# Oxidation of Ni-30Cr Alloy at Low Temperature and Low Oxygen Partial Pressure: Experimental Methods to Improve Kinetics Constants Determination

S. Bosonnet, X. Huang, L. Bataillou, L. Martinelli, Paul C M Fossati, Laurence Latu-Romain, Yves Wouters, C. Desgranges, Daniel Monceau

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S. Bosonnet, X. Huang, L. Bataillou, L. Martinelli, Paul C M Fossati, et al., Oxidation of Ni-30Cr Alloy at Low Temperature and Low Oxygen Partial Pressure: Experimental Methods to Improve Kinetics Constants Determination. High Temperature Corrosion of Materials, 2024, 10.1007/s11085-024-10270-x. [https://hal-04680433](https://hal-04680433)

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# Oxidation of Ni–30Cr Alloy at Low Temperature and Low Oxygen Partial Pressure: Experimental Methods to Improve Kinetics Constants Determination

S. Bosonnet¹ · X. Huang¹,² · L. Bataillou¹ · L. Martinelli¹ · Paul C. M. Fossati¹ · Laurence Latu-Romain² · Yves Wouters² · C. Desgranges¹ · D. Monceau³

Received: 15 July 2024 / Revised: 15 July 2024 / Accepted: 17 July 2024
© The Author(s) 2024

## Abstract

Ni–30Cr model alloy was used to study chromia-scale formation behaviour. During its formation the mass variation signal is weak and it is important to take specific care to measure oxidation kinetics by thermogravimetric analysis. Symmetrical design allows the determination of very small mass changes in compensating buoyancy effects and limiting measurement drift. The mass variation measurement comprises noise coming from different sources that affects the electronic signal. It must be minimised to improve accuracy. This involves keeping the room-temperature constant, strictly balancing the beam and minimising buoyancy effects. By this way it was possible to acquire kinetics and to measured rate constants, $k_p$, in a range from $3 \cdot 10^{-5}$ to $3 \cdot 10^{-10} \text{ mg}^2 \cdot \text{cm}^{-4} \cdot \text{s}^{-1}$ equivalent to $10^{-12}$ down to $10^{-17} \text{ cm}^2 \cdot \text{s}^{-1}$. Oxygen partial pressure ($P_{O_2}$) was monitor and revealed an abnormal consumption of oxygen at the beginning of the thermal exposure. Experiments with an inert material showed parasitic reactions identified by mass spectrometry as combustion of impurities. As oxygen consumption is not only due to oxidation of the sample, corrosion kinetics can’t be deduced from it. Hence, to determine whether the oxygen supply from the gas is a limiting parameter, a model, which quantifies oxygen consumption by sample oxidation within the thermobalance, is proposed.

**Keywords** Chromia forming alloy · Low $P_{O_2}$ · Thermogravimetric · Oxygen sensor · Mass spectrometry

## Introduction

Chromia-forming alloys are widely used in industrial applications because of their good behaviour in corrosive environments due to the formation of a protective chromia layer, which is compact and slow-growing. To illustrate, parabolic constants $k_p$

<footnote>Extended author information available on the last page of the article</footnote>
values obtained by thermogravimetric analysis (TGA) on Ni-30 Cr samples at dif-
ferent temperatures in low oxygen partial pressure atmosphere are shown in Fig. 1.
On this graph star marks correspond to experiments performed as part of this study
down to 500 °C [2]. These values are consistent with the literature [1, 3–10] and
change with temperature according an Arrhenius law with a pre-exponential fac-
tor $k_p^0$ of $2.4 \times 10^3$ mg$^2$.cm$^{-4}$.s$^{-1}$ equivalent to $8.8 \times 10^{-5}$cm$^2$.s$^{-1}$ and an activation
energy $E_a$ equal to 191 kJ.mol$^{-1}$. As in this study the mass variation signal is weak it
is important to take specific cares to measure oxidation kinetics by thermogravimet-
ric analysis (TGA).

