# Oxidation at 1250°C of Cr, Ta-rich carbides-strengthened Ni, Co-based alloys

Patrice Berthod, Jean-Paul Gomis, Lionel Aranda, Thierry Schweitzer

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Patrice Berthod, Jean-Paul Gomis, Lionel Aranda, Thierry Schweitzer. Oxidation at 1250°C of Cr, Ta-rich carbides-strengthened Ni, Co-based alloys. Materials and Corrosion / Werkstoffe und Korrosion, 2022, 10.1002/maco.202112770. hal-04768592

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Preprint version of:

“Oxidation at 1250°C of {Cr, Ta}-rich
carbides-strengthened {Ni, Co}-based
alloys”

Patrice Berthod, Jean-Paul Gomis, Lionel Aranda, Thierry Schweitzer

**Materials and Corrosion – Werkstoffe und Korrosion, 2022, 73(7), 1121–1131.**
Oxidation at 1250°C of {Cr, Ta}–Rich Carbides-strengthened
{Ni, Co}–Based Alloys

Patrice Berthod<fnref n="1" />,<fnref n="2" />*, Jean-Paul Gomis<fnref n="1" />, Lionel Aranda<fnref n="2" />, Thierry Schweitzer<fnref n="2" />

**Abstract.** Thermogravimetry tests were performed for 70 hours at 1250°C in air for six TaC-strengthened alloys with different Ni/Co ratio. The oxidation and chromia-volatilization rates were specified, and the formed oxides characterized. Metallography shows that the alloys rich in nickel (from ≈ 70 to ≈ 25wt.%Ni) stayed chromia-forming until the end of the 70 hours while catastrophic oxidation locally started in the case of the cobalt-based alloys which are too poor in Ni. The numerical exploitation of the mass gain files was done accordingly. Results clearly showed a regular increase in oxidation parabolic constant, as well as in chromia volatilization constant.

**Keywords :** superalloys; high temperature oxidation; mass gain kinetics; post-mortem characterization

The Authors state that:

**Data availability statement:** no data is available

**Funding statement:** this work did not benefit from any funding for this research

**Conflict of interest disclosure:** there is no conflict of interest associated to this work

**Ethics approval statement:** they approve the ethics

**Patient consent statement:** not applicable

**Permission to reproduce material from other sources:** not applicable

**Clinical trial registration:** not applicable

<footnote n="1">¹Université de Lorraine, Faculté des Sciences et Technologies, F-54500 Vandoeuvre-lès-Nancy, France</footnote>

<footnote n="2">²Université de Lorraine, CNRS, IJL, F-54000 Nancy, France</footnote>

<footnote>*Corresponding author's e-mail address: patrice.berthod@univ-lorraine.fr</footnote>
Introduction

Carbides are hard particles on which the high temperature mechanical resistance of some superalloys is based. This principle of reinforcement by a second phase was the main way used for the earliest superalloys. For these ones, which appeared near the middle of the last century, most of the concerned particles were chromium carbides [1,2]. Some of the more recent cast polycrystalline equiaxed superalloys are still reinforced by carbides. In many cases, these carbides are of various types in a same alloy: chromium carbides but also carbides involving other elements such as Ta, Ti, Nb... Some of these alloys, which contain MC carbides among their carbide populations, can be based on nickel [3–5] or on cobalt [6–9]. MC carbides can be also present in the oriented microstructures of Directionally Solidified (DS) nickel–based [10] or cobalt–based [11] superalloys. MC can be obtained as the single carbide phase present in the microstructure of cobalt–based alloys [12, 13] if the carbon and M weight contents are well rated. By respecting this condition, alloys containing exclusively eutectic TaC [14] or TiC [15] or NbC [16] and even only HfC [17] may be successfully produced. These MC carbides are mainly localized in grain boundaries and between dendrites. By basing the mechanical properties on these eutectic – but nevertheless very refractory – carbides one may obtain particularly creep–resistant polycrystalline superalloys for possible uses in a wide range of elevated temperatures, extending to 1200 and maybe 1250°C [18]. Indeed, at so high temperatures, many of these alloys are still 100°C and more below the start of their melting and MC carbides are still present in the microstructure. This is a decisive advantage over γ/γ' nickel–based single crystals which lose their reinforcing particles above 1100°C and also over superalloys strengthened by carbides of more classical type (e.g. Cr₇C₃ or (Cr,W)₂₃C₆) which also disappear at so high temperatures. One may also point out that, for working at around 1200°C, the conventionally MC–strengthened superalloys can apply to uses for which Oxide Dispersion Strengthened superalloys or alloys based on refractory elements (Nb, Mo, W...) cannot be produced as geometrically complex components.

Unfortunately, metals involved in the composition of MC carbides are generally also highly oxidable at high temperature [19, 20]. The presence, in alloys, of M metals in quantities high enough to allow developing MC carbide networks that are dense enough to achieve significant reinforcement, may influence the global oxidation behavior of the alloys. Indeed, for 0.5 wt.%C of carbon – content leading to a dense but not interconnected MC network – almost 8 wt.% of Ta or Hf are compulsory to obtain only TaC or HfC carbides in the microstructure. Such high M contents necessarily lead to the presence of many M atoms close to the surface. Here, they inevitably participate to the local oxidation phenomena, much more than for more usual alloys containing these elements in much lower quantities. Knowing that the M atoms are split between inter–grains/inter–dendrites boundaries (in primary carbides) and the matrix (in solid solution), their reaction when they are exposed to oxidation may be of several types. For the former ones a dissociation of carbides taking place at an increasing depth, followed by inter–crystals diffusion toward the oxidation front are expected. For the later ones, volume diffusion will be involved. One can think that the composition of the matrix may influence this volume diffusion, and consequently the participation – beside chromium – of the M elements in the global oxidation process. The composition of the matrix may vary with the chromium content, with the eventual presence of other elements in solid solution (M and other possible elements such as Mo or W), and of course with the base element. Indeed, many nickel–based alloys contain also iron or cobalt, many iron–based alloys contain also nickel and many cobalt–based alloys contain also nickel.

