Gamma iron even after it cooled down

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The 300 series of stainless steel is austenitic, characterized by gamma iron, which exhibits weak magnetism due to nickel content. The Curie temperature for iron, at 1000K or 730 degrees C, influences its magnetic properties. Nickel stabilizes the gamma allotrope of iron, while chromium, present in ferritic stainless steel, stabilizes the alpha allotrope. The ability of alloying elements to modify the host's crystal structure depends on the size and chemical similarity of the atoms involved. This phenomenon is a common characteristic of alloy systems, highlighting the complex interactions between different elements.
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The 300 series of stainless steel is austenitic meaning that the iron in the steel is gamma iron. This means that if it is magnetic it is only the weak magnetism from the nickel.

I read the wikipedia article on allotropes of iron and it says that gamma iron occurs when the iron is heated to 1000K or 730 degrees C. That is the curie temperature for iron.

But how does the nickel in the steel keep the iron in its gamma allotrope unlike ferric stainless steel where there is only chromium, iron, and carbon and it is in its alpha allotrope.
 
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As a rule of thumb, an alloying element in solid solution will tend to modify its host to its own crystal structure. In this case, pure nickel is cubic close packed and tends to stabilise the cubic close packed phase in iron ie the gamma phase.

The size of the effect is related to the the relative size of the host and solute atoms as well as their chemical similarity.

Similarly, pure chromium is body centred cubic and tends to stabilise the body centred cubic phase of iron ie alpha or ferrite. Above about 15% Cr, there is no gamma phase in an iron-chromium alloy with no nickel.

That's by no means a formally correct answer to your question nor an explanation for why this happens but it's a common feature of alloy systems
 

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