**3. Results**

### *3.1. Calculation of the Implanted Ion Range*

The SRIM is commonly used to simulate the ion sputtering process [26]. In this case, the ion range of all implanted ions in the simulation was calculated using dynamic simulation (TRIM) [27]. The impurity distributions of lanthanum and yttrium ions at ionic energies of 100 Kev and 105 Kev were simulated by TRIM. The results are shown in Figures 2 and 3, respectively. As shown in Figures 2a and 3a, each time an implanted ion collided with a target atom, a vacancy (lines of red dots) would be created, which would cause cascade damage (clusters of green dots) of the target atoms in steel. As shown in Figures 2b and 3b, the maximum ionic ranges of lanthanum and yttrium were 50 and 60 nm, respectively, and both had a normal distribution, which was consistent with the XPS results. Figures 2c and 3c show the ionization distribution in which lanthanum and yttrium ions lose their energy in steel samples, and it was observed that the host lattice arrangemen<sup>t</sup> of steel was damaged during the implantation of lanthanum and yttrium ions (Figures 2d and 3d).

**Figure 2.** TRIM simulation of lanthanum ion implantation for the (**a**) ion beam pattern, (**b**) ion ranges, (**c**) ionization distribution of ions, and (**d**) collision events.

**Figure 3.** TRIM simulation of yttrium ion implantation for the (**a**) ion beam pattern, (**b**) ion ranges, (**c**) ionization distribution of ions, and (**d**) collision events.

### *3.2. Chemical Composition and Structure of the Implanted Surface Layer*

Figure 4 shows the XPS spectra of the samples after La and Y ion implantation, where contaminants on the surface were removed by Ar<sup>+</sup> etching for 1 minute. Figure 4a,c show the full XPS spectra, which indicate that there are iron, oxygen, carbon, and silicon on the implanted lanthanum and yttrium surfaces, respectively. Compared with the binding energy of the standard absorbed carbon of 284.8 eV, the surface energy of the absorbed carbon in this study was 285.2 eV, which was 0.4 eV higher than that of 284.8 eV. The adjusted XPS data of La and Y are separately illustrated by Figure 4b,d respectively. Figure 4b shows the La 3d surface XPS spectrum. The three peaks correspond to La 3d3/2 (851.5 eV) and La 3d5/2 (835.1 eV). The spin-orbit splitting value was 16.4 eV, which clearly sugges<sup>t</sup> a typical La2O3 pattern [28]. The phenomenon was also observed by Jin et al. [29]. Figure 4d shows the Y 3d XPS spectrum, and the peaks at 158.0 eV and 155.9 eV correspond to the Y–Y bond, and the peak at 157.4 eV corresponds to Y2O3. Consequently, this result illustrate that lanthanum mainly exists as oxides, while yttrium exists as oxides and metallic Y in the RE implanted layer.

Figure 5 shows the depth profiles of the element content distribution of lanthanum and yttrium ion implantation samples from the XPS tests. Figure 5a,b show that the concentration of lanthanum and yttrium in the ion implantation layer present a normal distribution trend, and the peak concentration distributions are at depths of approximately 15 and 25 nm, with concentrations of 22.9 wt% and 21.2 wt%, respectively.

**Figure 4.** XPS spectra of sample surfaces—(**a**) survey spectrum and (**b**) La 3d spectrum of implanted La; (**c**) survey spectrum and (**d**) Y 3d spectrum of implanted Y.

**Figure 5.** Depth profiles of element content distribution obtained by XPS—(**a**) lanthanum implantation result and (**b**) yttrium implantation result.

As shown in Figure 6, due to the larger radius of rare earth and the internal stress introduced by ion implantation [30], all three diffraction peaks of α-Fe shift to the left and the peak intensity increased, which meant that the lattice distortion occurred on the surface of the implanted matrix, according to the Bragg equation [31].

