# Overview of Intermetallic Sigma (σ) Phase Precipitation in Stainless Steels

Authors: Chih-Chun Hsieh; Weite Wu
Journal: ISRN Metallurgy
 (2012)

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## Abstract

Theσ phase which exists in various series of stainless steels is a significant subject in steels science and engineering. The precipitation of the σ phase is also a widely discussed aspect of the science and technology of stainless steels. The microstructural variation, precipitation mechanism, prediction method, and effects of properties of σ phase are also of importance in academic discussions. In the first section, a brief introduction to the development and the precipitation characteristics (including morphologies and precipitation sites) of σ phase in stainless steels is presented. In the second section, the properties effect, prediction method, processing effect, elemental addition, retardation method and Thermo-Calc simulation of the σ phase in stainless steels are highlighted.


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## Body

## 1. Motivation

The precipitation of theσ phase, which is often observed in various series of stainless steels, is one of the main reasons for the deterioration of stainless steels’ properties, for example, mechanical property, corrosion resistance, and weldability. The σ phase can be precipitated under an elevated temperature environment, for example, casting, rolling, welding, forging, and aging. It is difficult to prevent the precipitation of the σ phase when the Cr content is above a certain level (above 20 wt.%) in stainless steels. The addition of a strong ferrite stabilizer into the stainless steels (Cr, Si, or Mo) rapidly leads to the formation of the σ phase. This means that the transformation from δ-ferrite to the σ phase can be accelerated when the Cr, Si, or Mo diffuse efficiently in δ-ferrite. Hence, understanding the mechanism of the δ→σ phase transformation is crucial to the prediction and control of stainless steels’ properties. This review paper presents a comprehensive overview of the precipitation of the σ phase in stainless steels, and it is hoped that it will result in some scientific contributions in the materials science and engineering of stainless steels.


## 2. Review of Sigma Phase (σ)

### 2.1. Development Progress of theσ Phase

(1)
In 1907, Treitschke and Tammann found that theσ phase in the Fe-Cr binary system was an intermetallic compound of 30 wt.% Cr~50 wt.% Cr [1].(2)
In 1927, Bain and Griffiths observed the successfulσ phase in the Fe-Cr-Ni ternary system. They found that the σ phase was a very hard and brittle compound which impacted the toughness of the steels. At that time, the σ phase was called the “B constituent” [2].(3)
In 1936, this Fe-Cr compound was called the “σ phase” by Jett and Foote, which became its official name [3].(4)
In 1951, the crystal structure of theσ phase in the Fe-Cr binary system was examined by Yano and Abiko They pointed out that the σ phase exhibited slower precipitation kinetics in the Fe-Cr alloy system than in the Fe-Cr-Mo and Fe-Cr-Si ternary systems [4].(5)
In 1966, theσ phase was observed by Hattersley and Hume-Rothery [5] and Hall and Algie [6] in austenitic stainless steels.(6)
By 1966, theσ phase had been found in over 50 transition alloys [6], including Cr-Ni, Fe-Cr-Ni, Fe-Cr-Mo, Fe-Cr-Mn, Fe-Cr-Ni-Mo, Fe-Cr-Si, Fe-V, Re-Cr, Mo-Re, Ta-Al, W-Te, Ta-V, Zr-Ir, Nb-Pd, Ti-Mn, and Nb-Fe.


### 2.2. Precipitation Characteristic of theσ Phase

Theσ phase is a tetragonal crystal structure, and its precipitation temperature is between 600°C and 1000°C [7–9]. The crystal information and chemical composition of the σ phase are listed in Table 1 [10]. The σ phase can increase the hardness and decrease the toughness, as well as the elongation, of steels [10]. The σ phase issues from the phase transformation of δ→σ (δ-ferrite to σ phase). When the δ→σ phase transformation occurs, the σ phase will precipitate in the high Cr-concentrated region of δ-ferrite and is formed directly in δ-ferrite particles. When the Cr content is below 20 wt.%, the precipitation of the σ phase is not readily observable in austenitic stainless steels [11]. However, the σ phase can be formed quickly when the Cr content is 25 wt.%~30 wt.%. Furthermore, the σ phase can also precipitate from γ-austenite when there is no δ-ferrite in the stainless steels [12]; albeit this is unlikely. The δ-ferrite is a Cr-rich region, compared to the γ-austenite, and it is a body-centered crystal (BCC) structure. Cr is easy to diffuse in δ-ferrite, and it is also a ferritic stabilizer. Hence, δ-ferrite is a beneficial site for the precipitation of the σ phase [13].Table 1
Chemical composition and lattice constant of theσ phase [10].
AlloyLattice parameter (Å)Composition of phase (wt%)FormulaFeCrNiMoSiFe-Cra0=8.799,
c0=4.544Fe-CrFe-Moa0=9.188, c0=4.812Fe-Mo17Cr-11Ni-2Mo-0.4Ti—304.390.817Cr-11Ni-0.9Mo-0.5Ti—334.55.40.7Type 316a0= 8.28~8.38, c0= 4.597~4.5995529511—(FeNi)x(CrMo)yType 316La0=9.21, c0=4.7820Cr-25-34Ni-6.5-8Moa0=8.87, c0=4.6135/3717/2615/2121/28—25Cr-20Ni—40469.4—3Shinohara et al. [14] pointed out that the precipitation of the σ phase was a diffusion-controlled phase transformation in 25% Cr-20% Ni stainless steel, and that the Cr atom had an important effect on the acceleration of the precipitation rate of the σ phase. The precipitation rate of the σ phase in δ-ferrite was higher (by about 100 times) than that of γ-austenite [15]. This meant that the diffusion velocity of the σ phase in δ-ferrite was faster than that in γ-austenite. The contents of Cr and Mo of δ-ferrite decreased and the Ni contents increased simultaneously after the σ phase precipitated. The above result led to the formation of secondary austenite phases (γ2) via the δ-ferrite [16].Figure1 shows the Time-Temperature-Transformation (TTT) curve of the σ phase in various series of stainless steels [17]. It can be seen that the nose of the TTT curve is located at a temperature range of 800°C~850°C, which means that this temperature range has the fastest precipitation rate. Furthermore, the σ phase precipitates at 0.1 h in AISI 309S stainless steel, which has a higher precipitation rate than other stainless steels because of its high Cr content, low C content, and high δ-ferrite (15%).TTT curves of theσ phase in various series of stainless steels (B: initial precipitation, H: intermediate stage, E: final precipitation stage [17].
(a)(b)(c)(d)(e)(f)(g)Barcik [18] reported on the precipitation behavior of the σ phase in Cr-Ni austenitic stainless steel. His study found that the precipitated order of the σ phase was in triple point: δ-ferrite, incoherent twin boundary, and inclusion grain. Sikka pointed out that the σ phase was easy to precipitate at the δ/γ interphase boundaries [19] because the δ/γ interphase was a high boundary energy place and so a beneficial site for the heterogeneous nucleation of the σ phase. Sato et al. [20] found that a high lattice coherent degree and low δ/γ boundary energy could suppress the precipitation of the σ phase. Na et al. [21] found that the σ phase formed in γ-austenite when the aging time was high; they constructed a schematic diagram to explain the precipitation behavior of the σ phase, as shown in Figure 2. For Case 1, the σ phase was formed in γ-austenite, but needed a higher aging temperature (above 1000°C), as shown in Figure 2(a). For Case 2, the σ phase precipitated at the δ/γ interphase boundary because this boundary was a region of high boundary energy, as displayed in Figure 2(b). For Case 3, the σ phase precipitated in δ-ferrite particle and was attributed to the high Cr region of δ-ferrite. This precipitation behavior was the least difficult condition to accomplish, as represented in Figure 2(c). Padilha and Rios [22] pointed out that the σ phase precipitating directly in γ-austenite was very slow (about several thousand hours) [23]. Three main reasons for this were as follows.(1)
Theσ phase was insoluble from C and N elements so that the precipitation time of the carbide and nitride was earlier than that of the σ phase.(2)
Theσ phase was a second phase of a rich substitutional element. The diffusion of the substitutional element was very slow in γ-austenite so that the nucleation of the σ phase in γ-austenite was difficult.(3)
The crystallography of theσ phase and γ-austenite was incoherent.Schematic diagram of theσ phase precipitation [21].
(a)(b)(c)


### 2.3. Microstructural Characteristic of theσ Phase

In 1978, Gray et al. [24] used an advanced magnetic etching technique to observe the δ→σ+γ2 phase transformation. Figures 3 and 4 show the microstructures of AISI 304 stainless steel aged at 595°C and 650°C for 31000 h, respectively, using magnetic etching. The plate σ phase and γ2 precipitate in δ-ferrite particles. Therefore, the precipitation of the σ phase is via the eutectoid decomposition of δ→σ+γ2. The σ phase has a similar precipitation mechanism when aged at 650°C for 31000 h, but the eutectoid decomposition of δ→σ+γ2 is more evident in this condition.Figure 3
Microstructural observation of theδ→σ+γ2 phase transformation in AISI 304 stainless steel (595°C, 31000 hr) [24].Figure 4
Microstructural observation of theδ→σ+γ2 phase transformation in AISI 304 stainless steel (650°C, 31000 hr) [24].This Section introduces the morphologies of theσ phase in austenitic, ferritic, and duplex stainless steels.


#### 2.3.1. Austenitic Stainless Steels

Figure5(a) shows the as-casting microstructure of the σ phase in AISI 309 LSi stainless steel, and then the σ phase precipitating in dendrite δ-ferrite [25]. This is the typical precipitation morphology of the σ phase. Figure 5(b) shows the microstructure of the σ phase in as-rolled AISI 316 stainless steel [26]. The σ phase is indicated by a lacy structure and precipitates with a fixed crystallographic direction because of the rolling function. Figure 5(c) shows the as-rolled microstructure of the σ phase with a 50% rolling ratio in AISI 304 stainless steel, and the σ phase exhibits dispersed globular morphologies [27]. This globular structure is a stable morphology.Microstructural observation of theσ phase with different working conditions in the austenitic stainless steels (a) as casting AISI 309 LSi stainless steel, (b) as rolled AISI 316 stainless steel, (c) with 50% rolling ratio in AISI stainless steel [25].
(a)(b)(c)


#### 2.3.2. Ferritic Stainless Steels

Generally, many secondary phases (e.g.,χ  phase, Lave phase, etc.) exist in ferritic stainless steels, so that a microstructural examination of the σ phase is necessary. The microstructures of the σ phase were studied in Fe-29Cr-8W ferritic stainless steel aged at 850°C for different aging times [28]. The σ phase can precipitate obviously above 10 h. However, the precipitation mechanism of the σ phase accompanies the χ  phase in the δ-ferrite matrixes as compared to austenitic stainless steels.