In this work, this is one of the different possible {MC network × Base elements} combinations which will be considered to investigate the effect of the chemical composition of the matrix on the oxidation process of an alloy rich in MC carbides of a single type – TaC – and with a matrix involving both cobalt and nickel for the base element position. A series of six alloys, all containing 25 wt.%Cr, 0.4 wt.%C and 6 wt.%Ta, with a Co content varying from 0 (cobalt–free Ni–based alloy) to 68.8 wt.% (nickel–free Co–based alloy) were tested in isothermal oxidation for 70 hours (almost 3 days) in a thermo–balance, followed the study of both metallographic and mass gain kinetic results
according to the Co/Ni ratio. The test temperature which was chosen for these investigations is the maximal one which can be reasonably expected for a still successful use of such MC-strengthened (Co, Ni)-based superalloys: 1250°C.

# Materials and methods

The technical details of this work are described below.

## Selection of the chemical compositions

The chemical compositions of the six alloys are 0Co-68.6Ni-R (called "0Co-69Ni"), 13.7Co-54.9Ni-R ("14Co-55Ni"), 27.4Co-41.4Ni-R ("27Co-42Ni"), 41.2Co-27.4Ni-R ("42Co-27Ni"), 54.9Co-13.7Ni-R ("55Co-14Ni") and 68.6Co-0Ni-R ("69Co-0Ni"), where "R" ("Rest") is composed by 25Cr, 0.4C and 6Ta in wt.%).

They were produced by melting charges composed of pure elements (purity: >99.9wt%), bought from Alfa Aesar. The apparatus for melting the prepared mix of elements was a 50kW-max high frequency induction furnace (CELES, France) and the atmosphere in the fusion chamber was composed of 300mbars of pure argon during operation. The heating was conducted with 100-110kHz and 4kV as current frequency and voltage. The obtained liquid alloys were maintained 5 minutes at the maximal temperature. Solidification and total cooling were achieved over about half an hour. Compact-shaped ingots of about 40 grams each were thus obtained.

## Cutting of the ingots and control of the obtained alloys

The ingots were cut in several parts by using a rotating metallographic saw. The obtained sections were subjected to visual control for verifying the internal metallurgical health. More accurate cutting was thereafter carried out for reaching the wished shapes and dimensions of the different samples destined for the different investigations and tests. The metallic parts destined to the as-cast microstructure characterizations were embedded (cold resin mixture, ESCIL France), ground (#240 to #1200 SiC papers, under water) and polished (spray of 1µm diamond particles).

The as-cast microstructures were examined using a Scanning Electrons Microscope (SEM) JSM-6010LA (JEOL, Japan) with an applied acceleration voltage equal to 20kV. The chemical compositions of the alloys were measured by Energy Dispersive Spectrometry (EDS), with the device attached to the SEM. The performed analyses were of an accuracy good enough for all elements except carbon. The ×250 and ×1000 magnifications were chosen for the SEM/BSE micrographs and the ×250 one was selected for the full frame EDS analyses. These EDS analyses were performed on five areas, for obtaining five results allowing the calculation of an average value and a standard deviation value of each element.

## Thermogravimetry runs and metallographic preparation of the oxidized samples

The dimensions of the parallelepipeds used for the oxidation tests were about 2 × 8 × 8 mm³. The edges, corners, main faces and lateral faces were smoothed/polished with #1200 SiC papers. The used apparatus was a TG92 thermobalance (SETARAM, France). The atmosphere characteristics and the thermal steps were respectively a 1.5 L/h flow of 80%N₂-20%O₂ synthetic air, and a +20K/min heating rate, an isothermal stage at 1250°C for 70 hours, and a cooling at -5K/min.

## Metallographic exploitation of the oxidized samples

After oxidation tests the external oxides formed on the surfaces of the samples were characterized by X-ray diffraction (XRD). The used apparatus was a Philips X-Pert Pro diffractometer (wavelength: copper Kα λ = 1.5406 Å, Angströms). After XRD, gold was deposited on all faces of the oxidized samples, by cathodic pulverization. This
was followed by nickel electrolytic deposition (in a Watt's bath maintained at 50°C, 16mA/cm² during about 3 hours). The coated samples were cut to obtain two halves. These ones were embedded, ground and polished following the same procedure as for the as-cast samples. Cross-sectional observation (SEM/BSE) and characterization (SEM/EDS) of the oxides externally and internally appeared, as well as of the subsurfacic parts modified by oxidation, were then carried out. The middle parts of the same cross-sectional samples were also observed (SEM/BSE) to examine the microstructure changes in the bulk due to the exposure at high temperature. The chemical compositions of the matrix (thus after stabilization at 1250°C) were also assessed (average of five EDS spot analyses).

