Grain boundary diffusion and oxidation processes

Solid State Ionics 117 (1999) 7–11

Grain boundary diffusion and oxidation processes Jean Philibert ´ Metallurgie Structurale, Universite´ de Paris-Sud, F-91405 Orsay Cedex, France Received 17 July 1997; accepted 16 September 1997

Abstract Oxidation kinetics are a complex phenomenon as they involve several elementary processes, related to the microstructure. Conversely this microstructure results from the interplay of all these processes. The role of grain boundary diffusion as a main factor at low temperatures in comparison with other short-circuits remains questionable.  1999 Elsevier Science B.V. All rights reserved. Keywords: Oxidation kinetics; Microstructure; Grain boundary diffusion

1. Introduction The basis of the kinetics of the oxidation of metals and alloys is well understood since the pioneering work of Wagner [1,2]. However Wagner’s model is an ideal one and, in most practical cases, the situation is not that simple, as the conditions for Wagner’s model to be valid are generally not fulfilled. The question can now be formulated as follows: can the oxidation kinetics of a given metal or alloy be predicted? This question deserves some discussion, as modelling of oxidation is required in many instances for technological purposes. Let us consider the simplest case: the oxidation of a pure metal. A simple parabolic oxidation kinetics is expected only if the reactions at the outer and the inner interface are not limiting the whole process. Oxidation belongs to the general class of Reactive Diffusion processes [3] that are controlled by: atomic transport of chemical species, including point defects, by diffusion through the reaction

product(s): intermetallic compound, oxide, sulphide . . . Diffusion (sometimes gas permeation) proceeds through the lattice as well as along grain boundaries and short circuits (pores, cracks, fissures or crevices, . . . ). Diffusion on surfaces and at metal / oxide interface are other paths of transport. interface reactions [4] since the reaction product is growing either at the inner (metal / oxide) or / and at the outer (oxide / atmosphere) interface. Transport by diffusion and interface reactions occur in series, so that the kinetics of the whole process (the thickness x or the mass of the reaction product) follow a parabolic law x 2 /k p 1 x /kl 5 t 2 to .

(1)

The now classical Wagner’s model allows the calculation of the parabolic rate constant knowing the self-diffusion coefficients of the cation and anion in the oxide and their dependence with the oxygen

0167-2738 / 99 / $ – see front matter  1999 Elsevier Science B.V. All rights reserved. PII: S0167-2738( 98 )00242-2

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J. Philibert / Solid State Ionics 117 (1999) 7 – 11

activity. Be this variation not too large, it can be neglected and an integral formula is more convenient, known as the Nernst equation [5]: k p 5 kclV D*(DG /kT )

(2)

where kcl is the average M concentration of the compound, V the molar volume per atom M, D* the M self-diffusion coefficient and DG the Gibbs free energy of the compound formation per M atom. For a stoichiometric compound, kclV51. This formula generalises easily when both species contribute to the growth process. In many instances it has been observed that k p was not a ‘constant’ but did vary with time during the course of the oxidation process. The usual explanation of this anomaly refers to the role of grain boundaries.

2. Grain boundary diffusion The microstructure of the reaction product(s) cannot be neglected, mainly at relatively low temperatures. In the simplest case the microstructure consists of columnar grains. Diffusion occurs through the lattice – i.e. the volume of the grains – and along the grain boundaries, so that it is determined by two parallel paths. The overall flux – the effective flux – is just the weighted sum of the lattice flux J and the GB flux J9, according to the relation: Jeff 5 (1 2 f )J 1 fJ9

(3)

where f is the volume fraction of GB sites, or with the conventional GB thickness d: f 5 3d /d

(4)

with the average grain size d. Formula (4) remains valid for equiaxed grains as demonstrated on a simplified model [6]. However, in many cases the microstructure is duplex, with an outer columnar zone and an inner equiaxed one, so that two different grain sizes are to be taken into account. Some migration of GBs is also possible that would ‘explain’ the time variation of k p . As the authors do not agree on this time dependence even in the ideal case of nickel oxidation ( [7,8] and A.M. Huntz, private

communication, 1997), the application of the above formulae (3–4) is not straightforward.

3. The nature of the short circuits The microstructure of oxide layers is most of the time very far from the simple schematic description of columnar and / or equiaxed grains. The surface appears more or less rough, evidencing individual grains, frequently with some facets, as a testimony of the individual growth of the oxide grains; in some cases regular corrugations appear, as a result of a mechanical instability – periodical buckling (see Fig. 3). This aspect varies with the oxidation duration and the surface tends to be smoother after longer times. Deeper defects are associated with this roughness: crevices, (interconnected) pores, dislocations, that make a lot of possible short-circuits for diffusion to proceed through the oxide layer. Some interesting experiments were performed on NiO scales produced on high purity nickel sheets. Nice diffusion profiles were obtained without any thermal treatment just after deposition of an aqueous solution of the tracer [9]. Autoradiographs evidenced the continuity of tracer penetration along some channels down to depths of more than 50 mm (Fig. 1) [9]. Such channels have been recently observed by transmission electron microscopy on NiO scales grown on Ni–1% Cr alloys oxidised at 10008C [10]. They seem to be related to the triple junctions between the oxide grains. Their development could be favoured by the presence of segregated elements as they are frequently observed in scales formed on alloys [14]. Very large channels are observed in steel scales (Fig. 2), probably in relation with the release of carbon dioxide, as oxidation and decarburization occur simultaneously. In the light of such results the model of GB diffusion as an important contribution becomes very questionable.

