# Nano-Structured Materials under Irradiation: Oxide Dispersion-Strengthened Steels

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{2}Ti

_{2}O

_{7}pyrochlore-like structure. However, the lattice structure of the smallest oxides is difficult to determine, but it is likely to be close to the atomic structure of the host matrix. Designed to serve in extreme environments—i.e., a nuclear power plant—the challenge for ODS steels is to preserve the nano-oxide dispersion under irradiation in order to maintain the excellent creep properties of the alloy in the reactor. Under irradiation, the nano-oxides exhibit different behaviour as a function of the temperature. At low temperature, the nano-oxides tend to dissolve owing to the frequent ballistic ejection of the solute atoms. At medium temperature, the thermal diffusion balances the ballistic dissolution, and the nano-oxides display an apparent stability. At high temperature, the nano-oxides start to coarsen, resulting in an increase in their size and a decrease in their number density. If the small nano-oxides coarsen through a radiation-enhanced Ostwald ripening mechanism, some large oxides disappear to the benefit of the small ones through a radiation-induced inverse Ostwald ripening. In conclusion, it is suggested that, under irradiation, the nano-oxide dispersion prevails over dislocations, grain boundaries and free surfaces to remove the point defects created by irradiation.

## 1. Introduction

- -
- 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. - -
- 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 t
^{1/3}, 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].

## 2. Materials and Methods

_{2}O

_{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.

^{+}self-ions with a flux of 2.6–2.8 × 10

^{12}ions·cm

^{−2}s

^{−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.

^{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

^{−2}s

^{−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].

## 3. Results

#### 3.1. Theoretical Background: The Irradiation Modified Gibbs–Thomson Relation

- -
- A quasi-stationary particle size distribution is approached asymptotically;
- -
- After the quasi-stationary condition is reached, the third power of the mean particle size increases linearly with time, with a unique slope, according to the following equation:

^{−3}dpa·s

^{−1}. The dashed line is the usual solubility for a curved interface—i.e., the conventional Gibbs–Thomson relation, $C\left(R\right)$—whereas the thick solid curve is the plot of the solute concentration at the precipitate interface under irradiation, ${C}^{I}\left(R\right)$. The coefficient values used to calculate the solubility are summarized in Table 2. Yttrium is considered as the rate-controlling element owing to its low diffusivity.

#### 3.2. Characterization of the Nano-Oxide Dispersion

^{23}m

^{−3}. The nano-oxides appear rather spherical, even though their shape remains difficult to appreciate considering their small size.

^{23}m

^{−3}, while the average diameter is found to be 2.0 nm. Those values are in good accordance with both the density and average diameter measured by TEM.

_{2}Ti

_{2}O

_{7}pyrochlore oxide is closely related to the fluorite structure, except that there are two cation sites and one-eighth of the anions are absent (8a). The Y and Ti metal cations occupy the 16d(1/2, 1/2, 1/2) and 16(0, 0, 0) sites, respectively, while the oxygen atoms are in the 48f(x, 1/8, 1/8) and 8b(3/8, 3/8, 3/8) positions [25]. Figure 7 illustrates the atomic arrangement of the pyrochlore-type lattice structure. Figure 6c shows an HRTEM image of a nano-oxide embedded in a matrix oriented along the $\langle 1\overline{1}0\rangle $ direction. In the FFT (Figure 6d), the additional spot corresponds to the atomic planes of the oxide. The zone axis corresponding to the precipitates displays $\langle 110\rangle $ fcc symmetry, while the two measured interplanar distances are found to be 0.254 nm and 0.304 nm. These values are in good accordance with the $\langle 400\rangle $ (0.25 nm) and the $\langle \overline{2}\overline{2}2\rangle $ (0.29 nm) pyrochlore distances [26]. The nano-oxide displays a cube-on-cube relationship with the matrix, as expected owing to the full coherency of the nanocluster parent phase (Figure 6a).

#### 3.3. Evolution of the Nano-Oxides Distribution during Thermal Annealing

^{23}m

^{−3}to 3.4 ± 0.7 × 10

^{22}m

^{−3}. To determine the extent to which the coarsening regime corresponds to this increase in size, we first need to calculate the interfacial energy of the nano-oxides.