#### 2.3.3. Duplex Stainless Steels

The microstructure of theσ phase was studied after heat treatment in A905 duplex stainless steel [26]. The σ phase (bright phase) precipitates in δ-ferrite grains when the aging condition is 30 min at 1100°C + 1 h at 900°C. However, σ+γ2 cellular structures form in δ-ferrite particles when the aging situation is 30 min at 1100°C + 10 h at 900°C. Finally, δ-ferrite is consumed by the σ+γ2 cellular structures completely when the aging condition is 30 min at 1100°C + 10 h at 800°C.


### 2.4. Classification of Morphologies of theσ Phase

In stainless steels, classification of the morphology of theσ phase can be divided into four types: (1) grain boundary precipitation, (2) triple point precipitation, (3) corner precipitation, and (4) cellular precipitation [29]. A discussion of these four morphologies follows.


#### 2.4.1.δ/γ Grain Boundary Precipitation

Theσ phase is easy to precipitate at the δ/γ phase boundary, which is a high Cr region. When a high Cr region forms, the depleted Cr region is also formed and leads to a decrease in the corrosion resistance at the same time. Furthermore, the δ/γ interphase boundary is a high interface energy site, and, as many defects concentrate there, it is a beneficial site for the heterogeneous nucleation of the σ phase. When the σ phase nucleates at the δ/γ interphase boundary, some defects disappear, which releases the free energy of the materials. Consequently, this decreases the activation energy barrier to form a coherent interface. Sato and Kokawa [30] pointed out that the σ phase forms preferentially at one side of the δ/γ interfaces along intergranular austenite in duplex stainless steel weld metal annealed at 1100 K. The crystallographic orientation relationships at the δ/γ interfaces are the σ phase forms which have deviated largely from the K-S relationship (ΔθK-S), as shown in Figure 6. The minimum deviation angle for the sigma phase formation decreases with increasing annealing time. Furthermore, the formation of the σ phase is strongly affected by the coherency and interfacial energy of the δ/γ interface.Figure 6
Effect of the deviation angleΔθK-S and the annealing time on the formation of σ phase at δ/γ interfaces in the weld metal [20].


#### 2.4.2. Triple Point Precipitation

Theσ phase precipitates at the triple point of the δ-ferrite boundary and this precipitation type, called the “triple point σ phase.” Barick [31] pointed out that the formation of the triple point σ phase must be aged below 600°C for 10000 h~15000 h. The triple point σ phase also forms at the incoherent twin boundaries and the intragranular inclusions.


#### 2.4.3. Corner Precipitation

The corner precipitation of theσ phase means that the σ phase forms directly in corner δ-ferrite particles because the δ-ferrite is a high Cr content phase, and σ phase prefers to nucleate and precipitate at that point. When the σ phase precipitates at the corner δ-ferrite, it consumes the Cr content of the δ-ferrite particles.


#### 2.4.4. Cellular Precipitation

Cellular precipitation means that theσ phase and secondary austenite (σ+γ2) precipitate as laminar precipitation in the δ-ferrite particles. This reaction is called the eutectoid decomposition of δ→σ+γ2. When the eutectoid decomposition of δ→σ+γ2 is finished, the σ phase consumes the Cr, Mo, and Si contents of the δ-ferrite particles.


### 2.5. Precipitation of theσ Phase in Austenitic, Superferritic, and Duplex Stainless Steels

Villanueva et al. [32] discussed the precipitation mechanism of the σ phase in the as-rolled plate of AISI 316L austenitic (17Cr-12Ni-2.4Mo), DIN 1.4574 superferritic (28Cr-4Ni-2.4Mo-0.31Nb), and UNS S31803 duplex (22Cr-5.4Ni-2.4Mo) stainless steels with various aging temperatures. Three schematic diagrams (Figures 7–9) can be used to explain the precipitation mechanism of σ phase.Precipitation mechanism of theσ phase in AISI 316L stainless steel [32].
(a)(b)(c)(d)Precipitation mechanism of theσ phase in DIN 1.4575 stainless steel [32].
(a)(b)(c)(d)Precipitation mechanism of theσ phase in UNS S31803 stainless steel [32].
(a)(b)(c)(d)Figures7(a)–7(d) show the precipitation mechanism of σ phase in AISI 316L stainless steel at different aging temperatures. Without heating (T0), the δ-ferrite is indicated by a lacy structure and precipitates at the δ/γ interphase boundary and γ phase. When the aging temperature is increased to T1, the σ and γ2 phases precipitate in δ-ferrite particles. When the aging temperatures are increased to  T2, the cellular σ+γ2 also forms in δ-ferrite particles, and the σ phase precipitates at the triple points and the δ/γ interphase boundaries. When the aging temperature is T3, the precipitation of the laminar σ+γ2 is more obvious than at the other aging temperatures.Figures8(a)–8(d) show the precipitation of σ phase in superferritic stainless steel. There is only δ-ferrite and no precipitation of the σ phase without heating (T0) in superferritic stainless steel. When the aging temperature is T1, the σ phase can occupy the triple points of the δ-ferrite grain boundaries. The σ phase grows at the δ-ferrite grain boundaries completely when the aging temperature increases to T2. Finally, the σ phase precipitates and extends to the inner δ-ferrite grain when the aging temperature is raised to T3.Figures9(a)–9(d) are the precipitation mechanism of σ phase in UNS S31803 duplex stainless steel. Here are δ and γ phases in UNS S31803 duplex stainless steel without heating (T0). Some laminar cellular structures (σ+γNew) are formed at the δ/γ interphase boundaries when the aging temperature is T1. Furthermore, the laminar cellular structures continue to grow when the aging temperature is increased to T2. Finally, the δ-ferrite is occupied completely.Villanueva et al. [32], in describing the above results, pointed out the precipitation level of the σ phase: Duplex stainless steel > Superferritic stainless steel > Austenitic stainless steel.


### 2.6. Effect of theσ Phase on the Properties of Stainless Steels

#### 2.6.1. Formation of Brittle Region

The embrittlement region of theσ phase forms in a temperature range of 650°C~900°C during the welding process in austenitic stainless steels. Hence, the welding energy and cooling rate must be controlled during welding in order to prevent the grain growth and precipitation of the brittle σ phase because the precipitation of the σ phase decreases the toughness and elongation. An embrittlement region of σ phase can be shown in Shaeffler diagram of Figure 10 [33]. Figure 10 of gray region is embrittlement region of σ phase, and this region is the widest in the mixed austenite plus ferrite phase region (A + F). On the other hand, the single austenite phase region (A) shows a small embrittlement range of the σ phase. Therefore, the possibility of the σ phase is lower in austenitic stainless steels. However, increasing the Cr content can promote the precipitation of the σ phase.Figure 10
Shaeffler diagram showing the embrittlement region of theσ phase [33].


#### 2.6.2. Extension of Hot Cracking during Welding

Konosu et al. [34] observed hot cracking in three stainless steel weld metals and the hot cracking extends along the γ/σ interface boundaries. The γ/σ interface boundaries are an initial fracture position of low elongation. This crack is a beneficial site and acts as a nucleated point of the σ phase. The growth of hot cracking cannot be neglected as it is very significant during the welding. Mataya and Carr [35] pointed out that hot cracking occurs because of the δ→σ phase transformation in the 21Cr-6Ni-9Mn austenitic stainless steel.


#### 2.6.3. Formation of Depleted Cr Region and Reduction of Corrosion Resistance

The precipitation of theσ phase reduces the corrosion resistances to the intergranular, pitting, and crevice. Reis et al. [36] reported that pitting corrosion resistance has an important relationship with the Cr content. Hence, pitting corrosion always happens at low Cr content points. Generally, the austenitic boundary is a preferential site for pitting corrosion because the austenite has a low Cr content. However, the depleted Cr zone disappears gradually as a function of Cr diffusion, which issues from the austenite but not the δ-ferrite. The σ phase always forms at the δ/γ interface boundaries and causes the formation of a depleted zone [37]. The σ phase and γ-austenite induce the galvanic effect, and the γ-austenite is corroded preferentially. Consequently, the corrosion potent is decreased. The fine σ phase has a more obvious effect on intergranular corrosion resistance than does the coarser σ phase because the fine σ phase forms a networked structure at the interface, and the coarse σ phase precipitates independently at the interface. Ravindranath and Malhotra [38] pointed out that intergranular corrosion resistance has an important effect on the formation of the networked σ phase. Besides, an independent coarse σ phase has no influence on intergranular corrosion resistance.


### 2.7. Prediction Methods of theσ Phase

Chemical composition can be used to predict the precipitation of theσ phase. Gow and Harder [39] pointed out an empirical formula to examine the precipitation tendency of the σ phase, as expressed in(1)(1)Ratiofactor=%Cr-16%C%Ni.If ratio factor >1.7, theσ phase can precipitate in stainless steels. When the C content is much higher, the ratio factor is much lower, and the precipitation tendency of the σ phase is decreased.Woodyatt [40] also pointed out a predicted formula of the σ phase via an electron vacancy number (at. %), as represented in(2)(2)Nv=0.66Ni+1.71Co+2.66Fe+4.66(Cr+Mo+W)+5.66V+6.66Zr+10.66Cb.When the electron vacancy number(Nv¯) > 2.52, the σ phase can be formed in stainless steels. According to Woodyatt’s theory, the Nv¯  in the AISI 310 stainless steel is equal to 2.88, so that this stainless steel indicates the precipitation of the σ phase. However, the interstitial elements (C and N) are neglected in this prediction formula.Hull [41] pointed out an empirical formula to predict the σ phase precipitation, as exhibited in (3). This equation has been widely used because it takes into account many alloy elements.(3)Creq=Cr+0.31Mn+1.76Mo+0.97W+2.02V+1.58Si+2.44Ti+1.70Cb+1.22Ta-0.266Ni-0.177Co.


### 2.8. Retardation Methods of theσ Phase

#### 2.8.1. Solid Solution Heat Treatment

The precipitation of theσ phase can be retarded by the use of the solid solution heat treatment. When stainless steels are heated to above 1050°C, the σ phase diffuses and dissolves into the γ-austenite matrix [42]. This dissolution process is called the “σ→γ phase transformation.”


