1. Introduction
Nanostructured materials, ranging from nanocrystalline and nanolayer to nanoporous and nanocomposite structures, are materials whose structural elements have dimensions in the range of 1–100 nm [
1]. Over the past decade, an explosion in both academic and industrial interest in these materials has arisen due to the remarkable and unique properties—such as fundamental electric, optical, magnetic and mechanical properties—that they exhibit in various fields [
1]. Oxide dispersion-strengthened steels can be considered to be examples of nanostructured materials owing to the high density of nano-oxides embedded in the ferritic matrix. The nano-oxides essentially serve as obstacles for dislocation motion and confer excellent mechanical strength properties to the alloy. Thus, these alloys are good contenders for applications in harsh environments as core component materials for the future generation of nuclear power plants. Therefore, maintaining this precipitation at a nanoscale in service conditions is of great interest to preserve the excellent mechanical properties and to guarantee the safe use of reactors. However, nanostructured ODS materials are far from equilibrium due to the high density of precipitate/matrix interfaces. Thus, the associated contribution of these interfaces to free energy constitutes a large driving force that leads the nano-oxides to coarsen even under irradiation. Therefore, to keep the benefits of nanoprecipitation by preventing the nano-oxides from coarsening, their irradiation stability has to be thoroughly understood in extreme conditions. Thus far, a number of studies have investigated the irradiation evolution of oxide nanoparticles in
bcc Fe-Cr-based oxide dispersion-strengthened steels [
2]. The main contributing mechanisms for nanoparticle evolution have been identified [
2,
3]: ballistic dissolution, Ostwald ripening, irradiation-enhanced diffusion and homogeneous nucleation. Of these four major themes explaining the irradiation response of the nanoparticles, this paper develops the two first themes.
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Ballistic dissolution refers to the displacement of a knock-on-atom to a position in the surrounding matrix outside the nano-oxide [
2]. An interfacial atom must be ejected more than one nearest-neighbour distance in the adjacent matrix to separate itself from the nano-oxide [
2]. The result is the total or partial dissolution of the nano-oxide dispersion. He et al. [
4] observed a significant decrease in size and number density of the nano-oxide distribution after 5 MeV Ni
2+ irradiation at 300 °C for a damage level of 100 dpa. If this phenomenon is normally expected at low temperature, some authors also reported dissolution at higher temperature. Li et al. [
5] observed nanoparticle shrinking under electron irradiation at 400 °C in a Fe-9Cr ODS. Swenson and Wharry [
6] observed the dissolution of the nano-oxides in Fe-9Cr ODS steels after neutron irradiation up to 3 dpa at the even higher temperature of 500 °C.
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Ostwald ripening under irradiation is similar to the well-known thermal process where small particles shrink to the benefit of large ones to minimize interfacial energy; the main difference is the irradiation cascades, which help in increasing interfacial solute concentration and enhance solute transport [
3]. Ostwald ripening can also be inverted, leading the small particles to grow at the expense of the large ones [
3]. In ODS steels, similar to those studied in this paper, Lescoat et al. [
7] proved that after irradiation, the average size of the nano-oxides increased while their density decreased. They show that the radius evolution kinetics of the nano-oxides can be scaled as
t1/3, with
t being the irradiation time, while the density decreased linearly with the inverse of the irradiation time, which is conformed to a classic Ostwald ripening process [
8]. Ostwald ripening was also reported in other studies [
9,
10]. Chen et al. [
11] distinguished the coarsening behaviour of coherent nano-oxides from incoherent ones. They found that coherent dispersoids were toward an equilibrium size at each temperature tested, and incoherent dispersoids are destroyed at low temperature but survived while shrinking in size at higher temperatures. In addition, the coarsening of nano-oxides was accompanied with a loss of the coherent atomic structure of the oxide/matrix interface [
12].
Therefore, all of these studies show that there are difficulties in retaining nano-oxide dispersion under irradiation at a nanoscale. This might lead the ODS steels to exhibit a possible loss of nanostructuration in service conditions. This paper proposes to detail the behaviour of the nano-oxides when the material is subjected to both thermal annealing and irradiation. A theoretical background is first proposed to introduce the enhanced and inverse Ostwald ripening mechanism.
2. Materials and Methods
All the results presented in this paper were obtained on ferritic ODS steels developed at CEA and elaborated by mechanical alloying. This process consisted of the milling under a hydrogen atmosphere of both pre-alloyed Fe-Cr-W-Ti powder and Y
2O
3 powder in an attritor. After powder milling, the alloy was hot extruded at 1100 °C and then annealed at 1050 °C for 1 h. The chemical compositions of the two studied materials are presented in
Table 1. Mn, Ni and Si elements were in minor concentrations that were initially present in the Fe-Cr-W-Ti powder, while C resulted from contamination. Those two alloys are called Fe-14Cr ODS and Fe-18Cr ODS hereafter.