#### 3.3.1. Interface Energy Calculation Deduced from Morphological Transition

_{2}Ti

_{2}O

_{7}mismatching plane, the resulting misfit strain is found to be 12.6% [25]. Therefore, by replacing those values in Equation (7) and by replacing the value of ${E}_{1}$ given elsewhere [25], we find that the interfacial energy of the nano-oxide embedded with cube-on-cube orientation is 290 mJ·m

^{−2}. By using a more accurate approach [25], the interface energy has been refined to a value of 260 mJ.m

^{−2}.

#### 3.3.2. Ostwald Ripening Process

^{2}is calculated. The better the linear regression fits the data, the closer the value of r

^{2}is to 1. We found that r

^{2}approaches 1 for the value $p$ = 3. However, all the plots presented in this graph, with $p$ ranging from 2 to 5, can be considered to have a linear slope, since all values of r

^{2}are very close to 1. Further, the plots rely on only three points, while more experimental values would have been required to correctly establish the value of $p$. Therefore, no clear conclusion is possible from this approach. In addition, since the density values are not available [28], the linear evolution of the density with the inverse of the annealing time cannot be assessed. However, since the value of r

^{2}is closer to 1 for $p$ = 3, it is considered in the following as a first approximation that the radius evolution scales as ${t}^{1/3}$ as expected by the LSW theory. Thus, Ostwald ripening is supposed to be the coarsening process of the nano-oxides. Figure 9b shows the evolution of the cube radius against time for 1250 °C, 1300 °C and 1400 °C aging temperatures. The linear evolution is also confirmed for coarsening at 1400 °C.

_{2}Ti

_{2}O

_{7}atom arrangement.

_{2}Ti

_{2}O

_{7}lattice structure are certainly at the root of the sluggish coarsening kinetics.

#### 3.4. Evolution of the Nano-Oxide Distribution under Irradiation

#### 3.4.1. Irradiation Response of the Nano-Oxides at Low Temperature

- Radiation-induced dissolution

^{2+}ion irradiation. This irradiation was conducted at room temperature where the ballistic effect could be isolated. After 5.6 h, the irradiation damage reached an average dose of 15 dpa within the first 100 nm, as depicted in Figure 1.

_{6}electron gun [30]. This takes into account the lack in definition of the particle perimeter caused by the imprecise focus setting during irradiation acquisition. The plot shows that the majority of the solute displaced atoms are ejected from the oxide at the beginning of the irradiation, during the first hour. After this, the particle slowly continues to dissolve until it reaches the steady state. However, the behaviour of more than 12 particles with radii ranging from 4 to 40 nm were followed during this in situ irradiation experiment. The results are not presented in this paper, but all the particles presented dissolution. Further, particles with same initial size presented comparable kinetics after 5.6 h of irradiation. Therefore, the oxide behaviour presented in Figure 11 can be considered as reliable, and the initial and final size of the oxide are correctly measured under stabilized conditions; however, the kinetics are imprecise owing to the difficulty to obtain correct conditions for image acquisition during irradiation.

#### 3.4.2. Irradiation Response of the Nano-Oxides at High Temperature

- Radiation-induced inverse Ostwald ripening

^{+}ions; the damage profile is described elsewhere [15]. Figure 12a shows a large oxide, with an initial diameter estimated at 48.5 nm. Figure 12b is the same oxide after irradiation up to 4 dpa, but it has shrunk as its diameter is now estimated at 46.3 nm. To illustrate this change in diameter, the initial diameter of the oxide is reported as a red circle in Figure 12b. As we previously observed, this dissolution is probably accompanied by an increase in solute concentration around the oxide that may diffuse toward surrounding particles and trigger their growth. Two nano-oxides are in the close vicinity of the oxide, as shown in Figure 12a and presented in high magnification in Figure 12c,e. Before irradiation, the characteristic length of the nano-oxide presented in Figure 12c is 2.3 nm, while the characteristic length of the other nano-oxide presented in Figure 12e is 3.75 nm. After irradiation, the TEM images suggest that both of these nano-oxides have grown. Figure 12d shows that the nano-oxide size has evolved from 2.3 nm to 4 nm, while Figure 12f shows that the other nano-oxide has evolved from 3.75 nm to 4.42 nm. Therefore, the shrinking of the large oxide combined with the growth of two neighbouring nano-oxides can be interpreted as an inverse Ostwald ripening, even if there is no clear evidence that the growth of the two neighbouring nano-oxides is due to the condensation of atoms ejected from the large oxides. Further, in Figure 12a, the nano-oxide contrast is poor but appears better in the dark-field contrast of Figure 12b, which limits the correct estimation of the initial size of the nano-oxides.