### Numerical treatment of the mass variation files

Concerning the oxidation kinetics, the mass gain by surface unit area was plot versus time for visualizing the type of kinetic (linear, parabolic, para-linear, other). This also allowed determining the linear constant of transient oxidation. If applicable (kinetic parabolic or not), the mass gain was plotted versus the square root of time and the parabolic constant of oxidation Kp was determined according to the classical procedure (Kp is equal to the average slope of the obtained m = f(t¹/²) curve multiplied by itself, then divided by 4). If applicable (external oxide scale made of chromia, exclusively or – at least – mainly), the mass gain multiplied by its derived value with respect to time was plotted versus the opposite value of mass gain (according to a method described in [21]). This allowed determining simultaneously the real value of the parabolic constant Kp and the value of the chromia volatilization constant Kv. One can remind that this later second constant is involved in the negative term - Kv × t expressing the continuous mass loss due to the re-oxidation of the solid Cr₂O₃ (formed over the sample) into gaseous CrO₃ which affects the mass of chromia-forming alloys when they are oxidized in air for temperatures higher than 1000°C (at the atmospheric pressure). As Kp, Kv tends increasing with temperature but it may also depend of the general characteristics of the chromia scale (compactness, porosities, presence of elements other than Cr and O ...) and needs to be assessed each time it is possible.

The equations, on which the two treatments of the mass gain files were thus based, are:

$$m = (2 \times Kp_{class})^{1/2} \times t^{1/2} \qquad (Eq. 1)$$

$$m \times dm/dt = Kv \times (-m) + Kp_{corr} \qquad (Eq. 2)$$

where m is the mass gain divided by the whole outer surface of the sample, t is time, Kp_class is the parabolic constant (proportionality coefficient between the mass gain rate and the inverse value of the mass gain, involved in the differential equation dm/dt = Kp_class/m), Kv the slope and Kp_corr the ordinate at the origin of the straight line obtained by plotting m × dm/dt versus -m.

To check the validity of the obtained values for the kinetic constant, mathematical curves plotted from the experimental value of mass gain recorded at the end of heating (m₀, e.g. 0.33 mg/cm² for the 0Co-69Ni alloy), step by step according to the following equation (Eq. 3), were compared to the experimental mass gain curves.

$$m_{n+1} = m_n + (Kp / m_n) \times \delta t - Kv \times \delta t \qquad (Eq. 3)$$

with δt being the time step of mass gain recording used for the thermogravimetry test (here 39 seconds for all tests), mₙ₊₁ the mass gain achieved 39 seconds after the previous one mₙ.

## Results
### Control of the obtained alloys: chemical compositions and as-cast microstructures

The chemical compositions were measured in EDS with acceptable accuracy (Table 1). The contents in all elements (except carbon, which cannot be analysed) meet rather well the targeted values. The contents in Ni, Co and Cr are in reasonably good agreement with the corresponding wished values. The tantalum content measured by EDS is systematically higher than the targeted values. This difference between the measured Ta contents and the real ones is usual when Energy Dispersion Spectrometry is used on alloys rich in TaC. They are attributed to the TaC carbides emerging in relief – even on the mirror-like polished samples – because of their much higher hardness than the metallic matrix. These carbides are thus much more exposed to the electron beam. This overestimation of Ta (and a little of chromium) mechanically induces slightly lower contents for Ni and Co. EDS is not able to bring consistent carbon content, because of the low molar mass and the low weight content of this element. The population of carbides, which will be observed just thereafter, is typical of a 0.4–0.5 wt.%C content. This suggests that the targeted carbon content is also reached, as usually observed for this elaboration procedure.

The microstructures of the alloys after their elaboration are illustrated by SEM/BSE micrographs in Figure 1 (low magnification for general aspect) and in Figure 2 (higher magnification for observing carbides details). All alloys are composed of a dendritic matrix and of carbides. These carbides, regardless to their natures, are all located in the grain or dendrites boundaries. They form a eutectic compound with the matrix. The carbides present in the three (0 to 27)Co-(69 to 42)Ni alloys are of two distinct natures: chromium carbides (darker than matrix when they are imaged with the SEM in BSE mode) and tantalum carbides (white). The three remaining alloys, the cobalt-richest ones, only contain tantalum carbides.

### Characterization of the oxidized states prior to cross-sectional preparation

After careful exiting of the oxidized samples out of the thermobalance, these ones were preliminarily observed with the naked eye. This allowed observing that oxides were obviously missing here and there on the oxidized surfaces. This was particularly true for the alloys rich in nickel (from 0Co-69Ni to 27Co-42Ni) and less for the ones rich in cobalt (from 69Co-0Ni to 42Co-27Ni). The oxidized samples were thereafter subjected to X-ray diffraction (XRD). The obtained XRD spectra are given in Figure 3 in the case of the three (0 to 27)Co-(69 to 42)Ni alloys, and in Figure 4 in the case of the three (42 to 69)Co-(27 to 0)Ni alloys. The diffraction peaks corresponding either to the nickel base matrix, or to the cobalt base matrix, are generally high and numerous. This is due to the loss of external oxide scales during cooling after the oxidation exposure. This is true for all alloys, but particularly for the two alloys which are the richest in nickel (0Co-69Ni and 14Co-55Ni). These two later alloys are still covered by oxides in other locations: $Cr_2O_3$ (chromia) and $CrTaO_4$. In fact, this is this second oxide, in which both chromium and tantalum are involved, that is the most present. In the third spectrum of Figure 3, in addition to the two oxides cited before, the $CoCr_2O_4$ spinel is present. Its appearance was promoted by the significant presence of cobalt beside nickel in the base element position. For the three alloys richer in cobalt than in nickel (from 69Co-0Ni to 42Co-27Ni), $CrTaO_4$, chromia and the spinel oxide are present together (Figure 4). The oxide scale formed over the sixth alloy, which is totally nickel-free, contains cobalt oxide in addition.