We will discuss the origin of the artefacts encountered during a TGA measure-
ment and show that P₀₂ measurement during oxidation test must be used with cau-
tion. We will then propose an oxygen consumption model that accounts for the typi-
cal artefacts and provides a better view of the kinetics of oxidation.

Experimental Procedures

Ni-30Cr samples were taken from an ingot manufactured by Ugine-Savoie Imphy
(France). Detailed composition analysis of the ingot from which the samples were
taken is given in [1]. The mechanical and thermomechanical treatments applied to
the alloy before being cut in 10 mm × 15 mm × 1 mm coupons is also described in
our previous work. The coupons were ground using SiC paper down to P500 grade,
in order to form only chromia with no nickel oxide as Gheno observed in [11].
Then, oxidation tests were carried out on Ni-30Cr samples at 500, 600, 700, 800
and 900 °C in a SETARAM TAG-24 symmetrical thermobalance [2] using argon as

<figure><img src="image_4.png" /><figcaption>**Fig. 1** Arrhenius plot of parabolic rate constants measured for Ni-30Cr alloy oxidised under different oxidising conditions in a symmetrical thermobalance. The “star” symbols relate to our new data. Values in brackets are the oxygen partial pressure</figcaption></figure>

<figure><img src="image_5.png" /></figure>
the oxidising atmosphere and helium as the carrier gas protecting the balance beam and the weight modulus. A schematic view of the configuration is shown in Fig. 2. In this symmetrical arrangement two samples are hung on both sides of the balance beam: the Ni-30Cr sample on one side and a reference inert material (platinum) on the other side. Each one is placed in two independent furnaces. The oxygen partial pressure ($P_{O_2}$) was monitored by two oxygen sensors: one in situ mounted in the furnace near the sample, another one ex situ located at the gas outlet. Argon was injected at the common inlet with a flow rate of 2 L.h$^{-1}$ and divided in each furnace, so that the flux into each furnace is 1 L.h$^{-1}$. Helium was directly injected in the weight modulus area with a flowrate of 0.5 L.h$^{-1}$. Helium was evacuated after flowing through both furnaces at a flow rate of 0.25 L.h$^{-1}$ in each furnace. The gas outlets of each furnace converge in a single pipe, where the ex situ $P_{O_2}$ was measured.

<figure><img src="image_6.png" /><figcaption>**Fig. 2** Schematic view of symmetrical thermobalance and gas circuits with external and internal $O_2$ sensors (in red) (Color figure online)</figcaption></figure>
The initial value, before heating, was 5.10<sup>-6</sup> atm. Gas with 99.998% purity from air products company were injected during the whole experiments with a global flow rate of 1.25 L·h<sup>-1</sup> in each furnace.

## Results and Discussion

Several phenomena involving different sources can affect the resulting signal. The most impactful is the buoyancy force exerted by the test gas on the sample, but other artefacts stemming from variations in the electromagnet which is affected by room temperature fluctuations, can affect measurement to a lesser extent.

## Measurement Artefact Due to Room Temperature Variations

This device is equipped with an electromagnetic compensation balance that includes electromagnets, consisting of copper coils and a magnet, to compensate the force generated by mass variations. Due to its coefficient of thermal expansion, the electrical resistivity, and therefore the electrical resistance of the coils, is sensitive to temperature variations so that the current required to hold the magnet in position varies. This phenomenon induces a parasitic signal as the weight modulus undergoes temperature variations. That is shown in Fig. 3 which shows in the same graph the weight gain and the room temperature monitoring during an oxidation test performed at 500 °C: fluctuations occur simultaneously for both signals. The phenomenon repeats with a frequency of 24 h, corresponding to a day-night cycle. This fluctuation results in an error of 3 µg in the thermobalance mass gain measurement, which is of the same order of magnitude as the analytical balance measurement. Given that the sample area in this study is around 4 cm², the accuracy of the chromia oxide layer thickness measurements is therefore of 5 nm. These day-night

<figure><img src="image_7.png" /><figcaption>Fig. 3 Weight gain measured in thermobalance and laboratory temperature monitoring</figcaption></figure>

<figure><img src="image_8.png" /></figure>
temperature fluctuations can then affect $k_p$ measurements for typical values of $k_p$ lower than $10^{-8} \text{ mg}^2\cdot\text{cm}^{-4}\cdot\text{s}^{-1}$.

