2019 Volume 60 Issue 5 Pages 678-687
The quantitative evaluation of vacancy mobility was conducted by analyzing the void denuded zone (VDZ) width formed near grain boundaries under neutron and electron irradiation. The microstructures of Fe–15Cr–xNi (x = 15, 20, 25, 30 mass%) alloys that were neutron irradiated at 749 K were examined, and the differences in the vacancy mobility among the four alloys were qualitatively investigated. We also investigated the VDZ widths formed under electron irradiation at various irradiation temperatures (576 K–824 K) in these alloys. The VDZ widths increased with increasing Ni content in both the neutron and electron irradiation experiments, which implies an increase of the vacancy mobility. The vacancy migration energies were estimated from the temperature dependence of the VDZ widths, and the estimated energies were 1.09, 0.97, 0.90, and 0.77 eV for the alloys containing 15, 20, 25, and 30 mass% Ni, respectively. It was confirmed that these estimated energies were approximately consistent with the ones estimated by well-known dislocation loop growth rate analysis through electron irradiation experiments. From the obtained vacancy migration energies by the VDZ analysis, the effective vacancy diffusivity and excess vacancy concentration were estimated using the analytical equation of the VDZ width, which quantitatively confirmed the increase of the vacancy mobility with increasing Ni content.
Fig. 8 Arrhenius plots of VDZ widths formed in electron-irradiated Fe–15Cr–xNi (x = 15–30 mass%) model alloys: experimental results (four symbols) and theoretical predictions (solid lines).
The nuclear core material in sodium-cooling-type fast breeder reactors, especially the fuel cladding tube, is required to suppress irradiation-induced void swelling. Effective approaches for void swelling suppression include the addition of alloying elements and the introduction of cold working to the alloys. In particular, in the development of austenitic stainless steels, high initial Ni contents in the matrix of Fe–Cr–Ni alloys has been shown to be effective for suppressing void swelling. Void swelling in Fe–Cr–Ni alloys containing approximately 45 mass% Ni content has been shown to be the smallest under high-energy particle irradiation.1,2) The nickel-dependent mechanism for suppressing void swelling (retarding the onset of steady-state swelling) was proposed by many researchers.2–8) The proposed mechanism is summarized below.
This mechanism has been widely accepted. However, a qualitative understandings, especially concerning the diffusion behavior of point defects, have been mostly covered using theoretical approaches, and systematic and experimental quantitative analysis of the diffusion behavior has seldom been performed.
In this study, an analysis method focused on the void denuded zone (VDZ) width was used to estimate the vacancy diffusion behavior in Fe–Cr–Ni alloys during irradiation and to clarify its nickel concentration dependence. The VDZ is known to form near grain boundaries under irradiation and depends on the vacancy diffusivity (Dv), recombination rate (μR), and displacement damage rate (Gdpa) under irradiation.9–13) First, microstructural observations of Fe–15Cr–xNi (x = 15, 20, 25, 30 mass%) model alloys that were neutron-irradiated in JOYO were performed using transmission electron microscopy (TEM). The microstructures of the voids and dislocations in the matrix as well as the VDZ widths and RIS near random grain boundaries (GBs) were investigated. Subsequently, electron irradiation experiments were performed using high-voltage electron microscopy (HVEM) to understand the fundamental behavior of the VDZ formation. After the VDZ width measurements, the vacancy migration energy (Ev) was estimated. We also estimated the vacancy migration energy using dislocation loop growth rate analysis and compared the results with those estimated using the VDZ width analysis. Through these analyses, the effect of the initial nickel content on the VDZ width and vacancy diffusion was quantitatively evaluated.
Fe–15Cr–xNi austenitic model alloys were used in this study. The chemical compositions of the alloys are listed in Table 1. Initial nickel contents of 15, 20, 25, and 30 mass% were selected. Before the irradiation, all the samples were solution annealed in a furnace.
The Fe–15Cr–xNi model alloys were irradiated up to the “steady-state” conditions such that the microstructures were expected to be under steady-state swelling. Thin disk specimens of 3-mm diameter were prepared before the neutron irradiation. The neutron irradiation was performed in the experimental fast reactor JOYO using the Core Material Irradiation Rig (CMIR). The irradiation temperature and fast neutron irradiation dose conditions are summarized in Table 2.
