must be accompanied by a morphological study of the oxide film on a fine scale (nanostructure study), in order to evaluate its diffusion behaviour. Results which are obtained without such microstructural observations have to be re-examined. It is clear that the effect of impurities should also be considered.

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Acknowledgement T h e authors w o u l d like t o . a c k n o w l e d g e C. D o l i n at C N R S B e l l e v u e for realising the S I M S analyses.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.

A.C.S. Sabioni, A.M. Huntz, J. Philibert, B. Lesage and C. Monty, J. Mat. Sci., 27, 4782 (1992). M. L¢ Gall, A.M. Huntz, B. Lesage, C. Monty and J. Bemardini, J. Mat. Sci., 30, 201 (1995). A.C.S. Sabioni, B. Lesage, A.M. Huntz, J.C. Pivin and C. Monty, Phil. Mag.A, 66, 333 (1992). A.C.S. Sabioni, A.M. Huntz, F. Millot and C. Monty, Phil. Mag.A, 66, 351 (1992). A.C.S. Sabioni, A.M. Huntz, F. Millot and C. Monty, Phil. Mag.A, 66, 361 0992). M. Le Gall, B. Lesage and J. Bemardini, Phil. Mag. A, 70, 761 (1994). D. Prot and C. Monty, Phil. Mag. A, 73, 899 (1996). M. Le Gall, A.M. Huntz, B. Lesage and C. Monty, Phil. Mag. A, 73, 919 (1996). D. Prot, M. Le Gall, B. Lesage, A.M. Huntz and C. Monty, Phil. Mag. A, 73, 935 (1996). C. Wagner, Z. Phys. Chem., B21, 25 (1933). S.C. Tsal, A.M. Huntz and C. Dolin, Oxid. Met., 43, 581 (1995). S.C. Tsal, A.M. Huntz and C. Dolin, Mat. Sci. Eng., A212, 6 (1996). M.J. Graham, J.l. Elridge, D.F. Mitchell and R.J. Hussey, Mater. Sci. Forum, 43, 207 (1989) (Trans Tech Publications, Switzerland). M.E. Lobnig, H.P. Schmidt, K.Hennesen and H.J. Grahke, Oxid. Met., 37, 81 (1992). J. Balmain and A.M. Huntz, submitted to Mat. Sci. Eng. D. Clemens, K. Bongartz, W.J. Quadakkers, H. Nickel, H. Holzbrecher and J.S. Becket, Fresenius J. Anal. Chem., 353, 267 (1995). J. Li, M.K. Loudjani, B. Lesage and A.M. Huntz, submitted to Phil. Mag. A. E.W. Hart, Acta Metall., 5, 597 (1957). J. Philibert, La Revue de M6tallurgie-ClT/Sci. et G6nie des Mat6riaux, 1601 (1993). R.R.Dils, Ph.D. Thesis, Stanford University, (1965). S.C. Tsal, Doctor Thesis, University Paris XI, France (1996). L.G. Harrison, Trans. Faraday Sot., 57, 74 (1961). S. Lartigue-Korinek, C. Carry, F. Dupau and L. Priester, Mat. Sci. Forum, vols 170-172, 409 (1994), Trans Tech. Publ., Switzerland. S. Lartigue-Korinek and F. Dupau, Acta Metall. Mater., vol.24, n° 1,293 (1994). M.J. Bennett, and D.P. Moon, "The Role of Active Elements in the Oxidation Behaviour of High Temperature Metals and Alloys", Edited by E. Lang, Elsevier Applied Sciences, London, 1! I (1988). A.M. Huntz, "The Role of Active Elements in the Oxidation Behaviour of High Temperature Metals and Alloys", Edited by E. Lang, Elsevier Applied Sciences, London, 81 (1988). E.G. Moya, F. Moya, A. Sami, D. Juv6, D. Tr6heux and C. Grattepain, Phil. Mag.A, 72, no.4, 861 (1995). Microscopy of Oxidation, 1- Eds. M.J. Bennett and G.W. Lorimer, (1990) and 2-Eds. S.B. Newcomb and M.J. Bennett, (1993), The Institute of Materials.