### Cross-sectional characterization of the formed oxides

Cross-sectional metallographic results are given in Figure 5 for the alloys which are free of any catastrophic oxidation start everywhere on their surfaces. These alloys are the four ones which are the richest in nickel, from 0Co-69Ni to 42Co-27Ni. These alloys all behaved as chromia-forming alloys, as showed by the chromia parts which remain here and there, despite a particularly intensive spallation which obviously induced the loss of a great part of this external oxide. Three of these four alloys contain internal white islands of $CrTaO_4$ in the internal alloy zones close to the surface. These {chromium + tantalum} oxides are closer to this scale/alloy interface when the cobalt
content is lower. In contrast, they are present deeper for higher cobalt content. The case of the 0Co-69Ni alloy is
rather particular since almost no internal island is present in the internal alloy zone close to the surface. The
corresponding micrograph given in **Figure 5** shows the absence of this white CrTaO₄ oxide while it forms a
continuous oxide separating the alloy and the external scale in other locations on the surface of the same sample.
The two last alloys (55Co-14Ni and 69Co-0Ni), richer in cobalt than the former ones, are affected here and there
by catastrophic oxidation while the behavior still remains chromia-forming elsewhere. Some micrographs illustrating
this variety of behaviors over a same sample are given in **Figure 6** for the 55Co-14Ni alloy and in **Figure 7** for the
69Co-0Ni one. For both of them, chromia is still present in some locations but this thick continuous oxide is covered
by a thin oxide layer composed of the CoCr₂O₄ spinel (with discrete presence of (Co,Ni)O or CoO). This thin oxide
layer separates the external side of chromia and hot air during the oxidation test. In other locations, chromia is more
irregular and thinner. It is located between the damaged alloy and the thick scales of mixed oxides (CoO or (Co,Ni)O,
CoCr₂O₄, complex oxides of Co, Ni and Cr simultaneously). For these 55Co-14Ni and 69Co-0Ni alloys the boundary
between alloy and oxides is irregular: the main part of this frontier is flat but there are some locations where the
alloy seems to be dig or mined. In the first places (flat frontier), chromia is the major external scale. Here oxidation
progressed by cationic diffusion with chromia growth taking place at the chromia/gas interface. In the second places
the alloy was oxidized directly at the alloy/oxide scale interface and the growth of the oxide scale proceeded at the
alloy/oxide scale interface. In the later case, this oxide scale is composed of a thin inner chromia scale and of a
thick oxide scale of complex composition.

Cross-sectional characterization of chemistry changes in extreme surface of the alloys

Thus, for these alloys, there are some surface locations where the local behavior was chroming-forming and some
locations where this behavior was obviously lost. This observation suggested that controlling the chromium contents
in the outermost alloy part may be interesting to verify whether the Cr content values in the outermost alloy part
were still high enough in the firstly mentioned areas and whether they became too low in the secondly mentioned
areas. This was done with five EDS spot analyses, carried out at about 2–3 µm from the alloy/oxide scale interface.
The obtained values were used to calculate the corresponding average values and the standard deviation values,
for the Cr contents and also for the Ta contents. They are given in Table 2. The four alloys which are the richest in
nickel (from 42Co-27Ni to 0Co-69Ni) all present chromium contents in the outermost alloy part which are equal to
– or higher than – 15wt.% Cr. However the average value tends constantly decreasing (from 19 to 15 wt.%) between
the 0Co-69Ni alloy and the 42Co-27Ni one. The acceptable low standard deviation value demonstrates that these
Cr contents are well representative of the alloys. When arriving to the two cobalt-richest alloys (55Co-14Ni and
69Co-0Ni), the results are much more scattered. Two populations are to be considered: locations knowing a
beginning of catastrophic oxidation (fourth results line of Table 2) and locations still free of such phenomenon (third
results line). In the third result line, the chromium contents are of the same level as the two medium alloys (27Co-
42Ni and 42Co-27Ni alloys) while the chromium contents are significantly lower (10 and even 3 wt.%Cr) where
general oxidation was progressing. The progressive decrease in average Cr content in the outermost alloy part
when nickel is more and more replaced by cobalt in the alloy (first line of Table 2) demonstrates that the chromia–
forming sustainability becomes lower and lower. At the end of the 70 hours of oxidation at 1250°C, the duration
before catastrophic oxidation start is expected to be lower and lower when more and more cobalt is present. In the
case of the two Co-richest alloys (55Co-14Ni and 69Co-0Ni) catastrophic oxidation had already started in some
places.

Concerning tantalum, its content in the metallic part close to the scale/alloy interface, is low for the four alloys which are the richest in cobalt (27Co-42Ni to 69Co-0Ni). This content is zero or less than 1wt.%. But it is a little higher for the 14Co-55Ni alloy (about 1.5 wt.%) and really higher for the 0Co-69Ni alloy (about 4wt.%). To finish with the metallographic results, one can first display cross-sectional micrographs with lower magnification to have a wider
look to the surfaces and to the internal alloy zones close to the surface. They allow verifying the representativeness of the previous descriptions as well as consolidating the knowledge of the inhomogeneity of oxidation behaviors (Figure 8 and Figure 9).

