Computation and application of the lattice Green function to dislocations in metals, intermetallics, and semiconductors

Dislocations are fundamental crystallographic defects that play key roles in determining material properties. The first step to understanding dislocations and being able to model them accurately is knowing their geometry. While the far-field geometry of a dislocation can be well described by anisotropic continuum elasticity theory, the elastic solution diverges close to the dislocation core. Methods such as density functional theory (DFT) are needed to accurately determine the geometry in the dislocation core; however, the long-range strain field of a dislocation is incompatible with periodic boundary conditions, making it challenging to perform DFT calculations of isolated dislocations. The flexible boundary condition (FBC) approach captures the correct long-range response of the dislocation by coupling the dislocation core to an infinite harmonic bulk through the lattice Green function (LGF). To improve the accuracy and efficiency of the FBC approach, we develop a numerical method to compute the LGF specifically for a dislocation geometry by directly accounting for its topology. This is in contrast to previous methods, where the LGF was computed for the perfect bulk as an approximation for the dislocation. The dislocation LGF computed using our method describes the response around the dislocation more accurately than the perfect bulk LGF, and relaxes dislocation core geometries efficiently when used within the FBC approach. We apply this method to compute the LGF for screw, edge, and mixed dislocations in metals, intermetallics, and semiconductors, and use them within the FBC approach coupled with DFT to accurately determine the equilibrium dislocation core structures. First, we compute the core structures of five different dislocations in BCC iron -- a₀/2[111] screw, a₀/2[111](1\bar{1}0) 71^\circ mixed, a₀[100](010) edge, a₀[100](011) edge, and a₀/2[\bar{1}\bar{1}1](\bar{1}10) edge dislocations, and find a dependence of the local magnetic moment on the local strain. Next, we compute the relaxed core structures of the \frac{a₀}{2}[1\bar{1}0] Ni screw dislocation and the a₀[1\bar{1}0] \NiAl\ superdislocation, demonstrating the first fully atomistic DFT calculation of an extended dislocation core structure in an intermetallic. Finally, we compute single-period, double-period, and quadruple-period dislocation core reconstructions of the 60^\circ Cd-core dislocation in CdTe. Through this work, we demonstrate the generality and versatility of our method to compute LGF and relax dislocation core structures in a wide range of technologically important material systems.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Materials Science & Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2018

Author dc:creator

• Tan, Anne Marie Zhao Hui

Contributors dc:contributor

• Trinkle, Dallas R.
• Johnson, Harley T.
• Schleife, André
• Zuo, Jian-Min

• dislocation
• lattice Green function
• computation
• simulation
• density functional theory
• multiscale modeling

Statement dc:rights

• Copyright 2018 Anne Marie Zhao Hui Tan

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/101646

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/101646