Theoretical Calculations and Experimental Study of the Nitrided Layer of 1Cr17Ni2 Steel

Abstract

Due to the harsh operating conditions experienced by 1Cr17Ni2 steel, efforts were made to optimize its performance by subjecting 1Cr17Ni2 stainless steel to nitriding treatments at temperatures of 460 °C, 500 °C, and 550 °C, each for durations of 8 and 16 h. The formation state of its cross section was observed through a metallurgical microscope and scanning electron microscope, and it was characterized by hardness measurement. Through a ball-on-disk wear experiment, the adhesive wear and friction coefficient of its non-lubricated sliding were measured. The phase composition of its surface was measured by XRD. The results revealed that nitriding led to the formation of a modified layer on the surface of the samples, with a depth of 130 μm after nitriding at 550 °C for 16 h. The hardness of the modified layer exceeded that of the matrix, reaching up to 1400 Hv_0.1. X-ray diffraction (XRD) analysis of the sample surfaces indicated the presence of high-hardness phases such as CrN, γ′-Fe₄N, and ε-Fe_2-3N. This article predicts the mechanical properties of nitrided phases in high-alloy martensitic stainless steel through first-principles computational methods. We provide a reference for improving the performance of high-alloy steel after nitriding through a combination of theoretical calculations and experiments.

1. Introduction

1Cr17Ni2 steel is a martensitic stainless steel with excellent characteristics, commonly used as a compressor blade for gas turbine jet engines. Its function is to compress and rectify air for a full reaction with fuel, so it will directly contact high-temperature and high-pressure gas fluid during operation. The temperature, pressure, and flow rate of the fluid flowing through its blades will change greatly under different conditions, and it is prone to fatigue damage under the action of periodic stress. Therefore, the strength, wear resistance, and fatigue resistance of 1Cr17Ni2 steel need to be greatly improved.

Plasma nitriding is a surface heat treatment method that can effectively improve the mechanical properties of materials. It is a chemical heat treatment technology that uses active nitrogen atoms in glow discharge plasma to perform nitriding, the glow discharge generated by high-voltage electric fields causes charged particles to bombard the surface of the workpiece, resulting in an increase in surface temperature, thus achieving the diffusion of nitrogen atoms. The nitrided phase formed on the surface after nitriding has high hardness and wear resistance, resulting in the improved mechanical properties of the surface. The findings of K. Ram Mohan Rao et al. [1] indicate that the presence of iron nitrides FexN (x = 2, 3, 4) has a significant impact on the performance of martensitic stainless steel. The existence of these iron nitrides can form a dense protective layer, effectively preventing corrosion media from corroding the metal matrix, thereby enhancing the material’s corrosion resistance and fatigue performance. This study provides new insights and methods for improving the engineering performance of martensitic stainless steel. Ram and others [2] also found that nitrogen permeation at 500 °C for 10 h generates a broader region known as the passivation zone, which has a beneficial effect on improving the corrosion resistance and fatigue performance of stainless steel.

Aizawa et al.’s [3] research indicates that the high-nitrogen, low-temperature plasma nitriding treatment of AISI420 at 400 °C results in the transformation of the original coarse grains and fully martensitic microstructure into a fine-grained α′-γ dual-phase structure under high nitrogen concentrations. Plastic strain from α′ to γ phase under high nitrogen occurs along slip lines, while geometric reshaping into rectangular and rhomboidal grains simultaneously takes place. This enhances the hardness and wear resistance of the original specimens. Castro et al. [4] studied the impact of plasma nitriding on the fatigue performance of titanium alloys and found that high-temperature plasma nitriding forms a nitrogen-rich hardening layer on the alloy surface, increasing the fatigue strength at low cycles. Zhongli Han [5] and others found that after the low-temperature plasma nitriding of 17-4 PH steel, the nitrided layer mainly consists of γ′-Fe₄N, with a layered and granular morphology. The strength increases with increasing nitriding temperature and nitriding time. Of these, the S phase gradually transforms into CrN, and the α′_N phase transforms into γ′-Fe₄N or CrN. L. Umemura et al. [6] studied the effect of low-temperature plasma nitriding and conventional ion nitriding on the tribological properties of 410S martensitic stainless steel. The study showed that nitriding can effectively improve the wear resistance of the material and achieve a lower friction coefficient. Ruijun He et al. [7] conducted plasma nitriding on AISI422 martensitic stainless steel suitable for steam turbine disks or blades for 20 h, and found that after tempering, the matrix mainly consisted of α-Fe. Upon nitriding, the surface contained γ′-Fe₄N, CrN, and α′_N phases, and the morphology of CrN gradually decreased in width with increasing nitriding depth, transitioning from obtuse angles to acute angles. Liu Yiqi et al. [8] found that CrN and Fe₂N were generated in the modified layer after the plasma nitriding of 1Cr17Ni2 martensitic stainless steel, and the hardness increased from 3.67 GPa to a maximum of 9.25 GPa, resulting in a significant improvement in mechanical properties. Darko Landek et al. [9] studied the effect of plasma nitriding at different temperatures and durations on the surface mechanical properties of AISI 316L stainless steel. They found that shorter durations of plasma nitriding (4–8 h) were advantageous for improving wear resistance and corrosion resistance. Patel [10] and others investigated the effect of active screen plasma nitriding on the microstructure, hardness, and wear loss of 347 H austenitic stainless steel. Their study found that active screen plasma nitriding at 500 °C, under relatively high temperatures, can improve the microstructure and hardness of the metal surface, thereby enhancing the wear resistance of the metal surface. Zhang et al. [11] treated 42CrMo steel with nitriding and laser composite process. They successfully predicted the depth of the modified layer through finite element calculation, and proved through calculation that the composite process greatly improves the fatigue life of 42CrMo steel. Furthermore, in further research [12,13,14,15,16], we have found that theoretical studies on the surface parameters of single crystals have become the main theme of many articles.