It is therefore essential to maintain the weight modulus at a constant temperature whether that is the temperature of the carrier gas flowing directly into it or the ambient temperature of the room.

Before starting the experiments, a stabilization sequence was performed to ensure that the test gas flow rates were as expected. Before introducing the gases, a primary vacuum was applied to the furnaces and to the weight modulus part to eliminate pollution. The stabilization sequence was carried out by flowing gas at ambient temperature long enough for the volume of the furnace to be renewed several times and by regulating at a low temperature, typically 30 °C, for the system to already have a temperature history for the adjustment of the regulation parameters PIDs during the first temperature rise.

## Measurement Artifact Due to Buoyancy

The thermobalance symmetrical design allows the determination of very small mass changes by compensating buoyancy effects thanks to the use of a reference sample set at the same conditions of gas flow and temperature as the test sample settings. As the volumes of both samples differ slightly, the buoyancy force exerted on each is different and the buoyancy effect is therefore not fully compensated. In fact, the difference in buoyancy forces changes with the gas density, e.g. during heating and cooling steps or if the gas composition is changed. Several means can be used to correct this buoyancy effect from mass gain curves. Examples are given below.

The graph in Fig. 4a shows raw and buoyancy-corrected specific gain mass versus time for a Ni–Cr sample oxidised during 50 h at 700 °C. This effect takes places only during the transitory stage. If only the isothermal stage is considered, the buoyancy correction can simply be done from the difference between the mass gain measured at the end of the isothermal stage and the one measured at the end of the cooling stage, when the sample reaches room temperature. This assumes that oxidation is negligible during cooling. This “direct method” is used to adjust the data on Fig. 4a.

<figure><img src="image_9.png" /><figcaption>Fig. 4 a Raw and “direct method” adjusted specific mass gain versus time and b Raw and adjusted by Monceau & Poquillon’s method, specific mass gains versus temperature of Ni–30Cr oxidised at 700 °C during 50 h [13]</figcaption></figure>
The method proposed by Monceau et Poquillon [12] consists in adjusting buoyancy as a function of temperature. The relation between weight gains difference and temperature they achieve is given in Eq. (1):

$$ \Delta_m(T) - \Delta_m(T_{amb}) = -\frac{1}{T}(V_{sam} - V_{ref})\frac{P_{gas}}{R} + \frac{1}{T_{amb}}(V_{sam} - V_{ref})\frac{PM_{gas}}{R}, \quad (1) $$

where $\Delta m$ is the mass gain (g), $V_{sam}$ and $V_{ref}$ the volumes of the test and reference samples, respectively (m³), $P_0$ the test pressure (Pa), $M_{gas}$ the molar weight of flowing gas (g·mol⁻¹), $R$ the gas constant (J·mol⁻¹·K⁻¹), $T$ and $T_a$ the test and ambient temperature, respectively (K).

The raw mass gain which is measured during the heating stage is not only the result of buoyancy but also of oxidation of the sample. In contrast it is only due to buoyancy during the cooling stage because oxidation is negligible, especially in the lower temperature range. Considering only the cooling stage measurements, an affine function can be fitted to $\Delta_m(T) - \Delta_m(T_{amb})$ as a function of $1/T$. We can then deduce $(V_{sam} - V_{ref})\frac{PM_{gas}}{R}$ from the slope and $\frac{1}{T_{amb}}(V_{sam} - V_{ref})\frac{PM_{gas}}{R}$ from the intercept. Figure 4b, shows the raw specific mass gain (blue line) and the values adjusted by this method (orange line) as a function of temperature. It becomes then possible by this method to extract the mass gain purely caused by oxidation from the overall mass change.

