There are two types of energy associated with a dislocation
- In-plane energy – decreases as dislocation width increases, so acts to spread the misfit strain over a larger region
- Misalignment energy – increases as the dislocation width increases, so acts to localise the misfit strains
- The dislocation width will be the value for which the sum of the two types of energy is a minimum
- w/b is strongly dependent on d/b, where b is the atom spacing parallel to the slip plane and d normal to it.
- Changes in misfit energy are the primary obstacle to dislocation motion.
- Using the atomistic model with a moving origin allows us to estimate the energy as the dislocation moves, hence we can determine the Peierls energy and the Peierls stress.
- Peierls stress increases exponentially as the dislocation width w/b decreases.
Derek Hull and, D.J.Bacon, Introduction to Dislocatioins (Volume 3 of Materials Science and technology, 5th Edition), Elsevier, 2011, ISBN: 008096673X, 9780080966731
H.J.Frost and M.F.Ashby, Deformation-mechanism maps: the plasticity and creep of metals and ceramics, First Edidtion, Pergamon Press, 1982, ISBN: 0080293379, 9780080293379, http://engineering.dartmouth.edu/defmech/
Ulrich Messerschmidt, Dislocation Dynamics During Plastic Deformation, Springer-Berlin, Heidelburg, 2010, ISBN: 978-3-642-03176-2, 978-3-642-03177-9, https://doi.org/10.1007/978-3-642-03177-9
Howie,P.R., Thompson, R.P., Korte-Kerzel,.S., & Clegg,W.J. (2017), Softening non-metallic crystals by inhomogenenous elasticity. Scientific Reports, 7(1), 11602. https://doi.org/10.1038/s41598-017-09453-1