How can σ-phase be precipitated in ferritic stainless steel?

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How can σ-phase be precipitated in ferritic stainless steels? The σ-phase in ferritic steels is a typical FeCr intermetallic compound with a chromium content of around 45%; it is non-magnetic, hard, and brittle. In pure Fe-Cr alloys, the σ phase can be formed when wCr > 20%. The presence of other alloying elements, particularly Mn, Si, Mo, W, etc., promotes the formation of the σ phase at lower Cr contents, and it can have a ternary composition.    Chromium is an element that narrows the austenite region; when its mass fraction is above about 12%, the austenite region disappears completely. This means that alloys with wCr>12% do not undergo a γ-α transformation, and therefore neither grain refinement nor hardening occurs. Cr is a strong ferrite-forming element; therefore, ferrite can precipitate from the liquid metal throughout the entire alloy range. When the Cr content is high, the brittle and hard σ phase begins to precipitate from δ-ferrite at around 820°C. The σ phase has a high Cr content, which leads to embrittlement.    In ordinary pure ferritic stainless steels with wCr > 21%, the σ phase can precipitate if heated for an extended period at temperatures between 520 and 820°C. The formation of the σ phase is related to factors such as the chemical composition and microstructure of the weld metal, heating temperature, holding time, and prior cold deformation. Elements in steel that promote the formation of ferrite, such as aluminum, silicon, molybdenum, titanium, and niobium, can strongly increase the tendency to form the σ phase ； Manganese reduces the chromium content required for the formation of the σ phase in high-chromium steel ； Carbon and nitrogen can stabilize the austenite phase and form compounds with chromium, which increases the chromium content required for the formation of the σ phase. Nickel can raise the temperature required to form the σ phase. Since the formation of the σ phase depends on the diffusion and migration of atoms such as Cr and Fe, its formation rate is relatively slow. Steel with wCr=17% begins to precipitate the σ phase only after being tempered at 550°C for 1000 hours. When 2% Mo is added, the precipitation time of the σ phase is significantly reduced; the σ phase appears after about 200 hours of tempering at 600°C. Therefore, sufficient attention must be paid to the welded high-temperature components of ferritic heat-resistant steels that are used for extended periods in the temperature range where the σ-phase forms.