## Oxygen Partial Pressure ($P_{O_2}$) monitoring during oxidation

To monitor the oxygen content during oxidation tests, the thermobalance is equipped with two oxygen probes as described above. The probes consist of a solid electrolyte made of zirconia doped with yttria which has the property of being an anionic conductor at high temperatures. One side of this electrolyte is then in contact with the gas, the other side is in contact with a reference environment. This reference environment is a metal-oxide mix whose equilibrium $P_{O_2}$ is temperature dependent, acting as a buffer mix. It is composed of a Pd/PdO mix for working temperatures between 500 °C and 700 °C or Ir/IrO₂ between 700 °C and 900 °C.

The electrical potential difference between each side is measured via two platinum contacts acting as electrodes. The relation between the oxygen partial pressure and the potential difference is given by Eq. (2):

$$ P_{O_2,gas} = P_{O_2,reference} \cdot \exp\left(\frac{4F}{RT}\Delta\psi_{gas}\right) \quad (2) $$

with $P_{O_2,gas}$ and $P_{O_2,reference}$ the oxygen partial pressures (atm) of the test gas and reference environment, respectively, $F$ the Faraday constant equal to 96 485 C·mol⁻¹, $R$ the gas constant equal to 8,314 J·mol⁻¹·K⁻¹, $T$ the temperature (K) and $\Delta\psi_{gas}$ the voltage measured between the gas-electrolyte and electrolyte-reference sides.

In order to increase the accuracy of the $P_{O_2}$ measurement, probes are calibrated beforehand.
The in situ probe is a customized fitted Setnag Micropoas®, directly immersed in the environment of the furnace at the nearest of the test sample. The ex situ probe is placed at the outlet. It is an oxygen analyser Setnag Jok'air® consisting of a Setnag Micropoas® with its own heating system and placed in the gas outlet. The analysed gas is the combination of the gases coming from both furnaces and P<sub>O<sub>2</sub></sub> corresponds to the average of the values in the two furnaces. Because of this location a time lag between the in situ and ex situ signals may also occur, which can result in differences between in situ and ex situ values of P<sub>O<sub>2</sub></sub>. Furthermore, as the probe does not operate below 500 °C, in situ probes cannot be used during the heating phase. However, because the ex situ probe integrates an independent heating system, its signal can be used throughout the duration of the oxidation test.

Oxygen partial pressure during oxidation using in situ and ex situ probes is shown in Fig. 5. Oxygen consumption can be used to monitor corrosion kinetics, assuming that it is due solely to oxidation of the material. However, the ex situ oxygen probe, which combines the gas flow from the two furnaces (reference furnace and test furnace), should give a value of half the oxygen content of the gas, i.e. of the order of 3 10<sup>-6</sup> atm, if all the oxygen from the test furnace had been consumed by the oxidation of the alloy. However, Fig. 5 shows that the ex situ oxygen probe gives values several orders of magnitude lower. Surprisingly, oxygen is therefore consumed in both furnaces.

## Oxygen Consumption and Gas Released During Heat Treatment With Inert Samples

In order to measure the oxygen consumption due solely to the oxidation of the sample, a blank test was carried out with two inert (alumina or platinum) samples suspended in each furnace of the symmetrical thermobalance. A mass spectrometer was added to identify species released during thermal cycles. The sampling capillary was directly introduced into the furnace via a specific coupling piece. Several experiments were performed to qualify produced gaseous species, the first measurement scans showed mainly an evolution of CO<sub>2</sub> and H<sub>2</sub>O signals.