This article studied and analyzed the microstructure and composition of 1Cr17Ni2 steel after plasma nitriding, revealing the influence of nitrogen penetration on its microstructure and tribological properties under harsh operating conditions. The wear mechanism of 1Cr17Ni2 steel after plasma nitriding was briefly discussed. The research results can provide reference for the process selection of high-alloy steel.

2. Materials and Methods

2.1. Experimental Methods

The material used in this study is 1Cr17Ni2 martensitic stainless steel, and the specific chemical composition is shown in

Table 1. The chemical composition of 1Cr17Ni2 (wt.%).

C	Fe	Si	Mn	Cr	Ni	S	P
0.14	Bal.	0.63	0.42	16.83	2.26	0.02	0.03

. The samples are in the form of circular discs with dimensions of 30 mm × 8 mm. They were quenched for 2 h at a temperature of 960 °C, followed by intermediate- or high-temperature tempering while nitriding at different nitriding temperatures. Prior to nitriding, all samples were carefully ground using manual processing with silicon carbide papers ranging from 240 to 800 grit to achieve an ideal surface condition. The final surface roughness of all samples was approximately 0.4 μm (Ra). Nitriding was performed in a 50 KW LDMC-50F pulsed plasma nitriding furnace in an NH₃ atmosphere with a fixed flow rate of 1.0L/min. Nitriding temperatures of 460 °C, 500 °C, and 550 °C were used, with nitriding times of 8 h and 16 h.

The microstructure of the nitrided layer was observed using a VHX-5000 digital microscope from China, and a copper sulfate hydrochloride aqueous solution was used as an etchant to reveal the fibrous microstructure of the shell layer. Using the TESCAN MIRA LMS Scanning Electron Microscope (SEM) from Czechia, the surface morphology of the sample is scanned in a vacuum environment. Microhardness was measured using an HDX-1000 digital microhardness tester from China with a 100 g load applied for 15 s. X-ray diffraction analysis was performed on the plasma-nitrided clean surfaces of samples treated with different nitriding times and temperatures to investigate their different phase compositions. The Rigaku D/max-2000 PC rotating anode X-ray diffractometer with Cu-Ka radiation was used in this experiment. The 2 theta angle range was set from 20° to 90° with a step size of 0.2°. The geometry of the measurement is Bragg–Brentano. The voltage and current were set at 40 kV and 30 mA, respectively. The CFT-I functional friction tester was used to measure the surface friction coefficient of samples after different process treatments. The grinding ball was a 6 mm diameter ball made of WC with a load of 20 N, and the hardness of WC ball was 2400 Hv_0.1, reciprocating friction; the sliding speed was 300 revolutions per minute; and it had a running length of 3 mm and a friction time of 3600 s.

2.2. Calculation Methods and Models

All first-principles calculations in this article are performed using the CASTEP program based on density functional theory. Density functional theory is a quantum mechanical modeling method that allows us to calculate the electronic structure and properties of materials. The exchange–correlation energy is described using the generalized gradient approximation (GGA-PBE). The interaction between ions and electrons was described using the Vanderbilt-type ultra-soft pseudo-potential [17], and the geometric optimization was performed using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method [18]. The plane wave truncation energy used in this experiment was 600 eV, and the grid used for Brillouin zone summation and integration was divided into 5 × 5 × 3. The elastic properties of the generated phases were calculated using a stress–strain method based on Hooke’s law [19]. First, a crystal cell that sufficiently indicates the atomic arrangement of the material was established using first-principle computational methods. Some of the Fe atoms in the cell are replaced with other alloy elements. Then, the influence of alloy elements on the stability of the crystal cell in alloy nitrides is calculated. For the convenience of calculation and analysis, the content of other elements in the configuration process is converted into Cr equivalents, according to the electronegativity rule. The established crystal cell system only contains the main metal elements Fe and Cr, as well as the doped N element. The valence electron configuration of Fe atom is 3d6 4s2, the valence electron configuration of Cr atom is 3d4 4s2, and the valence electron configuration of N atom is 2s2 2p3. All energy convergence accuracies in this experiment are at or above Fine. The energy convergence accuracy is 1 × 10⁻⁵ eV, and the gradient method is used to optimize the structure. The accuracy requirements are that the force acting on each atom is not greater than 0.03 eV/Å, the internal stress is not greater than 0.05 GPa, and the atomic displacement is not greater than 0.001 Å. In this study, the electronic structure and properties of the 1 Cr17Ni2 stainless steel during the nitriding process were calculated using DFT. The calculations involved the determination of the cohesive energy, formation energy, and density of states of α-Fe under different Cr and N contents. The model used in this study represents the crystal structure of the 1Cr17Ni2 stainless steel and is optimized for accurate calculations. The model takes into account the positions of the atoms in the crystal lattice, their connectivity, and the interaction between the atoms. It provides a framework for understanding the behavior of the material at the atomic level and allows for the analysis of the effects of Cr and N on the crystal structure and properties of the alloy. Since both Fe and Cr involved in the calculations are magnetic atoms, spin polarization is introduced to ensure the accuracy of the computed data and to analyze the influence of alloying elements on the system’s binding energy.

