Phase Transformation of δ→σ in 24Cr-14Ni Stainless Steels Under Nitrogen Atmospheric Aging Treatment

Abstract

This work investigates the δ→σ phase transformation in 24Cr-14Ni stainless steel, specifically focusing on how heat treatment temperature, time, and nitrogen atmospheric ratios (NARs) dictate microstructural stability. Understanding the formation mechanism of the σ phase is critical for alloy design, as it remains the most detrimental intermetallic phase in austenitic steels. The results show that δ-ferrite decomposes into σ and secondary γ₂ phases through a cellular eutectoid reaction driven by elemental diffusion. Higher Cr and Si levels stabilize δ-ferrite and promote σ phase precipitation, accelerating the δ→σ transformation. Furthermore, the σ phase exhibits the highest Cr_eq/Ni_eq ratio among all constituent phases. The σ phase fraction is highest with 0 vol.% NAR during 1–8 h of aging and decreases progressively with increasing NARs (20–40 vol.%), reaching a minimum at 80 vol.% under all conditions. JMAK model analysis (n ≈ 0.531, k ≈ 0.905) indicates that σ phase precipitation at 800 °C with 40 vol.% NAR is governed by diffusion-controlled growth with early nucleation site saturation in δ-ferrite. Consequently, rapid σ phase formation occurs, reaching ~21.3% within 1 h. This behavior is attributed to the instability of δ-ferrite and the faster diffusion of Cr and Si compared to austenite.

1. Introduction

Austenitic stainless steels in the Fe-Cr-Ni system continue to play a critical role in advanced engineering applications due to their excellent corrosion resistance, mechanical performance, and high-temperature stability [1,2,3,4,5,6]. However, the alloy design of austenitic stainless steels also leads to the retention of δ-ferrite during solidification and processing, which introduces significant complexity into their phase transformation behavior during subsequent thermal exposure [7,8,9].

Recent studies have demonstrated that δ-ferrite is metastable at intermediate temperatures and undergoes decomposition during aging through eutectoid-like reactions, forming the σ phase and secondary austenite (γ₂) [10,11,12,13]. This transformation is strongly dependent on diffusion-controlled processes, chemical partitioning, and local compositional heterogeneities [14,15,16].

The σ phase remains one of the most critical secondary phases in stainless steels due to its detrimental effects on material performance. Recent investigations have confirmed that the σ phase preferentially nucleates at δ/γ interfaces and δ-ferrite regions, where elemental segregation—particularly of chromium and molybdenum—enhances nucleation kinetics [17,18,19,20,21]. Furthermore, systematic studies have shown that σ phase precipitation is highly sensitive to aging temperature and alloy composition, typically occurring within 600–1000 °C and accelerating under conditions that promote elemental diffusion [18,19].

Nitrogen has emerged as a key alloying element in modern stainless steels, particularly in high-performance and high-strength applications. It acts as a strong austenite stabilizer and contributes to both solid solution strengthening and improved corrosion resistance [22,23]. Recent studies have highlighted that nitrogen not only suppresses δ-ferrite formation but also alters phase transformation pathways by influencing elemental partitioning and diffusion kinetics [24,25,26]. In nitrogen-containing environments, additional complexity arises due to possible nitride formation and interactions with chromium, which may either retard or promote σ phase precipitation depending on local thermodynamic conditions [27,28,29].

The evolution of microstructure during aging has a direct and significant impact on mechanical properties and corrosion behavior. Recent experimental studies have shown that σ phase precipitation leads to increased hardness but severely reduces ductility and toughness due to its brittle nature [30,31,32]. Moreover, chromium depletion associated with σ phase formation results in a marked deterioration in corrosion resistance, particularly in pitting and intergranular corrosion environments [33,34,35]. These degradation mechanisms are closely linked to the kinetics of phase transformation and the spatial distribution of secondary phases within the microstructure [36].

Previous studies on nitrogen-containing stainless steels have mainly focused on duplex stainless steels [37,38,39], in which nitrogen is typically introduced during alloying at the smelting stage. In this work, nitrogen is introduced through heat treatment under a controlled nitrogen atmosphere. Studies on 24Cr-14Ni stainless steel are relatively limited, and investigations under nitrogen atmospheric conditions are even less common. This study therefore aims to provide further understanding of its phase transformation behavior under such conditions.

