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Determination of Retained Austenite in Quenched Steel
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Qualitative determination of retained ausenite content in the heat treated steels is possible by X-ray diffraction technique. One of the basic approach is by comparing integrated intensities. 

 

The expression for the intensity diffracted by a single phase powder specimen in a diffractometer is given by:

 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»I«/mi»«mo»=«/mo»«mfenced»«mfrac»«mrow»«msub»«mi»I«/mi»«mi»o«/mi»«/msub»«msup»«mi»e«/mi»«mn»4«/mn»«/msup»«/mrow»«mrow»«msup»«mi»m«/mi»«mn»2«/mn»«/msup»«msup»«mi»c«/mi»«mn»4«/mn»«/msup»«/mrow»«/mfrac»«/mfenced»«mfenced»«mfrac»«mrow»«msup»«mi»§#955;«/mi»«mn»3«/mn»«/msup»«mi»A«/mi»«/mrow»«mrow»«mn»32«/mn»«mi»§#960;«/mi»«mi»r«/mi»«/mrow»«/mfrac»«/mfenced»«mfenced»«mfrac»«mn»1«/mn»«msup»«mi»§#957;«/mi»«mn»2«/mn»«/msup»«/mfrac»«/mfenced»«mfenced close=¨]¨ open=¨[¨»«mrow»«msup»«mfenced close=¨|¨ open=¨|¨»«mi»F«/mi»«/mfenced»«mn»2«/mn»«/msup»«mi»p«/mi»«mfenced»«mfrac»«mrow»«mn»1«/mn»«mo»+«/mo»«msup»«mi mathvariant=¨normal¨»cos«/mi»«mn»2«/mn»«/msup»«mn»2«/mn»«mi»§#952;«/mi»«/mrow»«mrow»«msup»«mi mathvariant=¨normal¨»sin«/mi»«mn»2«/mn»«/msup»«mi»§#952;«/mi»«mo»+«/mo»«/mrow»«/mfrac»«/mfenced»«/mrow»«/mfenced»«mfenced»«mfrac»«msup»«mi»e«/mi»«mrow»«mo»-«/mo»«mn»2«/mn»«mi»M«/mi»«/mrow»«/msup»«mrow»«mn»2«/mn»«mi»§#956;«/mi»«/mrow»«/mfrac»«/mfenced»«/math»

Above equation can be rewritten as:

 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»I«/mi»«mo»=«/mo»«mfrac»«mrow»«msub»«mi»K«/mi»«mn»2«/mn»«/msub»«mi»R«/mi»«/mrow»«mrow»«mn»2«/mn»«mi»§#956;«/mi»«mi»m«/mi»«/mrow»«/mfrac»«/math»

Where,

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»K«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mfenced»«mfrac»«mrow»«msub»«mi»I«/mi»«mi»o«/mi»«/msub»«msup»«mi»§#955;«/mi»«mn»3«/mn»«/msup»«mi»A«/mi»«/mrow»«mrow»«mn»32«/mn»«mi»§#960;«/mi»«mi»r«/mi»«/mrow»«/mfrac»«/mfenced»«mfenced close=¨]¨ open=¨[¨»«mrow»«msup»«mfenced»«mfrac»«msub»«mi»§#956;«/mi»«mi»o«/mi»«/msub»«mrow»«mn»4«/mn»«mi»§#960;«/mi»«/mrow»«/mfrac»«/mfenced»«mn»2«/mn»«/msup»«mfrac»«msup»«mi»e«/mi»«mn»4«/mn»«/msup»«msup»«mi»m«/mi»«mn»2«/mn»«/msup»«/mfrac»«/mrow»«/mfenced»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»R«/mi»«mo»=«/mo»«mfenced»«mfrac»«mn»1«/mn»«msup»«mi»§#957;«/mi»«mn»2«/mn»«/msup»«/mfrac»«/mfenced»«mfenced close=¨]¨ open=¨[¨»«mrow»«msup»«mfenced close=¨|¨ open=¨|¨»«mi»F«/mi»«/mfenced»«mn»2«/mn»«/msup»«mi»p«/mi»«msup»«mfenced»«mfrac»«mrow»«mn»1«/mn»«mo»+«/mo»«msup»«mi mathvariant=¨normal¨»cos«/mi»«mn»2«/mn»«/msup»«mn»2«/mn»«mi»§#952;«/mi»«/mrow»«mrow»«msup»«mi mathvariant=¨normal¨»sin«/mi»«mn»2«/mn»«/msup»«mi»§#952;«/mi»«mo»+«/mo»«/mrow»«/mfrac»«/mfenced»«mn»2«/mn»«/msup»«msup»«mi»e«/mi»«mrow»«mo»-«/mo»«mn»2«/mn»«mi»M«/mi»«/mrow»«/msup»«/mrow»«/mfenced»«/math»

 

K2 depends only on incident beam, but not on crysal structure.

 

R depends only on crystal structure, but not on surrounding phase.

 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«mi»§#956;«/mi»«/math» depends on both crystal structure and surrounding phase.

 

Thus for Austenite «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mi»§#947;«/mi»«mo»)«/mo»«/math» and Martensite «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mi»§#945;«/mi»«mo»)«/mo»«/math» above euation becomes: 

 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»I«/mi»«mi»§#947;«/mi»«/msub»«mo»=«/mo»«mfrac»«mrow»«msub»«mi»K«/mi»«mn»2«/mn»«/msub»«msub»«mi»R«/mi»«mi»§#947;«/mi»«/msub»«msub»«mi»C«/mi»«mi»§#947;«/mi»«/msub»«/mrow»«mrow»«mn»2«/mn»«mi»§#956;«/mi»«mi»m«/mi»«/mrow»«/mfrac»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»I«/mi»«mi»§#945;«/mi»«/msub»«mo»=«/mo»«mfrac»«mrow»«msub»«mi»K«/mi»«mn»2«/mn»«/msub»«msub»«mi»R«/mi»«mi»§#945;«/mi»«/msub»«msub»«mi»C«/mi»«mi»§#945;«/mi»«/msub»«/mrow»«mrow»«mn»2«/mn»«mi»§#956;«/mi»«mi»m«/mi»«/mrow»«/mfrac»«/math»

 

From these two equations:

 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«msub»«mi»I«/mi»«mi»§#947;«/mi»«/msub»«msub»«mi»I«/mi»«mi»§#945;«/mi»«/msub»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«msub»«mi»R«/mi»«mi»§#947;«/mi»«/msub»«msub»«mi»C«/mi»«mi»§#947;«/mi»«/msub»«/mrow»«mrow»«msub»«mi»R«/mi»«mi»§#945;«/mi»«/msub»«msub»«mi»C«/mi»«mi»§#945;«/mi»«/msub»«/mrow»«/mfrac»«/math»

In this equation we have to caluclate «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»C«/mi»«mi»§#947;«/mi»«/msub»«mo»/«/mo»«msub»«mi»C«/mi»«mi»§#945;«/mi»«/msub»«/math» to evoluate reatined austenite.

 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»I«/mi»«mi»§#945;«/mi»«/msub»«/math» and «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»I«/mi»«mi»§#947;«/mi»«/msub»«/math» are the integrated intensities for each of the diffraction line (area unde the curve after background substraction).

 

By considering «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»C«/mi»«mi»§#947;«/mi»«/msub»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«msub»«mi»C«/mi»«mi»§#945;«/mi»«/msub»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mn»1«/mn»«/math»we can find out the actual amount of each phase. By cosidering several pairs of austenite and matensite lines, we can obtain several values of retained austenite content.  

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