After limiting the calculation module and accuracy, the construction of a supercell model begins. In calculations, different supercell models are selected based on the solid solution atomic content. Generally, a larger supercell size corresponds to a closer approximation to the true value of the solid solution atomic concentration. However, when the supercell size becomes too large, the number of atoms increases, and the interactions between atoms become more complex, resulting in an exponential increase in computational complexity.

3. Results and Discussion

3.1. Microstructures of Nitride Layers

The cross-sectional microstructure of the 1Cr17Ni2 steel sample after nitriding is shown in Figure 1. Figure 2 shows the distribution of N element in the cross-section of the sample under different nitriding processes using EDS. As depicted in the figure, it is clear that with the increase in nitriding time, there is a significant increase in the thickness of the nitride layer. The steel surface forms a thin and uniform compound layer [1]. It can be seen from the figure that the nitride layer surface is composed of three parts, namely the diffusion zone, the heat-affected zone, and the substrate. The interface between the diffusion zone and the heat-affected zone is smooth, while the interface between the heat-affected zone and substrate is blurred. The depth of the nitrided layer for different nitriding processes is shown in

Table 2. Depth of plasma nitriding layer for different processes.

Nitriding Process	Depth (μm)
460 °C PN8h	84
460 °C PN16h	125
500 °C PN8h	101
500 °C PN16h	125
550 °C PN8h	109
550 °C PN16h	133

. It also confirmed that as the temperature rises, the depth of the nitrided layer in the sample nitrided for 8 h increases significantly with the increase in nitriding temperature, while the sample nitrided for 16 h shows an increasing trend, although this is not very obvious, with the increase in nitriding temperature, and the same situation also occurs in Landgraf’s study [20]. It can also be observed from the figure that as the temperature increases, the particles in the matrix gradually grow, which is due to the increase in the driving force for grain growth caused by the temperature increase. At the same time, with the extension in nitriding time, the modification depth also continues to deepen due to the introduction of more nitrogen into the material. Due to the influence of diffusion kinetics, nitrogen enters from the high-concentration part of the material into the lower-concentration part, and the higher temperature provides energy for nitrogen to diffuse inward, resulting in the further inward diffusion of nitrogen, which explains why the modification depth continuously increases with the extension in nitriding time.

As shown in Figure 3, the XRD spectra of samples with different nitriding processes exhibit significant differences in peak intensity. During the nitriding process, the diffusion and chemical reactions of Fe, Cr, Ni, and N elements lead to changes in the surface phase composition of the samples. The nitride layer mainly consists of a compound layer and a diffusion zone. The compound layer is primarily composed of γ′-Fe₄N, a small amount of ε-Fe_2-3N, and CrN, while the diffusion zone is primarily composed of α′_N-Fe [21,22], where N and C atoms dissolve interstitially in the α-Fe lattice. The composition of the nitride layer is the same as the phase composition obtained by Li junyang et al. for 2Cr13 martensitic stainless steel after ion nitriding [23]. γ′-Fe₄N is formed due to the diffusion of N atoms into Fe during the nitriding process. It is worth noting that the diffraction peaks of the γ′-Fe₄N phase show a slight shift towards lower angles, mainly due to chemical reactions and element diffusion during nitriding. On one hand, the formation of nitrides and metal compounds reduces the content of pure metal phases. On the other hand, N atoms as external interstitial atoms enter the metal, while alloying elements usually act as substituting atoms, resulting in the expansion of lattice parameters. This is consistent with the increase in equilibrium lattice constant observed in the experimental calculations in Section 3.3 of this paper. Alloying elements diffuse and interact atomically during the nitriding process, leading to the formation of metal compounds, and they play a special role in phase transformations. It is worth noting that at lower nitriding temperatures and shorter nitriding times, the peak intensity of γ′-Fe₄N is higher. With an increase in nitriding temperature and extension of nitriding time, the peak intensity of γ′-Fe₄N gradually weakens while the peak intensity of ε-Fe_2-3N increases. This is because an increase in nitriding temperature and time leads to an increase in the concentration of N solid solution into the matrix. At the same time, the higher nitriding temperature makes the nitriding kinetics more active, which allows for a sufficient amount of N to react and form nitrides. Also, with an increase in N concentration, the reaction between γ′-Fe₄N and N favors the formation of ε-Fe_2-3N. Furthermore, a narrowing of the peaks is observed, indicating that the grain has grown to a certain extent, which is consistent with the observations in Figure 1. Additionally, due to the high Cr content of the 1Cr17Ni2 stainless steel, the surface phase of the sample contains CrN. The theoretical reaction products of Cr and N include CrN and Cr₂N. However, only CrN is observed in the XRD pattern, which agrees with the experimental and theoretical results. According to the first-principle calculations, the energy change for the precipitation of CrN is −0.19 eV, while that of Cr₂N is 9.86 eV [24]. This suggests that the precipitation of CrN can occur spontaneously, while the precipitation of Cr₂N is more difficult. This also explains why CrN is preferentially precipitated in the nitriding layer on the surface of 1Cr17Ni2 stainless steel.