- 2.
- Radiation-enhanced Ostwald ripening

^{22}m

^{−3}. By comparing the histogram before (Figure 3d) and after irradiation (Figure 3f), it is observed that irradiation induced a shift of the distribution toward the larger diameter accompanied with the disappearing of the smallest nano-oxides; i.e., particle coarsening occurred. In addition, one may notice that the nano-oxide distribution after irradiation at 500 °C (Figure 3f) is similar to the nano-oxide distribution after thermal aging at 1300 °C over 1 h (Figure 3e). Further, the shape of the nano-oxide has also evolved from a sphere to near-cubical shape. Table 6 resumes the results obtained after irradiation conducted on both Fe-14Cr ODS [9] and Fe-18Cr ODS [7] at various damage doses.

^{−1}is close to thermal annealing performed at a temperature ranging between 1250 and 1300 °C. The difference in the coarsening rate kinetics observed between Fe-14Cr ODS and Fe-18Cr ODS remains unexplained; the slight difference in the initial nano-oxide size could possibly explain it because, as discussed below, the nano-oxide interface can remove the defect created by irradiation and decrease the diffusion coefficient. Further, difference in matrix composition can also modify the element diffusivity. One may also consider that the nano-oxides are initially non-stoichiometric compounds [7]; this particularity may affect the growth kinetics under irradiation. However, it has been proven that irradiation tends to make the nano-oxides increasingly stoichiometric since the ratio Y:Ti is close to 1 after 150 dpa at 500 °C [7].

#### 3.4.3. Irradiation Response of the Nano-Oxides at Medium Temperature

- The temperature of apparent stability

^{2+}ion irradiation up to 100 dpa. In the 14YWT ODS steels irradiated up to 100 dpa at 450 °C and 600 °C, the TEM observation performed by Certain et al. [34] revealed a nano-oxide population that was undistinguishable from that of the unirradiated sample.

## 4. Discussion

^{−21}m

^{−1}s

^{−1}molK

^{−1}. Figure 15 is the plot of $\frac{{D}^{th}{C}_{\infty}}{T}$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 $\frac{{D}^{irr}{C}_{\infty}^{irr}}{{T}^{irr}}$, 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 ${C}_{\infty}^{irr}\left({T}^{irr}\right)={C}_{\infty}\left(1270\xb0\mathrm{C}\right)$, we can calculate the diffusion coefficient of the rate-controlling element for this irradiation condition; we found a value of ${D}^{irr}$= 8.5 × 10

^{−14}m

^{2}s

^{−1}.

^{−3}dpa·s

^{−1}[7] and $\tau $ is the time for a vacancy to reach a sink. Therefore, after the substitution of Equation (14) into Equation (13), the time $\tau $ is equal to [7]

^{−6}s. After calculating the vacancy diffusion coefficient ${D}_{v}$ as proposed in [7], the corresponding global sink strength ${k}^{2}$ is found to be equal to 3.8 × 10

^{16}m

^{−2}.

^{14}m

^{−2}in similar ferritic ODS steels [28]. The sink strength of the free surfaces in thin foil can be calculated as [43] ${k}_{s}^{2}=3/{l}^{2}$ by considering that $\sum}_{i}{k}_{i}l\to 0$, where $\sum}_{i}{k}_{i$ 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 ${k}_{gb}^{2}=60/{d}^{2}$ by considering that $\sum}_{i}{k}_{i}d\to 0$ [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.