<figure><img src="image_10.png" /><figcaption>Fig. 5 P<sub>O<sub>2</sub></sub> ex and in situ during oxidation of Ni-30Cr in pure Ar in TGA (a) from 500 to 700 °C and (b) from 800 to 900 °C</figcaption></figure>
Figure 6 shows the results of a test carried out with alumina samples; tests with platinum samples gave the same results. For this experiment, the samples are inserted into the furnaces and heated as for an oxidation test. Then temperature is decreased and increased again, as shown by the temperature profiles in Fig. 6, without removing the sample from the furnace. The in situ oxygen probe only works at temperatures above 700 °C. Signals are therefore cut off at lower temperatures. At the start of the first cycle, a sharp drop in $P_{O_2}$ is accompanied by the release of $CO_2$ and $H_2O$, highlighting the combustion of carbonaceous species ($CH_4$, for example). All the signals return to a steady state after an hour, regardless of the temperature. The impurities absorbed on the surface of the sample and on the walls of the furnace are therefore assumed to have all been consumed. However, during the second cycle, the peaks in $O_2$ consumption and $CO_2$ and $H_2O$ release reappear. This highlights the combustion of new impurities that may have been brought by the circulation of Ar between the two cycles at ambient temperature.

## Oxygen Consumption Modelling for Ni-30Cr Oxidation in Thermobalance

Zancanaro & al. [14] proposed a 2D modelling of the gaseous flows across a thermobalance using computational fluids dynamics. Here, to quantify the oxygen consumption due to sample oxidation at high temperature in the thermobalance, a 1D model is proposed. In this model, it is supposed that the oxygen fed by the flow of

<figure><img src="image_11.png" /><figcaption>Fig. 6 Changes in temperature, oxygen partial pressure and the intensity of the $CO_2$ and $H_2O$ signals during heating of an $Al_2O_3$ sample to 700, 800 and 900 °C over two cycles in a symmetrical thermobalance</figcaption></figure>

<figure><img src="image_12.png" /></figure>
Ar containing O₂ is consumed by the oxidation of the sample in the middle of a high temperature tubular furnace.

Oxidation causes a gradient of oxygen partial pressure in the furnace, and the diffusion equation in one dimension in space, is written (3):

$$ \frac{\partial}{\partial t} \left( \frac{P_{O_2}}{P^0} \right) = D_{O_2} \frac{\partial^2}{\partial x^2} \left( \frac{P_{O_2}}{P^0} \right) - \frac{T}{T_a} \frac{Q}{S_t} \frac{\partial}{\partial x} \left( \frac{P_{O_2}}{P^0} \right) - \frac{b \rho_{O_x}}{2n^0 M_{O_x}} \cdot \frac{A}{S_t l_x} \frac{de}{dt}, \quad (3) $$

where P⁰ is the standard pressure (atm), t the oxidation time (s), D₀₂ the oxygen diffusion coefficient in Ar (cm²·s⁻¹), x the position in the furnace (cm), T the furnace temperature (K), Tₐ the ambient temperature (K) and Q the volumetric flow rate of the gas Ar-O₂ (cm³·s⁻¹) in direction x, Sₜ the area of the tube section (cm²), b the stoichiometric coefficient of MₐO₉ oxide, ρ₀ₓ the density of the oxide (g·cm⁻³), M₀ₓ the molar mass of the oxide (g·mol⁻¹), A the surface area of the sample (cm²), lₘ the sample length (cm) along the x axis, e the thickness of the oxide (cm), n⁰ the concentration of all gaseous species at the standard pressure (mol·cm⁻³).

In Eq. (3), the three terms on the right represent, respectively, the supply of oxygen by diffusion in a heterogeneous medium, the supply of oxygen by an oxygen-rich flow imposed on an oxygen-poor medium and the consumption of oxygen by oxidation of the sample. Equation (3) is solved numerically using the finite difference method.