3.2. Microhardness after Nitriding

As shown in Figure 4, measuring the hardness along the surface towards the center of the sample and taking the average of the hardness of three test points at the same depth every 10 μm as the hardness at that depth, the microhardness profiles of the nitride layer profile after nitriding treatment at different temperatures for 1Cr17Ni2 steel show a parabolic distribution overall, reaching a peak hardness of approximately 1000 Hv_0.1. The surface hardness of the nitride layer was greatly improved after nitriding treatment. It can be seen from the figure that as the depth of the nitride layer increases, the hardness first increases, reaches a peak, and then slowly decreases before suddenly dropping. A hardness gradient distribution appears at the interface between the nitride layer and the substrate, and the gradient becomes more gradual as the temperature increases. Upon the careful observation of Figure 4a,b, it can be seen that a peak in microhardness occurs within a depth range of 30 μm to 90 μm, which coincides with the depth range of the white bright layer when compared to Figure 1. The sample nitride at 460 °C for 16 h exhibits the highest surface hardness, reaching 1338 Hv_0.1. Comparing the samples that were nitrided for 8 h and 16 h, it can be seen that samples nitride at 460 °C generally have the highest surface hardness. According to Figure 3, it can be seen that there are a large amount of high-hardness α′_N, ε-Fe_2-3N, γ′-Fe₄N, and a small amount of CrN phases generated in the surface phase at 460 °C, while the CrN content is higher in the surface phase at 500 °C and 550 °C, reducing the surface hardness at these two temperatures [25]. Meanwhile 460 °C is more suitable for nitrogen solid solution, while at 500 and 550 °C, a small amount of compound precipitation occurs, resulting in a slight decrease in hardness [26].

3.3. Friction and Wear Mechanism of 1Cr17Ni2 Steel after Plasma Nitriding

This study used a friction tester to determine the friction coefficients of specimen surfaces after different processing techniques. As shown in Figure 5, the friction coefficients of different samples generally increased over time before stabilizing. The significant changes in friction coefficients among different techniques mainly occurred within the first 800 s of wear, after which they gradually stabilized. The original specimen exhibited the lowest friction coefficient, with an overall trend of initially increasing and then decreasing.

The variation in friction coefficient during wear depends on several factors, including the phase composition, the hardness of the worn surface, and the wear mechanisms. The local fluctuations in friction coefficient during wear can be explained by the mechanism of “oxidation–separation–reoxidation” in oxidative wear [27]. Heat generated by friction during wear causes debris to oxidize, forming a dense oxide film that effectively prevents direct contact between the mating surfaces, thus lubricating and reducing the friction coefficient.

The wear rate of the nitrided surface layer initially increases and then decreases as the nitriding temperature rises, and this phenomenon holds true when nitriding for 16 h as well. As evident from the graph, the wear rate decreases with the increase in nitriding time. Observing the changes in the stable friction coefficient, it is evident that its variation is inversely proportional to the surface wear rate: as time progresses, the friction coefficient of the 16 h nitrided surface is consistently higher than that of the 8 h nitrided samples. The wear resistance after nitriding experiences a significant improvement compared to unnitrided samples. Specifically, the wear rate of the original sample is 2.31 × 10⁻⁵ mm³/(N·m), whereas the wear rates of the nitrided samples decrease by two orders of magnitude compared to the original sample.

Moreover, as depicted in Figure 6, under the same nitriding temperature, the wear rate of samples nitrided for 16 h is generally lower than that of samples nitrided for 8 h. Concurrently, the friction coefficient of the 16 h nitrided samples is generally higher than that of the 8 h nitrided samples. This indicates that the friction performance of the samples improves significantly with the increase in nitriding time.

The three-dimensional morphology of wear after 2400 s at 300 rpm for different nitriding processes is depicted in Figure 7, showing similar wear profiles for all specimens without significant macroscopic plow grooves.

Table 3. Scratch depth under different nitriding processes.

Nitriding Process	Scratch Depth/μm
original	47.34
460 °C PN8h	27.98
460 °C PN16h	21.91
500 °C PN8h	31.97
500 °C PN16h	31.02
550 °C PN8h	40.8
550 °C PN16h	30.58

provides the depths of wear marks under different processes, indicating a significant reduction in wear mark depth after nitriding compared to the original specimen. At the same sliding speed, the depth of wear marks increased with time and temperature. Among them, nitride at 460 °C exhibited the lowest wear mark depth, which increased with nitriding temperature, leading to an increase in both wear rate and wear mark depth.

A comparison between the wear rate and hardness revealed an inverse relationship, indicating that increasing hardness can significantly reduce wear rate and improve wear resistance [28,29]. However, hardness is not the sole determinant of wear resistance, as co-nitrided layers with optimal toughness exhibit the best wear resistance.

As shown in Table 3, the wear scar of the nitrided sample is significantly reduced compared to the original sample. At the same sliding speed, the depth of the wear scar increases with the increase in time and temperature. Among them, the 460 °C has the shallowest wear scar, and the wear scar depth increases with the increase in nitriding temperature, resulting in an increase in both wear rate and wear scar depth. At the same time, through the comparison of wear rate and hardness, it is found that the wear rate is roughly inversely proportional to the hardness, and increasing the hardness can significantly reduce the wear rate and improve the wear resistance.

In order to observe the micro-morphology of the wear scar in more depth and analyze the micro-mechanism of wear in detail. The surface friction and wear morphology of the nitrided Figure 8 1Cr17Ni2 steel was analyzed.

Table 4. Energy spectrum analysis results of points in Figure 8b.