This study aims to systematically elucidate the δ→σ transformation behavior in 24Cr-14Ni stainless steel under varying nitrogen atmospheric ratios, aging temperatures, and times by integrating microstructural characterization with JMAK kinetic modeling. The innovation of this study lies in investigating the relationship between σ precipitation and phase transformation kinetics, providing a foundation for understanding the σ phase precipitation mechanism through nitrogen atmospheric aging heat treatment. This comprehensive understanding directly supports the development of optimized heat treatment and welding strategies to improve engineering performance.

2. Experimental Procedures

The test material used in this research was a 24Cr-14Ni stainless steel billet. The chemical composition of this steel is shown in

Table 1. Chemical compositions of test materials (wt.%).

Materials	Element (wt.%)
24Cr-14Ni Stainless Steel	Cr	Ni	C	Si	Mn	Mo	Cu	P	S	Fe
	24.69	13.34	0.03	0.72	1.69	0.14	0.20	0.01	0.01	Bal.

. The test material was sampled from a billet 10 mm × 10 mm in size. The billet was heat-treated in a tubular furnace at different aging temperatures of 600 °C, 700 °C, 800 °C, 900 °C, 1000 °C, and 1200 °C and at different aging times of 1 h, 2 h, 4 h, and 8 h. The atmosphere was N₂ with volume ratios of 0 vol.%, 20 vol.%, 40 vol.%, and 80 vol.% relative to the air. In this study, the volume percentages of different nitrogen atmospheres relative to air (N₂/Air) are abbreviated and shortened as NARs (nitrogen atmospheric ratios). The hardness of specimens under different aging conditions was tested using a Rockwell hardness tester (HRB, Mitutoyo, Tokyo, Japan). A 1/16″ hard steel ball indenter was used to measure the Rockwell hardness value to investigate the changes in hardness value of 24Cr-14Ni stainless steel under different proportions of nitrogen atmospheric ratios after heat treatment.

After the aging treatment, the samples were quenched in water, ground with SiC paper, and polished with Al₂O₃ powder paste. The Groesback etchant was prepared using 4 g of KMnO₄ plus 4 g of NaOH and 100 mL of deionized water for the etching. The phase fraction of the δ-ferrite, σ phase, and γ-phase was analyzed with Thermo-Calc Software (Version 2026a, Thermo-Calc Software AB, Solna, Sweden) and an image analyzer (Media Cybernetics Image-Pro plus 6.0).

Microstructural observations of the δ-ferrite, σ phase, γ-phase, and γ₂-phase were carried out for the heat-treated samples using an optical microscope (OM, ZEISS Axioskop 2 MAT, Carl Zeiss, Göttingen, Germany). An electron probe microanalyzer (EPMA, JXA-8900R, JEOL Ltd., Akishima, Tokyo) plus the wavelength dispersive spectrometer (WDS) helped the analysis of transformation behavior of the δ-ferrite, σ phase, γ-phase, and γ₂-phase and their chemical compositions. The schematic diagram of the experimental procedure in this study is shown in Figure 1.

3. Results and Discussion

3.1. Effect of NARs on the δ→σ Phase Transformation

Nitrogen is a strong austenitic stabilizer and plays a significant role in determining the phase stability and transformation behavior of duplex microstructures. To discuss the influence of NARs on the evolution of δ-ferrite and σ phase, the variables of temperature and aging time must be carefully controlled. If the aging temperature is excessively high (e.g., above 800 °C and close to the solution treatment temperature), δ-ferrite may already decompose and the δ→γ transformation may approach completion. Similarly, prolonged aging times (>4–8 h) can lead to morphological stabilization of ferrite from dendritic to spherical structures. Therefore, appropriate aging conditions are essential for investigating the effect of nitrogen atmosphere on phase transformation behavior.

The microstructural evolution of δ-ferrite and σ phase aged at 900 °C for 1 h under different NARs is shown in Figure 2a–d. Under a nitrogen-free atmosphere (0 vol.% N₂), a significant amount of dendritic δ-ferrite can be observed, as indicated in Area 1 of Figure 2a. Limited decomposition of δ-ferrite is also present, as shown in Area 2, while numerous σ phase precipitates nucleate within the δ-ferrite matrix. Under this condition, the relatively stable δ-ferrite provides favorable nucleation sites for σ phase formation.