### Cross-sectional characterization: little glance at the bulk microstructures changes

One can also have a look to the microstructures of the oxidized samples far from the surfaces, to take benefit from the oxidation tests for studying how these microstructures evolved at high temperature. Indeed these oxidation tests for the alloys' surfaces also consist in thermal tests for the core of the samples. Knowing how microstructures behaved is of importance since the mechanical properties of the alloys closely depend on the morphology of the hardening carbide particles. Obviously, in addition to the microstructure changes induced by oxidation in the internal alloy zones close to the surface of the alloys (disappearance of the carbides, Figure 8 and Figure 9), significant modifications also occurred for the carbides under the effect of the very high temperature of the thermal tests. Figure 10 (SEM/BSE micrographs taken at low magnification) and Figure 11 (higher magnification) should be compared to Figure 1 and Figure 2 respectively. Coalescence and coarsening of chromium carbides as well as of tantalum carbides obviously occurred significantly. Such phenomena are known to be detrimental for the mechanical properties at high temperature of the alloys. Besides the present characterization of the high temperature oxidation behavior it can be useful to evaluate the consequences of the observed carbides' morphology changes on the static, fatigue or creep resistances. This must be investigated in the frame of a mechanical study. The chemical composition of the matrix were measured by spot EDS analysis. The average values of the five results per alloy are graphically presented in Figure 12. One can see that the Ni and Co contents in the matrix follow the contents in the whole alloys. Concerning the tantalum content decreases rapidly from the 0Co-89Ni alloy (about 4wt.%Ta) to the 27Co-42Ni alloy (about 1.7wt.%Ta) and remains constant for the three Co-richest alloys. This is clearly the result of the increase in TaC carbide fraction (more Ta involved in carbides thus less Ta in solution in the matrix). A similar phenomenon can be seen concerning chromium: with the disappearance of the chromium carbides from the Ni-richest alloys to the Co-richest ones, the Cr content in the matrix takes several wt.%Cr.

### Kinetic study of oxidation: general shape of the mass gain curves

The mass gains of the six alloys are plotted together in a same figure (Figure 13). Except one, the mass gains of all alloys are parabolic, and one can see that the mass gain rate increases from the 0Co-69Ni alloy to the 69Co-Ni alloy. In fact, there are two groups, the two nickel-richest alloys (0Co-69Ni and 14Co-55Ni) and the two medium alloys (27Co-42Ni and 42Co-27Ni) for which the kinetics are quite similar for both alloys. The 55Co-14Ni alloy oxidized faster than the previously evocated alloys, following the same logic concerning the Co content effect. In contrast, the mass gain kinetic of the last alloy, the nickel-free cobalt-based one (69Co-0Ni), is similar to the ones of the two nickel-richest alloys (14Co-55Ni and 0Co-69Ni) for the first half of the total duration. Thereafter, the mass gain of the 69Co-0Ni alloy accelerates and the kinetic evolves from parabolic to linear, in contrast with the mass gains of the two nickel-richest alloys (14Co-55Ni and 0Co-69Ni) which stay parabolic.

### Kinetic study of oxidation: strategy for the constants determination according to the natures of the formed oxides

The metallographic results presented in the previous section suggested that chromia grew during the oxidation of all alloys during the thermogravimetry runs, and was the main oxide in all cases. Because of scale spallation at cooling, the chromia layer was not seen over the four nickel-richest alloys (42Co-27Ni to 0Co-69Ni), except some remaining small parts. The chromia scales were much more kept by the two cobalt-richest alloys (69Co-0Ni to 55Co-14Ni) and it was thus possible to observe them. But some other oxides were present too, notably the ones involving cobalt, alone or together with nickel or chromium (spinel). Taking these metallographic observations (the four Co-richest alloys) and deductions (the two Ni-rich alloys) into account, it was decided in all cases to analyze
the isothermal parts of the mass gain files to try determining both the real (i.e. not underestimated) parabolic constant Kp, and the linear constant Kv characterizing chromia volatilization. In parallel, the classical Kp determination (i.e. as the average slope of the mass gain curve plotted versus the square root of time) was also carried out for the alloys for which the Kp–Kv determination was probably not suitable because of the presence of zones where catastrophic oxidation started sooner or later locally (i.e. the two cobalt–richest alloys).

### Kinetic study of oxidation: values obtained for the different oxidation kinetic constants

An example of {m dm/dt versus -m} plot is given in Figure 14 (case of the 0Co-69Ni alloy). The equation of the straight line gives the values of real Kp (slope: 265 × 10⁻¹² g² cm⁻⁴ s⁻¹) and of Kv (ordinate at origin: 205 × 10⁻¹⁰ g cm⁻² s⁻¹). These values were used to plot a mathematical curve. This one fits much better the experimental mass gain curve than the ones plotted using the Kp value classically determined, as this can be seen in Figure 15. In contrast, the values of Kp and Kv determined for the two cobalt–richest alloys (69Co-0Ni to 55Co-14Ni) lead to a mathematical value which is not able to represent the experimental curve (Figure 16). In this case, the curve plotted using the classically determined Kp value fits better the experimental curve. The volatilization–corrected Kp and Kv constants were determined over only a part of the m × dm/dt versus -m plotted curve (see “1/” in the upper graph of Figure 16). This part, unfortunately too short, corresponds to the first hours of isothermal oxidation preceding the start of local oxidation with a linear kinetic. This later local linear oxidation logically results in a tilted straight line (see “2/” in the upper part of Figure 16) oriented differently to the previous one (“1/”) since this corresponds to a mass gain (fast linear oxidation) instead a mass loss by volatilization of chromia. The fit with the experimental curve was thus corrected for only the first fifth of total duration, while severe divergence occurred afterwards. The curve plot with a Kp value classically determined over the whole isothermal stage duration necessarily fits the experimental curve much better, but still insufficiently.

