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Dislocation (like screw or edge dislocation) is not a 'real' thing, while Newton's laws only apply to a real object (no matter macroscopic, like stars, or microscopic, like atoms).

In the derivation of Peach-Koehler force (stress acting on a dislocation), I understand that the force is actually acting on those atoms around the dislocation, which is equivalent to acting on the dislocation in the mathematical sense. However, based on the above point (treating dislocation as a 'real' thing), some books directly use force balance and other mechanical analysis on dislocation.

Can we treat dislocation as a 'real' thing in all mechanical cases just as the void in a solid when analysing electrical properties? Is there some way to think about it easily other than a complicated mathematical argument?

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Although the mathematical theory of dislocations was developed long before the development of the electron microscope (EM), the invention of the EM enabled materials scientists to image dislocations. We have pictures of crystal dislocations, and can measure their effects upon electrical as well as many other physical properties - so to me that means dislocations are 'real.'

Perhaps your question is actually whether mathematical models of dislocations in a continuum (these are based on Newtonian Mechanics) are accurate representations of dislocations in a crystal lattice. They can be accurate, and sometimes very useful for predicting macroscopic properties that are influenced by dislocations.

I believe there have also been computer models of dislocations and other crystal defects developed based upon a more 'realistic' analysis of a lattice, atomic bonds, quantum-effects etc.

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