#### 2.8.2. Subsequent Rolling Process

Gill et al. [43] reported that the dendrite σ phase is an unstable morphology and can lead to embrittlement of the stainless steels. The subsequent rolling process can be used to refine the σ phase particles from an unstable dendrite into stable globular morphologies. Hence, the embrittlement of the σ phase is decreased in the stainless steels by the subsequent rolling process.


#### 2.8.3. Addition of Alloy Elements

In recent years, Ni has been used to replace N and decrease the N addition because the price of the Ni in steel continues to improve. Lin et al. [44] reported that N addition decreases the δ-ferrite content during the nitrogen atmospheric aging heat treatment and retards the phase transformation from δ to σ. However, C has a similar effect on the suppression of the σ phase, but its addition leads to the precipitation of the nitride and causes sensitization and embrittlement.Brandis et al. [45] pointed out that Nitrogen had a better effect on the retardation of the σ phase than Carbon. Smuk et al. [46] studied the powder metallurgy of duplex stainless steels and found that Cu particles could pin the σ/γ2 interface boundaries, as shown in Figure 11. This meant that the Cu particles could prevent the motion of the σ/γ2 interface boundaries and can change the morphologies of the σ phase. Consequently, the δ→σ phase transformation could be suppressed efficiently.Figure 11
Cu particles can pin and prevent the motion of theσ/γ2 interface [46].


### 2.9. Thermo-Calc Simulation of theσ Phase

Besides the metallographic technique and quantitative analysis, the precipitation examination of theσ phase can also be predicted using a Thermo-Calc software simulation. This thermodynamic simulation only needs the input of the element contents and experimental temperatures to produce the phase diagrams. This simulation method is called Calculation of Phase Diagrams (CALPHAD).The simulation methods of the Thermo-Calc software in theσ phase have three databases: Steel & Fe-Alloys Database (TCFE), SGTE Solution Database (SSOL) [47] + Lindholm [48], and Modified SSOL [49]. Erneman et al. [49] used the three Thermo-Calc databases (TCFE, SSOL + Lindholm, Modified SSOL) to calculate the σ phase fraction in AISI 347 stainless steel at 700°C. The σ phase has a lesser volume fraction, which means a lower grain growth according to the TCFE simulation result. The simulation result of the Modified SSOL indicates a higher volume fraction of the σ phase, which means a higher grain growth. The simulation data of SSOL was in between the TCFE and SSOL databases. Saunders and Miodownik [50] used the Thermo-Calc software to simulate the precipitation quality of the σ phase with Mo, Mn, So, N, and C in Fe-22Cr-5.5Ni stainless steel between 670°C and 850°C. The series of simulation results were shown in Figures 12(a)–12(f). However, by adding 3% Mo into the original stainless steel, this steel becomes Fe-22Cr-5.5Ni-3Mo stainless steel, as shown in Figure 12(b). This CAPLAD result indicates that the σ phase has the highest content of all temperatures at 800°C. Moreover, Mo addition can extend the precipitation range to 900°C.CALPHAD result of the phases (a) Original Fe-22Cr-5.5Ni, (b) Fe-22Cr-5.5Ni-3MoFe-22Cr-5.5Ni, (c) Fe-22Cr-5.5Ni-3Mo-1.7MnFe-22Cr-5.5Ni, (d) Fe-22Cr-5.5Ni-3Mo-1.7Mn-0.4Si, (e) Fe-22Cr-5.5Ni-3Mo-1.7Mn-0.4Si-0.14N, and (f) Fe-22Cr-5.5Ni-3Mo-1.7Mn-0.4Si-0.14N-0.24C stainless steels [46].
(a)(b)(c)(d)(e)(f)By adding 1.7% Mn into the Fe-22Cr-5.5Ni-3Mo stainless steel, this steel becomes Fe-22Cr-5.5Ni-3Mo-1.7Mn stainless steel. The CALPHAD result shows that Mn has a competitive effect with Cr and Mo, so it can promote the precipitation of theσ phase, as shown in Figure 12(c). By adding 0.4% Si into the Fe-22Cr-5.5Ni-3Mo-1.7Mn, this steel becomes Fe-22Cr-5.5Ni-3Mo-1.7Mn-0.4Si stainless steel. The CALPHAD result shows that Si is a strong ferrite stabilizer which can raise the σ phase content, as indicated in Figure 12(d). Hence, it can be concluded that Si promotes the δ→σ phase transformation. By continuing to add 0.14N into the Fe-22Cr-5.5Ni-3Mo-1.7Mn-0.4Si, this steel becomes Fe-22Cr-5.5Ni-3Mo-1.7Mn-0.4Si-0.14N stainless steel. When N is added, the nitride (M2N) forms, and the σ phase content decreases at the same time, as shown in Figure 12(e). This is because N addition promotes the δ→γ phase transformation and retards the δ→σ phase transformation.Similarly, by adding 0.24C to the Fe-22Cr-5.5Ni-3Mo-1.7Mn-0.4Si-0.14N, this steel becomes Fe-22Cr-5.5Ni-3Mo-1.7Mn-0.4Si-0.14N-0.24C stainless steel. The CALPHAD result shows that C addition leads to the formation of M23C6, as shown in Figure 12(f). The content of carbide is higher, and the content of σ phase is lower in stainless steels. Furthermore, the σ phase fraction with the C addition is lower than that with Mn, Si or N additions.


### 2.10. Effect of Various Processes on theσ Phase

#### 2.10.1. Effect of Solid Solution-Treated Temperature and Cooling Rates on theσ Phase

Chen and Yang [51] studied 2205 duplex stainless steel as the solid solution treated at 1020°C with different cooling rates (1°C s−1, 0.5°C s−1, 0.25°C s−1, and 0.1°C s−1). The results showed that there was no σ phase when cooling rates were 1°C s−1 and 0.5°C s−1. The cooling rates of 0.25°C s−1 and 0.1°C s−1 indicated a slight σ phase and a lot of  σ phases, respectively. On the other hand, the precipitation of the σ phase was concentrated mainly at the δ/γ interface boundaries and δ-ferrite. However, Chen and Yang [51] also observed the precipitation of the σ phase at two solid solution temperatures, 1020°C and 1080°C. Experimental result indicated that the content of the σ phase was higher with the cooling rate at 1020°C than at 1080°C. Finally, Chen and Yang [51] used a solid solution temperature (1200°C) at a fixed cooling rate (0.1°C s−1) to discuss the precipitation of the σ phase. The experimental result showed that the Cr, Mo, and Si elements at 1200°C were higher than at 1080°C or 1200°C. This meant that the elemental diffusion of the Cr, Mo, and Si had an increasing effect on the precipitation of the σ phase at 1200°C at a cooling rate of 0.1°C s−1, as represented in Table 2 [51].Table 2
EDS analysis ofδ, σ, and γ phases at various solid solution temperatures and a fixed cooling rate of 0.1°C s−1[51].
ElementFeCrNiMoMnSiSolution treated at 1020°C and cooled at 0.1°C s−1σ61.7±0.525.7±0.63.46±0.066.84±0.081.15±0.041.15±0.04δ66.6±0.724.1±0.43.60±0.064.09±0.061.15±0.040.44±0.02γ68.0±0.720.8±0.46.45±0.082.42±0.061.45±0.040.32±0.02Solution treated at 1080°C and cooled at 0.1°C s−1σ62.7±0.525.2±0.63.92±0.065.90±0.081.14±0.041.13±0.04δ66.7±0.724.0±0.43.68±0.064.05±0.061.15±0.040.43±0.02γ68.3±0.720.9±0.46.39±0.082.45±0.061.44±0.040.33±0.02Solution treated at 1200°C and cooled at 0.1°C s−1δ67.0±0.723.6±0.43.83±0.083.96±0.061.16±0.040.41±0.02γ68.2±0.721.3±0.46.25±0.082.54±0.061.33±0.040.35±0.02


#### 2.10.2. Effect of Tensile Strain Rate and Time on theσ Phase

Hong and Han [52] conducted a high-temperature tensile test in superduplex stainless steel (Fe-24Cr-7Ni-3Mo-0.14N) at 850°C with a strain rate of 3.16×10-3s-1. The grain size of the σ phase increased in a deformed sample and maintained a constant value in the undeformed sample. This was because the controlled grain boundaries slip-strain induced the grain growth [53, 54] during the super-plasticity. Chandra and Kuchlmayr [55] reported that the σ phase content decreased with an increase in strain rate when the aging temperature was 900°C in Fe-19Cr-5Ni-2.7Mo stainless steel.


#### 2.10.3. Effect of Cold Rolling Ratios on theσ Phase

Abe et al. [56] reported on the effect of various cold rolling ratios on the precipitation of the σ phase in Fe-10Cr-30Mn stainless steel. Experimental result indicated the LAXRD (Low-angle X-Ray Diffraction) analysis at 923 K under various cold rolling ratios and aging times (30% CW-10 h, 30% CW-100 h, 30% CW-1000 h, and 80% CW-1000 h). The CW is an abbreviation of the “Cold Working.” The diffraction angle (2θ) of the LAXRD analysis is smaller than 85°, and this analytical method can show a clear diffraction signal. Many σ diffracted peaks can be detected, and there is no diffracted peak in the second phases. The diffracted peak of the σ phase is more obvious with 30% CW with an increase in aging time, which means that the precipitation of the σ phase does not decrease. Hence, cold rolling promotes the precipitation of the σ phase. Other diffracted peaks (σ(410), σ(212)) of the σ phase were examined when the cold rolling ratio increased to 80% CW, and the σ(312) peak was higher.Figure13 shows the TEM image in Fe-10Cr-30Mn stainless steel heat treated at 923 K for 3600 ks after cold rolling with various cold rolling ratios. The result shows that the grain size of the σ phase becomes smaller with increases in the cold rolling ratio, but that the distribution density of the σ phase increases. However, recrystallization only occurs above 30% CW, and there is no recrystallization with 10% CW. The σ phase only precipitates at the grain boundaries and triple points, as shown in Figure 13(a). A complete recrystallization happens with 60% CW and 80% CW, and then partial recrystallization occurs with 30% CW, as indicated in Figures 13(b)–13(d).The effect of various cold rolling ratios on distribution and grain size of theσ phase (a) 10% CW, (b) 30% CW, (c) 60% CW, and (d) 80% CW [56].
(a)(b)(c)(d)Huang and Chen [57] pointed out that cold working promoted the formation of the σ phase because the recrystallized and cold working boundaries were nucleated sites for the σ phase at low temperatures. At high temperatures, fine recrystallized grains formed and increased the area of the grain boundary so that the σ phase nucleated easily. Duhaj et al. [7] reported that the formation of the σ phase accelerated when the cold working degree was increased and that the σ phase content increased at the same time. It was concluded that the defects of stacking fault and twin acted as nucleation sites of the σ phase.Figures14(a)–14(c) show the relationship between recrystallization and the σ phase precipitation [56]. Initially, the σ phase nucleates at the recrystallized boundaries when crystallization occurs during cold rolling, as shown in Figure 14(a). This precipitation of the σ phase occurs because of the minimum strain energy during cold rolling. When the σ phase is formed, the recrystallized boundaries move to the deformed grains as a function of the recrystallized driving force (fR). A recrystallized reacting force (-fp) is also applied to the front of the recrystallized boundaries, as indicated in Figure 14(b). This recrystallized reacting force is due to the difference of the dislocation density from two sides of the recrystallized boundaries. Finally, the σ phase finishes the nucleation and grain growth and then escapes the recrystallized boundaries, as shown in Figure 14(c).Nucleation and grain growth ofσ phase at the recrystallized boundaries (fR: recrystallized driving force, -fp: recrystallized reacting force) [56].
(a)(b)(c)Koutsoukis et al. [58] studied the precipitation of the σ phase in S32654 super austenite stainless steel, cold rolled and aged at 850°C during cold rolling. The experimental result showed that the dispersion of the σ phase was more obvious when the cold rolling ratios were increased from 20% CW to 60% CW. The precipitation of the σ phase increased the hardness value about 500 HV with 60% CW when aged at 650°C.