### Kinetic study of oxidation: values obtained for the different oxidation kinetic constants

The Kp–Kv method using the {m dm/dt versus -m} plot was thus applied to the four alloys 0Co-69Ni to 42Co-27Ni. For the two other alloys, even if values of Kp and Kv are provided (for verifying that they are not realistic), this is the classically determined Kp value which must be taken in consideration. Table 3 gathered all these values with, in addition, the ones of the slope of the line tangent to the parabolic curve at the beginning of the isothermal stage (Kl). The Kp and Kv values determined for the four alloys 0Co-69Ni to 42Co-27Ni alloys are given in bold characters, and their Kp values classically calculated are given in normal characters, to clearly show that the Kp and Kv values are the kinetic constants to be taken into consideration for these four nickel–richest alloys. Indeed, knowing the volatilization constant allows knowing the real Kp value and thus the real kinetic of deterioration of the alloy by oxidation. In contrast, the Kp values classically calculated are the ones which must be kept (bold character), at the expense of the ones issued from the Kp–Kv method (italic characters, followed by the * symbol), for the two cobalt–richest 55Co-14Ni and 69Co-0Ni alloys. Despite that these classically determined Kp values describe kinetics of alloy deterioration by oxidation which are slower than in reality, they are to be preferred.

Concerning the linear KI constant – which can be taken as an estimation of the linear oxidation constant at the arrival to 1250°C (first results line of Table 3) – no systematic variation can be noticed versus the Co/Ni balance in the alloy. In contrast the evolution of the classically determined Kp value versus the cobalt content in alloy is more interesting: globally it increases when the Co content increases. One can find again this evolution for the Kp value corrected from chromia volatilization (265 to 445 × 10⁻¹² g² cm⁻⁴ s⁻¹ from 0Co-69Ni to 42Co-27Ni). These values are significantly higher than the corresponding classic Kp. The reason is that these volatilization–corrected values of the parabolic constant are not underestimated; they really describe the damage kinetic of the alloys by oxidation. At the same time, the Kv constant decreases from 205 to 171 × 10⁻¹⁰ g cm⁻² s⁻¹). This is different for the two Co–
richest alloys (55Co-14Ni and 69Co-0Ni) for which not realistic values of Kv and of volatilization-corrected Kp were obtained. This is the reason why these values are written in italic and pointed out by the * symbol.

Discussion

The progressive replacement of Ni by Co in a nickel-based alloy led thus to the conversion of the nature of the
primary carbides. From a dense carbide network made of tantalum carbides and chromium carbides in similar
quantities in absence of cobalt, the increasing Co addition induced the development of a TaC network of similar
density, as this was seen in Figure 1. This difference in carbides nature remained later during the stage at 1250°C
since the Ni-richest alloys still contained chromium carbides and tantalum carbides (both becoming coalesced and
rounder than initially) and the Co-richest alloys still contained only TaC (becoming more and more fragmented). In
the first case (nickel-rich alloys) tantalum was distributed in equivalent quantities between matrix in which it was
present in solid solution, and in the second case (cobalt-rich alloys) tantalum was mainly present as TaC carbides
while only a minor quantity was present in solid solution in the matrix (Figure 12). There were thus possibly two
opposite effects of the Co/Ni ratio on the chromium diffusion acting during high temperature oxidation. One the one
hand, knowing that Cr diffusion is easier in a nickel matrix than in a cobalt matrix, diffusion was more difficult when
more and more cobalt was present in the alloy and thus in the matrix. But, on the other hand, more cobalt allowed
decreasing the quantity of tantalum in solution in the matrix, with as result a lower hindering effect of tantalum for
Cr diffusion through the matrix. Obviously, this was the first factor which played the predominant role since this was
for the cobalt-richest alloys that the loss of chromia-forming behavior started the first.

Indeed, the nickel-richest alloys clearly behaved as veritable chromia-forming alloys, as demonstrated by the slow
parabolic kinetics of mass gain (Figure 13) and by the oxidation products principally made of chromia (and CrTaO₄
oxide) that XRD (Figure 3) and cross-sectional BSE imaging and EDS spot analysis (Figure 5) allowed identifying.
So, during their isothermal oxidation, these nickel-richest alloys did not suffer from insufficient supply in chromium
along the oxidation front. In contrast, the cobalt-richest alloys, with a matrix with globally the same Co/Ni ratio as
the whole alloys (Figure 12), oxidized much faster (Figure 13) and their external oxides were continuous too, but
thicker and made of chromia but also of other oxides (XRD spectra in Figure 4, micrographs in Figure 6 and Figure
7), including spinels, of significant quantities. Clearly, in their cases, chromium did not succeeded in diffusing quickly
enough towards the oxidation front to allow a chromia growth and thickening fast enough to preserve the base
elements from oxidation.

The separation of alloy and oxidizing atmosphere by a continuous external scale in all cases allowed the parabolic
shape of the mass gain curves but the kinetic constants were significantly different between the Ni-richest alloys
(low Kp values) and the Co-richest ones (high Kp values). The Kp values as classically determined (from the slope
of the mass gains plotted versus the square root of time) constantly increased with the content in Co at the expense
of Ni: from 130 to around 300 × 10⁻¹² g² cm⁻⁴ s⁻¹ from the 0Co-69Ni cobalt-free Ni-based alloy to the 69Co-0Ni
nickel-free Co-based alloy.