^{15}m

^{−2}when taking into account ${k}_{NO}^{2}$ (TEM) and is equal to 1.8 × 10

^{16}m

^{−2}when taking into account ${k}_{NO}^{2}$ (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 ${k}_{NO}^{2}>{k}_{s}^{2}>{k}_{disl}^{2}>{k}_{gb}^{2}$, with ${k}_{NO}^{2}$ 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.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Depth profile of irradiation damages (displacement per atom) in Fe calculated by Iradina [14] using 4000 keV-Au

^{2+}ions with a fluence of 4.0 × 10

^{15}ions·cm

^{−2}.

**Figure 2.**Dependence on the irradiation temperature irradiation of the yttrium solute concentration produced by recoil resolution and by thermal solubility for pyrochlore-type precipitate.

**Figure 3.**Bright field TEM image with its corresponding histogram: (

**a**,

**d**) as-received material, (

**b**,

**e**) after thermal annealing (1300 °C, 1 h), (

**c**,

**f**) after irradiation up to 150 dpa at 500 °C.

**Figure 4.**Chemical map of the nano-oxides from EDS acquisition: (

**a**) ADF STEM image, (

**b**) Y L ac-quisition, (

**c**) Ti K acquisition, and (

**d**) O K acquisition.

**Figure 5.**Three-dimensional APT reconstruction of as-received Fe-14Cr ODS: (

**a**) an iso-composition surface >5 at.% of O+Y+Ti in blue was used to highlight nano-oxides, (

**b**–

**e**) zoomed in insert of region of interest showing map of Fe, O, Y and Ti atoms in as-received Fe-14Cr ODS steel.

**Figure 6.**HRTEM images of both nano-cluster (<1.5 nm) and nano-oxide embedded within the ferritic matrix: (

**a**) HRTEM image of a nano-cluster, (

**b**) corresponding FFT, (

**c**) HRTEM image of a nano-oxide, (

**d**) corresponding FFT.

**Figure 7.**Pyrochlore-type lattice structure: (

**a**) general view, (

**b**) observed along the $\mathrm{(001)}$ direction, (

**c**) observed along the $\mathrm{(111)}$ direction, (

**d**) observed along the $\mathrm{(011)}$ direction.

**Figure 9.**Ostwald ripening of the nano-oxides: (

**a**) evolution of the radius elevated at the power p (p = 2, 3, 4, 5) against time for a thermal annealing at 1300 °C; (

**b**) evolution of the cube radius against time for thermal annealing at 1250 °C, 1300 °C and 1400 °C; (

**c**) plot of the calculated and experimental radii against temperature for various annealing durations.

**Figure 10.**In situ observation of the evolution of a nano-oxide during 4 MeV Au

^{2+}irradiation: (

**a**) before irradiation, (

**b**) after 0.5 h (1.3 dpa), (

**c**) after 1.1 h (3 dpa), (

**d**) after 2 h (5 dpa), (

**e**) after 2.9 h (8 dpa), (

**f**) after 3.8 h (10 dpa), (

**g**) after 4.3 h (12 dpa), and (

**h**) after 5.6 h (15 dpa).

**Figure 11.**Experimental and theoretical dissolution rate of the nano-oxide presented in Figure 9 during in situ 4 MeV Au

^{2+}ion irradiation.

**Figure 12.**Radiation-induced inverse Ostwald ripening after 150 keV Fe

^{+}ion irradiation: (

**a**) bright-field image of a large oxide surrounded by nano-oxides before irradiation, (

**b**) dark-field image of the same particles after irradiation (4 dpa), (

**c**) a neighbouring nano-oxide before irradiation, (

**d**) the same neighbouring nano-oxide after irradiation (4 dpa), which appears larger, (

**e**) another neighbouring nano-oxide before irradiation, (

**f**) the same nano-oxide after irradiation (4 dpa), which appears larger.

**Figure 13.**Radius and density evolution after 0, 75 and 150 dpa in both Fe-14Cr ODS and Fe-18Cr ODS: (

**a**) evolution of the cube diameter against irradiation damage, (

**b**) evolution of the inverse of the density against irradiation damage.

**Figure 14.**Evolution of the nano-oxides’ normalized radii after irradiation at RT, 300 °C, 400 °C and 500 °C.

**Figure 15.**Evolution of $\frac{{D}^{th}{C}_{\infty}}{T}$ against temperature, used in order to determine the equivalent temperature.

