The nominal composition of the Ni-Cr-Mo alloy obtained by chemical analysis is given in Table 1. A widely known Monte-Carlo simulation-based software SRIM [23] has been used to estimate the depth profile of the distribution of implanted He ions and vacancies formed during irradiation and the same is shown in Fig. 1. The irradiation damage has been evaluated in terms of dpa (displacements per atom) using the following formula:
$$\:dpa=\left({{\nu\:}}_{\text{N}\text{R}\text{T}}\:\times\:{10}^{8}\times\:D\right)/{N}_{o}$$
1
where D signifies the irradiation fluence (ions/cm2), No denotes the atom density of the target material in atoms/cm³, and νNRT stands for the number of displaced atoms per Å per ion determined by the method outlined by Stoller et al. using Eq. 2 [24].
$$\:{{\nu\:}}_{\text{N}\text{R}\text{T}}=(0.8\times\:{T}_{dam})/(2\times\:{E}_{d})$$
2
where \(\:{T}_{dam}\) represents the total damage energy calculated from the phonon contribution to the ions and recoils. The estimated peak damage for the samples irradiated with fluences 3×1016, 2×1017, and 7×1017 ions/cm2 is 1.5, 9.6, and 33.9 dpa, respectively. The number density of He atoms implanted during the irradiation experiments for a fluence equivalent to a dose of 7×1017 ions/cm2 is 2x1022 ions/cm3. Figure 1 shows that irradiation damage is extended up to a depth of ~ 350 nm with a peak at around 200 nm. The peak becomes more pronounced with an increase in irradiation dose.
In order to probe the damage region which is confined up to a depth of 350 nm from the surface using GIXRD, the effective penetration depth (\(\:{x}_{\alpha\:}\)) of an X-ray beam was calculated using Eq. (3).
$$\:{x}_{\alpha\:}=\frac{-\text{l}\text{n}(1-G)}{\mu\:(\frac{1}{Sin\alpha\:}+\frac{1}{Sin(2\theta\:-\alpha\:)})}$$
3
where G is the fraction of the incident beam that is absorbed up to a depth of \(\:{x}_{\alpha\:}\), µ is the linear attenuation coefficient of the material,\(\:\:\alpha\:\) is the grazing angle, and 2\(\:\theta\:\) is the diffraction angle. In this study, the fraction of unabsorbed X-rays is taken as 1/e and the diffraction angle of the most intense peak corresponding to the (111) plane is taken as 2\(\:\theta\:\). The mass attenuation coefficient of Ni-45Cr-1.4Mo (wt.%) alloy is 110 cm2/g for CuKα X-rays. Based on Eq. 3, the grazing angle of 1.5º was found to be most appropriate to investigate the irradiation-induced microstructural changes up to a depth of 350 nm and therefore GIXRD experiments were carried out at 1.5º angle of incidence.
3.1. Microstructure prior to irradiation
The microstructure of the pristine alloy is presented in Fig. 2. An overview of the gross microstructural features of the alloy can be obtained from Fig. 2a. The irregularly shaped precipitates seen in Fig. 2a correspond to alpha-Cr. A non-uniform distribution of such precipitates was noticed within the matrix phase with grain boundaries acting as the preferred site for nucleation. The volume fraction of the precipitates was found to be small with their sizes varying between 100–300 nm. The average composition of the precipitates was estimated to be Cr-10.3Ni-3.5Mo (wt.%) through EDS analysis. The matrix phase showed an average composition of Ni-43.4Cr-1.1 Mo (wt.%). The micrograph shown in Fig. 2b was obtained under two-beam diffracting condition. It depicts the planar arrangement of dislocations within the matrix phase without any sort of dislocation interaction or entanglement.
3.2. X-Ray Diffraction Line Profile analysis
Figure 3 shows a typical GIXRD profile for the un-irradiated and irradiated NiCrMo alloy samples. The peaks observed in the diffractogram before and after irradiation are indexed to the fcc γ-Ni phase. It can be concluded from these diffractograms that no new phases have formed after irradiation. Figure 4 shows the enlarged view of the strongest intensity (111) peak before and after irradiation. This figure suggests that this peak shifts gradually to a lower 2θ value with an increase of irradiation dose, indicating an increase in the lattice spacing with the increase in the irradiation dose. Indeed, other peaks were also observed to shift to lower diffraction angle with an increase in irradiation dose. Therefore, it could be inferred that the He ion irradiation caused lattice expansion in the irradiated samples.
