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21.12: Summary

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    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.

    Going further


    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,

    Ulrich Messerschmidt, Dislocation Dynamics During Plastic Deformation, Springer-Berlin, Heidelburg, 2010, ISBN: 978-3-642-03176-2, 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.

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