After neutron irradiation, the specimens were electropolished and analyzed using TEM and energy-dispersive X-ray spectrometry (EDS) using a JEOL JEM-2010F (200-kV). For the TEM observations, the void distribution near the random GBs was investigated, and the widths of the VDZ were evaluated as the average distance between the GB and voids closest to the GB. Subsequently, the RIS of the solute atoms near the GBs was investigated using EDS to clarify the relationship between the VDZ and RIS widths.
2.3 Electron irradiation and post-irradiation experiment for VDZ width analysisThin foil specimens of the Fe–15Cr–xNi model alloys were prepared using electropolishing and then electron-irradiated with 1-MeV electrons using a Hitachi H-1300 high-voltage electron microscope (HVEM). Electron irradiation was performed at various temperatures to evaluate the vacancy migration energy from the relationship between the VDZ width and irradiation temperature. The displacement rate was approximately 2.0 × 10−3 dpa/s, and the irradiation dose was up to 7.2 dpa. The irradiation conditions are summarized in Table 3. It has been previously reported that the irradiation dose does not affect the VDZ width;9,10) therefore, the relatively low irradiation doses that enabled steady-state conditions to be reached were selected in the present experiments.
Electron irradiation areas including random GBs were selected. All the irradiated areas had a sufficiently thick foil thickness (approximately 400 nm) to minimize the effect of the surface sink. The vacancy migration energies in each alloy were estimated from the analysis of the temperature dependence of the VDZ width, as described in Ref. 10–13.
2.4 Dislocation loop growth rate analysis under electron irradiationTo confirm the validity of the vacancy migration energies estimated from the VDZ width analysis, the vacancy migration energies were also estimated using the dislocation loop growth rate analysis method proposed by Kiritani et al.14,15) The dislocation loop growth for the Fe–15Cr–xNi model alloys was performed using 1.25-MeV electrons using a JEOL ARM-1300HVEM. The displacement rate was approximately 1.0 × 10−3 dpa/s, and the temperature range and irradiation dose were 591–835 K and up to 0.56 dpa, respectively (see Table 4). The diameters of observed dislocation loops were measured from a time series of TEM images, and the average growth rates of the dislocation loops were estimated at each temperature.
Typical TEM images of the microstructures of the neutron-irradiated Fe–15Cr–xNi alloys at 749 K up to 18.0 dpa are presented in Fig. 1. In all the alloys, many voids and dislocations are homogeneously distributed in the matrix. The dislocation density, void diameter, void number density, and void swelling of the alloys are summarized in Fig. 2. The void number density, dislocation density, and magnitude of the void swelling decreased with increasing initial nickel content of the alloys. However, the void size was independent of the initial nickel content. These results are consistent with previous research findings,2,5–7) and it was confirmed that the point defect behavior would be correlated to the initial nickel content.
Typical TEM images of the microstructures of Fe–15Cr–xNi (x = 15–30 mass%) model alloys that were neutron irradiated at 749 K to 18.0 dpa. The top images show the void distributions, and the bottom images show the dislocation distributions.
Average dislocation density, void diameter, void number density, and void swelling of Fe–15Cr–xNi (x = 15–30 mass%) model alloys neutron irradiated at 749 K to 18.0 dpa evaluated for three area microstructures (TEM images) in each alloy.
Next, we examined three areas (VDZ1, VDZ2, and VDZ3 in Fig. 3) near random GBs in the neutron-irradiated Fe–15Cr–15Ni model alloys. The formation of the VDZ was apparent near every GB. The widths of the VDZs formed in these areas were measured: half the distance between the centers of the voids closest to the GB in both grains was defined as the VDZ width. In Fig. 3, the measured VDZ widths in the three areas were almost the same (∼160 nm), which indicates that the VDZ width would be not strongly affected by the GB nature and that the widths of VDZs formed near random GBs should be regarded as constant.16)
Three TEM images (VDZ 1, VDZ 2, and VDZ 3 images) of microstructures in Fe–15Cr–15Ni model alloy neutron irradiated at 749 K to 18.0 dpa. The random GB is indicated by a solid white line, and the boundaries of the formed VDZ are indicated by white dotted lines.