When the NAR increases to 20 vol.% N₂ (Figure 2b), the dendritic morphology of δ-ferrite remains relatively intact. At this stage, elemental partitioning and interdiffusion of Cr and Ni occur between the δ and γ phases. The diffusion of Cr toward the γ-phase corresponds to the δ→γ transformation, whereas Ni diffusion toward δ-ferrite corresponds to the γ→δ transformation. These diffusion processes promote compositional redistribution and gradually destabilize δ-ferrite, leading to its partial decomposition.

With a further increase of NAR to 40 vol.% N₂ (Figure 2c), the interdiffusion-driven decomposition behavior becomes more pronounced. In addition to the δ→γ transformations, the δ→σ phase transformation occurs. The increase in nitrogen atmospheric ratio accelerates the kinetics of these phase transformations, resulting in enhanced decomposition of δ-ferrite.

When the NAR reaches 80 vol.% N₂, the phase transformation processes gradually approach completion. As shown in Figure 2d, the morphology of δ-ferrite evolves into fine ribbon-like and dispersed spherical structures. The increase in nitrogen significantly accelerates the decomposition of δ-ferrite and enhances the δ→γ transformation behavior. Meanwhile, the precipitation of δ-ferrite is suppressed, thereby reducing the probability of δ→σ transformation and consequently decreasing both the amount of σ phase precipitation and the overall transformation rate.

Overall, increasing the nitrogen atmospheric ratio modifies the elemental partitioning and interdiffusion behavior between δ and γ phases, which accelerates the decomposition of δ-ferrite while suppressing the nucleation and growth of the σ phase.

To further clarify the decreasing trend and decomposition of δ-ferrite at 900 °C, thermodynamic simulations were performed using Thermo-Calc over a temperature range of 400–1600 °C. The calculated volume fractions of α, δ, σ, and γ phases as a function of temperature are shown in Figure 3.

The simulation results indicate that the volume fraction of δ-ferrite decreases around 900 °C, while the fraction of the σ phase correspondingly decreases. This behavior suggests that, at this temperature range, the thermodynamic stability of δ-ferrite becomes relatively higher, leading to the partial dissolution or suppression of the σ phase.

As the temperature further increases beyond 1200 °C, the fraction of δ-ferrite gradually decreases. At these higher temperatures, the σ phase is nearly absent, indicating that the σ phase is thermodynamically unstable in the high-temperature region. At elevated temperatures above a critical range (typically 950–1050 °C), the σ phase becomes thermodynamically unstable and redissolves into the austenite. As a result, it is not present in the high-temperature region under equilibrium conditions.

Overall, the thermodynamic calculations reveal that the phase stability of δ-ferrite and σ phase is strongly temperature dependent, and the decrease in δ-ferrite fraction near 900 °C is consistent with the observed microstructural evolution.

3.2. The Mechanism of σ Phase Precipitation

Figure 4 shows the morphological evolution of the σ phase in 24Cr-14Ni stainless steel aged at 800 °C under a 40 vol.% N₂ under different aging times. In the microstructure, the black particles correspond to δ-ferrite, while the reddish-brown particles represent σ phase. In general, δ-ferrite forms a chromium-rich region relative to the austenitic matrix. Because δ-ferrite has a BCC crystal structure, which facilitates the diffusion of Cr, it provides a favorable environment for the precipitation of σ phase that requires a high Cr concentration. As a result, σ phase preferentially nucleates and precipitates along the δ-ferrite particles.

The influence of aging time on the morphology of σ phase was also investigated. As shown in Figure 4a, when the aging time is 1 h, the δ-ferrite exhibits a network-like dendritic morphology (Area 1) within which numerous σ phase precipitates can be observed. When the aging time increases to 2 h, δ-ferrite begins to undergo outward diffusion and gradual decomposition, as shown in Figure 4b. As the δ-ferrite decomposes, the σ phase that initially nucleated within the δ-ferrite region also tends to redistribute toward the surrounding austenitic matrix. Consequently, metallographic observations reveal that σ phase precipitates remain closely associated with the δ-ferrite regions, which serve as Cr-enriched zones favorable for σ phase nucleation.

With further extension of the aging time to 4 h, the original network-like δ-ferrite structure largely decomposes and diffuses into the austenitic matrix, as shown in Figure 4c. Correspondingly, the σ phase precipitates become more dispersed throughout the microstructure. When the aging time reaches 8 h, most of the δ-ferrite has dissolved into the austenite phase, as shown in Figure 4d. As a result, the probability of σ phase nucleation within δ-ferrite is significantly reduced, leading to a noticeable decrease in the amount of σ phase precipitation.