#### 2.10.4. Effect of Hot Rolling Ratios on theσ Phase

Hsieh et al. [59] studied the precipitation mechanism of the σ phase in 19Cr-9Ni-2Mn austenitic and 18Cr-0.75Si ferritic stainless steels, hot rolled at 800°C under hot rolling ratios of 0%, 50%, and 75%. The experimental results indicated that the precipitation tendencies of the σ phase increased gradually with increase of the hot rolling ratio.Experimental results show the morphological variations of theσ phase with hot rolling ratios of 0%, 50%, and 75% in 19Cr-9Ni-2Mn stainless steel. The morphologies of the σ phase changed from complete dendrites into fine globular structures when the hot rolling ratio was increased from 0% to 75%, with similar results in 18Cr-0.7Si stainless steel.Hsieh et al. [60] pointed out that the dendrite σ phase was an unstable morphology and that the globular σ phase was a stable morphology. Gill et al. [61] also reported that the globular σ phase resulted from a refinement of the unstable σ phase. The globular σ phase consumed the Cr content of the δ-ferrite completely. Hence, the globular σ phase was maintained in the rolled state samples. Furthermore, the dendrite σ phase occurred because of the partial consumption of the Cr content of the δ-ferrite.


## 2.1. Development Progress of theσ Phase

(1)
In 1907, Treitschke and Tammann found that theσ phase in the Fe-Cr binary system was an intermetallic compound of 30 wt.% Cr~50 wt.% Cr [1].(2)
In 1927, Bain and Griffiths observed the successfulσ phase in the Fe-Cr-Ni ternary system. They found that the σ phase was a very hard and brittle compound which impacted the toughness of the steels. At that time, the σ phase was called the “B constituent” [2].(3)
In 1936, this Fe-Cr compound was called the “σ phase” by Jett and Foote, which became its official name [3].(4)
In 1951, the crystal structure of theσ phase in the Fe-Cr binary system was examined by Yano and Abiko They pointed out that the σ phase exhibited slower precipitation kinetics in the Fe-Cr alloy system than in the Fe-Cr-Mo and Fe-Cr-Si ternary systems [4].(5)
In 1966, theσ phase was observed by Hattersley and Hume-Rothery [5] and Hall and Algie [6] in austenitic stainless steels.(6)
By 1966, theσ phase had been found in over 50 transition alloys [6], including Cr-Ni, Fe-Cr-Ni, Fe-Cr-Mo, Fe-Cr-Mn, Fe-Cr-Ni-Mo, Fe-Cr-Si, Fe-V, Re-Cr, Mo-Re, Ta-Al, W-Te, Ta-V, Zr-Ir, Nb-Pd, Ti-Mn, and Nb-Fe.


## 2.2. Precipitation Characteristic of theσ Phase

Theσ phase is a tetragonal crystal structure, and its precipitation temperature is between 600°C and 1000°C [7–9]. The crystal information and chemical composition of the σ phase are listed in Table 1 [10]. The σ phase can increase the hardness and decrease the toughness, as well as the elongation, of steels [10]. The σ phase issues from the phase transformation of δ→σ (δ-ferrite to σ phase). When the δ→σ phase transformation occurs, the σ phase will precipitate in the high Cr-concentrated region of δ-ferrite and is formed directly in δ-ferrite particles. When the Cr content is below 20 wt.%, the precipitation of the σ phase is not readily observable in austenitic stainless steels [11]. However, the σ phase can be formed quickly when the Cr content is 25 wt.%~30 wt.%. Furthermore, the σ phase can also precipitate from γ-austenite when there is no δ-ferrite in the stainless steels [12]; albeit this is unlikely. The δ-ferrite is a Cr-rich region, compared to the γ-austenite, and it is a body-centered crystal (BCC) structure. Cr is easy to diffuse in δ-ferrite, and it is also a ferritic stabilizer. Hence, δ-ferrite is a beneficial site for the precipitation of the σ phase [13].Table 1
Chemical composition and lattice constant of theσ phase [10].
AlloyLattice parameter (Å)Composition of phase (wt%)FormulaFeCrNiMoSiFe-Cra0=8.799,
c0=4.544Fe-CrFe-Moa0=9.188, c0=4.812Fe-Mo17Cr-11Ni-2Mo-0.4Ti—304.390.817Cr-11Ni-0.9Mo-0.5Ti—334.55.40.7Type 316a0= 8.28~8.38, c0= 4.597~4.5995529511—(FeNi)x(CrMo)yType 316La0=9.21, c0=4.7820Cr-25-34Ni-6.5-8Moa0=8.87, c0=4.6135/3717/2615/2121/28—25Cr-20Ni—40469.4—3Shinohara et al. [14] pointed out that the precipitation of the σ phase was a diffusion-controlled phase transformation in 25% Cr-20% Ni stainless steel, and that the Cr atom had an important effect on the acceleration of the precipitation rate of the σ phase. The precipitation rate of the σ phase in δ-ferrite was higher (by about 100 times) than that of γ-austenite [15]. This meant that the diffusion velocity of the σ phase in δ-ferrite was faster than that in γ-austenite. The contents of Cr and Mo of δ-ferrite decreased and the Ni contents increased simultaneously after the σ phase precipitated. The above result led to the formation of secondary austenite phases (γ2) via the δ-ferrite [16].Figure1 shows the Time-Temperature-Transformation (TTT) curve of the σ phase in various series of stainless steels [17]. It can be seen that the nose of the TTT curve is located at a temperature range of 800°C~850°C, which means that this temperature range has the fastest precipitation rate. Furthermore, the σ phase precipitates at 0.1 h in AISI 309S stainless steel, which has a higher precipitation rate than other stainless steels because of its high Cr content, low C content, and high δ-ferrite (15%).TTT curves of theσ phase in various series of stainless steels (B: initial precipitation, H: intermediate stage, E: final precipitation stage [17].
(a)(b)(c)(d)(e)(f)(g)Barcik [18] reported on the precipitation behavior of the σ phase in Cr-Ni austenitic stainless steel. His study found that the precipitated order of the σ phase was in triple point: δ-ferrite, incoherent twin boundary, and inclusion grain. Sikka pointed out that the σ phase was easy to precipitate at the δ/γ interphase boundaries [19] because the δ/γ interphase was a high boundary energy place and so a beneficial site for the heterogeneous nucleation of the σ phase. Sato et al. [20] found that a high lattice coherent degree and low δ/γ boundary energy could suppress the precipitation of the σ phase. Na et al. [21] found that the σ phase formed in γ-austenite when the aging time was high; they constructed a schematic diagram to explain the precipitation behavior of the σ phase, as shown in Figure 2. For Case 1, the σ phase was formed in γ-austenite, but needed a higher aging temperature (above 1000°C), as shown in Figure 2(a). For Case 2, the σ phase precipitated at the δ/γ interphase boundary because this boundary was a region of high boundary energy, as displayed in Figure 2(b). For Case 3, the σ phase precipitated in δ-ferrite particle and was attributed to the high Cr region of δ-ferrite. This precipitation behavior was the least difficult condition to accomplish, as represented in Figure 2(c). Padilha and Rios [22] pointed out that the σ phase precipitating directly in γ-austenite was very slow (about several thousand hours) [23]. Three main reasons for this were as follows.(1)
Theσ phase was insoluble from C and N elements so that the precipitation time of the carbide and nitride was earlier than that of the σ phase.(2)
Theσ phase was a second phase of a rich substitutional element. The diffusion of the substitutional element was very slow in γ-austenite so that the nucleation of the σ phase in γ-austenite was difficult.(3)
The crystallography of theσ phase and γ-austenite was incoherent.Schematic diagram of theσ phase precipitation [21].
(a)(b)(c)


## 2.3. Microstructural Characteristic of theσ Phase

In 1978, Gray et al. [24] used an advanced magnetic etching technique to observe the δ→σ+γ2 phase transformation. Figures 3 and 4 show the microstructures of AISI 304 stainless steel aged at 595°C and 650°C for 31000 h, respectively, using magnetic etching. The plate σ phase and γ2 precipitate in δ-ferrite particles. Therefore, the precipitation of the σ phase is via the eutectoid decomposition of δ→σ+γ2. The σ phase has a similar precipitation mechanism when aged at 650°C for 31000 h, but the eutectoid decomposition of δ→σ+γ2 is more evident in this condition.Figure 3
Microstructural observation of theδ→σ+γ2 phase transformation in AISI 304 stainless steel (595°C, 31000 hr) [24].Figure 4
Microstructural observation of theδ→σ+γ2 phase transformation in AISI 304 stainless steel (650°C, 31000 hr) [24].This Section introduces the morphologies of theσ phase in austenitic, ferritic, and duplex stainless steels.