Figure 4 shows the VDZ formations near random GBs in the Fe–15Cr–xNi model alloys. In the Fe–15Cr–20Ni, Fe–15Cr–25Ni, and Fe–15Cr–30Ni alloys, the VDZ widths in both grains differed and were asymmetric with respect to the GB, which would be caused by grain boundary migration (GBM) during neutron irradiation. Evidentially, for the Fe–15Cr–25Ni and Fe–15Cr–30Ni alloys, some small voids were nucleated at the inner side of the VDZ in which large voids exist. The VDZ widths were evaluated with the exception of small voids. The VDZ widths clearly increased with increasing initial nickel content. It has been reported that VDZ widths are proportional to the 1/4 power of the vacancy diffusivity for the recombination dominant case.10) Thus, wider VDZ widths would lead to faster vacancy diffusion in the matrix in high-nickel-content alloys. These results are also supported by the RIS behavior near the present GBs (see Fig. 5). In every GB, the amounts of the major elements such as iron, nickel, and chromium in the VDZ regions fluctuated; in particular, nickel segregation and chromium depletion occurred at the GBs. Such areas of fluctuation were enlarged with increasing initial nickel content, which suggests that the diffusion of point defects (vacancies as well as interstitials) would be enhanced with increasing initial nickel content.
Typical TEM images of microstructures of Fe–15Cr–xNi (x = 15–30 mass%) model alloys neutron irradiated at 749 K to 18.0 dpa. The red line indicates the direction of the EDS line analysis. The distance from the grain boundary was ∼450 to ∼700 nm.
Main element profiles near GBs obtained from EDS line analyses of the microstructures of the Fe–15Cr–xNi (x = 15–30 mass%) model alloys shown in Fig. 4. The blue circle represents Ni, the red square represents Fe, and the black diamond represents Cr. The yellow hatching indicates the areas where VDZ formation was observed.
The neutron irradiation experiments described in Section 3.1 qualitatively indicated that the vacancy diffusivities changed with the initial nickel content of the alloys. However, it must be evaluated whether wider VDZ widths with increasing initial nickel content were the essential phenomena; therefore, in situ observation of VDZ formation under electron irradiation was performed. Figure 6 presents TEM images near random GBs in the Fe–15Cr–xNi model alloys that were electron irradiated at approximately 723 K. Despite the differences in the degree of irradiation damage such as the irradiation dose rate and knock-on procedure (Frenkel defects or cascade damage) between electron and neutron irradiation, VDZ formations were also observed under electron irradiation. This finding clearly indicates that the VDZ widths increased with increasing initial nickel content similar to in the neutron irradiation case. It was also confirmed that the void number density tended to decrease with increasing initial nickel content. This tendency corresponded to that observed for neutron irradiation, and the diffusivity of the point defects would be also enhanced with increasing initial nickel content during electron irradiation.
TEM images of microstructures of Fe–15Cr–xNi (x = 15–30 mass%) model alloys electron irradiated at approximately 723 K.
We then attempted to estimate the vacancy migration energy under electron irradiation based on the temperature dependences of the VDZ width. Figure 7 presents TEM images near an identical random GB in the electron-irradiated Fe–15Cr–15Ni model alloy at 625 K to 824 K. It was clarified that the VDZ widths increased with increasing irradiation temperature. The same tendency was confirmed in every model alloy used in the present study. Using analytical equation (1) for the relationship between the VDZ width and vacancy diffusivity,10) Arrhenius plots of the obtained VDZ widths were generated, as shown in Fig. 8.
| \begin{equation} w (r_{\text{gb}}) = (D_{\text{v}}/4G_{\text{dpa}}\mu_{\text{R}})^{1/4}\propto (D_{\text{v}})^{1/4} \end{equation} | (1) |
| \begin{equation} D_{\text{v}} = D_{0}\exp (-E_{\text{v}}/k_{\text{B}}T), \end{equation} | (2) |
TEM images of microstructures of Fe–15Cr–15Ni model alloy electron irradiated at approximately 625–824 K.
Arrhenius plots of VDZ widths formed in electron-irradiated Fe–15Cr–xNi (x = 15–30 mass%) model alloys: experimental results (four symbols) and theoretical predictions (solid lines).
As observed in Fig. 8, a linear relationship between the logarithmic VDZ widths (w) and the reciprocal temperature (1/T) was obtained for all the alloys except Fe–15Cr–30Ni. The VDZ widths of the Fe–15Cr–20Ni model alloy were narrower than those of the Fe–15Cr–15Ni model alloy, which is inconsistent with the results shown in Fig. 6. This error occurred because the irradiated GB was inclined in the Fe–15Cr–20Ni alloy; however, it does not affect the analysis of the temperature dependence of the VDZ width. Then, the activation energy (Q) of VDZ width was evaluated from the fitted curves, as shown in Fig. 8. Here, the VDZ width of the Fe–15Cr–30Ni model alloy at high temperature (775 K) was excluded from the fitted curve of the VDZ width. As will be described later, the vacancy mobility in this alloy becomes very large, such that it was predicted that disappearance to the surface sink will predominate, especially at higher temperature. Therefore, the VDZ width at 775 K was eliminated from the activation energy estimation in the Fe–15Cr–30Ni model alloy. The estimated vacancy migration energies are summarized in Table 5. For the Fe–15Cr–15Ni model alloy, the estimated vacancy migration energy of 1.09 ± 0.14 eV was almost the same as the previously reported value of approximately 1.05 eV.11–13) This similarity indicates that the analysis of the VDZ width gives the correct vacancy migration energy. In addition, it was clarified that the vacancy migration energy was decreased (the vacancy mobility was enhanced) with increasing initial nickel content up to 30 mass% nickel.