Further examination of Areas 2 and 3 is presented in the magnified images shown in Figure 4e,f, corresponding to Figure 4c,d. The results indicate that σ phase precipitation proceeds via a cellular σ + γ₂ eutectoid decomposition mechanism. After an aging time of 8 h, σ phase precipitation becomes less pronounced, which can be attributed to an increased δ→γ phase transformation rate, thereby promoting a more extensive decomposition process. This phase transformation, specifically the cellular σ + γ₂ eutectoid decomposition, effectively reduces the atomic diffusion distance.

3.3. Effect of Aging Temperatures on the Enrichment Elements of δ, σ, and γ Under NARs

Using the mapping analysis of an electronic probe micro-analyzer, the elemental enrichment behavior of δ-ferrite, σ phase, and γ-phase was investigated under various temperatures, while maintaining a fixed nitrogen atmospheric ratio and holding time (40 vol.% N₂, 4 h). In addition, concentration distribution analyses of Cr, Ni, Si, and Fe were performed. Figure 5 and Figure 6 illustrate the enrichment characteristics of these phases under the specified nitrogen atmospheric ratio (NAR) and duration.

At an aging temperature of 600 °C for 4 h, chromium enrichment was observed in δ-ferrite; however, no σ phase precipitation was detected. This does not imply that σ phase formation is impossible at 600 °C; rather, the probability of σ phase nucleation within δ-ferrite is relatively low, and the overall precipitation amount remains limited. This behavior can be attributed to the insufficient driving force for phase transformation at this temperature, as the eutectoid decomposition reaction is not sufficiently pronounced to promote the transformation of δ-ferrite into the σ phase.

Furthermore, Si-enriched regions were predominantly localized within δ-ferrite, indicating that Si promotes the stabilization and formation of δ-ferrite. In contrast, Ni enrichment was primarily observed in the γ-phase, with minimal Ni detected in δ-ferrite. This observation confirms that the γ-phase is a Ni-rich and Cr-depleted phase.

Because no significant eutectoid decomposition occurs at 600 °C, δ-ferrite does not substantially dissolve into the γ-phase. As a result, the γ-phase retains relatively higher concentrations of Ni and Fe without being diluted by δ-ferrite transformation.

Figure 6 shows the microstructure at 700 °C under a fixed NAR (40 vol.% N₂, 4 h). At this temperature, σ phase nucleation is clearly observed within the δ-ferrite matrix. The backscattered electron image (BEI) reveals two contrast regions within δ-ferrite (dark and gray). Cr mapping indicates that the gray regions are enriched in Cr, whereas the dark regions exhibit lower Cr content, identifying them as σ phase and δ-ferrite, respectively. This result confirms that the σ phase is richer in Cr and preferentially precipitates within δ-ferrite. As δ-ferrite is a Cr-rich phase, it provides favorable sites for heterogeneous σ phase nucleation, accompanied by the formation of surrounding Cr-depleted zones.

Si mapping shows a reduced enrichment level compared to that at 600 °C, due to partial σ phase precipitation within δ-ferrite. Since Si is a δ-ferrite stabilizer, it is more strongly enriched in δ-ferrite than in the σ phase. In addition, Si promotes eutectoid decomposition, thereby accelerating the δ→σ transformation. However, under a 40 vol.% N₂ atmosphere, the δ→σ transformation is suppressed, while the δ→γ transformation is promoted. Ni and Fe mappings reveal that their enrichment in the γ-phase at 700 °C is less pronounced than at 600 °C. This is attributed to eutectoid decomposition, where dispersed δ-ferrite and σ phase partially dissolve into the γ-phase, reducing the Fe and Ni concentrations in the matrix.

3.4. Quantitative Analysis of δ, σ, and γ Phases Under Different NARs

To clarify the effect of aging temperature on the elemental distributions of the δ, σ, and γ phases, the nitrogen atmospheric ratio and aging time were fixed at 40 vol.% N₂ and 4 h, respectively. The variations in elemental compositions of δ, σ, and γ phases at different temperatures (800 °C, 1000 °C, and 1200 °C) and their relationships with phase transformations are presented in Figure 7.