Point	Element (wt.%)
	Cr	Fe	Ni	W	C	O
A	11.34	44.15	0.83	25.19	4.86	9.14
B	11.90	45.34	1.39	24.08	6.37	7.44
C	17.18	76.54	2.43	0.53	2.28	0.36

shows the surface morphology of the original sample after friction and wear, and Figure 8b shows the EDS test results for points A, B, and C. As can be seen from the figure, as the friction and wear progress, the surface of the wear scar is covered with an oxide film, which is formed by the compaction of wear debris generated during the wear process during movement. This oxide film can effectively prevent direct contact between the sample and the friction pair, thereby reducing the friction coefficient. The results of energy spectrum analysis also indicate that the wear debris contains oxides, suggesting that the type of oxide is Fe₂O₃. With the cycle of the friction process, the oxide film gradually thickens and fatigue cracks are generated. Over time, the fatigue cracks gradually increase and fatigue peeling occurs, exposing a new surface to contact with the friction pair, eventually reaching an equilibrium. There are shallow ploughing grooves on the surface of the wear scar (point A in Figure 8a), indicating that there is abrasive wear on the surface. Meanwhile, observing point B in Figure 8a, it can be seen that there is slight tearing on the surface of the wear scar, indicating that there may be adhesive wear on the surface. The adhesive ensures that the surface wear rate does not increase rapidly. In summary, the main wear mechanisms of 1Cr17Ni2 steel in the quenched state are slight abrasive wear and oxidative wear, in addition to slight adhesive wear.

In order to reveal the wear mechanism, it is necessary to observe the wear behavior first. Figure 9 shows the surface friction and wear morphology after different nitriding processes, with typical areas of wear scars enlarged. As shown in Figure 9a, there is a slight ploughing groove inside the wear scar, indicating that there is slight abrasive wear during the wear process. By magnifying the edge morphology of the wear scar, it can be seen that there are obvious plastic deformation zones and crack generation zones at the edge of the wear scar, indicating that fatigue wear has occurred at the edge of the wear scar. From Figure 9b, it can be seen that there is a clear ploughing pattern inside the wear scar, indicating that there is abrasive wear during the wear process. At the same time, by zooming in on the image of the edge of the wear scar, it can be seen that there are significant plastic deformation zones and crack formation zones at the edge of the wear scar, indicating that fatigue wear has occurred at the edge of the wear scar. Compared to the wear effect of the original sample, there are no cracks at the center of the wear scar after nitriding, indicating that the nitrided layer has good fatigue performance. The reason for the formation of cracks at the edge is that the wear debris in the center and the oxides generated during the wear process are pushed to the edge of the wear scar by the friction pair during the wear process and are compacted. As the friction and wear test time increases, the compacted wear debris at the edge of the wear scar has poor fatigue performance and gradually produces fatigue cracks. As time further increases, the cracks expand and eventually fall off. In summary, the main wear mechanisms of the sample nitrided at 500 °C for 8 h are particle wear and oxidative wear. Upon observation of Figure 9c, it is evident that the wear morphology of 550 °C nitriding for 8 h bears a resemblance to that of 460 °C nitriding for 16 h. However, in terms of wear depth and wear rate, the 460 °C nitriding for 8 h exhibits a lower wear rate and a shallower wear depth, potentially related to the surface phase structure. By comparing the SEM images of the three processes, it can be concluded that as the nitriding temperature increases, the wear mechanism changes from abrasive wear and oxidative wear to oxidative wear.

Figure 10 shows the surface and edge micro-morphology of the friction and wear experiments after nitriding at 500 °C for 8 h and 500 °C for 16 h. From Figure 10b, it can be seen that the ploughing shape inside the wear scar has decreased, and almost no obvious ploughing marks are visible, indicating that no abrasive wear has occurred at this time. Cracks also appear on the edge of the wear scar, and the mechanism of occurrence is consistent with that of 500 °C nitriding for 8 h, indicating that the main wear mechanism of the 500 °C nitriding for 16 h sample is oxidative wear. It can be seen that with the extension of nitriding time, the wear mechanism changes from abrasive wear and oxidative wear to oxidative wear.

3.4. Crystal Cell Optimization

α′_N (over-saturated nitrogen martensite) is the martensitic structure formed when nitrogen is in a supersaturated state solidly dissolved in the octahedral interstitial sites of α-Fe. Therefore, this study selects α-Fe as the basis for constructing the model. Many studies on surfaces have focused on the atomic level, including surface segregation and surface magnetic structures of iron-chromium alloys. Therefore, we adopt the surface structure of the bcc Fe-Cr system as a model reference for the surface of 1Cr17Ni2 stainless steel [16,30]. The body-centered cubic (bcc) structure of α-Fe allows the interstitial atoms to more easily occupy octahedral sites and maintain a relatively stable structure. Alloying elements in martensitic stainless steel mainly exist in the form of substitutional solid solution. As the temperature increases, the energy of the system also increases, making it easier for alloying elements to move, thus increasing the likelihood of reacting with nitrogen. However, most alloying elements have significantly different crystal structures from α-Fe. Therefore, it is almost impossible for the reaction to occur when the temperature cannot reach the critical value. First-principles calculations are based on the system energy at absolute zero, so it is assumed that the Cr atoms are randomly and disorderly distributed, while nitrogen is always located in octahedral interstitial sites. Therefore, based on the Cr content in the 1Cr17Ni2 martensitic stainless steel, a 2 × 2 × 2 supercell is established as the calculation model.

To investigate the influence of different concentrations of nitrogen solid solution on the nitriding of 1Cr17Ni2 martensitic stainless steel, a nitriding model was established for the supercell due to the mass percentage range of 16% to 18% for chromium (Cr) in 1Cr17Ni2 stainless steel. The model was Fe₁₃Cr₃, with a mass percentage of 17.65% for Cr, which is close to the real composition. Three original Fe atoms in the supercell were replaced by Cr atoms, taking into account the symmetry of the crystal structure. Additionally, varying numbers of N atoms were added to the octahedral interstitial sites. The nominal chemical formula for this series of structures is Fe₁₃Cr₃N_n. The optimized structure model of Fe₁₃Cr₃N_n after computational structural optimization is shown in Figure 11. Meanwhile, the composition table of Cr and N contents in the Fe₁₃Cr₃N_n structural series with varying nitrogen contents is shown in

Table 5. Composition table of Cr and N contents in Fe₁₃Cr₃N_n structural series.