Figure 7 shows the TEM image of the surface layer of the samples, with and without ion implantation. It can be observed from Figure 7a,b that that there are some crystal defects in the 20Cr2Ni4A matrix, such as dislocation entanglement and dislocation grid, which form a stable defect network. The RE ion implantation caused lattice damage to the body-centered cubic (BCC) Fe matrix. From the observation of Figure 7c–f, the matrix implanted with rare earth ions forms high density dislocation entanglement compared to that of the non-implanted sample. Especially after yttrium

ion implantation, the matrix was almost full of high-density dislocations, which accumulated and tangled [30].

**Figure 6.** XRD patterns of the implanted surface with and without rare earth (RE) implantation—(**a**) XRD spectra; (**b**) diffraction angle of the (110) peak; (**c**) diffraction angle of the (200) peak; and (**d**) diffraction angle of the (211) peak.

**Figure 7.** TEM observation of non-carburized samples after ion implantation—(**<sup>a</sup>**,**b**) non-implanted sample; (**<sup>c</sup>**,**d**) lanthanum-implanted sample; and (**<sup>e</sup>**,**f**) yttrium-implanted sample.

### *3.3. Phase and Microstructure of the Carburized Layer After Ion Implantation*

The phase on the surface of the carburized samples was measured by XRD, as shown in Figure 8. The carburized layers of the three samples are composed of a martensite phase with a body-centered cubic (BCC) structure and retained austenite with a face-centered cubic (FCC) structure. Due to the limitation of the phase detection spatial resolution with XRD, there are no diffraction peaks from lanthanum and yttrium. However, it was found that the strongest diffraction peaks from the lanthanum and yttrium-implanted samples shift to the left by 0.26 and 0.20 degrees, respectively, compared with that of the non-implanted sample. The other two peaks of martensite migrated to the left at the same time. In addition, the intensity of all crystal planes after lanthanum and yttrium implantation were stronger than those from the non-implanted sample. X-ray stress analyses also revealed that the content of the retained austenite in the carburized layer decreased slightly with the implantation of RE ions, as shown in Table 2.

**Figure 8.** XRD spectra of the carburized layers of the three samples—(**a**) XRD spectra; (**b**) diffraction angle of the (110) peak; (**c**) diffraction angle of the (200) peak; and (**d**) diffraction angle of the (211) peak.

**Table 2.** Retained austenite content in the carburized surface layer of the three samples by XRD.


In this section, the microstructures of the carburized layers of different samples carburized in vacuum for 5 hours at 920 ◦C are discussed. Figure 9a,c,e show the layers from conventional carburizing and carburizing with REs lanthanum and yttrium, respectively. Figure 9a shows that the microstructure of the carburized layer was composed of a martensite matrix, and granular carbides were dispersed in it and retained austenite, which were not transformed into martensite. However, ultrafine acicular martensite and fine dispersed grain carbides were obtained in the carburized layer after the ion implantation of lanthanum and yttrium, as shown in Figure 9c,e, respectively. Figure 9b,d,f show that the core microstructures of the three samples were tempered martensite and free ferrite. According to the GB/T 25744-2010 metallographic standard, the core microstructures of the non-implanted sample were equivalent to grade 4, while those of the samples with RE ion implantation were equivalent to grade 3.

**Figure 9.** Microstructure of the carburized layer on the three samples—(**a**) carburized surface layer without RE; (**b**) core after carburizing without RE; (**c**) carburized surface layer after La implantation; (**d**) core after La implantation; (**e**) carburized surface layer after Y implantation; and (**f**) core after Y implantation.