Figure 7a shows the WDS quantitative analysis of δ, σ, γ, and γ₂ phases, with detailed results summarized in

Table 2. WDS quantitative analysis of δ, σ, γ, and γ₂ phases in 24Cr-14Ni stainless steel at 800 °C (4 h, 40 vol.% N₂).

Point	Element (wt.%)	Cr	Ni	Si	Mo	Mn	C	Cu	Fe	Creq/Nieq
	Phase
1	δ	34.71	5.11	0.57	0.35	1.35	0.07	0.01	57.84	4.39
2	γ	19.88	14.23	0.39	0.09	1.62	0.06	0.26	63.47	1.20
3	σ	40.60	5.10	0.31	0.41	1.24	0.06	0.01	52.66	5.62
4	γ2	22.12	14.20	0.32	0.09	1.61	0.05	0.23	63.36	1.35

. The Cr content in δ-ferrite is approximately 34.7 wt.%, whereas that in the σ phase reaches about 40.6 wt.%, indicating that Cr-enriched σ phase is likely to form under aging at 800 °C. The precipitation of σ phase from δ-ferrite leads to Cr depletion in δ-ferrite. The γ-phase contains approximately 19.8 wt.% Ni, indicating a Ni-rich and Cr-depleted phase, while exhibiting a higher Fe content than both δ and σ phases. These findings are consistent with the elemental mapping results. In terms of Si distribution, δ-ferrite exhibits a higher Si content than σ and γ phases. Combined with the WDS analysis, this confirms that Si plays a more direct and effective role in stabilizing δ-ferrite compared to σ phase. A higher Si content suppresses the δ→γ transformation rate, thereby reducing the δ→γ transformation kinetics and promoting the δ→σ transformation. Regarding Mo, the σ phase contains a higher Mo content than δ-ferrite, further confirming that in 24Cr-14Ni stainless steel, the σ phase is enriched in both Cr and Mo, whereas δ-ferrite is enriched in Cr and Si. Additionally, Cu and Mn, known austenite stabilizers, are more concentrated in the γ-phase than in δ and σ phases. The chemical composition of γ₂ is similar to that of γ; however, γ₂ is formed via eutectoid decomposition of δ-ferrite, and therefore contains slightly higher Cr content than γ.

Figure 7b presents the WDS quantitative analysis of δ, σ, and γ phases at 1000 °C, as summarized in

Table 3. WDS quantitative analysis of δ and γ phases in 24Cr-14Ni stainless steel at 1000 °C (4 h, 40 vol.% N₂).

Point	Element (wt.%)	Cr	Ni	Si	Mo	Mn	C	Cu	Fe	Creq/Nieq
	Phase
1	δ	31.20	7.14	0.87	0.15	1.70	0.56	0.10	57.67	1.52
2	γ	22.85	12.66	0.75	0.07	1.85	0.69	0.15	62.82	1.01

. At this temperature, δ-ferrite is in a decomposed state, and the δ→γ transformation is more pronounced than the δ→σ transformation. Consequently, σ phase becomes difficult to observe near the solution treatment temperature, as most δ-ferrite has dissolved into the γ matrix. The Cr content in δ-ferrite is approximately 31.2 wt.%, slightly lower than that at 800 °C. This decrease is attributed to the dissolution of δ-ferrite into the matrix at 1000 °C. Although higher Cr content at 800 °C stabilizes δ-ferrite and promotes δ→σ transformation, the extent of Cr depletion caused by δ→γ transformation at 1000 °C is more significant, resulting in an overall reduction in Cr content. Furthermore, the γ-phase exhibits higher Ni content compared to that at 800 °C, due to the completion of δ→γ transformation, leading to a fully austenitic structure.

Figure 7c shows the WDS quantitative analysis at 1200 °C, with results listed in

Table 4. WDS quantitative analysis of δ and γ phases in 24Cr-14Ni stainless steel at 1200 °C (4h, 40 vol.% N₂).