Molecular Formula	Content of Cr (at.%)	Content of Cr (wt.%)	Number of N Atoms	Content of N (at.%)	Content of N (wt.%)
Fe13Cr3	18.75	17.65	0	0	0
Fe13Cr3N2	16.65	17.11	2	11.1	3.07
Fe13Cr3N4	15.0	16.60	4	20	5.96
Fe13Cr3N6	13.62	16.12	6	27.3	8.68

.

Since there are two main forms of alloy elements in steel, most of the alloy elements will replace the lattice points of iron to form substitutional solid solutions; in addition, there will be alloy elements undergoing precipitation reactions to form alloy nitrides. Due to the significant difference in lattice constants between most alloy nitrides and the -Fe matrix, the formation of such alloy nitrides requires a significant driving force, making it generally difficult for them to form. The results obtained from first-principles calculations are based on the assumption that alloy elements in the alloy are randomly distributed and nitrogen atoms are located in the interstitial positions at 0 K. When constructing the Fe-Cr system, the influence of chromium element content on the stability of nitrogen-containing martensitic phase needs to be considered first, so the content of other elements is transformed into chromium equivalents according to the electronegativity rules.

Assuming that the chromium content remains unchanged in each model, a body-centered cubic (BCC) structure of α-Fe single crystal cell is established, and an ideal Fe-Cr series structure is then constructed based on this. Under the premise of maintaining symmetry, the different amounts of nitrogen atoms are sequentially added to the octahedral interstitial positions around the BCC atoms. The total energy of the supercell for different Fe-Cr-N systems is calculated through first-principle calculations, and the effect of nitrogen on the stability of the system structure is analyzed. The equilibrium lattice constants obtained after structure optimization are shown in

Table 6. The equilibrium lattice constants of the Fe₁₃Cr₃N_n series structure.

Molecular Formula	a (Å)	b (Å)	c (Å)	V (Å)
Fe13Cr3	5.7155	5.7155	5.7155	186.7125
Fe13Cr3N2	5.1071	5.1071	7.5728	197.5149
Fe13Cr3N4	6.9139	6.9139	5.0318	240.5328
Fe13Cr3N6	6.6812	6.6812	6.6812	298.2366

.

By analyzing the data in Table 6, it is easy to determine that the original α-Fe single crystal cell has a standard body-centered cubic structure. Under the condition of maintaining symmetry, by sequentially adding N atoms to the octahedral interstitial sites of the α-Fe supercell, the significant distortion of the original crystal structure can be observed, resulting in a transformation from cubic system to tetragonal system. Moreover, with an increase in nitrogen content, there is a continuous expansion in the cell volume. This also corresponds to the leftward shift of the γ′-Fe₄N diffraction peak in the XRD.

3.5. Structural Stability Analysis of the Fe-Cr-N Series

The total energy of the supercell system obtained from first-principles calculations provides an intuitive representation of the variation in structural energy of the Fe-Cr-N system. In this study, the cohesive energy (E_c) and the formation energy (E_f) were used to measure the thermodynamic stability and the ease of formation of the Fe-Cr-N system structures.

Formation energy refers to the energy released or absorbed when a reaction occurs between stable existing solid-state reactants and products. For exothermic reactions, the formation energy is negative. Cohesive energy refers to the energy released or absorbed when individual atoms combine from their free state to form a crystalline structure. The smaller the absolute value of cohesive energy, the less stable the system.

For a compound with the molecular formula A_xB_yC_n, the calculation formulas for cohesive energy and formation energy are as follows [31,32]:

$$E_f={\displaystyle \frac{1}{x+y+n}}\left(E_{tot}-x{E}_{soild}^A-y{E}_{soild}^B-n{E}_{soild}^C\right)$$

(1)

$$E_c={\displaystyle \frac{1}{x+y+n}}\left(E_{tot}-x{E}_{atom}^A-y{E}_{atom}^B-n{E}_{atom}^C\right)$$

(2)

where E_tot is the total energy of the supercell (eV) calculated by first principles [33,34]; E_solid is the average energy (eV) of a single atom under the condition of stable solid crystal formation from a single substance; E_atom is the energy of a single atom in a free state (eV); and x, y, and n are the number of A, B, and C atoms (where A is Fe, and the range of values for x is 13; B is Cr, and the range of values for y is 3; and C is N, and the range of values for n is 0, 2, 4, 6). The specific energy values required for the calculations are shown in

Table 7. Energy values of individual atoms of Fe, Cr, and N, as well as average atomic energies in solid crystals.

Molecular Formula	Total Energy Etot (eV)
Fesolid	−862.9728
Nsolid	−276.4335
Crsolid	−2400.4393
Featom	−855.8269
Natom	−267.9488
Cratom	−2393.2261

.

Regarding the calculations of binding energy and formation energy in the iron–chromium–nitrogen system, we found that in the series of iron–chromium–nitrogen structures, the total energy of the system decreases as the nitrogen atoms are incorporated. From the energy

Table 8. The energy value of Fe₁₃Cr₃N_n (n = 0, 2, 4, 6).

