Why are dislocations unstable thermodynamically contrary to that of point defects?
This question was answered on quora:
https://www.quora.com/Why-are-point-defects-thermodynamically-stable-but-dislocations-are-not
There is a good book about dislocations http://ru.b-ok.org/book/2275731/29c803
Dear Rajorshi Koyal,
I have mentioned few Research articles on why are dislocations unstable thermodynamically contrary to that of point defects.
I hope articles will help you.
01. Chapter The Elastic Field of Point Defects
02. http://www.gpcet.ac.in/wp-content/uploads/2017/03/I-II-ME-MSE-UNIT-I-LN.pdf
03. https://www3.nd.edu/~amoukasi/CBE30361/Lecture_Defects_2014.pdf
04. https://www.coursehero.com/file/8207442/Chapter-5b-Crystal-Imperfections-dislocations/
I hope I have answered your question.
With Best Wishes,
Samir G. Pandya
Although the answer on Quora (Link provided by Gert Van) explains this partially, it does not systematically address the non-equilibrium nature of dislocations. The author of that answer has derived the free energy change as a function of the mole fraction of vacancies. That part shows that a certain concentration of point defects are energetically favorable in any crystal. Of course this is purely due to the comparative increase in configurational entropy, which offsets the increase in enthalpy from broken bonds that are associated with vacancies. The second part of the answer by the author is incomplete. I will try to complete the missing pieces of the answer here.
As a thought experiment, a similar thermodynamic calculation for increase in entropy via-a-vis the enthalpy can be performed for dislocations. However, since the dislocation is a line defect, which implies that entire rows of atoms have broken bonds, the enthalpic penalty per unit length is significantly higher than the increase in entropy. Therefore the equilibrium concentration of dislocations that is calculated from this trade off is about 3 orders of magnitude lesser than what is typically observed in crystals. Given that this paradox cannot be resolved by thermodynamic arguments, dislocations are considered as non-equilibrium defects. This implies that if sufficient energy is supplied to the crystal over time, dislocations would get eliminated over time. This is the reason why dislocations get annihilated during annealing although the converse occurs in the context of point defects.
Note: Strain energy perspectives are involved in dislocations as well as point defects. Therefore the answer provided in Quora is partially incorrect as well. However, he is correct in pointing out that the strain energy associated with dislocations will be higher
Dear Narayan R.L. , well I wouldn't say that the answer on Quora is incorrect or even incomplete (the part about dislocations). The reason why there is no dislocations at equilibrium is exactly related to their (very) high free energies compared to point defects, as mentioned on Quora. The corresponding calculated concentration is then so low that it is completely negligible.
The fact that there are often dislocations in real crystals is related to their growth or synthesis, which are non equilibrium processes. Once dislocations are introduced, they are difficult to remove (comparatively to point defects). Also note that it is possible to synthesize certain materials with no dislocations at all (silicon for instance). It is therefore not really a paradox.
Dear Laurent Pizzagalli , Thank you for the response. I do not have a problem with the free energy part of the answer in Quora. But since the author of that post mentions that its the strain energy which leads to high self energy of the dislocations, it could mislead people into assuming that point defects do not have stress fields associated with them. Otherwise, it is quite an insightful answer. Thank you for the clarification in this regard.
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Materials Science