In addition to the shift in Bragg’s peak, width of the peak also changes with irradiation. The broadening of Bragg peaks is mainly due to a change in domain size and microstrain after accounting for the broadening due to instrumental parameters. Line profile analysis of the diffractograms can bring out important microstructural parameters such as the root mean square microstrain and the average domain size, which help in understanding the irradiation effect on these samples. In this study, Williamson–Hall method based on whole powder pattern fitting technique has been employed.
3.2.1 Modified Williamson Hall Method
The method assumes that the contributions to the broadening of Bragg peaks due to the domain size and the microstrain effects are linearly superimposed and independent of each other. Under these assumptions, Williamson and Hall (WH) relationship between the broadening (β), the volume weighted average domain size (D), and the maximum microstrain (\(\:\epsilon\:\)) is given by Eq. 4.
$$\:\frac{\beta\:\:Cos\:\theta\:}{\lambda\:}=\:\frac{1}{D}+2\epsilon\:\:\left(\frac{2\:Sin\:\theta\:}{\lambda\:}\right)$$
4
Thus, Dv and ε can be determined from the linear plot of \(\:\frac{\beta\:\:Cos\:\theta\:}{\lambda\:}\:\left({\Delta\:}\text{K}\right)\) vs\(\:\frac{2\:Sin\:\theta\:}{\lambda\:}\left(\text{K}\right)\) as shown in Fig. 5 for both unirradiated and irradiated samples. It is apparent that the data points in the WH plots are scattered and therefore, not suitable for linear fitting with acceptable accuracy. In the WH method, it is assumed that the micro-strain is isotropic along the crystallographic axes. The highly scattered data points in the WH plots reveal the existence of anisotropic broadening in the samples. The scattering tendency of the data points is also observed to increase with the increase in dose, suggesting that the micro-strain anisotropy along the different crystallographic planes increases with dose. To take care of such anisotropies, Ungár et. al.[25–27] suggested a modified version of the W-H method that is described by the Eq. 5.
$$\:{\Delta\:}\text{K}=\:\frac{1}{D}+\:{\left(\frac{\pi\:{b}^{2}\rho\:}{2B}\right)}^{1/2}K{C}^{1/2}$$
5
here b is the magnitude of the Burgers vector, \(\:\rho\:\) is the dislocation line density, B is a constant considered to be 10 over a wide range of dislocation distribution and C is the average contrast factor of the dislocations based on their positions relative to the diffraction vector [25–27]. The C factor for a cubic crystal is a linear function of the fourth-order invariant of the hkl indices of the various reflections and depends on the Burgers vector, line vectors characterizing the dislocations, the elastic anisotropy constant, Ai and the ratio of C12/C44, where C11, C12 and C44 are the elastic constants. Using C44 = 1.25 and Ai = 2.54, C is calculated employing the procedure given in ref [28]. However, the C factor in the modified Williamson-Hall method (Eq. 5) incorporates only the anisotropy component of strain. According to Warren [29], if a sample contains stacking faults or twin boundaries, or both, then apparent domain size is less than the actual domain size. Therefore, the presence of planar defects also influences the broadening of the diffraction peaks. Ungár et al.[30] included the effect of twinning and stacking faults in the modified W-H plot. With this change, Eq. (5) can be rewritten as
$$\:\:\:\:{\Delta\:}\text{K}-{\upvarsigma\:}\text{W}\left(\text{k}\right)=\:\frac{1}{D}+\:{\left(\frac{\pi\:{b}^{2}\rho\:}{2B}\right)}^{1/2}K{C}^{1/2}$$
6
where the parameter, \(\:{\upvarsigma\:}\) represents the density of twin boundaries and deformation faults and it is set as a fitting parameter. The value of the parameter W(k) for fcc unit cell is determined by Ungár et al. [28] for different peaks. Figure 6 shows linear fitting of data points in the plot of\(\:\:{\Delta\:}\text{K}-{\upvarsigma\:}\text{W}\left(\text{k}\right)\) vs. \(\:K{C}^{1/2}\) for all the samples. The domain size and dislocation density were evaluated from these plots using Eq. (6) and their variation as a function of irradiation dose is given in Table 2.