Molecular Formula	Total Energy Etot (eV)	Formation Energy Ef (eV)	Cohesive Energy Ec (eV)
Fe13Cr3	−18,419.5482	0.0260	−7.1325
Fe13Cr3N2	−18,972.3787	0.0251	−7.2807
Fe13Cr3N4	−19,518.0172	0.3841	−7.0397
Fe13Cr3N6	−20,061.4951	0.7760	−6.7443

system, we can see that the binding energies are negative, indicating that this series of structures can be formed by the combination of free atoms.

As the number of nitrogen atoms increases, the difficulty of binding increases. Looking at the formation energy, in the original α-Fe supercell and the supercell where only one Fe atom is replaced by a Cr atom, the formation energies for systems without nitrogen atoms and with two incorporated nitrogen atoms are negative, indicating good stability of these two structures. The formation energies for four and six incorporated nitrogen atoms are positive, but their values are small, suggesting the possibility of forming metastable states of these structures. In the supercell systems where two to four Fe atoms are replaced by Cr atoms, all the formation energies are positive. However, when the nitrogen content is two atoms, the formation energy decreases, and the absolute value of the binding energy increases significantly, indicating that the supercell with a nitrogen content of two atoms is more stable than the original supercell structure. But looking at the trend, for the same supercell system, the formation energy increases as the number of incorporated nitrogen atoms increases, and nitrideing systems with a lower nitrogen content have better stability. The absolute value of the binding energy gradually decreases as the number of nitrogen atoms increases, indicating that systems with lower nitrogen solubility have better stability. The specific energy calculation values for the relevant unit cells are shown in Table 8.

3.6. Analysis of Fe-Cr-N State Density and Differential Charge Density of Fe-Cr-N

The Fermi level (EF) is the highest energy level occupied by electrons at absolute zero temperature, and many properties of crystals are determined by the distribution of valence electrons near the Fermi level. Two peaks can be observed on both sides of the Fermi level, and the DOS between the two peaks is non-zero. This low-energy DOS region is called a pseudo-gap, which is typically represented by a V-shaped structure [33]. The stability of a system can be judged to some extent by the presence of a pseudo-gap near the Fermi level, or by the magnitude of the electron density of states M(EF) near the Fermi level. The higher the coincidence between the pseudo-gap and the Fermi level, or the lower the electron density of states near the Fermi level, the lower the system energy, indicating a more stable state.

The comparison chart of total density of states for the Fe₁₃Cr₃N_n (n = 0, 2, 4, 6) series of structures is shown in Figure 12. Pseudo-gaps exist near the Fermi level for Fe₁₃Cr₃ systems with different nitrogen contents. It can be seen that the introduction of nitrogen atoms in the system causes a density of states peak at around −16 eV. The Fe₁₃Cr₃ and Fe₁₃Cr₃N₂ systems in the figure show a pseudo-gap that coincides with the Fermi level. By comparison, increasing the nitrogen content causes fluctuations in the electron density near the Fermi level. M(EF) increases when two nitrogen atoms are introduced but starts to decrease when four nitrogen atoms are introduced. Moreover, the pseudo-gap peak shifts away from the Fermi level towards higher energy. This indicates that when only two nitrogen atoms are added to the system, the large lattice distortion reduces the structural symmetry, leading to a decrease in system stability. As the nitrogen content continues to increase, the symmetry of the unit cell partially recovers, but the stability of the system decreases, consistent with the previously calculated formation energy and binding energy results.

The partial density of states for Fe, Cr, and N in the Fe₁₃Cr₃N_n system is shown in Figure 13. The PDOS peaks near the Fermi level for the Fe₁₃Cr₃ alloy appear at around ±1.4 eV, with a peak value of approximately 33 e/eV. For the Fe₁₃Cr₃N₂ alloy, the PDOS peaks near the Fermi level appear at around ±1.3 eV, reaching a peak value of around 30 e/eV. The PDOS peaks near the Fermi level for Fe₁₃Cr₃N₄ appear at around ±2 eV, with a peak value close to 36 e/eV. For the Fe₁₃Cr₃N₆ alloy, the PDOS peaks near the Fermi level appear at around ±2.1 eV, with a peak value of approximately 40 e/eV. The majority of these alloy’s PDOS peaks originate from the 3d orbitals of Fe and Cr atoms. In the Fe₁₃Cr₃N_n alloy, the peak at −72 eV mainly originates from the s orbital of Cr atoms, the peak at −43 eV mainly comes from the p orbital of Cr atoms, and the peak at −16 eV mainly originates from the s orbital of N atoms. The DOS curve at 11eV primarily originates from the p orbitals of Fe and Cr atoms. At −7 eV, there is a hybridization phenomenon between the p orbitals of N atoms and the s orbitals of Fe and Cr atoms, indicating a strong covalent interaction among Fe, Cr, and N atoms. The overlap of DOS near the −7 eV level with the Fermi level for Fe₁₃Cr₃N₄ indicates a relatively stable structure. The narrowing of the DOS width for Fe₁₃Cr₃N₆ suggests a decrease in covalent interaction.

As shown in Figure 14, it can be observed that in the Fe_xCr_yN_n series structures, in series structures such as Fe₁₃Cr₃N_n, there is a strong bonding interaction between Fe and Cr atoms on different crystal planes. In the Fe_xCr_yN_n system with n = 0, Cr atoms gain electrons and carry negative charges, while Fe atoms lose electrons and carry positive charges. After the N atoms infiltrate into the crystal cell, the bonding interaction between Fe and Cr atoms weakens, and the bonding interaction between Cr-N and Fe-N atoms strengthens. When only two N atoms enter the system, Cr atoms are still in a relatively electron-attracting state, while Fe atoms gradually transition from being electron-losing to electron-attracting. As the number of N atoms in the system increases, N becomes the side that is more prone to losing electrons. When six N atoms are infiltrated, Fe atoms in the face-centered position are more likely to gain electrons compared to Cr atoms, carrying a higher negative charge. The analysis of Fe-Cr-N state density and differential charge density of Fe-Cr-N explains the mechanism of surface modification hardening.