### 2.3.1. Austenitic Stainless Steels

Figure5(a) shows the as-casting microstructure of the σ phase in AISI 309 LSi stainless steel, and then the σ phase precipitating in dendrite δ-ferrite [25]. This is the typical precipitation morphology of the σ phase. Figure 5(b) shows the microstructure of the σ phase in as-rolled AISI 316 stainless steel [26]. The σ phase is indicated by a lacy structure and precipitates with a fixed crystallographic direction because of the rolling function. Figure 5(c) shows the as-rolled microstructure of the σ phase with a 50% rolling ratio in AISI 304 stainless steel, and the σ phase exhibits dispersed globular morphologies [27]. This globular structure is a stable morphology.Microstructural observation of theσ phase with different working conditions in the austenitic stainless steels (a) as casting AISI 309 LSi stainless steel, (b) as rolled AISI 316 stainless steel, (c) with 50% rolling ratio in AISI stainless steel [25].
(a)(b)(c)


### 2.3.2. Ferritic Stainless Steels

Generally, many secondary phases (e.g.,χ  phase, Lave phase, etc.) exist in ferritic stainless steels, so that a microstructural examination of the σ phase is necessary. The microstructures of the σ phase were studied in Fe-29Cr-8W ferritic stainless steel aged at 850°C for different aging times [28]. The σ phase can precipitate obviously above 10 h. However, the precipitation mechanism of the σ phase accompanies the χ  phase in the δ-ferrite matrixes as compared to austenitic stainless steels.


### 2.3.3. Duplex Stainless Steels

The microstructure of theσ phase was studied after heat treatment in A905 duplex stainless steel [26]. The σ phase (bright phase) precipitates in δ-ferrite grains when the aging condition is 30 min at 1100°C + 1 h at 900°C. However, σ+γ2 cellular structures form in δ-ferrite particles when the aging situation is 30 min at 1100°C + 10 h at 900°C. Finally, δ-ferrite is consumed by the σ+γ2 cellular structures completely when the aging condition is 30 min at 1100°C + 10 h at 800°C.


## 2.3.1. Austenitic Stainless Steels

Figure5(a) shows the as-casting microstructure of the σ phase in AISI 309 LSi stainless steel, and then the σ phase precipitating in dendrite δ-ferrite [25]. This is the typical precipitation morphology of the σ phase. Figure 5(b) shows the microstructure of the σ phase in as-rolled AISI 316 stainless steel [26]. The σ phase is indicated by a lacy structure and precipitates with a fixed crystallographic direction because of the rolling function. Figure 5(c) shows the as-rolled microstructure of the σ phase with a 50% rolling ratio in AISI 304 stainless steel, and the σ phase exhibits dispersed globular morphologies [27]. This globular structure is a stable morphology.Microstructural observation of theσ phase with different working conditions in the austenitic stainless steels (a) as casting AISI 309 LSi stainless steel, (b) as rolled AISI 316 stainless steel, (c) with 50% rolling ratio in AISI stainless steel [25].
(a)(b)(c)


## 2.3.2. Ferritic Stainless Steels

Generally, many secondary phases (e.g.,χ  phase, Lave phase, etc.) exist in ferritic stainless steels, so that a microstructural examination of the σ phase is necessary. The microstructures of the σ phase were studied in Fe-29Cr-8W ferritic stainless steel aged at 850°C for different aging times [28]. The σ phase can precipitate obviously above 10 h. However, the precipitation mechanism of the σ phase accompanies the χ  phase in the δ-ferrite matrixes as compared to austenitic stainless steels.


## 2.3.3. Duplex Stainless Steels

The microstructure of theσ phase was studied after heat treatment in A905 duplex stainless steel [26]. The σ phase (bright phase) precipitates in δ-ferrite grains when the aging condition is 30 min at 1100°C + 1 h at 900°C. However, σ+γ2 cellular structures form in δ-ferrite particles when the aging situation is 30 min at 1100°C + 10 h at 900°C. Finally, δ-ferrite is consumed by the σ+γ2 cellular structures completely when the aging condition is 30 min at 1100°C + 10 h at 800°C.


## 2.4. Classification of Morphologies of theσ Phase

In stainless steels, classification of the morphology of theσ phase can be divided into four types: (1) grain boundary precipitation, (2) triple point precipitation, (3) corner precipitation, and (4) cellular precipitation [29]. A discussion of these four morphologies follows.


### 2.4.1.δ/γ Grain Boundary Precipitation

Theσ phase is easy to precipitate at the δ/γ phase boundary, which is a high Cr region. When a high Cr region forms, the depleted Cr region is also formed and leads to a decrease in the corrosion resistance at the same time. Furthermore, the δ/γ interphase boundary is a high interface energy site, and, as many defects concentrate there, it is a beneficial site for the heterogeneous nucleation of the σ phase. When the σ phase nucleates at the δ/γ interphase boundary, some defects disappear, which releases the free energy of the materials. Consequently, this decreases the activation energy barrier to form a coherent interface. Sato and Kokawa [30] pointed out that the σ phase forms preferentially at one side of the δ/γ interfaces along intergranular austenite in duplex stainless steel weld metal annealed at 1100 K. The crystallographic orientation relationships at the δ/γ interfaces are the σ phase forms which have deviated largely from the K-S relationship (ΔθK-S), as shown in Figure 6. The minimum deviation angle for the sigma phase formation decreases with increasing annealing time. Furthermore, the formation of the σ phase is strongly affected by the coherency and interfacial energy of the δ/γ interface.Figure 6
Effect of the deviation angleΔθK-S and the annealing time on the formation of σ phase at δ/γ interfaces in the weld metal [20].


### 2.4.2. Triple Point Precipitation

Theσ phase precipitates at the triple point of the δ-ferrite boundary and this precipitation type, called the “triple point σ phase.” Barick [31] pointed out that the formation of the triple point σ phase must be aged below 600°C for 10000 h~15000 h. The triple point σ phase also forms at the incoherent twin boundaries and the intragranular inclusions.


### 2.4.3. Corner Precipitation

The corner precipitation of theσ phase means that the σ phase forms directly in corner δ-ferrite particles because the δ-ferrite is a high Cr content phase, and σ phase prefers to nucleate and precipitate at that point. When the σ phase precipitates at the corner δ-ferrite, it consumes the Cr content of the δ-ferrite particles.


### 2.4.4. Cellular Precipitation

Cellular precipitation means that theσ phase and secondary austenite (σ+γ2) precipitate as laminar precipitation in the δ-ferrite particles. This reaction is called the eutectoid decomposition of δ→σ+γ2. When the eutectoid decomposition of δ→σ+γ2 is finished, the σ phase consumes the Cr, Mo, and Si contents of the δ-ferrite particles.


## 2.4.1.δ/γ Grain Boundary Precipitation

Theσ phase is easy to precipitate at the δ/γ phase boundary, which is a high Cr region. When a high Cr region forms, the depleted Cr region is also formed and leads to a decrease in the corrosion resistance at the same time. Furthermore, the δ/γ interphase boundary is a high interface energy site, and, as many defects concentrate there, it is a beneficial site for the heterogeneous nucleation of the σ phase. When the σ phase nucleates at the δ/γ interphase boundary, some defects disappear, which releases the free energy of the materials. Consequently, this decreases the activation energy barrier to form a coherent interface. Sato and Kokawa [30] pointed out that the σ phase forms preferentially at one side of the δ/γ interfaces along intergranular austenite in duplex stainless steel weld metal annealed at 1100 K. The crystallographic orientation relationships at the δ/γ interfaces are the σ phase forms which have deviated largely from the K-S relationship (ΔθK-S), as shown in Figure 6. The minimum deviation angle for the sigma phase formation decreases with increasing annealing time. Furthermore, the formation of the σ phase is strongly affected by the coherency and interfacial energy of the δ/γ interface.Figure 6
Effect of the deviation angleΔθK-S and the annealing time on the formation of σ phase at δ/γ interfaces in the weld metal [20].


## 2.4.2. Triple Point Precipitation

Theσ phase precipitates at the triple point of the δ-ferrite boundary and this precipitation type, called the “triple point σ phase.” Barick [31] pointed out that the formation of the triple point σ phase must be aged below 600°C for 10000 h~15000 h. The triple point σ phase also forms at the incoherent twin boundaries and the intragranular inclusions.


## 2.4.3. Corner Precipitation

The corner precipitation of theσ phase means that the σ phase forms directly in corner δ-ferrite particles because the δ-ferrite is a high Cr content phase, and σ phase prefers to nucleate and precipitate at that point. When the σ phase precipitates at the corner δ-ferrite, it consumes the Cr content of the δ-ferrite particles.


## 2.4.4. Cellular Precipitation

Cellular precipitation means that theσ phase and secondary austenite (σ+γ2) precipitate as laminar precipitation in the δ-ferrite particles. This reaction is called the eutectoid decomposition of δ→σ+γ2. When the eutectoid decomposition of δ→σ+γ2 is finished, the σ phase consumes the Cr, Mo, and Si contents of the δ-ferrite particles.


## 2.5. Precipitation of theσ Phase in Austenitic, Superferritic, and Duplex Stainless Steels

Villanueva et al. [32] discussed the precipitation mechanism of the σ phase in the as-rolled plate of AISI 316L austenitic (17Cr-12Ni-2.4Mo), DIN 1.4574 superferritic (28Cr-4Ni-2.4Mo-0.31Nb), and UNS S31803 duplex (22Cr-5.4Ni-2.4Mo) stainless steels with various aging temperatures. Three schematic diagrams (Figures 7–9) can be used to explain the precipitation mechanism of σ phase.Precipitation mechanism of theσ phase in AISI 316L stainless steel [32].
(a)(b)(c)(d)Precipitation mechanism of theσ phase in DIN 1.4575 stainless steel [32].
(a)(b)(c)(d)Precipitation mechanism of theσ phase in UNS S31803 stainless steel [32].
(a)(b)(c)(d)Figures7(a)–7(d) show the precipitation mechanism of σ phase in AISI 316L stainless steel at different aging temperatures. Without heating (T0), the δ-ferrite is indicated by a lacy structure and precipitates at the δ/γ interphase boundary and γ phase. When the aging temperature is increased to T1, the σ and γ2 phases precipitate in δ-ferrite particles. When the aging temperatures are increased to  T2, the cellular σ+γ2 also forms in δ-ferrite particles, and the σ phase precipitates at the triple points and the δ/γ interphase boundaries. When the aging temperature is T3, the precipitation of the laminar σ+γ2 is more obvious than at the other aging temperatures.Figures8(a)–8(d) show the precipitation of σ phase in superferritic stainless steel. There is only δ-ferrite and no precipitation of the σ phase without heating (T0) in superferritic stainless steel. When the aging temperature is T1, the σ phase can occupy the triple points of the δ-ferrite grain boundaries. The σ phase grows at the δ-ferrite grain boundaries completely when the aging temperature increases to T2. Finally, the σ phase precipitates and extends to the inner δ-ferrite grain when the aging temperature is raised to T3.Figures9(a)–9(d) are the precipitation mechanism of σ phase in UNS S31803 duplex stainless steel. Here are δ and γ phases in UNS S31803 duplex stainless steel without heating (T0). Some laminar cellular structures (σ+γNew) are formed at the δ/γ interphase boundaries when the aging temperature is T1. Furthermore, the laminar cellular structures continue to grow when the aging temperature is increased to T2. Finally, the δ-ferrite is occupied completely.Villanueva et al. [32], in describing the above results, pointed out the precipitation level of the σ phase: Duplex stainless steel > Superferritic stainless steel > Austenitic stainless steel.