Cr | W | Ti | Mn | Si | Ni | C | Y_{2}O_{3} | Fe |
---|---|---|---|---|---|---|---|---|

14 | 1 | 0.3 | 0.3 | 0.3 | 0.15 | 0.05 | 0.3 | Bal. |

18.05 | 0.95 | 0.26 | 0.3 | 0.3 | 0.19 | 0.03 | 0.56 | Bal. |

**Table 2.**Values used to calculate the solute concentration according to Equation (4). ${D}_{0}$ is the Y diffusion pre-exponential factor, ${E}_{m}$ is the diffusion activation energy of Y, ${C}_{\infty}$ is the equilibrium solubility of Y in the α-Fe matrix, ${E}_{s}$ is the equilibrium solubility activation energy of Y, $q\varphi $ is the irradiation damage rate, $\lambda $ is the mean displacement of Y ejected atoms, $\gamma $ is the interface energy of Y

_{2}Ti

_{2}O

_{7}nano-oxide and ${V}_{m}$ is the Y

_{2}Ti

_{2}O

_{7}molar volume.

${\mathit{D}}_{0}\text{}({\mathbf{m}}^{2}\xb7{\mathbf{s}}^{-1})$ | ${\mathit{E}}_{\mathit{m}}\text{}\left(\mathbf{eV}\right)$ | ${\mathit{C}}_{\mathit{\infty}}\text{}(\mathbf{mol}\xb7{\mathbf{m}}^{-3})$ | ${\mathit{E}}_{\mathit{s}}\text{}\left(\mathbf{eV}\right)$ | $\mathit{q}\mathit{\varphi}\text{}(\mathbf{dpa}\xb7{\mathbf{s}}^{-1})$ | $\mathit{\lambda}\left(\mathbf{nm}\right)$ | $\mathit{\gamma}$ | ${\mathit{V}}_{\mathit{m}}\text{}({\mathbf{m}}^{3}\xb7{\mathbf{mol}}^{-1})$ |
---|---|---|---|---|---|---|---|

5.7 × 10^{−7} [23] | 2 [23] | 5.4 [24] | 1.5 [24] | 6.5 × 10^{−3} [7] | 0.35 [7] | 0.26 [25] | 7.71 × 10^{−5} [24] |

T (°C) | t (h) | R (nm) | s | R (nm) TEM |
---|---|---|---|---|

1250 | 0 | 1.4 [28] | 0.5 [28] | 1.3 [28] |

1 | 1.6 [28] | 0.5 [28] | ||

1300 | 0 | 1.4 [28] | 0.5 [28] | 1.3 [28] |

1 | 2.0 [28] | 0.7 [28] | ||

3 | 2.6 [28] | 0.9 [28] | ||

1400 | 0 | 1.4 [28] | 0.5 [28] | 1.3 [28] |

1 | 3.0 [28] | 0.9 [28] | 2.4 [28] | |

3 | 4.4 [29] | 0.03 [29] |

T (°C) | ${\mathit{K}}_{\mathit{t}\mathit{h}}\left(\mathit{T}\right)\text{}\times \text{}{10}^{-3}\text{}({\mathbf{nm}}^{3}\xb7{\mathbf{s}}^{-1})$ |
---|---|

1250 | 0.7 |

1300 | 1.6 |

1400 | 7.5 |

$2{\mathit{R}}_{0}\left(\mathbf{nm}\right)$ | $\mathit{L}$ | ${\mathit{S}}_{0}(\mathbf{dpa}\xb7{\mathbf{s}}^{-1})$ | ${\mathit{\lambda}}_{\mathit{m}}\left(\mathbf{nm}\right)$ | ${\mathit{R}}_{\mathit{m}}\left(\mathbf{nm}\right)$ | $\mathit{B}$ |
---|---|---|---|---|---|