Figure 7 shows the result of this modelling for the oxidation of a Ni-30Cr sample of size 15×10×1 mm under impure Ar containing a nominal O₂ content equal to 7 10⁻⁵ atm. The hatched area is the oxidation zone, where the sample is located. The temperature rose from 40 °C to 900 °C in 22 min and then stabilised at 900 °C. High

<figure><img src="image_13.png" /><figcaption>Fig. 7 P₀ₓ At 900 °C under 20 mL·min⁻¹ of sweeping Ar for oxidation of Ni-30Cr sample with 15×10×1 mm dimension. The nominal value of P₀ₓ is 7×10⁻⁵ atm. x is the position in the furnace and t the oxidation time. The direction of gas flow is in the direction of increasing x. The centre of the sample is positioned at the abscissa origin. The hatched area is the oxidation zone, where the sample is located</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>**Fig. 8** Evolution of $P_{O_2}$ (a) at the furnace exit as a function of oxidation time (b) within the furnace after 2 h of oxidation. The hatched area is the oxidation zone, where the sample is located. Conditions of the calculation: $20 \text{ mL.min}^{-1}$ of sweeping Ar, $15 \times 10 \times 1$ mm dimension of the sample, nominal value of $P_{O_2}$ is $7 \times 10^{-5}$ atm. *x* is the position in the furnace and *t* the oxidation time. The direction of gas flow is in the direction of increasing *x*. The centre of the sample is positioned at the abscissa origin</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>**Fig. 9** Evolution of $P_{O_2}$ (a) at the furnace exit as a function of oxidation time (b) within the furnace after 2 h of oxidation. The hatched area is the oxidation zone, where the sample is located. Conditions of the calculation: temperature is 900 °C, $15 \times 10 \times 1$ mm dimension of the sample, nominal value of $P_{O_2}$ is $7 \times 10^{-5}$ atm. *x* is the position in the furnace and *t* the oxidation time. The direction of gas flow is in the direction of increasing *x*. The centre of the sample is positioned at the abscissa origin</figcaption></figure>

temperature oxidation rapidly consumes the oxygen in the reaction chamber, but the oxygen content gradually increases as the oxidation rate decreases, according to the oxide parabolic growth law.

Figure 8, 9 and 10 show the effects of temperature, Ar flow rate and $P_{O_2}$ at the inlet of the thermobalance, respectively on the $P_{O_2}$ evolution at the furnace exit (as a function of time, *t*) or within the furnace as a function of the location *x*. Oxygen consumption is greater at high temperatures. The same trend was found with the experimental results (Fig. 5). This is the consequence of the higher oxidation rate (Fig. 8). A high flow rate (Fig. 9) or high $P_{O_2}$ nominal (Fig. 10) value prevents the decrease in oxygen consumption due to the sample oxidation.

The oxygen partial pressure becomes negative at the start of oxidation at high temperature (Fig. 8a, low flow rate (Fig. 9a or low nominal $P_{O_2}$ (Fig. 10a. This is because the oxygen supply rate, which results from the Ar flow rate and diffusion caused by the gradient, is too low compared with the oxygen consumption rate
<figure><img src="image_16.png" /><figcaption>**Fig. 10** Evolution of $P_{O_2}$ (a) at the furnace exit as a function of oxidation time (b) within the furnace after 2 h of oxidation. The hatched area is the oxidation zone, where the sample is located. Conditions of the calculation: temperature is 900 °C, 20 mL.min$^{-1}$ of sweeping Ar, 15×10×1 mm dimension of the sample. *x* is the position in the furnace and *t* the oxidation time. The direction of gas flow is in the direction of increasing *x*. The centre of the sample is positioned at the abscissa origin</figcaption></figure>