Point	Element (wt.%)	Cr	Ni	Si	Mo	Mn	C	Cu	Fe	Creq/Nieq
	Phase
1	δ	34.40	5.13	1.05	0.19	1.01	0.94	0.01	57.25	1.33
2	γ	23.80	12.60	0.79	0.08	1.53	0.79	0.25	60.76	0.80

. The Cr content is higher than that at 1000 °C, which can be attributed to the increased Si content at 1200 °C. The higher Si content enhances the stability of δ-ferrite, and since Cr is a key indicator of δ-ferrite stability, Si addition helps maintain Cr at a stable level within δ-ferrite. It can therefore be inferred that 1200 °C is close to the solution treatment temperature, at which δ-ferrite becomes a stable phase. As a stable phase, δ-ferrite no longer undergoes eutectoid decomposition, and thus both δ→γ and δ→σ phase transformations are effectively suppressed at this temperature.

3.5. Effect of δ→σ Phase Transformation on Hardness at Aging Temperatures and NARs

Following the WDS quantitative analysis presented in Section 3.4, hardness measurements were conducted to further evaluate the effect of δ→σ phase transformation on mechanical properties. Under a fixed nitrogen atmospheric ratio and aging time (40 vol.% N₂, 4 h), the hardness evolution of 24Cr-14Ni stainless steel at different temperatures (800 °C, 1000 °C, and 1200 °C) is shown in Figure 8a.

The results indicate that the hardness decreases from HRB 84 at 800 °C to HRB 82 at 1000 °C, and further to HRB 80 at 1200 °C. As discussed in Section 3.2, temperature significantly influences the initial morphology and stability of δ-ferrite. At 800 °C, pronounced δ→σ transformation occurs, with substantial σ phase precipitation within δ-ferrite, leading to increased hardness.

At 1000 °C, δ-ferrite exhibits a dispersed spheroidized microstructure, with most δ-ferrite dissolving into the matrix. At this stage, δ→γ transformation becomes dominant over δ→σ transformation, resulting in reduced δ-ferrite content and limited σ phase formation, thereby lowering the hardness. At 1200 °C, near the solution treatment temperature, δ→γ transformation is nearly complete and δ-ferrite becomes thermodynamically stable without further phase transformation. Consequently, the absence of σ phase precipitation leads to the lowest hardness observed.

Figure 8b shows the hardness at 800 °C under different NARs. This experiment was carried out to examine the effect of the δ→σ transformation on hardness. The hardness is relatively high (HRB 89) without nitrogen. As the NAR increases to 20–40 vol.%, the hardness gradually decreases, which is attributed to the suppression of σ phase precipitation. At 80 vol.% NAR, the hardness further decreases to HRB 80.

3.6. Effect of Nitrogen Atmospheric Aging on the δ, σ, and γ Phases and the Chromium-Nickel Equivalent Ratio (Cr_eq/Ni_eq Ratio)

To predict the solidification mode, a quantitative compositional analysis was conducted using a wavelength dispersive spectrometer (WDS) equipped with an electron probe micro-analyzer. The Cr and Ni equivalent ratios (Cr_eq/Ni_eq) were calculated based on the measured elemental compositions. Among the available methods, the modified formulation proposed by Hammar and Svensson [40] is the most widely accepted for determining the Cr_eq/Ni_eq ratio which is illustrated by Equations (1) and (2):

Cr_eq = %Cr + 1.37 × (%Mo) + 1.5 × (%Si) + 2 × (%Nb) + 3 × (%Ti)

(1)

Ni_eq = %Ni + 0.31 × (%Mn) + 22 × (%C) + 14.2 × (%N) + %Cu

(2)

Accordingly, the Cr_eq/Ni_eq ratios of 24Cr-14Ni stainless steel were evaluated at aging temperatures of 800 °C, 1000 °C, and 1200 °C under a fixed nitrogen atmospheric ratio and holding time (40 vol.% N₂, 4 h).

As shown in Figure 9, the σ phase exhibits a relatively high Cr_eq/Ni_eq ratio at 800 °C, whereas at 1000 °C and 1200 °C, the ratio approaches near-zero values with a relatively flat distribution. This behavior indicates that the σ phase is enriched in chromium and molybdenum, resulting in a higher Cr_eq/Ni_eq ratio. When the Cr_eq/Ni_eq ratio exceeds 1.95, the sogen atlidification mode is fully ferrite, suggesting that the σ phase preferentially precipitates from δ-ferrite regions with elevated Cr_eq/Ni_eq ratios. At 800 °C, the δ-ferrite exhibits a lower Cr_eq/Ni_eq ratio than the σ phase, which can be attributed to chromium depletion in δ-ferrite during σ phase precipitation.

