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My professor, when discussing about Random Walk model during diffusion in metals said that "Vacancies are equilibrium defects but dislocations are not". I could not understand why. Why is it so?

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  • $\begingroup$ researchgate.net/post/… $\endgroup$
    – user14407
    Commented Nov 11, 2018 at 16:27
  • $\begingroup$ @SolarMike , what has equilibrium have to do with a defect like vacancy? $\endgroup$
    – Nitz
    Commented Nov 11, 2018 at 16:38

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Imagine you have two boxes separated by a removable partition. Each box is filled with a different pure monatomic gas. When you remove the partition, the gases mix. Their equilibrium state tends toward an equitable mixture at every point in time. The likelihood of the gases spontaneously separating is essentially zero for any appreciable number of atoms. This is modeled by statistical mechanics, and occurs for any similar system consisting of multiple mobile components.

Solids are no different from gases in that they obey the principles of statistical mechanics. In the case of a crystal lattice, vacancies are lattice points with no atom, i e. empty space. All solids are constantly exposed to empty space at their surface, and tend to mix with it. This may sound strange, but remember that atoms in a lattice are mobile, and can shift lattice positions if a neighboring space is available. All of the lattice points at the surface have lots of space available outside the crystal. The same applies at grain boundaries and at dislocations. So by random atomic movement, empty space can diffuse into the lattice and create vacancies. As we established with the two-gas setup, the empty space and solid tend to be in some mixed equilibrium, i.e. the equilibrium concentration of vacancies is non-zero. The only detail remaining is that the mixture isnt equal because the atoms of the solid have strong cohesive forces binding them together. Unlike gases the crystal doesn't evenly diffuse about the room and instantly vaporize. At least, in equilibrium it wouldn't (discounting vapor pressure)!

As for dislocations, their equilibrium concentration is zero because they don't spontaneously form, but can spontaneously leave crystals. Recall that dislocations form in response to a net shear creating an "excess" half plane of atoms, or alternately an "excess" half plane of vacancies. This occurs by a process called "slip". Slip does not occur in equilibrium. Getting a half plane of vacancies into the crystal, all organized along a plane, and done spontaneously, is simply not going to happen by chance. In contrast, an existing dislocation can move spontaneously by absorbing or emitting dislocations in a process called "climb". If a vacancy is absorbed, the half-plane of atoms decreases in number, moving the dislocation line in that direction. If a vacancy is emitted, the opposite occurs. If the dislocation line reaches the surface, it is no longer a dislocation. Thus dislocations can leave the crystal, but can't enter, resulting in a net equilibirum concentration of zero.

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Nature will always try to minimize the number of dislocations and grain-boundaries, whereas in the case of vacancies, there is an optimum number that will lead to the lowest Gibbs energy.

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