In section 3.2, we estimated the vacancy migration energy by analyzing the changes in the VDZ width under electron irradiation. To evaluate the validity of the vacancy migration energy estimated using this method, the vacancy migration energy was also estimated using the well-known Kiritani’s method, which is based on a relationship between the dislocation loop growth rate and irradiation temperature14,15) during in situ electron irradiation.
Figure 9 presents Arrhenius plots of the measured dislocation loop growth rates and the reciprocal temperature in the Fe–15Cr–xNi model alloys. The vacancy migration energies (Ev) estimated using the dislocation loop growth rate, which is proportional to Dv1/2, also decreased with increasing initial nickel content of the alloys similar to those in the VDZ width analysis. The migration energy obtained using each method fell within the range of the statistical error. That is, the high accuracy of the estimation of the vacancy migration energy from the VDZ width was confirmed (see Fig. 10).
Arrhenius plots of dislocation loop growth rates obtained from electron in situ observation for Fe–15Cr–xNi (x = 15–30 mass%) model alloys: experimental results (four symbols) and theoretical predictions (solid lines).
Relationship between estimated vacancy migration energies determined using VDZ width analysis (white circle symbols) and dislocation loop growth rate analysis (black square symbols) for electron irradiated Fe–15Cr–xNi (x = 15–30 mass%) model alloys.
As mentioned in the introduction, it has generally been suggested that increasing Ni content in Fe–Cr–Ni alloys would induce the enhancement of vacancy diffusion, thereby affecting void swelling. In the present study, microstructural changes focusing on voids, dislocations, VDZ, and RIS after neutron irradiation at 749 K up to 18 dpa were investigated in Fe–15Cr–xNi (x = 15, 20, 25, 30 mass%) alloys. The void number density and swelling were confirmed to decrease with increasing Ni content, which agrees well with the findings of previous reports.2,5–7) Therefore, it is suggested that the vacancy diffusivity would be increased. However, the VDZ widths and RIS regions near the GBs increased with increasing nickel content. The RIS width depends on the square root of the product of the vacancy diffusivity (Dv) and concentration (Cv) in the matrix,11) and vacancy flow toward the GBs would be high in high-nickel alloys. Such increases of the vacancy flow would enhance not only the recombination of vacancies and interstitials but also the annihilation of the vacancies into internals sinks, resulting in a decrease of the excess vacancy concentration such that void swelling would be suppressed.
4.2 Change of vacancy mobility in high-Ni alloyIn this study, the vacancy migration energies were examined using electron irradiation experiments and both VDZ width and dislocation loop growth rate measurements. Both approaches confirmed that the estimated values in all the model alloys were almost the same and that the vacancy migration energy decreased with increasing Ni content up to 30 mass% (see Fig. 10). Chakraborty et al. reported that the vacancy migration barrier in fcc Ni–Fe–Cr alloy was reduced to 0.44 eV under the condition which vacancy–vacancy pairs (di-vacancies) exist;17) such a situation can easily occur in irradiated materials. Thus, the fact that the vacancy migration energy of approximately 1.09 eV in 15 mass% Ni decreased to 0.77 eV in the 30 mass% Ni alloy according to the present VDZ width analysis is acceptable. The reason why the vacancy migration energy decreases with increasing Ni content can be attributed to the effect of the increased Ni atom content, which reduced the migration barrier needed for a site exchange between vacancies and solute atoms under the irradiation.
Additionally, using the vacancy migration energy obtained from the VDZ width analysis, the vacancy diffusivity (Dv), excess vacancy concentration (Cv), and their product (DvCv) under neutron irradiation were estimated using analytical equations and the physical parameter data set in Ref. 11. In this estimation, the irradiation temperature was 749 K, the displacement rate was 8.3 × 10−7 dpa/s, and the experimentally obtained dislocation sink densities in Fig. 2 were used. The other constants such as the lattice constant and vacancy jump frequency via solute atoms were obtained from previous research.11) The results are presented in Table 6. It was quantitatively confirmed that the vacancy diffusivity and vacancy mobility increased with increasing Ni content but that the excess vacancy concentration would decrease.