## 2.6. Effect of theσ Phase on the Properties of Stainless Steels

### 2.6.1. Formation of Brittle Region

The embrittlement region of theσ phase forms in a temperature range of 650°C~900°C during the welding process in austenitic stainless steels. Hence, the welding energy and cooling rate must be controlled during welding in order to prevent the grain growth and precipitation of the brittle σ phase because the precipitation of the σ phase decreases the toughness and elongation. An embrittlement region of σ phase can be shown in Shaeffler diagram of Figure 10 [33]. Figure 10 of gray region is embrittlement region of σ phase, and this region is the widest in the mixed austenite plus ferrite phase region (A + F). On the other hand, the single austenite phase region (A) shows a small embrittlement range of the σ phase. Therefore, the possibility of the σ phase is lower in austenitic stainless steels. However, increasing the Cr content can promote the precipitation of the σ phase.Figure 10
Shaeffler diagram showing the embrittlement region of theσ phase [33].


### 2.6.2. Extension of Hot Cracking during Welding

Konosu et al. [34] observed hot cracking in three stainless steel weld metals and the hot cracking extends along the γ/σ interface boundaries. The γ/σ interface boundaries are an initial fracture position of low elongation. This crack is a beneficial site and acts as a nucleated point of the σ phase. The growth of hot cracking cannot be neglected as it is very significant during the welding. Mataya and Carr [35] pointed out that hot cracking occurs because of the δ→σ phase transformation in the 21Cr-6Ni-9Mn austenitic stainless steel.


### 2.6.3. Formation of Depleted Cr Region and Reduction of Corrosion Resistance

The precipitation of theσ phase reduces the corrosion resistances to the intergranular, pitting, and crevice. Reis et al. [36] reported that pitting corrosion resistance has an important relationship with the Cr content. Hence, pitting corrosion always happens at low Cr content points. Generally, the austenitic boundary is a preferential site for pitting corrosion because the austenite has a low Cr content. However, the depleted Cr zone disappears gradually as a function of Cr diffusion, which issues from the austenite but not the δ-ferrite. The σ phase always forms at the δ/γ interface boundaries and causes the formation of a depleted zone [37]. The σ phase and γ-austenite induce the galvanic effect, and the γ-austenite is corroded preferentially. Consequently, the corrosion potent is decreased. The fine σ phase has a more obvious effect on intergranular corrosion resistance than does the coarser σ phase because the fine σ phase forms a networked structure at the interface, and the coarse σ phase precipitates independently at the interface. Ravindranath and Malhotra [38] pointed out that intergranular corrosion resistance has an important effect on the formation of the networked σ phase. Besides, an independent coarse σ phase has no influence on intergranular corrosion resistance.


## 2.6.1. Formation of Brittle Region

The embrittlement region of theσ phase forms in a temperature range of 650°C~900°C during the welding process in austenitic stainless steels. Hence, the welding energy and cooling rate must be controlled during welding in order to prevent the grain growth and precipitation of the brittle σ phase because the precipitation of the σ phase decreases the toughness and elongation. An embrittlement region of σ phase can be shown in Shaeffler diagram of Figure 10 [33]. Figure 10 of gray region is embrittlement region of σ phase, and this region is the widest in the mixed austenite plus ferrite phase region (A + F). On the other hand, the single austenite phase region (A) shows a small embrittlement range of the σ phase. Therefore, the possibility of the σ phase is lower in austenitic stainless steels. However, increasing the Cr content can promote the precipitation of the σ phase.Figure 10
Shaeffler diagram showing the embrittlement region of theσ phase [33].


## 2.6.2. Extension of Hot Cracking during Welding

Konosu et al. [34] observed hot cracking in three stainless steel weld metals and the hot cracking extends along the γ/σ interface boundaries. The γ/σ interface boundaries are an initial fracture position of low elongation. This crack is a beneficial site and acts as a nucleated point of the σ phase. The growth of hot cracking cannot be neglected as it is very significant during the welding. Mataya and Carr [35] pointed out that hot cracking occurs because of the δ→σ phase transformation in the 21Cr-6Ni-9Mn austenitic stainless steel.


## 2.6.3. Formation of Depleted Cr Region and Reduction of Corrosion Resistance

The precipitation of theσ phase reduces the corrosion resistances to the intergranular, pitting, and crevice. Reis et al. [36] reported that pitting corrosion resistance has an important relationship with the Cr content. Hence, pitting corrosion always happens at low Cr content points. Generally, the austenitic boundary is a preferential site for pitting corrosion because the austenite has a low Cr content. However, the depleted Cr zone disappears gradually as a function of Cr diffusion, which issues from the austenite but not the δ-ferrite. The σ phase always forms at the δ/γ interface boundaries and causes the formation of a depleted zone [37]. The σ phase and γ-austenite induce the galvanic effect, and the γ-austenite is corroded preferentially. Consequently, the corrosion potent is decreased. The fine σ phase has a more obvious effect on intergranular corrosion resistance than does the coarser σ phase because the fine σ phase forms a networked structure at the interface, and the coarse σ phase precipitates independently at the interface. Ravindranath and Malhotra [38] pointed out that intergranular corrosion resistance has an important effect on the formation of the networked σ phase. Besides, an independent coarse σ phase has no influence on intergranular corrosion resistance.


## 2.7. Prediction Methods of theσ Phase

Chemical composition can be used to predict the precipitation of theσ phase. Gow and Harder [39] pointed out an empirical formula to examine the precipitation tendency of the σ phase, as expressed in(1)(1)Ratiofactor=%Cr-16%C%Ni.If ratio factor >1.7, theσ phase can precipitate in stainless steels. When the C content is much higher, the ratio factor is much lower, and the precipitation tendency of the σ phase is decreased.Woodyatt [40] also pointed out a predicted formula of the σ phase via an electron vacancy number (at. %), as represented in(2)(2)Nv=0.66Ni+1.71Co+2.66Fe+4.66(Cr+Mo+W)+5.66V+6.66Zr+10.66Cb.When the electron vacancy number(Nv¯) > 2.52, the σ phase can be formed in stainless steels. According to Woodyatt’s theory, the Nv¯  in the AISI 310 stainless steel is equal to 2.88, so that this stainless steel indicates the precipitation of the σ phase. However, the interstitial elements (C and N) are neglected in this prediction formula.Hull [41] pointed out an empirical formula to predict the σ phase precipitation, as exhibited in (3). This equation has been widely used because it takes into account many alloy elements.(3)Creq=Cr+0.31Mn+1.76Mo+0.97W+2.02V+1.58Si+2.44Ti+1.70Cb+1.22Ta-0.266Ni-0.177Co.


## 2.8. Retardation Methods of theσ Phase

### 2.8.1. Solid Solution Heat Treatment

The precipitation of theσ phase can be retarded by the use of the solid solution heat treatment. When stainless steels are heated to above 1050°C, the σ phase diffuses and dissolves into the γ-austenite matrix [42]. This dissolution process is called the “σ→γ phase transformation.”


### 2.8.2. Subsequent Rolling Process

Gill et al. [43] reported that the dendrite σ phase is an unstable morphology and can lead to embrittlement of the stainless steels. The subsequent rolling process can be used to refine the σ phase particles from an unstable dendrite into stable globular morphologies. Hence, the embrittlement of the σ phase is decreased in the stainless steels by the subsequent rolling process.


### 2.8.3. Addition of Alloy Elements

In recent years, Ni has been used to replace N and decrease the N addition because the price of the Ni in steel continues to improve. Lin et al. [44] reported that N addition decreases the δ-ferrite content during the nitrogen atmospheric aging heat treatment and retards the phase transformation from δ to σ. However, C has a similar effect on the suppression of the σ phase, but its addition leads to the precipitation of the nitride and causes sensitization and embrittlement.Brandis et al. [45] pointed out that Nitrogen had a better effect on the retardation of the σ phase than Carbon. Smuk et al. [46] studied the powder metallurgy of duplex stainless steels and found that Cu particles could pin the σ/γ2 interface boundaries, as shown in Figure 11. This meant that the Cu particles could prevent the motion of the σ/γ2 interface boundaries and can change the morphologies of the σ phase. Consequently, the δ→σ phase transformation could be suppressed efficiently.Figure 11
Cu particles can pin and prevent the motion of theσ/γ2 interface [46].


## 2.8.1. Solid Solution Heat Treatment

The precipitation of theσ phase can be retarded by the use of the solid solution heat treatment. When stainless steels are heated to above 1050°C, the σ phase diffuses and dissolves into the γ-austenite matrix [42]. This dissolution process is called the “σ→γ phase transformation.”


## 2.8.2. Subsequent Rolling Process

Gill et al. [43] reported that the dendrite σ phase is an unstable morphology and can lead to embrittlement of the stainless steels. The subsequent rolling process can be used to refine the σ phase particles from an unstable dendrite into stable globular morphologies. Hence, the embrittlement of the σ phase is decreased in the stainless steels by the subsequent rolling process.