This experiment also calculated the elastic properties of the nitride phases of 1Cr17Ni2 steel using first-principles computational methods to further verify the experimental results. The mechanical properties of Fe₁₃Cr₃N_2, γ′-Fe₄N, ε-Fe_2-3N, and CrN were calculated, including bulk modulus (B), shear modulus (G), Young’s modulus (E), Pugh ratio (G/B), Poisson’s ratio (V), and hardness (Hv). According to the generalized Hooke’s law, the stiffness coefficient calculation results and mechanical property calculation results are shown in

Table 9. The calculated elastic constants Cij (GPa) of the phases.

Molecular Formula	C11	C12	C13	C14	C33	C44	C66
Fe13Cr3N2	509.88	152.72	164.36	---	539.83	158.90	107.71
γ′-Fe4N	316.22	134.93	---	63.62	---	---	---
ε-Fe3N	330.22	112.813	139.41	---	280.90	99.93	---
CrN	369.69	167.74	---	17.90	---	---	---

and

Table 10. Calculated results of elastic modulus and B/G ratio of the phases formed by ion nitriding of 1Cr17Ni2 steel.

Molecular Formula	B (GPa)	G (GPa)	E (GPa)	G/B	V	HV (GPa)	H/E	H3/E2
Fe13Cr3N2	280.28	154.22	382.417	0.55	0.28	16.53	0.042	0.029
γ′-Fe4N	195.36	74.43	198.13	0.38	0.33	5.02	0.025	0.003
ε-Fe2-3N	184.94	90.53	235.33	0.48	0.29	9.92	0.042	0.017
CrN	235.06	38.91	110.61	0.16	0.42	1.59	0.014	0.0003

.

As shown in Table 10, the Fe₁₃Cr₃N₂ phase exhibits the highest hardness, reaching up to 16.53 GPa, which is in good agreement with the actual measurement values obtained by Yixue Wang. The Pugh ratio G/B of different nitrided phases in 1Cr17Ni2 steel is less than 0.57, so they all have good toughness and are good ductile phases. At the same time, Poisson’s ratio v indicates that Fe₁₃Cr₃N₂ and ε-Fe_2-3N have strong rigidity and high microhardness, which also matches the phase composition of the high-hardness nitrided surface at 460 °C. The ratio of hardness to Young’s modulus can better display the wear resistance of materials than a single hardness. The higher the value of H/E, the better the wear resistance of the material [35]. The higher the value of H³/E², the lower the probability of plastic deformation. From Table 10, it can be seen that Fe₁₃Cr₃N₂ and ε-Fe_2-3N phases have lower wear rates, which can also be verified by the wear rate calculated in Figure 6. It can be inferred that by adjusting the nitriding temperature and time, a nitrided layer with excellent toughness and hardness can be obtained. This result is also consistent with the conclusion reached by Gonzalez-Moran in this article that nitrogen-expanded martensite has excellent wear resistance and is a rigid elastic solid with high elastic properties and resistance to plastic deformation [36,37,38,39,40].

4. Conclusions

This article focuses on the study of plasma nitriding of 1Cr17Ni2 steel at different temperatures and times. Combining first-principles calculations, the effects of temperature, time, and nitrogen-to-hydrogen ratio on the nitriding of 1Cr17Ni2 stainless steel using low-temperature and low-nitrogen hydrogen flow ratio were investigated. The specific findings are summarized as follows:

(1)

After plasma-nitriding treatment, a clear diffusion layer is formed between the surface layer and the matrix, with a thickness ranging from 89 μm to 110 μm. With an increase in nitriding temperature and time, the depth and hardness of the nitrided layer both increase to a certain extent, with hardness reaching up to 1400 Hv0.1. At the same time, the wear rate gradually decreases, with the wear rate decreasing by an order of magnitude compared to the original sample.

(2)

After nitriding at different temperatures, nitrides and solid solutions are formed on the surface, with the main phases being α′_N, ε-Fe_2-3N, γ′-Fe₄N, and CrN, etc. With the increase in temperature, the surface ε-Fe_2-3N content gradually increases. In summary, the sample nitrided at 460 degrees Celsius for 16 h has the best surface friction and hardness properties.

(3)

The structure of Fe₁₃Cr₃N_n (n = 0, 2, 4, 6) expands due to the addition of N atoms, and the total energy of the structure decreases with the increase in nitrogen content, and the binding energy is negative. The absolute value of the binding energy decreases with the increase in N content. The formation energy structure stability decreases with the increase in nitrogen content and tends to be metastable. The structural expansion is consistent with the XRD diffraction peak shift results.

(4)

The electronic density of states near the Fermi level of the Fe₁₃Cr₃N_n (n = 0, 2, 4, 6) structure is mainly derived from the 3d electrons of the metal atoms, and is affected by the concentration of N atoms, leading to severe orbital hybridization and a strong bond between metal and non-metal atoms. The addition of N is beneficial to the improvement of hardness, which is consistent with the experimentally measured microhardness values.

(5)

Through the calculation of the elastic modulus of the nitrided phase of 1Cr17Ni2 steel, it is shown that Fe₁₃Cr₃N₂ and ε-Fe_2-3N have strong rigidity and high microhardness, as well as good wear resistance, and have a low probability of plastic deformation, which is consistent with experimental results.