The domain size decreases significantly from 356 Å to 136 Å when irradiated at highest dose of 33.9 dpa. The domain size is seen to decrease with increase in irradiation dose and the rate of its decrease is ~ 74 Å /dpa, 42.5 Å /dpa, and 5.7 Å /dpa at doses of 1.5 dpa, 9.6 dpa, and 33.9 dpa, respectively. This indicates that the maximum reduction in domain size occurred during the initial phase of irradiation and approaches saturation as the dose of irradiation increases.
3.3. Transmission electron microscopy of irradiated samples
The irradiated samples were investigated in TEM to reveal the geometric configurations attained by the clusters of point defects generated by irradiation. The bright-field TEM micrographs of Figs. 7(a-b) and 7(c-d) show the defect microstructures of irradiated samples recorded under two-beam diffraction imaging conditions at doses of 9.6 dpa and 33.9 dpa, respectively. Two different diffraction g-vectors were used to image the defect structure. A network of dislocation loops could be observed in both the irradiated samples very clearly besides small, black dot-like feature which represents defect clusters/small dislocation loops. No discernible difference could be noticed in terms of the density of the loops in the two samples (9.6 vis-à-vis 33.9 dpa) although more of dot-like feature was observed in the 9.6 dpa sample in contrast to 33.9 dpa when imaged with 200 diffraction vector (Fig. 7(a) vs. 7(c)). This suggested towards an increase in the size of the defect clusters/small dislocation loops with irradiation dose, leading to the attainment of a more distinct loop-like character. Although the nature of the loops has not been determined in the present work, it is expected to be similar to that exhibited by the microstructure of any irradiated fcc material with predominance of faulted (Frank) loops (1/3 < 111 > Burgers vector) over perfect loops (1/2 < 110 > Burgers vector) owing to lower stacking fault energy.
It is to be noted that all these defect features are an outcome of the irradiation process alone, as the unirradiated sample imaged under similar diffracting condition did not exhibit any of these features except for a few isolated planar dislocations (Fig. 2(b)). Another major irradiation effect on the microstructure of the alloy, which became apparent through TEM examination, was the dissolution of the native alpha-Cr precipitates. The alpha-Cr precipitates present in the unirradiated matrix (Fig. 2(a)) were hardly visible after irradiation; Only their leftover vestiges were noticed as shown encircled in Fig. 8. The dissolution of alpha-Cr precipitates got accompanied by a corresponding increase in the Cr- and Mo-content of the matrix phase to 44.7 wt.% and 1.8 wt.%, respectively from that of 43.4 wt.% and 1.1 wt.% in the unirradiated condition. Elemental analysis carried out on the precipitate remnants showed composition very close to that of the irradiated matrix namely Ni-47Cr-2.3Mo (wt.%), thereby proving their dissolution. However, the re-precipitation of alpha-Cr phase was not observed. It should be noted that pristine samples were heat treated in such a way so as to minimize the precipitate volume fraction during processing. Thus, the dissolution of small fraction of pre-existing precipitate may not be considered detrimental for application purpose.
Focus-series experiments were performed on the highest dose (33.9 dpa) sample to examine the generation of voids on account of irradiation. In such experiments, the presence of voids gets evinced as black dots surrounded by a white fringe in over focused image (under positive defocus of the objective lens) and as white dots surrounded by a dark fringe in under focused image (under negative defocus of the objective lens). The features encircled in Figs. 9(a) and (b), present near the sample’s edge, showed this sort of contrast reversal, which established unequivocally the presence of voids in the irradiated sample. The size of the voids was observed to be in the range of ~ 2 to 6 nm. He has a negligible solubility in metals and have the ability to stabilize vacancy clusters thereby leading to the formation of voids [10]. In Ni-based alloys, bubble formation due to He ion implantation has been studied by several authors [31–35]. Van et al. studied the growth of helium bubbles and the formation of blisters during low energy He ion irradiation in nickel and amorphous Metglass alloy (Fe40Ni38Mo4B8) in the temperature range of -73 °С to 327 °С and dose range of 5x1020 He/m2-1x1022 He/m2. In crystalline nickel even at 0 °С, the bubbles grew to a saturation value of mean diameter equal to 2.5 nm [36].