Overall, 800 °C corresponds to the temperature range where eutectoid decomposition becomes pronounced, marking the onset of the δ→σ transformation. At this stage, both δ and σ phases retain relatively high Cr_eq/Ni_eq ratios. In contrast, at 1000 °C and 1200 °C, the δ→γ transformation becomes dominant, and both δ and σ phases progressively diffuse into the austenitic matrix, leading to a reduction in the Cr_eq/Ni_eq ratio. When the ratio decreases below 1.25, the solidification mode shifts to fully austenitic. Therefore, for the γ-phase at aging temperatures of 800 °C, 1000 °C, and 1200 °C, the Cr_eq/Ni_eq ratio remains below 1.25, confirming that the γ-phase is a nickel-rich and chromium-depleted phase.

3.7. Cr_eq/Ni_eq Ratios of δ, σ, and γ Phases Under Different NARs

The elemental analyzed results of δ-ferrite, σ phase, and γ-phase under different NARs (0, 20, 40, 60, and 80 vol.% N₂) were analyzed at 800 °C for 4 h. The influence of the NAR on the chromium-nickel equivalent ratio (Cr_eq/Ni_eq) was further evaluated, as summarized in Figure 10.

Both δ-ferrite and σ phase exhibit relatively high Cr_eq/Ni_eq ratios as shown in Figure 9 under the condition of 800 °C for 4 h at 0 vol.% N₂. This is attributed to the absence of nitrogen, resulting in no suppression of δ and σ phase precipitation. In contrast, the γ-phase shows a lower Cr_eq/Ni_eq ratio due to its Ni-rich and Cr-depleted phase, making it the phase with the lowest ratio among the three.

From 20 to 40 vol.% N₂, the Cr_eq/Ni_eq ratios of δ-ferrite and σ phase decrease compared to those at 0 vol.% N₂, indicating a more pronounced suppression of δ and σ phase precipitation. The γ-phase still exhibits the lowest Cr_eq/Ni_eq ratio owing to its inherent compositional characteristics.

When the N₂/Air ratio increases to 60 vol.%, the Cr_eq/Ni_eq ratios of δ-ferrite and σ phase further decrease relative to those at 0 and 40 vol.% N₂, suggesting an enhanced inhibitory effect on δ and σ phase formation. Additionally, the Cr_eq/Ni_eq ratio of the γ-phase also decreases. This reduction is likely associated with increased austenitization induced by the higher nitrogen content, which progressively lowers the overall Cr_eq/Ni_eq ratio.

Finally, the lowest Cr_eq/Ni_eq is obtained at 80 vol.% N₂ among all conditions, indicating that this nitrogen content most effectively suppresses the precipitation of δ and σ phases during aging. Under this condition, the γ phase also exhibits its minimum Cr_eq/Ni_eq ratio, corresponding to the most pronounced austenitization and resulting in the overall lowest Cr_eq/Ni_eq. Nevertheless, σ phase precipitation can still occur at 80 vol.% N₂, as it retains a relatively high Cr_eq/Ni_eq ratio (4.78).

3.8. Phase Transformation Kinetics of δ→σ Under Different NARs

Figure 11 presents the σ phase fraction in 24Cr-14Ni stainless steel aged at 800 °C under N₂/Air ratios ranging from 0 to 80 vol.%. The highest σ phase fraction is observed without a nitrogen atmospheric ratio (0 vol.% NAR) over aging times of 1–8 h. With increasing NAR (20–40 vol.%), the σ phase fraction gradually decreases, reaching its lowest value at 80 vol.% among all conditions.

To further examine the δ→σ transformation behavior, the precipitation kinetics were evaluated using the Johnson–Mehl–Avrami–Kolmogorov (JMAK) model (Equation (3)) [41,42], which describes the σ phase fraction (f) as a function of aging time (t), where k is the rate constant and n is the Avrami exponent. The analysis was focused on the condition of 800 °C with 40 vol.% NAR, as this condition exhibits a relatively higher Cr_eq/Ni_eq ratio (Figure 9).

f = 1 − exp(−ktⁿ)

(3)