TEM observations were conducted on a JEOL-2100 microscope (JEOL LTD, Tokyo, Japan) operating at 200 kV, while HRTEM was performed on both JEOL-2010F and CS-corrected (probe and image) JEOL-neoARM microscopes operating at 200 kV. Chemical analysis was performed using the neoARM microscope equipped with double-Centurio EDS (Energy Dispersion Spectroscopy) detectors (JEOL LTD, Tokyo, Japan). TEM disks were punched from 60 µm-thick, mechanically polished foils and electropolished using a 10% perchloric acid, 90% ethanol solution at −10 °C in a Struers Tenupol thinning device. The Focused Ion Beam (FIB) technique was also used to extract a standard cross-section preparation from a virgin ODS sample with an FEI Helios SEM/FIB dual beam microscope (Thermo Fisher Scientific, Waltham, MA, USA).
Atom Probe Tomography (APT) analysis was performed on a CAMECA LEAP 4000X HR (Ametek, Inc., Berwyn, PA, USA) in laser pulsing mode; a base temperature of 50 K, laser pulse energy of 80 pJ and pulse repetition rate of 250 kHz were used during the experiments.
The ion irradiations were conducted at the CEA-JANNuS Saclay facility (CEA, Saclay, France) [
13] using 500 keV Fe
+ self-ions with a flux of 2.6–2.8 × 10
12 ions·cm
−2s
−1. The specimens had a thin-foil geometry; were maintained at nominal temperatures of 300 °C, 400 °C and 500 °C; and were tilted by 15° with respect to the incoming ion beamline. The depth profile of irradiation damage using 500 keV Fe
+ ions can be found in [
7]. The mean doses reached within the first 100 nm were estimated to be roughly 75 dpa [
7] and 150 dpa [
7] for a fluence of 4.4 × 10
16 ions·cm
−2 and 8.9 × 10
16 ions·cm
−2, respectively.
In situ ion irradiations were conducted at the JANNuS-Orsay facility (Université Paris-Saclay, Orsay, France) [
13] at IJClab equipped with a FEI Tecnai G
2 20 TEM (Thermo Fisher Scientific, Waltham, MA, USA) operating at 200 kV and coupled with the ARAMIS ion accelerator. Irradiations were performed at room temperature and at 500 °C. At room temperature, the irradiations were conducted using 4000 keV Au
2+ ions with a flux of 2.0 × 10
11 ions·cm
−2s
−1. The depth profile of the irradiation damage was calculated using Kinchin–Pease mode from the Iradina software [
14] with 40 eV displacement energy. The irradiation damage profile is presented in
Figure 1. At 500 °C, the irradiations were conducted using 150 keV Fe
+ ions with a flux of 2.9 × 10
12 ions·cm
−2·s
−1. The corresponding irradiation profile is presented elsewhere [
15].
4. Discussion
In this paper, we demonstrated that irradiation can affect the nano-oxide dispersion in ODS steels. When subjected to ion bombardment, the nano-dispersion dissolves at low temperature; in contrast, the oxides coarsen at high temperature. The coarsening mechanism is supposed to be radiation-enhanced Ostwald ripening, where the excess of point defects created by irradiation enhances the thermal diffusion and the ballistic jumps assist the thermal Gibbs–Thomson effect to increase the interfacial solute concentration. Further, the larger oxide tends to dissolve to the benefit of the smaller ones through an inverse Ostwald ripening mechanism. In the end, when thermal and ballistic atomic fluxes compensate each other, the nano-oxides exhibit an apparent stability. Therefore, except at low temperature where the nano-oxides are likely to dissolve completely after a long irradiation, it can be concluded that the nanoprecipitation is generally preserved for the irradiation condition presented in this paper since the nano-oxide average diameter reached a value of only 5.6 nm after the longest irradiation (150 dpa at 500°C).
Now we know that the nanosize of the oxides is retained under irradiation, there is a functionality that needs to be highlighted: nano-oxides are supposed to act as sinks for point defects [
35,
36]. This means that point defects created under irradiation can be lost at the nano-oxide interfaces. We use the result obtained in this paper to support this point. To do this, we need to calculate the sink strength of the ODS steel.
First, we have to calculate the diffusion coefficient under irradiation. For this, we consider that the Ostwald ripening under irradiation is close to the classic Ostwald ripening regime since we proved the coarsening kinetic scale to be
. Therefore, we can deduce an equivalent irradiation temperature
by assuming
which can be formulated after simplification as
This equation has to be considered as a first approximation to rationalize the radiation-enhanced coarsening, as explained in [
37]. This gives some clues to understand key parameters controlling coarsening under irradiation. From
Table 7, it can be seen that
is equal to 5.26 × 10
−21 m
−1s
−1molK
−1.