linked to oxidation. This is of course unrealistic as $P_{O_2}$ cannot be negative. In reality, when the consumption of oxygen becomes too great in relation to its supply (by diffusion and convection), the oxidation of the alloy decreases (the $k_p$ becomes dependent on the external $P_{O_2}$) until it stops when the external $P_{O_2}$ becomes equal to the equilibrium $P_{O_2}$ between the alloy and the oxide, limiting the oxidation of the material. In the simple model shown in this study, $k_p$ is constant, whatever the $P_{O_2}$. The next step towards a more realistic model will be to adjust the $k_p$ to the external $P_{O_2}$ decrease, so that the $k_p$ becomes zero when the external $P_{O_2}$ becomes equal to the alloy/oxide equilibrium $P_{O_2}$. In this case, $P_{O_2}$ can no longer become negative. This improvement to the model is one of the perspectives of this work. However, this simple model shows that the shape of the drops of $P_{O_2}$ observed in experiments and depending on temperature (Fig. 5) is related to the oxidation of the sample (Fig. 8). The combustion of the carbonaceous species adsorbed on the wall of the furnaces and tubes of the thermobalance cannot explain such shapes of drops. Moreover, the model shows the effect of flow rate (Fig. 9) and nominal $P_{O_2}$ (Fig. 10) on the drop of $P_{O_2}$.

In conclusion, the $P_{O_2}$ decreases at the start of oxidation and the time required for the $P_{O_2}$ to rise increase with the oxidation temperature. Oxidation could be limited by oxygen supply at the start of oxidation at high temperature, low flow rate or low nominal $P_{O_2}$.

## Conclusion

Ni-30 Cr alloy oxidation at low temperature and in low oxygen partial pressure is a typical case, where very slow oxidation kinetics needs to be evaluated as accurately as possible. Possible sources of loss in accuracy were investigated by equipping the thermobalance with oxygen sensors. Most TGA devices work with a compensation electromagnetic balance that is sensitive to room temperature variations. Keeping the room at a constant temperature reduces the magnitude of this artefact. Taking
care to balance the beam accurately (below ± 1 mg difference between the two sides) before starting the test further reduces some part of the electronic noise by minimising current offset. That is essential to get rid of this artefact when measuring very low mass gain. For Ni-30Cr oxidised in argon, a drop in oxygen partial pressure was observed during the test. It is not solely attributable to oxygen consumption by the sample but also to parasitic reactions which occur in furnaces with impurities contained in the gas. It is therefore doubtful to use the evolution of the partial pressure of oxygen to determine whether it is the limiting factor for oxidation. However, a simple model was proposed to quantify the effect of sample oxidation on oxygen consumption. It shows that the high oxygen consumption that delays the rise in oxygen pressure is due to oxidation of the sample. It also shows that oxidation of Ni-30Cr alloys at low $P_{O_2}$ or low flux can be limited by oxygen supply during a thermobalance test.

**Author Contributions** All authors reviewed the manuscript.

**Funding** Open access funding provided by Commissariat à l'Énergie Atomique et aux Énergies Alternatives.

**Data Availability** No datasets were generated or analysed during the current study.

**Declarations**

**Conflict of interest** The authors declare that they have no conflict of interest.

**Open Access** This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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## Authors and Affiliations

S. Bosonnet<fnref n="1" /> · X. Huang<fnref n="1" />,<fnref n="2" /> · L. Bataillou<fnref n="1" /> · L. Martinelli<fnref n="1" /> · Paul C. M. Fossati<fnref n="1" /> · Laurence Latu-Romain<fnref n="2" /> · Yves Wouters<fnref n="2" /> · C. Desgranges<fnref n="1" /> · D. Monceau<fnref n="3" />

<figure><img src="image_17.png" /></figure>

X. Huang
xian-huang@outlook.com

S. Bosonnet
sophie.bosonnet@cea.fr

L. Martinelli
laure.martinelli@cea.fr

<footnote n="1">¹ Université Paris-Saclay, CEA, S2CM, 91191 Gif Sur Yvette, France</footnote>

<footnote n="2">² Université Grenoble Alpes, CNRS, SIMaP, 38000 Grenoble, France</footnote>

<footnote n="3">³ CIRIMAT, Université de Toulouse, CNRS, INPT, UPS, Ensiacet, 4 allée Emile Monso, 31030 Toulouse Cedex 4, France</footnote>