What is the relationship between the Kernel Average Misorientation (KAM) and the dislocation density in the materials?
Hello,
A KAM map provides a quantitative measurement of the local lattice curvature around each measurement in an EBSD map and therefore will give some indication of the local variations of geometrically necessary dislocation (GND) densities. However, it will not provide quantitative GND density information and won’t reveal anything about the nature of the dislocations.
Regards.
Source: Oxford Instruments (https://www.oxinst.com/)
The Kernel Average Misorientation is often used as an approximate measure for the local crystallographic lattice curvature, a value which is typically retrieved from electron back scatter diffraction data.
The KAM value can be calculated for different neighborhood spheres, where aspects such as the number of spheres / pixels / shells considered, the resolution of the EBSD mappings and the homogeneity of the curvature (one crystal spin or backward / forward etc) etc play important roles for the fidelity and usefulness of the extracted GND data.
The main scientific consideration behind that however is always the same namely that any inelastic lattice curvature in a crystal must be accommodated by a corresponding kinematic defect carrier (such as a dislocation a twin etc) with uni-directionally polarized Burgers vectors.
(fun task to better understand the kinematics here: calculate the number of dislocations u need to wind a Au wire of 1 mm thickness around ur finger....)
In other words any lattice curvature in a crystal translates exactly to a certain number of dislocations with the same net orientation of its total b vector. In kinematic language you could also say that the local anti-symmetric portion of the displacement gradient tensor must be matched by a corresponding number of dislocations which can be seen as the kinematic quantization (elementary inelastic rotation unit) of inelastic lattice curvature.
For this basic kinematic relationship you should start with the original paper of: The deformation of plastically non-homogeneous materials, M. F. Ashby, Philosophical Magazine 21 (170):399-424 (1970). and works of Nye etc. There is all u need as a starter.
Irrespective of these rather straightforward relationships you should however be careful as the GND density does not linearly translate to the total dislocation density because the former depends on the total lattice curvature after a deformation while the latter depends on the homogeneity of the dislocation patterning and the total deformation history etc . (here: read e g this book: Thermodynamics and Kinetics of Slip Volume 19 of Progress in materials science ; Authors, U. F. Kocks, Ali S. Argon, M. F. Ashby ; it is here: http://kocks.ucsd.edu/docs/KAA.PDF)
I attach a few papers that might give you a bit more background.
Good luck!
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