It was revealed that the VDZ width analysis can be used to evaluate the vacancy diffusion behavior from TEM microstructures after irradiation experiments. However, the temperature dependence of the VDZ widths under neutron irradiation were not investigated in the present study because of the absence of samples irradiated over wide temperature ranges and approaching steady-state doses. Therefore, the evaluation of the vacancy migration energy under neutron irradiation should be performed as future work to account for not only the difference between charged particles (electrons) and uncharged particles (neutrons) but also the change in the di-vacancy concentration, as di-vacancies are expected to be formed under neutron irradiation.
4.3 Difference in VDZ widths between neutron and electron irradiationComparing the VDZ widths formed under neutron irradiation (see Fig. 4) and electron irradiation (see Fig. 6), it is apparent that the VDZ widths formed under neutron irradiation were wider despite the almost same irradiation temperature range (723 K to 749 K). The differences are shown in Fig. 11. To clarify the origin of this difference, the theoretical VDZ widths were calculated using the analytical equation of the defect free zone (DFZ) width (eq. (3)).11)
| \begin{equation} w (r_{\text{gb}}) = (D_{\text{v}}C_{\text{v}}/2G_{\text{dpa}})^{1/2} \end{equation} | (3) |
VDZ widths for neutron (black square symbol) and electron (white circle symbol) irradiation of Fe–15Cr–xNi (x = 15–30 mass%) model alloys. The straight line indicates the theoretical VDZ width, which is expected to be formed in the neutron irradiation case and was calculated using the rate theory equation using the vacancy migration energies obtained in the present study. The dotted line indicates the theoretical VDZ width for electron irradiation.
The theoretical VDZ widths were almost the same as the experimentally obtained widths for neutron irradiation. A slight overestimation of the experimental width in the Fe–15Cr–15Ni alloy was confirmed. This suggests that the used value of vacancy migration energy, which was 1.09 eV and has relatively large error ranges, might being overestimated. When the value is set as 1.05 eV in the calculation, the theoretical width can correspond to the experimental one. Furthermore, a slight underestimation of the experimental width in the Fe–15Cr–30Ni alloy was indicated and would be also due to the slight difference of the used vacancy migration value in the calculation. In addition, this finding may imply that a saturated vacancy concentration would be affected by other internal sinks such as voids and decreased because of the annihilation there.
For electron irradiation, the theoretical VDZ widths reproduced the trend of the experimentally determined Ni content dependence, although the VDZ widths were narrower than the experimentally obtained widths. The underestimation of the experimental widths suggests a flow of excessive vacancies toward the GB. Nevertheless, the experimental widths showed a reliable temperature dependence and Ni content dependence. Thus, the additional vacancy flow would be independent of temperature and Ni content. A vacancy concentration gradient may induce the additional vacancy flow. Because an electron beam has a broadening Gaussian intensity profile, and the intensity of the beam central position is relatively higher than that of the outer position, it is suggested that the displacement rate (dpa/s) in the central parts irradiated by the electron beam should be always higher than that in the outer parts. Therefore, the excess vacancy concentration in the central parts would be increased compared with that in the outer parts, such that a vacancy concentration gradient would be present. For more precise estimation of the theoretical VDZ width, an improvement of the rate theory equations to account for the existence of this vacancy concentration gradient would be required.
Consequently, it is found that evaluation of the vacancy diffusion behavior from VDZ width analysis could be possible not only in Fe–15Cr–xNi (x = 15, 20, 25, 30 mass%) alloys but also in other fcc metals and alloys. However, it is necessary to consider the contribution of the annihilation of point defects to internal sinks under neutron irradiation, the validity of the experimentally obtained values such as the sink density and VDZ width, and the characteristics of the irradiation conditions in both neutron and electron irradiation.
To quantitatively estimate the vacancy diffusion behavior in high-nickel Fe–Cr–Ni alloys during irradiation, we investigated the VDZ formation in neutron and electron irradiation experiments for Fe–15Cr–xNi (x = 15, 20, 25, 30 mass%) alloys. We also estimated the vacancy migration energies by analysis of the VDZ width changes under electron irradiation. Using the estimated vacancy migration energies, the effective vacancy diffusivity, excess vacancy concentration, and vacancy mobility were evaluated. The results are summarized below.
