By Vasily Bulatov, Wei Cai
This ebook offers a huge choice of types and computational equipment - from atomistic to continuum - utilized to crystal dislocations. Its function is to aid scholars and researchers in computational fabrics sciences to procure functional wisdom of correct simulation tools. simply because their habit spans a number of size and time scales, crystal dislocations current a standard floor for an in-depth dialogue of numerous computational techniques, together with their relative strengths, weaknesses and inter-connections. the main points of the coated equipment are offered within the kind of "numerical recipes" and illustrated through case experiences. a set of simulation codes and knowledge records is made on hand at the book's web site to assist the reader "to learn-by-doing" via fixing the workout difficulties provided within the ebook.
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Additional info for Computer Simulations of Dislocations
Finally, F (ρi ) is an embedding function deﬁning the energy required to embed atom i into an envi√ ronment with electron density ρi . For example, the form F (ρ) =−A ρ is used in the Finnis–Sinclair (FS) potential . Other similar potentials, such as effective medium theory (EMT) models, use somewhat different forms for the electron density contribution function f (r) and the embedding function F (ρ) . Because the embedding function is non-linear, the EAM-like potentials include many-body effects that cannot be expressed by a superposition of pair-wise interactions.
3). g. eq. 6), the convention is to add half of every pair-wise interaction term (such as in the LJ potential) and one third of every three-body term (such as in the SW potential) to the local energy of each participating atom. For the EAM-like potentials, the local energy of atom i can be deﬁned as Ei = j 1 φ(|ri − rj |) + F (ρi ). 11) It is easy to check that the sum of local energies of all atoms is equal to the total potential energy, eq. 8), as it should be. 3 Computational Cost of Interatomic Interaction Models As has already been mentioned, the ﬁrst principles theory describes the interatomic interactions more accurately than the interatomic potentials but at a much higher computational cost.
For a mixed dislocation, the edge component of the Burgers vector determines how many atoms need to be inserted or removed during climb motion. Consider a general dislocation with Burgers vector b, which moves on a plane with normal vector n and sweeps out an area A ( A is positive if the dislocation moves in the direction of n × ξ ). Let V = (b · n) A. If V > 0, then material of volume V has to be inserted. If V < 0, then material of volume | V | has to be removed. 20 I N TRODUC T ION TO C RYSTAL D ISLO CATIO N S The number of atoms to be inserted or removed can then be obtained by dividing V by the volume of the primitive cell and multiplying by the number of atoms in the basis.