Phase Imaging Annihilation of Dislocation at Crystal Surface

Dislocations are arguably the most important defect in crystals. They determine the material’s strength, destroy electronic devices and degrade sensors, among other things. Interestingly, at their core is an undefined point, a singularity created by having a one atomic plane displacement, i.e., the Burgers vector, B , representing a 2π phase shift over a 360-degree rotation. Moreover, crystal surfaces cannot hold strain, which must somehow destabilize the dislocation when it annihilates at the surface. Recently, the core of the dislocation has been able to be phase imaged by the interference of two symmetrically Bragg diffracted beams [1]. As well, the bottom surface of the crystal has recently been phase imaged using differential phase contrast [2]. These two new phase imaging capabilities reported here have been used to image a dislocation passing from the top to the bottom surfaces of a gold specimen (Fig. 1). As the dislocation approaches the bottom surface, the dislocation can be seen to become unstable and then split to form a triple point (Fig. 2). The partial dislocations formed wrap around a 3D defect, likely a pit (Fig. 2). It is hypothesized that the dislocations at the triple point cross-slip from (111) onto three equivalent {111} planes. The partial dislocations form stacking faults, which are the surfaces of the pit (Fig. 3). The dislocations at three edges are shared among the three surfaces, which reduces their formation energy, E, by one half, i.e., E = 3 x 1/6 d<211> (Fig. 3), which is equivalent to half the Burgers vector of the original dislocation, E = ½ B<110> for FCC gold. The other half of the dislocation strain relaxes the structure providing energy to nucleate the 3D volume of the pit. The relaxed structure is too small to hold its Au atom, ejecting it, likely onto the surface of the crystal (Fig. 3). Thus, the energy required to nucleate the pit is ½ E/B<110l> where E is the material’s elastic modulus. For Au, the pit formation energy is ½ 76 GPa / 0.235 nm = 1.6 nN. Pits are known to exist on the surface of materials as traditionally seen by etching. This is the first time that their formation has been seen from the perspective of the inside of the crystal to the surface. A model is proposed based upon the destabilization of a dislocation to form three connected stacking fault surfaces to form a 3D pit. Simulations are still required to verify the proposed pit formation mechanism from this experimental observation [3]. – a) Bright field TEM image of a dislocation in Au specimen at exact Bragg diffraction, b) schematic of interfering symmetrically diffracted beams using an electron biprism, c) interferogram of dislocation in a). – a), Reconstructed phase image of dislocation in Fig. 1 showing annihilation of 2π shift at top (T) and bottom (B) surfaces, b) Magnified view of bottom surface showing unstable strain (US) along the dislocation just before creating a pit, c) 3x phase enhancement revealing triple point (TP) within circle formed by partial dislocations, which create three surfaces forming the pit. – Stacking fault surfaces outlined by red, green, and blue lines formed from partial dislocations having <211> Burgers vectors and {111} habit planes. The relaxation of the surfaces by ½ B ejects the corner atom to establish the nucleation of the 3D volume of the pit.

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