Critical Size for Edge Dislocation Free Free-Standing Nanocrystals by Finite Element Method
As the size of a free-standing crystal approaches a few tens of nanometers, the image force experienced by a dislocation can exceed the Peierls force. This will lead to dislocations leaving the nanocrystal without the application of an external stress and thus making it dislocation free. In this investigation a finite element methodology is developed for the calculation of the critical size at which a free-standing crystal becomes edge dislocation free. A simple edge dislocation is simulated using Finite Element Method (FEM) by feeding-in the appropriate stress-free strain in an idealized domains corresponding to the introduction of an extra half-plane of atoms. The image force experienced by the edge dislocation is calculated as the gradient of the plot of the energy of the system as a function of the position of the simulated dislocation. In nanocrystals, due to the proximity of multiple surfaces, the net image force due to multiple images has to be calculated. Additionally, surface or/and domain deformations have to be taken into account in nanocrystals; which can drastically alter the image force. For the crystal to become dislocation free, the minimum image force experienced by the dislocation, has to exceed the Peierls force. Minimum image force values calculated from the FEM models are compared with the Peierls stress values obtained from literature to determine the critical domain size at which crystal becomes edge dislocation free.
P. Khanikar and A. Subramaniam, "Critical Size for Edge Dislocation Free Free-Standing Nanocrystals by Finite Element Method", Journal of Nano Research, Vol. 10, pp. 93-103, 2010