The linear fitting results of precipitation kinetics of σ phase in 24Cr-14Ni stainless steels at 800 °C with 40 vol.% NAR with the JMAK model are shown in Figure 12a,b. After linear fitting, the Avrami exponent (n) and rate constant (k) are obtained as n = 0.531 and k = 0.905, respectively. This means that the σ phase nucleates precipitates and grows in δ-ferrite. The growth process of σ phase is controlled by atomic diffusion when the n value is close to 0.5. The nucleation sites of the σ phase were already saturated in the early stages of the phase transformation. Therefore, the σ phase forms rapidly, reaching a fraction of 21.3% within 1 h when the rate constant (k) is 0.905. This is because δ-ferrite is an unstable phase, and the diffusion rates of Cr and Si within the δ-ferrite are much faster than those of austenite, causing the σ phase to rapidly form at 800 °C. This also indicates that Si promotes σ phase precipitation, as evidenced by the EMPA mapping results shown in Figure 5 and Figure 6. The growth mode with n = 0.531 is one-dimensional growth. The σ phase does not grow into a spherical shape but rather develops along a specific “line”. In 24Cr-14Ni stainless steel billets, this line is usually a dendrite boundary or a dislocation line. The σ phase precipitates along the remaining δ-ferrite, eventually forming a continuous or semi-continuous network structure at the grain boundaries. This result confirms the microstructural observation (Network σ phase) of region 1 in Figure 4a in Section 3.2. However, the δ-ferrite in the 24Cr-14Ni stainless steel billet is a continuous network structure. As long as the σ phase precipitates along the edges of these networks, it will form a continuous brittle path. This result implies that billets kept at 800 °C are prone to cracking during subsequent processing. The detailed kinetic parameters and JMAK model calculations for the σ phase precipitation are summarized in

Table 5. Kinetic parameters and precipitation data of σ phase in 24Cr-14Ni stainless steels at 800 °C.

Time t (h)	σ Phase Fraction (%)	f	ln(t)	1 − f	ln(1 − f)	−ln(1 − f)	ln[−ln(1 − f)]	Remarks
1	21.3	0.213	0.000	0.787	−0.239	0.239	−1.433	Initial stage of σ precipitation
2	24.6	0.246	0.693	0.754	−0.282	0.282	−1.266	Gradual increase in σ fraction
4	30.1	0.301	1.386	0.699	−0.358	0.358	−1.028	Accelerated transformation stage
8	32.7	0.327	2.079	0.673	−0.396	0.396	−0.927	Transformation approaching saturation

Notes: f represents the transformation fraction of the σ phase. The kinetic analysis is based on the Johnson–Mehl–Avrami (JMAK) model, expressed as: f = 1 − exp(−ktⁿ), where k is the kinetic rate constant and n is the Avrami exponent. The linear relationship between ln[−ln(1 − f)] and ln(t) indicates that the σ phase transformation follows JMAK kinetics. The fitted kinetic parameters are n = 0.531 and k = 0.905.

.

4. Conclusions

The phase transformation of δ→σ in 24Cr-14Ni stainless steel under various aging temperatures, aging times, and N₂/Air ratios (NARs) was investigated. The main findings of this study can be summarized as follows:

(1)

As the aging time increased from 1 to 8 h, the morphology of δ-ferrite gradually transformed from dendritic to globular and decomposed progressively.

(2)

Significant σ phase precipitation was observed at 800 °C, whereas it was largely suppressed at temperatures above 1000 °C.

(3)

The eutectoid decomposition of δ into δ + γ₂ was most pronounced at 800 °C with 40 vol.% NAR.

(4)

Si promotes the δ→σ phase transformation during aging at 700–800 °C due to its enrichment in δ-ferrite.

(5)

At 80 vol.% NAR, σ phase precipitation was retarded at 800 °C after 4 h of aging, which is associated with a relatively low Cr_eq/Ni_eq ratio (4.78).

(6)

The JMAK analysis of σ phase precipitation at 800 °C (40 vol.% NAR) yielded an Avrami exponent (n) of 0.531 and a rate constant (k) of 0.905, indicating a site-saturated nucleation mechanism with diffusion-controlled growth. The σ phase preferentially nucleates within δ-ferrite and grows along one-dimensional paths, such as dendrite boundaries or dislocation lines, leading to the formation of a network-type σ structure.

(7)

The relatively high kinetic constant (k = 0.905) demonstrates that σ phase precipitation proceeds rapidly at 800 °C, reaching 21.3% within 1 h due to the fast diffusion of Cr and Si in δ-ferrite. The resulting continuous or semi-continuous σ network promotes the formation of brittle paths, implying that billets held at 800 °C are highly susceptible to cracking during subsequent processing.