Computer Simulation of Creation and Motion of Edge Dislocations in Face Centered Crystals
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INTRODUCTION It is well known that creation, motion and interaction of dislocations play an important role in the plastic deformation of crystalline solids. It is important to know how the dislocations are atomistically created and move in thin films. In this paper creation and motion of dislocations were simulated by use of molecular dynamics. Dislocations in face centered cubic metals are usually dissociated into Heidenreich-Shockley partial dislocations. The width of the dissociated partial dislocations depends on the repulsive force between two partial dislocations and attractive force due to stacking faults. Edge dislocations in a face centered cubic metal were automatically dissociated by the molecular dynamics method. Holding the displacements in < 12 I> a complete edge dislocation can be created in a face centered metal. Aluminum was chosen as an example in this paper, because it has a face centered cubic lattice and is one of the most important metals for thin films. INTERATOMIC POTENTIALS In metals, the conduction electrons travel from one atom to another atom and the interaction cannot be represented by a pairwise potential but by many body potentials. The interaction between the i-th atom and the j-th atom depends on not only the distance between them but also other factors. By the embedded atom function, surface problems can be treated. The n-body embedded function proposed by Oh and Johnson [1,2] was used in this paper. The total energy is given by EtowaI= Ei (1) rij = Iri - rjI E i =F( p i) +(I/'-) ZEID(rij)
(2) (3)
F(p)= a(P/pe)n+b(P/pe)
(4)
(5) Pi= E f(rij) Here Etota! is the total internal energy. E i is the internal energy associated with atom i. p i is the electron density at atom i due to all other atoms. F( p i) is the embedding energy of the atom 111 Mat. Roes. Soc. Symp. Proc. Vol. 356 0 1995 Materials Research Society
into electron density p i.
D (r ii) is the two body central potential between atoms i and j
separated by r ij" f (r ij) is the contribution to the electron density at atom i due to atom j at the distance r i from atom i. f (r) = fold (t) - f c (r)
(6)
fold feexpi - f (r/re)- 1) f e (r) = f old r c) + g(r)f 'old(r c)/g '(r)
(7) (8)
(D(r) = (Dold(r)4
Dold(r) =
(Dc(r) g(r)
=
4)
c(r)
(9)
(Deexp{" y(r/re -1)1
(?old(rd)+g(r) 4)'old (rc)/ g'(rc) 1-exp I 3(r/re)-rc/r e))
(10) (11) (12)
For aluminum Oh and Johnson [I]give ,?=5, y =10.5, 0 =20, r c =1. 9 r e, 9e= 0 " 12 53 8 eV, a = -4.8144, b = 0.47685, n = 0.39948, and p e= 12.793. 3. SPECIMENS Specimens A and B are rectangular parallelepipeds, thin films, having (Ill). (11), (101), (10T),(121) and (12"1) faces. The slip plane (11) is parallel to one of the surfaces (Fig. I). The slip direction is taken to be [101]. DEFORMATION Near the center of the (101) plane of Specimen A, a step was created [Fig. 1). The height of the step was increased. A stepwise displacement of 0.08d ( d = the nearest neighbor distance ) was given, all the atoms in the crystal were relaxed 100 cycles, then another stepwise displacement wa
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