In fact, these classically determined Kp values do not report objectively the real damage caused by oxidation since
they are underestimated. In contrast with oxidation of chromia-forming alloys at 1000°C and less, the forming
chromia does not stay in full on the sample since a part is lost as CrO₃ gas. The mass gain is thus undervalued and
the Kp too. Applying the method illustrated by Figure 14 allowed accessing to much more realistic Kp values for the
Ni-richest alloys: around 260 – 270 × 10⁻¹² g² cm⁻⁴ s⁻¹ (Table 3) as is to say a little higher than for a model Ni-30Cr
alloy earlier oxidized in similar conditions (245 × 10⁻¹² g² cm⁻⁴ s⁻¹ at 1300°C [21]). The two sets of results are
consistent since, in the present case it is clear that the internal oxidation of Cr and Ta in significant quantities of
CrTaO₄ oxide contributed significantly to the mass gain from which real Kp and Kv were calculated. Concerning the Kv constant representing the chromia mass loss by its partial re-oxidation and gasification, the values determined for the Ni-richest alloys here (around 200 × 10⁻¹⁰ g cm⁻² s⁻¹, Table 3) are also consistent with the Kv values obtained for the binary at this level of temperature (168 and 367 × 10⁻¹⁰ g cm⁻² s⁻¹ for 1200°C and 1300°C [21]). So, one can consider that the degradation of the Ni-richest alloys of this study by oxidation was not significantly worse than the oxidation-resistant Ni-30Cr alloy taken in reference, with only a limited deleterious role of tantalum and no real effect of the added cobalt.

Unfortunately, for the Co-richest alloys, it was not possible to access, as for the Ni-richest alloys, to a realistic parabolic constant by taking chromia volatilization into account using the same method ([21], Figure 14). Indeed, the presence of many other oxides did not allowed applying it in the required conditions with consequently not valid results: this was attempted but this led to unexpected {m × dm/dt versus -m} curves (Figure 15) and false results (Table 3). The parabolic but fast mass gains (and high values of classically determined Kp) and even starts of para-linear oxidation (Figure 13), the presence of (Co,Ni)Cr₂O₄ spinels and even (Co,Ni)O mono-oxides (Figure 6 and Figure 7) and the high values, unquestionably suggested that these alloys were undergoing fast oxidation-induced degradation, which were even preparing to catastrophically oxidize.

## Conclusion

In addition to its effect on the population of primary carbides, the Ni/Co ratio may greatly influence the oxidation of the alloys at 1250°C. The cobalt-free or low cobalt nickel-based alloys well resist oxidation while oxidation is fast from the beginning of the isothermal exposure to air for the low nickel or nickel-free cobalt-based alloys. In fact, for the {chromia-forming} behavior and the {TaC as single carbide}-criterion there is obviously the same threshold for the Ni/Co ratio: it is equal to 1. Below this value, the alloy benefits from a potential good creep-resistance thanks to a maximal fraction in TaC carbides, but it is unfortunately threatened by imminent destruction by generalized oxidation. Above this value, the alloy correctly resists against oxidation but it is mechanically weakened by only low TaC presence and by a softer matrix more based on nickel than on cobalt. In their present state, such alloys are usable at this very high level temperature but either in not chemically aggressive environment or in conditions of not high applied stresses. These alloys may potentially represent a good alternative to other alloys offering better performances but much more expensive or difficult to produce as components with complex geometries.

## Data Availability statement

No data corresponding to this work is available.

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TABLES

<table><caption>Table 1. Weight chemical composition of the studied alloys (average and standard deviation values calculated from five EDS x250 full frame measurements)</caption><thead><tr><th>Alloys :<br>Co/Ni-25Cr<br>-0.4C-6Ta</th><th>0Co-69Ni</th><th>14Co-55Ni</th><th>27Co-42Ni</th><th>42Co-27Ni</th><th>55Co-14Ni</th><th>69Co-0Ni</th></tr></thead><tbody><tr><th>Cr</th><td>25.6 ±0.2</td><td>26.2 ±0.2</td><td>24.9 ±0.5</td><td>25.9 ±0.3</td><td>26.2 ±0.3</td><td>25.4 ±0.2</td></tr><tr><th>Co</th><td>/</td><td>13.2 ±0.2</td><td>25.9 ±0.4</td><td>41.1 ±0.7</td><td>52.8 ±0.5</td><td>66.8 ±0.3</td></tr><tr><th>Ni</th><td>66.4 ±0.6</td><td>52.6 ±0.5</td><td>38.8 ±0.2</td><td>25.4 ±0.3</td><td>13.1 ±0.3</td><td>/</td></tr><tr><th>Ta</th><td>7.9 ±0.7</td><td>7.9 ±0.4</td><td>10.3 ±0.3</td><td>7.6 ±0.2</td><td>7.8 ±0.4</td><td>7.7 ±0.5</td></tr><tr><th>C</th><td>0.4</td><td>0.4</td><td>0.4</td><td>0.4</td><td>0.4</td><td>0.4</td></tr></tbody></table>