4. Diffusivity in scales It was thought – and claimed – that for a reliable prediction of the parabolic rate constant, it should be better to start from the diffusion coefficients mea-

J. Philibert / Solid State Ionics 117 (1999) 7 – 11

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Fig. 1. 63 Ni autoradiographs after deposition of an aqueous solution of radioactive 63 NiCl on the surface of a polished NiO scale, at two different depths (3.7 and 50 mm); each pore (labelled a to h) may be tracked up to the original surface. After [9].

Fig. 2. Eutectoid steel (0.8% C, 1% Mn, 1% Si) oxidised 1 h at 11508C in 7% O 2 110% H 2 O atmosphere. From bottom to top: eutectoid steel, decarburised layer, silicate and FeO scales with cavities (dark grey), upper layer of Fe 3 O 4 . Courtesy P. Henry (IRSID).

sured on these scales rather than on bulk materials, single crystals (for lattice D) or polycrystalline specimens (for grain boundary D9) [11]. The advantage of this approach would lie in the specificity of

the oxide microstructure. The reality appeared rapidly quite challenging, because of the complexity of the microstructure that makes these specimens very poor ones from the point of view of the determi-

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J. Philibert / Solid State Ionics 117 (1999) 7 – 11

Fig. 3. Ridge model of scale surfaces: black and hatched parts refer to lattice diffusion for, respectively, corrugated and flat surfaces [15].

nation of diffusion coefficients (Fig. 3). In the preceding paragraph I mentioned the pseudo-diffusion observations performed on NiO scales (see Fig. 1). To the author’s knowledge the question of grain boundary diffusion in NiO is still open to discussion. Some experiments on NiO bicrystals failed to detect GB nickel diffusion at temperatures where it was determined according to the former literature. I refer ´ the reader to a critical review by Dechamps and Barbier [12]. In these conditions the agreement claimed by Atkinson [7] between diffusion data and oxidation rate constant between 300 and 9008C is dubious. A more recent and detailed study discards GB diffusion as an important factor in the kinetics of nickel oxidation [8]: but contradictory results have been reported about the isothermal variation of k p due to grain growth (A.M. Huntz, private communication, 1997). Surface diffusion (outer and pore surfaces) should probably play an important role at temperatures lower than 9008C where the scales present some roughness and porosity. Molecular oxygen permeation towards the inner interface through fissures or pores would be a possible contribution to the overall process as suggested by 18 O observations [13,14]. The situation is still more critical in the case of chromia or alumina former alloys as the scales are only a few mm thick and the diffusivities very low. The literature reveals a disagreement about the nature of the fastest component, i.e. the cation or the anion, that would dominate the oxidation process. The determination of diffusion coefficients in the

scales appeared as a real challenge. Even when reproducible diffusion profiles (penetration curves of the tracer) were obtained, their interpretation was not straightforward and the comparison with the data obtained on bulk specimens risky. It was realised that the tracer diffusion proceeds only in a very thin superficial layer of the scale. As the scale surface is convoluted, the true exchange surface may be quite larger than the cross section (Fig. 3) [15]. Fig. 4 shows the surface of alumina scale after oxidation at 12008C of two FeCrAl alloys with close compositions [16]. Clearly the second one lends to better diffusion measurements (in the present case 18 O and 54 Cr as a substitute to Al, due to the absence of a convenient radiotracer for aluminium). Actually

Fig. 4. SEM micrographs of the outer surface of alumina scales after oxidation at 12008C of two Fe–Cr–Al alloys (about 4.5% Al) [16].

J. Philibert / Solid State Ionics 117 (1999) 7 – 11

the results obtained on such a specimen – and only on such specimens – did agree with bulk specimen determinations extrapolated from higher temperatures (where conventional determinations were performed because of the smallness of the diffusivities) and allowed a fair prediction of the parabolic rate constant [16,17]. Let us point out that outer scale convolutions are not the result of a local decohesion. The inner interface remains adherent although it is no more a flat one. Probably intense plastic deformation was active during the oxide growth perhaps because of strong compressive stresses and interface segregation. But the origin of these processes remain obscure. Let us recall that such a dislocation activity is not particular to these alloys. Evidence of local recrystallisation of the metallic substrate close to the inner interface was observed in the past, depending critically on the purity of the metal at very low levels [18,19]. These important observations have been more or less forgotten and their importance subsequently neglected. The number and the complexity of the processes occurring within the scales and at the interfaces do not lend to any reliable prediction about the oxidation kinetics. We are unable to define some criterion relative to the roughness or convolution of the scales. In these conditions one can wonder whether it is worthwhile continuing endless discussions of the models addressing the role of the so-called active elements as each alloy is a particular system! These added elements slow down the oxidation rate and improve the adhesion of the scales: do they segregate to the grain boundaries and modify the respective part of the cation and anion diffusion or do they modify the inner interface reaction?

the grain boundaries. But unfortunately these required determinations appear insufficient for a reliable modelling of the growth of most scales. The microstructure depends on many factors: composition of the alloy, nature of the atmosphere, shape of the specimen . . . as well as on all the elementary processes involved during oxidation: lattice and short-circuit diffusion, interface reactions, stress generation and relaxation . . . This reciprocal relationship oxidation process–microstructure evolution is the key to a true understanding of the kinetics and related properties. Its complexity leads us to a rather pessimistic view about a possible modelling of oxidation processes as an answer to the demand from the technical applications. Many questions could remain without any answer for a long time and empiricism would still be the rule for improving the high temperature corrosion resistance of industrial alloys.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]

5. Conclusion Belonging to the class of reactive diffusion processes, oxidation is a quite specific case. Among the reasons for this peculiarity, one must mention that the system is less constrained because of the presence of a free surface, that can generate a lot of defects and consequently increase the complexity of the microstructure generation and evolution. More data are required on the diffusion coefficients in oxides at rather low temperatures in the lattice and in

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[13] [14] [15] [16] [17] [18] [19]

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