## 2.8.3. Addition of Alloy Elements

In recent years, Ni has been used to replace N and decrease the N addition because the price of the Ni in steel continues to improve. Lin et al. [44] reported that N addition decreases the δ-ferrite content during the nitrogen atmospheric aging heat treatment and retards the phase transformation from δ to σ. However, C has a similar effect on the suppression of the σ phase, but its addition leads to the precipitation of the nitride and causes sensitization and embrittlement.Brandis et al. [45] pointed out that Nitrogen had a better effect on the retardation of the σ phase than Carbon. Smuk et al. [46] studied the powder metallurgy of duplex stainless steels and found that Cu particles could pin the σ/γ2 interface boundaries, as shown in Figure 11. This meant that the Cu particles could prevent the motion of the σ/γ2 interface boundaries and can change the morphologies of the σ phase. Consequently, the δ→σ phase transformation could be suppressed efficiently.Figure 11
Cu particles can pin and prevent the motion of theσ/γ2 interface [46].


## 2.9. Thermo-Calc Simulation of theσ Phase

Besides the metallographic technique and quantitative analysis, the precipitation examination of theσ phase can also be predicted using a Thermo-Calc software simulation. This thermodynamic simulation only needs the input of the element contents and experimental temperatures to produce the phase diagrams. This simulation method is called Calculation of Phase Diagrams (CALPHAD).The simulation methods of the Thermo-Calc software in theσ phase have three databases: Steel & Fe-Alloys Database (TCFE), SGTE Solution Database (SSOL) [47] + Lindholm [48], and Modified SSOL [49]. Erneman et al. [49] used the three Thermo-Calc databases (TCFE, SSOL + Lindholm, Modified SSOL) to calculate the σ phase fraction in AISI 347 stainless steel at 700°C. The σ phase has a lesser volume fraction, which means a lower grain growth according to the TCFE simulation result. The simulation result of the Modified SSOL indicates a higher volume fraction of the σ phase, which means a higher grain growth. The simulation data of SSOL was in between the TCFE and SSOL databases. Saunders and Miodownik [50] used the Thermo-Calc software to simulate the precipitation quality of the σ phase with Mo, Mn, So, N, and C in Fe-22Cr-5.5Ni stainless steel between 670°C and 850°C. The series of simulation results were shown in Figures 12(a)–12(f). However, by adding 3% Mo into the original stainless steel, this steel becomes Fe-22Cr-5.5Ni-3Mo stainless steel, as shown in Figure 12(b). This CAPLAD result indicates that the σ phase has the highest content of all temperatures at 800°C. Moreover, Mo addition can extend the precipitation range to 900°C.CALPHAD result of the phases (a) Original Fe-22Cr-5.5Ni, (b) Fe-22Cr-5.5Ni-3MoFe-22Cr-5.5Ni, (c) Fe-22Cr-5.5Ni-3Mo-1.7MnFe-22Cr-5.5Ni, (d) Fe-22Cr-5.5Ni-3Mo-1.7Mn-0.4Si, (e) Fe-22Cr-5.5Ni-3Mo-1.7Mn-0.4Si-0.14N, and (f) Fe-22Cr-5.5Ni-3Mo-1.7Mn-0.4Si-0.14N-0.24C stainless steels [46].
(a)(b)(c)(d)(e)(f)By adding 1.7% Mn into the Fe-22Cr-5.5Ni-3Mo stainless steel, this steel becomes Fe-22Cr-5.5Ni-3Mo-1.7Mn stainless steel. The CALPHAD result shows that Mn has a competitive effect with Cr and Mo, so it can promote the precipitation of theσ phase, as shown in Figure 12(c). By adding 0.4% Si into the Fe-22Cr-5.5Ni-3Mo-1.7Mn, this steel becomes Fe-22Cr-5.5Ni-3Mo-1.7Mn-0.4Si stainless steel. The CALPHAD result shows that Si is a strong ferrite stabilizer which can raise the σ phase content, as indicated in Figure 12(d). Hence, it can be concluded that Si promotes the δ→σ phase transformation. By continuing to add 0.14N into the Fe-22Cr-5.5Ni-3Mo-1.7Mn-0.4Si, this steel becomes Fe-22Cr-5.5Ni-3Mo-1.7Mn-0.4Si-0.14N stainless steel. When N is added, the nitride (M2N) forms, and the σ phase content decreases at the same time, as shown in Figure 12(e). This is because N addition promotes the δ→γ phase transformation and retards the δ→σ phase transformation.Similarly, by adding 0.24C to the Fe-22Cr-5.5Ni-3Mo-1.7Mn-0.4Si-0.14N, this steel becomes Fe-22Cr-5.5Ni-3Mo-1.7Mn-0.4Si-0.14N-0.24C stainless steel. The CALPHAD result shows that C addition leads to the formation of M23C6, as shown in Figure 12(f). The content of carbide is higher, and the content of σ phase is lower in stainless steels. Furthermore, the σ phase fraction with the C addition is lower than that with Mn, Si or N additions.


## 2.10. Effect of Various Processes on theσ Phase

### 2.10.1. Effect of Solid Solution-Treated Temperature and Cooling Rates on theσ Phase

Chen and Yang [51] studied 2205 duplex stainless steel as the solid solution treated at 1020°C with different cooling rates (1°C s−1, 0.5°C s−1, 0.25°C s−1, and 0.1°C s−1). The results showed that there was no σ phase when cooling rates were 1°C s−1 and 0.5°C s−1. The cooling rates of 0.25°C s−1 and 0.1°C s−1 indicated a slight σ phase and a lot of  σ phases, respectively. On the other hand, the precipitation of the σ phase was concentrated mainly at the δ/γ interface boundaries and δ-ferrite. However, Chen and Yang [51] also observed the precipitation of the σ phase at two solid solution temperatures, 1020°C and 1080°C. Experimental result indicated that the content of the σ phase was higher with the cooling rate at 1020°C than at 1080°C. Finally, Chen and Yang [51] used a solid solution temperature (1200°C) at a fixed cooling rate (0.1°C s−1) to discuss the precipitation of the σ phase. The experimental result showed that the Cr, Mo, and Si elements at 1200°C were higher than at 1080°C or 1200°C. This meant that the elemental diffusion of the Cr, Mo, and Si had an increasing effect on the precipitation of the σ phase at 1200°C at a cooling rate of 0.1°C s−1, as represented in Table 2 [51].Table 2
EDS analysis ofδ, σ, and γ phases at various solid solution temperatures and a fixed cooling rate of 0.1°C s−1[51].
ElementFeCrNiMoMnSiSolution treated at 1020°C and cooled at 0.1°C s−1σ61.7±0.525.7±0.63.46±0.066.84±0.081.15±0.041.15±0.04δ66.6±0.724.1±0.43.60±0.064.09±0.061.15±0.040.44±0.02γ68.0±0.720.8±0.46.45±0.082.42±0.061.45±0.040.32±0.02Solution treated at 1080°C and cooled at 0.1°C s−1σ62.7±0.525.2±0.63.92±0.065.90±0.081.14±0.041.13±0.04δ66.7±0.724.0±0.43.68±0.064.05±0.061.15±0.040.43±0.02γ68.3±0.720.9±0.46.39±0.082.45±0.061.44±0.040.33±0.02Solution treated at 1200°C and cooled at 0.1°C s−1δ67.0±0.723.6±0.43.83±0.083.96±0.061.16±0.040.41±0.02γ68.2±0.721.3±0.46.25±0.082.54±0.061.33±0.040.35±0.02


### 2.10.2. Effect of Tensile Strain Rate and Time on theσ Phase

Hong and Han [52] conducted a high-temperature tensile test in superduplex stainless steel (Fe-24Cr-7Ni-3Mo-0.14N) at 850°C with a strain rate of 3.16×10-3s-1. The grain size of the σ phase increased in a deformed sample and maintained a constant value in the undeformed sample. This was because the controlled grain boundaries slip-strain induced the grain growth [53, 54] during the super-plasticity. Chandra and Kuchlmayr [55] reported that the σ phase content decreased with an increase in strain rate when the aging temperature was 900°C in Fe-19Cr-5Ni-2.7Mo stainless steel.


### 2.10.3. Effect of Cold Rolling Ratios on theσ Phase

Abe et al. [56] reported on the effect of various cold rolling ratios on the precipitation of the σ phase in Fe-10Cr-30Mn stainless steel. Experimental result indicated the LAXRD (Low-angle X-Ray Diffraction) analysis at 923 K under various cold rolling ratios and aging times (30% CW-10 h, 30% CW-100 h, 30% CW-1000 h, and 80% CW-1000 h). The CW is an abbreviation of the “Cold Working.” The diffraction angle (2θ) of the LAXRD analysis is smaller than 85°, and this analytical method can show a clear diffraction signal. Many σ diffracted peaks can be detected, and there is no diffracted peak in the second phases. The diffracted peak of the σ phase is more obvious with 30% CW with an increase in aging time, which means that the precipitation of the σ phase does not decrease. Hence, cold rolling promotes the precipitation of the σ phase. Other diffracted peaks (σ(410), σ(212)) of the σ phase were examined when the cold rolling ratio increased to 80% CW, and the σ(312) peak was higher.Figure13 shows the TEM image in Fe-10Cr-30Mn stainless steel heat treated at 923 K for 3600 ks after cold rolling with various cold rolling ratios. The result shows that the grain size of the σ phase becomes smaller with increases in the cold rolling ratio, but that the distribution density of the σ phase increases. However, recrystallization only occurs above 30% CW, and there is no recrystallization with 10% CW. The σ phase only precipitates at the grain boundaries and triple points, as shown in Figure 13(a). A complete recrystallization happens with 60% CW and 80% CW, and then partial recrystallization occurs with 30% CW, as indicated in Figures 13(b)–13(d).The effect of various cold rolling ratios on distribution and grain size of theσ phase (a) 10% CW, (b) 30% CW, (c) 60% CW, and (d) 80% CW [56].
(a)(b)(c)(d)Huang and Chen [57] pointed out that cold working promoted the formation of the σ phase because the recrystallized and cold working boundaries were nucleated sites for the σ phase at low temperatures. At high temperatures, fine recrystallized grains formed and increased the area of the grain boundary so that the σ phase nucleated easily. Duhaj et al. [7] reported that the formation of the σ phase accelerated when the cold working degree was increased and that the σ phase content increased at the same time. It was concluded that the defects of stacking fault and twin acted as nucleation sites of the σ phase.Figures14(a)–14(c) show the relationship between recrystallization and the σ phase precipitation [56]. Initially, the σ phase nucleates at the recrystallized boundaries when crystallization occurs during cold rolling, as shown in Figure 14(a). This precipitation of the σ phase occurs because of the minimum strain energy during cold rolling. When the σ phase is formed, the recrystallized boundaries move to the deformed grains as a function of the recrystallized driving force (fR). A recrystallized reacting force (-fp) is also applied to the front of the recrystallized boundaries, as indicated in Figure 14(b). This recrystallized reacting force is due to the difference of the dislocation density from two sides of the recrystallized boundaries. Finally, the σ phase finishes the nucleation and grain growth and then escapes the recrystallized boundaries, as shown in Figure 14(c).Nucleation and grain growth ofσ phase at the recrystallized boundaries (fR: recrystallized driving force, -fp: recrystallized reacting force) [56].
(a)(b)(c)Koutsoukis et al. [58] studied the precipitation of the σ phase in S32654 super austenite stainless steel, cold rolled and aged at 850°C during cold rolling. The experimental result showed that the dispersion of the σ phase was more obvious when the cold rolling ratios were increased from 20% CW to 60% CW. The precipitation of the σ phase increased the hardness value about 500 HV with 60% CW when aged at 650°C.


