A connected question is: what is known (or measured experimentally) about the electromagnetic fields round an elastic-plastic crack that propagates quasi-statically in metallic materials?
Based on quantum mechanical calculations, an electric potential round a dislocation in metals has been suggested and an estimate provided ( see in Nabarro, "Theory of Crystal Dislocations", Oxford University Press, Oxford, 1967). As a direct consequence and by superposition, there would exist electromagnetic fields round an elastic-plastic crack that propagates quasi-statically in metallic materials (see Anongba, ResearchGate). Can people comment about this matter?
Normally, in metals charges are screened on an atomic scale by the free electrons, so no static electrical fields can exist beyond this scale. The same is true for quasi-static crack propagation.
What are the reasons for your question?
Do you believe in the existence of an electric potential round an edge dislocation in metals?( see relation (9.11), p.615 in Nabarro, "Theory of Crystal Dislocations", Oxford University Press, Oxford, 1967)
I have accepted this result as a consequence of the distortion of the lattice and a redistribution of the free electrons. The potential is that of a line dipole.
If the answer is yes, then the reasons of my questions in the Q&A seem intelligible, in particular: what is known (or measured experimentally) about the electromagnetic fields round an elastic-plastic crack that propagates quasi-statically in metallic materials?
Indeed Nabarro claims the existence of electrical potential around dislocations in metals. His arguments is given in the following:
The inhomogeneous dilatation ∆D (x) r ( x position vector) of the lattice due to the dislocation leads to a redistribution r of the conduction electrons. As a result, an electric potential VD(x)and r electric fieldED(x)are built round a dislocation; furthermore the relation linking ∆D and VD is linear.
Patrick and Tapan, the redistribution of free electrons can occur ONLY as a result of an electric field Eo(x) created by the local lattice distortion (the field of bound electrons).
The reaction of the free electrons will be such as to kill this field Eo(x) and make the TOTAL field equal to zero. If one calculates the electric potential created by the redistribution of electrons ONLY and forgets about Eo(x), one finds a field -Eo(x).
In equilibrium the total field must be zero, otherwise there will be a force acting on all other free electrons and it will not be a stationary state. Isn't this obvious?
Do you mean that any distortion, of increasing magnitude, of the lattice would result in zero electric potential? Your view is for a perfect lattice. Remember: The potential is that of a line dipole(zero macroscopic electric charge) .
Many people have added to the theory: Nabarro, Cottrell, Ziman, Friedel, Landauer, Seeger... The theory of the electric resistivity produced by dislocations in cold-worked materials makes use of this electric potential round a dislocation. It is also observed that foreign charged atoms are attracted by dislocations in metals. Nabarro (1967, page 405) noted: The first experimental evidence of the importance of electrostatic interactions in alloys came from a study (Weinig and Machlin, Acta metall. 4 (1956) 262) of the alloys of aluminium with magnesium, copper, zinc, germanium, silver and cadmium (please refer to the corresponding section for detailed explanation).
Dear Patrick and Tapan, after more thinking about the subject, I understood that you were right and I was wrong. Indeed, an electric field will exist in a metal around dislocations and other lattice distortions.
My mistake was due to the incorrect assumption that an electric field in a conductor will necessarily result in an electron current. In fact, a non-homogeneous electron concentration will result in a diffusion current too. Absence of current requires that the gradient of the electrochemical potential (not of the electric potential) is zero.
This is well known for all sort of contact phenomena. Consider for example an A-B-A structure, where A and B are different conductors. (If the B layer is very thin, this can be viewed as a local distortion of the A lattice). There will be electric fields around the contact regions, as wall as variations of the electron concentration. In equilibrium, the diffusion and field currents cancel each other (no gradient of electrochemical potential!), however there certainly will exist electric fields and voltage drops in the contact regions.
The contact voltages cannot be directly measured by a voltmeter (because in equilibrium there will be no current through our voltmeter), however there are other ways to experimentally establish their existence. I believe that the same applies to electric fields around dislocations.
It would extremely interesting to check whether we can verify the existence of the electric potential around dislocation experimentally. May be there are already such experiments and it is likely that Nabarro's book (unfortunately I cannot get that book here) gives such information. After all dislocation is a very old field of research.
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