<table><caption>Table 2. Weight contents in Cr and in Ta in the outermost part of the alloys (* value obtained only in one location)</caption><thead><tr><th>Alloys<br>wt.%</th><th>0Co-69Ni</th><th>14Co-55Ni</th><th>27Co-42Ni</th><th>42Co-27Ni</th><th>55Co-14Ni</th><th>69Co-0Ni</th></tr></thead><tbody><tr><th>Cr</th><td>19.2 ±0.7</td><td>18.7 ±1.0</td><td>16.6 ±1.1</td><td>14.8 ±1.3</td><td>11.5 ±4.0</td><td>13.8 ±2.9</td></tr><tr><th>Ta</th><td>4.0 ±0.6</td><td>1.6 ±0.5</td><td>0.5 ±0.4</td><td>0.7 ±0.6</td><td>0.3 ±0.4</td><td>0.6 ±0.4</td></tr><tr><th>Cr max</th><td></td><td></td><td></td><td></td><td>13.0 ±1.0</td><td>16.0 ±1.5</td></tr><tr><th>Cr min</th><td></td><td></td><td></td><td></td><td>2.8 *</td><td>11.2 ±1.0</td></tr></tbody></table>

<table><caption>Table 3. The obtained values for the different kinetic constants</caption><thead><tr><th></th><th>0Co-69Ni</th><th>14Co-55Ni</th><th>27Co-42Ni</th><th>42Co-27Ni</th><th>55Co-14Ni</th><th>69Co-0Ni</th></tr></thead><tbody><tr><th>xCo - (69-x)Ni<br>-25Cr-0.4C-6Ta</th><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>Transient<br>oxidation<br>K<sub>l</sub> stage start<br>(x10<sup>-8</sup>g cm<sup>-2</sup> s<sup>-1</sup>)</th><td>138</td><td>95</td><td>102</td><td>119</td><td>226</td><td>79.3</td></tr><tr><th>Kp (classically<br>determined)<br>(x10<sup>-12</sup>g cm<sup>-4</sup> s<sup>-1</sup>)</th><td>134</td><td>275</td><td>277</td><td>293</td><td>360</td><td>293</td></tr><tr><th>Kp (Kv-<br>corrected)<br>(x10<sup>-12</sup>g cm<sup>-4</sup> s<sup>-1</sup>)</th><td>265</td><td>258</td><td>425</td><td>445</td><td>860*</td><td>308*</td></tr><tr><th>Kv<br>(x10<sup>-10</sup>g cm<sup>-2</sup> s<sup>-1</sup>)</th><td>205</td><td>191</td><td>171</td><td>171</td><td>497*</td><td>348*</td></tr></tbody></table>

<footnote>(*: values not realistic since the Kp-Kv method is not applicable in these two cases)</footnote>
<figure><img src="image_2.png" /><figcaption>Figure 1. General view of the microstructures of the studied alloys (SEM/BSE x250)</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Figure 2. Detailed view of the carbides morphologies in the studied alloys (SEM/BSE x1000)</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Figure 3. Diffractograms acquired on one face of the oxidized samples (here: the three nickel-richest oxidized)</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Figure 4. Diffractograms acquired on one face of the oxidized samples (here: the three cobalt-richest oxidized)</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Figure 5. The oxidized surface states from the 0Co-69Ni alloy (a: CrTaO₄-free zone, b: zone still having CrTaO₄) to the 42Co-27Ni alloy (SEM/BSE x1000; identification by EDS spot analysis)</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Figure 6. Oxidized surface states of the 55Co-14Ni alloy: 1/zones still mainly chromia-forming (top) and 2/ local catastrophic oxidation (SEM/BSE x1000; identification by EDS spot analysis)</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Figure 7. Illustration of the oxidized surface states of the 69Co-0Ni alloy: 1/zone still mainly chromia-forming (left) and 2/ local catastrophic oxidation (right); (SEM/BSE x1000; identification by EDS spot analysis)</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Figure 8. General view of the sub-surfaces states of the four first alloys for evidencing the development of the carbide-free zones (SEM/BSE x250)</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>Figure 9. General view of the sub-surfaces states of the two Co-richest alloys: dependence of the carbide-free depth on the local oxidation behavior: still chromia forming (top) and catastrophic oxidation started (bottom) (SEM/BSE x250)</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Figure 10. General view of the {70h, 1250°C}-aged microstructures of the six alloys (SEM/BSE, magnification: x250)</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>Figure 11. Detailed view of the morphologies of the carbides in the six {70h, 1250°C}-aged alloys (SEM/BSE, magnification: x1000)</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Figure 12. Matrix compositions of the alloys in their {1250°C, 70h}-aged states
(SEM EDS, average of five values)</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>Figure 13. The mass gain curves of the six alloys plotted together</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Figure 14. An example of the curves obtained by plotting m × dm/dt versus -m, which allows deducing the real Kp constant and the Kv constant when the behavior is mainly chromia-forming (here: the Ni-richest alloy 0Co-69Ni)</figcaption></figure>
<figure><img src="image_16.png" /></figure>

Figure 15. Example of comparison between the experimental mass gain curve (thick gray) and curves plotted with the obtained values Kp classically determined (thin dotted red) or with the real Kp and Kv values determined according to Figure 11 (thin black); here: the Ni-richest alloy (0Co-69Ni)
<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /><figcaption>Figure 16. Example of {m x dm/dt versus -m} plot (top) and of lack in consistency (bottom) between the experimental curve (thick gray) and the curve plotted with the real Kp and Kv values determined according to Figure 13 (thin black) when the behavior is not mainly chromia-forming; here: the Co-richest alloy (69Co-0Ni)</figcaption></figure>