3.4. Positron annihilation spectroscopy study
The variation of S-parameter as a function of mean positron implantation depth (S(Z) profiles) from the sample surface is presented in Fig. 10 for both unirradiated and irradiated samples. The experimental S-Z profiles could be analyzed using the variable energy positron fit (VEPFIT) software [37–39]. The solid line shows the fitting of VEPFIT program. It can be seen that the S-parameter of the unirradiated sample increase sharply close to the surface, before mean implantation depth of 50 nm. This behavior is generally observed in metallic samples and is attributed to the back diffusion of positrons towards the surface, which results in the formation of a positronium-like state that has higher S-parameter values [40]. The S-parameter values of the irradiated samples are higher than that of unirradiated samples throughout the depth and the S-parameter value increases as the dose increases. The S-W plot is analyzed to identify the defects that have been produced by ion implantation. The typical S-W plots for the sample irradiated to the highest dose of 33.9 dpa is shown in Fig. 11.
3.5. Nano indentation
The hardness H of the samples before and after irradiation were evaluated using nano-indentation. The inset in Fig. 12(a) shows the average nanoindentation hardness as a function of depth. The hardness of all irradiated samples was observed to be higher than that of the unirradiated sample together with a progressive increase in hardness with irradiation dose. There is a decrease in the hardness of all the samples with increasing indentation depth in irradiated as well in unirradiated samples. This is attributed to the ‘indentation size effect’ (ISE) which can be described by Nix–Gao model based on geometrically necessary dislocations [41, 42] using Eq. 7.
$$\:\frac{H}{{H}_{0}}=\sqrt{1+\frac{{h}^{*}}{h}}$$
7
where H is the measured hardness corresponding to indentation depth h, H0 is the hardness corresponding to infinite depth which is also known as the bulk equivalent hardness or ISE free hardness, \(\:{h}^{*}\) is the characteristic constant of indention depth which depends on the indenter shape and shear modulus. In evaluating the hardness of shallow-depth low-energy ion-irradiated materials, the estimated hardness often turns out to be a convoluted hardness having contributions from both the hard-irradiated surface and the underneath soft unirradiated substrate. An approach developed by Kasada et al. [43] allows one to evaluate the hardness of irradiated region without interference from the unirradiated substrate.
A fitting of H2 against 1/h of the hardness data was carried out for depths beyond 125 nm and the same is shown in the Fig. 12. For all irradiated samples, the plot of H2 versus 1/h exhibits an inflection at a critical indentation depth (hc) and this inflection point is more pronounced at higher dose of 33.9 dpa and can be seen at around 300 nm. The hardness of the irradiated samples, H0, and h* evaluated by fitting the data in the range of 125 nm < h < hc are given in Table 3. It is observed that the value of H0 increases and h* decreases with increase in irradiation dose.
In order to understand the effect of He ion irradiation on the mechanical properties, the change in the average nanohardness value (∆H), defined as ∆H = Hirradiated - Hunirradiated was evaluated and shown in Table 3. The hardening rates at 1.5 dpa, 9.6 dpa and 33.9 dpa were found to be 347 MPa/dpa, 195 MPa/dpa and 25 MPa/dpa, respectively. This shows that the hardening rate is higher at lower irradiation doses. The irradiation hardening can be fairly assumed to be mainly due to a change in dislocation density and therefore dislocation density can be estimated using Eq. 8.
$$\:\rho\:={\left(\frac{{H}_{0}}{MC\alpha\:Gb}\right)}^{2}$$
8
where M is the Taylor factor (3.06 for cubic lattice) and α (= 0.5) is defect barrier strength (dependent on dislocation structures) [44, 45]. G represents the shear modulus (87 GPa, [1]), b represents the magnitude of the Burgers vector, and C represents the Tabor's factor. For metals C = 3 can be considered [44, 45]. Using Eq. (8), the dislocation density was calculated for each sample and given in Table 3. It is observed that the dislocation density estimated from nano-hardness is higher than that estimated from XRD analysis.