14.4 | 50 | 9.9 × 10^{−4} | 7 | 5.7 | 0.2 |

Damage Dose (dpa) | Mean Diameter (nm) | Density (m^{−3}) | |
---|---|---|---|

Fe-14Cr ODS [9] | 0 | 2.2 (±0.5) | 2.9 ± 0.5 × 10^{23} |

75 | 4.5 (±0.2) | 1 ± 0.3 × 10^{23} | |

150 | 5.6 (±0.2) | 1.2 ± 0.4 × 10^{22} | |

Fe-18Cr ODS [7] | 0 | 3.0 (±0.5) | 2.3 ± 0.7 × 10^{23} |

75 | 3.5 (±0.5) | 1.1 ± 0.3 × 10^{23} | |

150 | 4.1 (±0.5) | 0.9 ± 0.3 × 10^{23} |

**Table 7.**Comparison between experimental and calculated nano-oxide diameter after radiation-enhanced Ostwald ripening in (a) Fe-14Cr ODS steel and (b) Fe-18Cr ODS steel.

(a) | |||

K_{irr}(T) × 10^{−3} (nm^{3}.s^{−1}) | Damage dose (dpa) | $\mathrm{Experimental}\text{}\mathrm{diameter}\text{}2R$ (nm) | $\mathrm{Calculated}\text{}\mathrm{diameter}\text{}2R$ (nm) |

0.87 | 0 | 2.2 (±0.5) | - |

75 | 4.50 (±0.2) | 4.52 | |

150 | 5.60 (±0.2) | 5.58 | |

(b) | |||

K_{irr}(T) × 10^{−3} (nm^{3}.s^{−1}) | Damage dose (dpa) | $\mathrm{Experimental}\text{}\mathrm{diameter}\text{}2R$ (nm) | Calculated diameter $2R$ (nm) |

0.17 | 0 | 3.0 (±0.5) | - |

75 | 3.5 (±0.5) | 3.51 | |

150 | 4.1 (±0.5) | 3.90 |

${\mathit{k}}_{\mathit{N}\mathit{O}}^{2}\text{}\left(\mathbf{TEM}\right)\text{}\left({\mathbf{m}}^{-2}\right)$ | ${\mathit{k}}_{\mathit{N}\mathit{O}}^{2}\text{}\left(\mathbf{APT}\right)\text{}\left(\mathbf{m}{\mathbf{m}}^{-2}\right)$ | ${\mathit{k}}_{\mathit{d}\mathit{i}\mathit{s}\mathit{l}}^{2}\text{}\left({\mathbf{m}}^{-2}\right)$ | ${\mathit{k}}_{\mathit{s}}^{2}\text{}\left({\mathbf{m}}^{-2}\right)$ | ${\mathit{k}}_{\mathit{g}\mathit{b}}^{2}\text{}\left({\mathbf{m}}^{-2}\right)$ |
---|---|---|---|---|

4.0 × 10^{15} | 1.6 × 10^{16} | 5.0 × 10^{14} | 1.2 × 10^{15} | 2.4 × 10^{14} |

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**MDPI and ACS Style**

Ribis, J.; Mouton, I.; Baumier, C.; Gentils, A.; Loyer-Prost, M.; Lunéville, L.; Siméone, D.
Nano-Structured Materials under Irradiation: Oxide Dispersion-Strengthened Steels. *Nanomaterials* **2021**, *11*, 2590.
https://doi.org/10.3390/nano11102590

**AMA Style**

Ribis J, Mouton I, Baumier C, Gentils A, Loyer-Prost M, Lunéville L, Siméone D.
Nano-Structured Materials under Irradiation: Oxide Dispersion-Strengthened Steels. *Nanomaterials*. 2021; 11(10):2590.
https://doi.org/10.3390/nano11102590

**Chicago/Turabian Style**

Ribis, Joël, Isabelle Mouton, Cédric Baumier, Aurélie Gentils, Marie Loyer-Prost, Laurence Lunéville, and David Siméone.
2021. "Nano-Structured Materials under Irradiation: Oxide Dispersion-Strengthened Steels" *Nanomaterials* 11, no. 10: 2590.
https://doi.org/10.3390/nano11102590