Figure 15 is the plot of
against the temperature. The plot has been realized by using the theoretical value of the diffusion coefficient [
23] and solubility [
24], as previously given in
Table 2. By reporting on this plot the value found for
, we can deduce the equivalent annealing temperature; that is, the temperature that would have produced the same result as irradiation but in pure thermal annealing conditions. We found that an irradiation at 500 °C for 9.5 h (i.e., 150 dpa) is equivalent to a thermal annealing at 1270 °C for the same duration. This theoretical result appears to be in good accordance with the theoretical results presented in
Figure 9c, showing that a thermal annealing of 10 h at 1270 °C leads the nano-oxides to grow from a radius of 1.4 nm to a radius of about 3 nm. Therefore, if we assume that
, we can calculate the diffusion coefficient of the rate-controlling element for this irradiation condition; we found a value of
= 8.5 × 10
−14 m
2s
−1.
From a theoretical point of view, irradiation enhances the diffusion coefficient
relative to the purely thermal valued
by [
38]
where
is the concentration of vacancies under irradiation, and
is the equilibrium concentration of vacancies under purely thermal conditions. In ODS steels, the sink density is high enough to consider that interstitials find the sink before they find vacancies [
39]. Therefore, we can approximate the concentration of vacancies as
where
is the defect production equal to a rate of 6.4 × 10
−3 dpa·s
−1 [
7] and
is the time for a vacancy to reach a sink. Therefore, after the substitution of Equation (14) into Equation (13), the time
is equal to [
7]
With
—the vacancy formation energy—equal to 2.2 eV [
40],
is the global sink strength and
is the vacancy diffusion coefficient. After calculating
at 50 0°C from the values given in
Table 2, we found that
is equal to 1.2 × 10
−6 s. After calculating the vacancy diffusion coefficient
as proposed in [
7], the corresponding global sink strength
is found to be equal to 3.8 × 10
16 m
−2.
Considering that nano-oxide dispersion, dislocations, free surfaces and grains are the main sinks for point defects [
41], we can try to estimate which of these sinks is the principal contributor to the loss of point defects. The sink strength
for the nano-oxides (NO) can be calculated as
[
41], where
and
are the radius and number density of the nano-oxides and
Y is a constant related to the bias for defect trapping [
41], which is reported to be equal to 1 [
41]. The sink strength
is estimated by considering the average radius and number density from both TEM (this study) and APT measurement [
42]. The sink strength for the dislocations can be calculated as
, where
is the atomic site for defect capture according to the dislocation line intercepted with a crystal plane [
41] and
is the dislocation density. For the calculation, we approximate the dislocation sink strength as being similar to the dislocation density [
41]. The dislocation density was estimated to be 5.0 × 10
14 m
−2 in similar ferritic ODS steels [
28]. The sink strength of the free surfaces in thin foil can be calculated as [
43]
by considering that
, where
is the sink strength of all other microstructural defect sinks within the foil and
l is the half of the foil thickness, estimated at 50 nm. Concerning the grain, the sink strength can be expressed as
by considering that
[
41], with
d being the diameter of the grains, which is equal to 0.5 µm in the studied ODS steels [
44].
Table 8 presents the result for all the sink strength.
The sum of all the sink strengths
is equal to 5.9 × 10
15 m
−2 when taking into account
(TEM) and is equal to 1.8 × 10
16 m
−2 when taking into account
(APT). The sink strength calculated based on the APT measurement matches the sink strength value found previously (3.8 × 10
16 m
−2), which validates this method over the TEM measurement. Thus, as Aydogan et al. [
41] found, one may note that
, with
one order of magnitude higher than the other sink strength. Hence, it can be concluded that the nano-oxides are likely to be the main mechanism of defect removal under irradiation.
From this sink calculation, the removal of point defects by the sample surface appears to be significant. Since thin foil geometry was used to irradiate the ODS samples, the loss of point defects at the free surface should modify the kinetics of growth in the case where the thermal effects predominate over the ballistic effects. Thus, at 500 °C, the growth of the nano-oxides may be over or underestimated due to the effect of free surfaces.
In conclusion, in addition of being obstacles to the dislocation motion, nano-oxides also act as sinks for the point defects created under irradiation and allow their population to be reduced. This functionality requires the stability of the atomic configuration of the interfaces, but recent results [
12] showed that interfaces of nano-oxides exhibit instabilities only for high irradiation damage while remaining stable otherwise.