In addition, the SEM images of the carbides in the carburized layer and their corresponding size and distribution histograms are shown in Figure 10. Figure 10a shows that the majority of the carbides are granular and unevenly distributed in the interstices between the martensites and are accompanied by large diameter bar carbides. However, compared to that in the non-implanted layer, the carbide distribution in the carburized layer of the sample after ion implantation was finer and more uniform. Among the non-implanted and implanted layers, the carbides implanted with yttrium were the finest. The EDS measurements of the carbide particles in the three samples showed that the carbides were mainly composed of carbon, iron, chromium, nickel, and manganese, while lanthanum and yttrium were found in the carbides in the ion-implanted samples. The size distribution of the carbide particles was estimated by using Nano Measurer 1.2 software and Gaussian fitting (v1.2, Wan An Intelligent Technology, Wuhan, China). At least 150 particles were counted from each SEM image. The carbide particles in SEM photos were labeled and statistical reports were derived [32]. The average diameter of carbides on the surface of the non-implanted samples was 0.35 μm. Among them, 81.2% of the carbides were within 0.6 μm in diameter, and the length of a portion of the large strip carbides was more than 5 μm. However, the average diameters of the carbides on the surface of the carburized layer after ion implantation of lanthanum and yttrium were 0.25 and 0.17 μm, respectively. The diameters of most carbides were from 0.1 to 0.3 μm. The results showed that ion implantation of the REs reduced the particle size of carbides on the carburized layer surface. The effect of yttrium ion implantation was better than that of the lanthanum ion implantation because yttrium implantation resulted in a minimum particle size of 0.06 μm and a maximum particle size of 0.36 μm. In other words, RE ion implantation pretreatment played an important role in refining the structure of the carburized layer and promoting the dispersion of the fine carbide precipitates.

**Figure 10.** Diameter of the granular carbides in the carburized surface layer—(**a**) carbide morphology and energy dispersive spectroscopy (EDS) results without RE and (**b**) its carbide diameter distribution; (**c**) carbide morphology and EDS results with La implantation and (**d**) its carbide diameter distribution; (**e**) carbide morphology and EDS results with Y implantation, and (**f**) its carbide diameter distribution.

### *3.4. Hardness Distribution and E*ff*ective Hardening Depth of the Carburized Layer*

Figure 11 shows the results of the Rockwell hardness measurements. The surface Rockwell hardness of the non-implanted sample was 58.3 HRC, and the hardness of RE-implanted samples was higher than the previous value, especially samples with the yttrium addition. After vacuum carburization, the Rockwell hardness of the yttrium-implanted sample increased to 61.8 HRC at the subsurface layer; this value was higher than that of the lanthanum-implanted sample (60.5 HRC). In contrast, the core hardness value did not change significantly. The smaller error bar value indicated that there was no significant difference in the range of surface hardness.

**Figure 11.** Rockwell hardness of the carburized layer and the core of the three samples.

Figure 12 shows the microhardness results of the samples after carburization, with and without the RE ions. The fluctuation of the error bars were not more than 25 HV1. It could be seen that the microhardness of the carburized layer after RE ion implantation was higher than that treated by conventional vacuum carburization at 920 ◦C, and the change in the hardness gradient was minor. The maximum hardness of the carburized layer after ion implantation of lanthanum and yttrium occurred at 0.1 mm and 0.2 mm from the surface and was 805 HV1 and 822 HV1, respectively, which was higher than the value of 778 HV1 at 0.2 mm from the surface, after conventional carburizing. Osman Asi suggested that the enhancement in hardness was mainly caused by the diffusion of carbon atoms [33]. According to the GBT 9450-2005 standard, the effective hardening depths of the non-implanted, La-implanted, and Y-implanted samples were 1.36 mm, 1.44 mm, and 1.47 mm, respectively, as shown by the arrows in Figure 12. RE ion implantation increased the hardness of the carburized layer of the 20Cr2Ni4A steel but did not cause a significant increase in the depth of the effective hardened layer. Hence, the results showed that the microhardness of the carburized layer obtained by vacuum carburizing with yttrium was the highest, and the change was the most uniform among the samples considered herein.

