Especially the C12, C44, and Ai values for ferrite pearlite microstructure.
Thanks
Overview:
The most common approach to determine the screw/edge character of dislocations in a bulk sample is to study the elastic strain anisotropy with modified Williamson-Hall (mWH) analysis. The three papers below are good starting points.
General Experimental Procedure:
You must take a high-resolution and low-noise scan of several peaks of your steel. Often, the first six peaks are used, i.e. for a Cu scan you will collect a 2theta range of 40 to 150 degrees, giving you a scan of the following ferrite peaks: {011}, {002}, {112}, {022}, {013}, and {222} . You must also take a scan of a standard reference material such as fully annealed ferritic steel or lanthanum hexaboride (LaB6) - this "standard'' scan will be used to quantify the instrument's "broadening". You will account for the instrumental broadening using "Voigt correction".
Post-Experiment Analysis:
Please see the work of Ungar below.
Comment on Uncertainty
With correct application of the mWH method, you will be able to determine dislocation density, crystallite (subgrain) size, and dislocation character (nominal fraction of screw versus edge). As a caveat, the method is fairly laborious and subject to bias error if you do a bad job of sample preparation or analysis. Be careful and perform your analysis on multiple replicates. I also recommend confirming your results with another technique like TEM or EBSD (micro-orientation based approaches like kernel average misorientation can also help you to achieve a greater understanding of dislocation content/microstrain and grain/subgrain size).
Good luck!
References:
An Improved X-ray Diffraction Analysis Method to Characterize Dislocation Density in Lath Martensitic Structures by Hajyakbary et. al. and The contrast factors of dislocations in cubic crystals: the dislocation model of strain anisotropy in practice by Ungar et. al. Use of the Voigt Function in a Single-Line Method for the Analysis of X-ray Diffraction Line Broadening by De Keijser et. al. Papers attached here. Article An Improved X-ray Diffraction Analysis Method to Characteriz...
Article The contrast factors of dislocations in cubic crystals: The ...
Article Use of the Voigt Function in a Single-Line Method for the An...
Dislocation density and micro strain .
Dislocation density 1/D ^2 X 10^-3 (nm ^-2)
D is crystallite size
Overview:
The most common approach to determine the screw/edge character of dislocations in a bulk sample is to study the elastic strain anisotropy with modified Williamson-Hall (mWH) analysis. The three papers below are good starting points.
General Experimental Procedure:
You must take a high-resolution and low-noise scan of several peaks of your steel. Often, the first six peaks are used, i.e. for a Cu scan you will collect a 2theta range of 40 to 150 degrees, giving you a scan of the following ferrite peaks: {011}, {002}, {112}, {022}, {013}, and {222} . You must also take a scan of a standard reference material such as fully annealed ferritic steel or lanthanum hexaboride (LaB6) - this "standard'' scan will be used to quantify the instrument's "broadening". You will account for the instrumental broadening using "Voigt correction".
Post-Experiment Analysis:
Please see the work of Ungar below.
Comment on Uncertainty
With correct application of the mWH method, you will be able to determine dislocation density, crystallite (subgrain) size, and dislocation character (nominal fraction of screw versus edge). As a caveat, the method is fairly laborious and subject to bias error if you do a bad job of sample preparation or analysis. Be careful and perform your analysis on multiple replicates. I also recommend confirming your results with another technique like TEM or EBSD (micro-orientation based approaches like kernel average misorientation can also help you to achieve a greater understanding of dislocation content/microstrain and grain/subgrain size).
Good luck!
References:
An Improved X-ray Diffraction Analysis Method to Characterize Dislocation Density in Lath Martensitic Structures by Hajyakbary et. al. and The contrast factors of dislocations in cubic crystals: the dislocation model of strain anisotropy in practice by Ungar et. al. Use of the Voigt Function in a Single-Line Method for the Analysis of X-ray Diffraction Line Broadening by De Keijser et. al. Papers attached here. Article An Improved X-ray Diffraction Analysis Method to Characteriz...
Article The contrast factors of dislocations in cubic crystals: The ...
Article Use of the Voigt Function in a Single-Line Method for the An...
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