### 2.10.4. Effect of Hot Rolling Ratios on theσ Phase

Hsieh et al. [59] studied the precipitation mechanism of the σ phase in 19Cr-9Ni-2Mn austenitic and 18Cr-0.75Si ferritic stainless steels, hot rolled at 800°C under hot rolling ratios of 0%, 50%, and 75%. The experimental results indicated that the precipitation tendencies of the σ phase increased gradually with increase of the hot rolling ratio.Experimental results show the morphological variations of theσ phase with hot rolling ratios of 0%, 50%, and 75% in 19Cr-9Ni-2Mn stainless steel. The morphologies of the σ phase changed from complete dendrites into fine globular structures when the hot rolling ratio was increased from 0% to 75%, with similar results in 18Cr-0.7Si stainless steel.Hsieh et al. [60] pointed out that the dendrite σ phase was an unstable morphology and that the globular σ phase was a stable morphology. Gill et al. [61] also reported that the globular σ phase resulted from a refinement of the unstable σ phase. The globular σ phase consumed the Cr content of the δ-ferrite completely. Hence, the globular σ phase was maintained in the rolled state samples. Furthermore, the dendrite σ phase occurred because of the partial consumption of the Cr content of the δ-ferrite.


## 2.10.1. Effect of Solid Solution-Treated Temperature and Cooling Rates on theσ Phase

Chen and Yang [51] studied 2205 duplex stainless steel as the solid solution treated at 1020°C with different cooling rates (1°C s−1, 0.5°C s−1, 0.25°C s−1, and 0.1°C s−1). The results showed that there was no σ phase when cooling rates were 1°C s−1 and 0.5°C s−1. The cooling rates of 0.25°C s−1 and 0.1°C s−1 indicated a slight σ phase and a lot of  σ phases, respectively. On the other hand, the precipitation of the σ phase was concentrated mainly at the δ/γ interface boundaries and δ-ferrite. However, Chen and Yang [51] also observed the precipitation of the σ phase at two solid solution temperatures, 1020°C and 1080°C. Experimental result indicated that the content of the σ phase was higher with the cooling rate at 1020°C than at 1080°C. Finally, Chen and Yang [51] used a solid solution temperature (1200°C) at a fixed cooling rate (0.1°C s−1) to discuss the precipitation of the σ phase. The experimental result showed that the Cr, Mo, and Si elements at 1200°C were higher than at 1080°C or 1200°C. This meant that the elemental diffusion of the Cr, Mo, and Si had an increasing effect on the precipitation of the σ phase at 1200°C at a cooling rate of 0.1°C s−1, as represented in Table 2 [51].Table 2
EDS analysis ofδ, σ, and γ phases at various solid solution temperatures and a fixed cooling rate of 0.1°C s−1[51].
ElementFeCrNiMoMnSiSolution treated at 1020°C and cooled at 0.1°C s−1σ61.7±0.525.7±0.63.46±0.066.84±0.081.15±0.041.15±0.04δ66.6±0.724.1±0.43.60±0.064.09±0.061.15±0.040.44±0.02γ68.0±0.720.8±0.46.45±0.082.42±0.061.45±0.040.32±0.02Solution treated at 1080°C and cooled at 0.1°C s−1σ62.7±0.525.2±0.63.92±0.065.90±0.081.14±0.041.13±0.04δ66.7±0.724.0±0.43.68±0.064.05±0.061.15±0.040.43±0.02γ68.3±0.720.9±0.46.39±0.082.45±0.061.44±0.040.33±0.02Solution treated at 1200°C and cooled at 0.1°C s−1δ67.0±0.723.6±0.43.83±0.083.96±0.061.16±0.040.41±0.02γ68.2±0.721.3±0.46.25±0.082.54±0.061.33±0.040.35±0.02


## 2.10.2. Effect of Tensile Strain Rate and Time on theσ Phase

Hong and Han [52] conducted a high-temperature tensile test in superduplex stainless steel (Fe-24Cr-7Ni-3Mo-0.14N) at 850°C with a strain rate of 3.16×10-3s-1. The grain size of the σ phase increased in a deformed sample and maintained a constant value in the undeformed sample. This was because the controlled grain boundaries slip-strain induced the grain growth [53, 54] during the super-plasticity. Chandra and Kuchlmayr [55] reported that the σ phase content decreased with an increase in strain rate when the aging temperature was 900°C in Fe-19Cr-5Ni-2.7Mo stainless steel.


## 2.10.3. Effect of Cold Rolling Ratios on theσ Phase

Abe et al. [56] reported on the effect of various cold rolling ratios on the precipitation of the σ phase in Fe-10Cr-30Mn stainless steel. Experimental result indicated the LAXRD (Low-angle X-Ray Diffraction) analysis at 923 K under various cold rolling ratios and aging times (30% CW-10 h, 30% CW-100 h, 30% CW-1000 h, and 80% CW-1000 h). The CW is an abbreviation of the “Cold Working.” The diffraction angle (2θ) of the LAXRD analysis is smaller than 85°, and this analytical method can show a clear diffraction signal. Many σ diffracted peaks can be detected, and there is no diffracted peak in the second phases. The diffracted peak of the σ phase is more obvious with 30% CW with an increase in aging time, which means that the precipitation of the σ phase does not decrease. Hence, cold rolling promotes the precipitation of the σ phase. Other diffracted peaks (σ(410), σ(212)) of the σ phase were examined when the cold rolling ratio increased to 80% CW, and the σ(312) peak was higher.Figure13 shows the TEM image in Fe-10Cr-30Mn stainless steel heat treated at 923 K for 3600 ks after cold rolling with various cold rolling ratios. The result shows that the grain size of the σ phase becomes smaller with increases in the cold rolling ratio, but that the distribution density of the σ phase increases. However, recrystallization only occurs above 30% CW, and there is no recrystallization with 10% CW. The σ phase only precipitates at the grain boundaries and triple points, as shown in Figure 13(a). A complete recrystallization happens with 60% CW and 80% CW, and then partial recrystallization occurs with 30% CW, as indicated in Figures 13(b)–13(d).The effect of various cold rolling ratios on distribution and grain size of theσ phase (a) 10% CW, (b) 30% CW, (c) 60% CW, and (d) 80% CW [56].
(a)(b)(c)(d)Huang and Chen [57] pointed out that cold working promoted the formation of the σ phase because the recrystallized and cold working boundaries were nucleated sites for the σ phase at low temperatures. At high temperatures, fine recrystallized grains formed and increased the area of the grain boundary so that the σ phase nucleated easily. Duhaj et al. [7] reported that the formation of the σ phase accelerated when the cold working degree was increased and that the σ phase content increased at the same time. It was concluded that the defects of stacking fault and twin acted as nucleation sites of the σ phase.Figures14(a)–14(c) show the relationship between recrystallization and the σ phase precipitation [56]. Initially, the σ phase nucleates at the recrystallized boundaries when crystallization occurs during cold rolling, as shown in Figure 14(a). This precipitation of the σ phase occurs because of the minimum strain energy during cold rolling. When the σ phase is formed, the recrystallized boundaries move to the deformed grains as a function of the recrystallized driving force (fR). A recrystallized reacting force (-fp) is also applied to the front of the recrystallized boundaries, as indicated in Figure 14(b). This recrystallized reacting force is due to the difference of the dislocation density from two sides of the recrystallized boundaries. Finally, the σ phase finishes the nucleation and grain growth and then escapes the recrystallized boundaries, as shown in Figure 14(c).Nucleation and grain growth ofσ phase at the recrystallized boundaries (fR: recrystallized driving force, -fp: recrystallized reacting force) [56].
(a)(b)(c)Koutsoukis et al. [58] studied the precipitation of the σ phase in S32654 super austenite stainless steel, cold rolled and aged at 850°C during cold rolling. The experimental result showed that the dispersion of the σ phase was more obvious when the cold rolling ratios were increased from 20% CW to 60% CW. The precipitation of the σ phase increased the hardness value about 500 HV with 60% CW when aged at 650°C.


## 2.10.4. Effect of Hot Rolling Ratios on theσ Phase

Hsieh et al. [59] studied the precipitation mechanism of the σ phase in 19Cr-9Ni-2Mn austenitic and 18Cr-0.75Si ferritic stainless steels, hot rolled at 800°C under hot rolling ratios of 0%, 50%, and 75%. The experimental results indicated that the precipitation tendencies of the σ phase increased gradually with increase of the hot rolling ratio.Experimental results show the morphological variations of theσ phase with hot rolling ratios of 0%, 50%, and 75% in 19Cr-9Ni-2Mn stainless steel. The morphologies of the σ phase changed from complete dendrites into fine globular structures when the hot rolling ratio was increased from 0% to 75%, with similar results in 18Cr-0.7Si stainless steel.Hsieh et al. [60] pointed out that the dendrite σ phase was an unstable morphology and that the globular σ phase was a stable morphology. Gill et al. [61] also reported that the globular σ phase resulted from a refinement of the unstable σ phase. The globular σ phase consumed the Cr content of the δ-ferrite completely. Hence, the globular σ phase was maintained in the rolled state samples. Furthermore, the dendrite σ phase occurred because of the partial consumption of the Cr content of the δ-ferrite.


## 3. Summary

The above review has presented a clear overview of the precipitation of theσ phase in stainless steels. This review paper has provided the metallographic characteristics, precipitation mechanisms, properties effects, and prediction methods of the σ phase in stainless steels. The precipitation of the σ phase is the main reason for the degradation of stainless steels. Understanding the precipitation of the σ phase will allow for some control over the properties of stainless steels.



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*Source: 732471-2012-03-08.xml*