**Figure 12.** The microhardness distribution of the carburized layer along the depth direction.

### *3.5. Calculation of the Carbon Di*ff*usion Coe*ffi*cient*

As can be seen from Figure 13, the carbon concentration on the carburized surface without ion implantation was about 0.84%, and the carbon concentration varied unevenly. After ion implantation, the carbon content on the carburized surface reached more than 0.9%, and the carbon concentration gradient changed more gently. The hardness gradient distribution of the three carburized specimens was approximately the same as that of the carbon element distribution measured by the EPMA.

**Figure 13.** Carbon concentration along the depth of the carburized layers.

During the vacuum carburization process, acetylene gas was the carbon source. The diffusion of carbon atoms followed Fick's second law and was considered a one-dimensional plane diffusion phenomenon. If the diffusion coefficient did not change with the carbon concentration (or average diffusion coefficient), the carbon concentration distribution in the infiltration process satisfied Equation (1) [12]:

$$\frac{\partial \mathbf{c}(\mathbf{x}, t)}{\partial t} = D \frac{\partial^2 \mathbf{c}(\mathbf{x}, t)}{\partial \mathbf{x}^2} \tag{1}$$

where *<sup>c</sup>*(*<sup>x</sup>*, *t*) is the volume concentration of carbon, *x* is the distance from any point in the sample to the surface of the sample, *t* is the diffusion time, and *D* is the carbon diffusion coefficient.

With the extension of the carburizing time, the carbon concentration *c*s on the steel surface gradually increased from the original carbon content *c*0 to a constant level and was in equilibrium with the carbon potential *c*p of the furnace gas, which indicated that it had entered the stage of carbon diffusion. At the beginning of the carburization process, the initial and boundary conditions of Equation (1) were marked as *c*0 = (*<sup>x</sup>*, 0) and *c*s = (0, *t*). The solution of Fick's second law, which provided the curve of the carbon diffusion concentration, was as Equation (2):

$$\frac{\mathbf{c}\_{\mathbf{x}} - \mathbf{c}\_{0}}{\mathbf{c}\_{\mathbf{s}} - \mathbf{c}\_{0}} = 1 - \operatorname{erf}\left(\mathbf{x} / 2\sqrt{Dt}\right) \tag{2}$$

where *erf* (*x*/2 √*Dt*) is the error function. When the specified value of *cx* was higher than *c*0.35%, the obtained depth of the hardened layer could be described as Equation (3):

$$
\mathbf{x} = \mathcal{ZK}\sqrt{\mathbf{D}t} \tag{3}
$$

where *K* is a constant (constant carbon potential).

Therefore, based on the depth of the carburized layer shown in Figure 12, when the carburizing temperature and time were the same, the diffusion coefficient relation of the carburized layer with or without RE ions could be obtained by Equation (3), as shown in Equations (4) and (5):

$$1.44/1.36 = \sqrt{D\_{920^\circ \text{C}}^{La}/D\_{920^\circ \text{C}}}\tag{4}$$

$$1.47/1.36 = \sqrt{D\_{\text{g20}^{\circ}\text{C}}^{\circ}/D\_{\text{g20}^{\circ}\text{C}}}\tag{5}$$

where *D*920◦ , *<sup>D</sup>*La920◦ , and *<sup>D</sup>*Y920◦ are the carbon diffusion coefficients of 20Cr2Ni4A steel without ion implantation and with lanthanum or yttrium implantation before vacuum carburizing, respectively. Finally, the relations were shown in Equations (6) and (7):

$$D\_{920^\circ \text{C}}^{La} / 1.12 D\_{920^\circ \text{C}} \tag{6}$$

$$D\_{920^{\circ}\text{C}}^{Y} / 1.17 D\_{920^{\circ}\text{C}} \tag{7}$$

In short, the carbon diffusion coefficients after lanthanum and yttrium implantation were 1.12 and 1.17 times higher, respectively, than those of the non-implanted samples when the vacuum carburizing temperature was 920 ◦C and the carbon potential was 1.2%. This was consistent with the results of the hardness gradient distribution and the carbon concentration distribution of the carburized layer.
