# Interaction of Dislocations and Interfaces in Crystalline Heterostructures: A Review of Atomistic Studies

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## Abstract

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## 1. Introduction

- In Section 2, TBs of metals and alloys interact with screw and non-screw lattice dislocations.
- Section 3 focuses on the interaction of dislocations with low-angle grain boundaries (LAGBs) and high-angle grain boundaries (HAGBs).
- In Section 4, the interaction of bimetal interfaces— covering coherent, semi-coherent, and incoherent interfaces—with dislocations is reviewed.
- Section 5 focuses on metal/nonmetal interfaces interacting with both metal dislocations and nonmetal dislocations.

## 2. The Interaction of Dislocations and TBs

#### 2.1. Screw Dislocations Interacting with Coherent TBs

#### 2.2. Non-Screw Dislocations Interacting with Coherent TBs

## 3. The Interaction of Dislocations and GBs

#### 3.1. Dislocations Interacting with LAGBs

#### 3.2. Dislocations Interacting with HAGBs

#### 3.3. Dislocation Pile-Ups Interacting with GBs

## 4. The Interaction of Dislocations and Bi-Metal Interfaces

#### 4.1. The Interaction of Dislocations and Coherent Interfaces

#### 4.2. The Interaction of Dislocations and Semi-Coherent Interfaces

#### 4.3. The Interaction of Dislocations and Incoherent Interfaces

## 5. The Interaction of Dislocations and Metal/Non-Metal Interfaces

#### 5.1. Interaction of Metal Dislocations and Metal/Non-Metal Interfaces

#### 5.2. Interaction of Non-Metal Dislocations with Metal/Nonmetal Interfaces

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

Molecular dynamics | MD |

face-centered-cubic | fcc |

body-centered-cubic | bcc |

twin boundary | TB |

grain boundary | GB |

low-angle grain boundary | LAGB |

high-angle grain boundary | HAGB |

grain boundary dislocation | GBD |

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**Figure 1.**Configuration of a twinned bi-crystal for simulating the interaction between (

**a**) an incident screw dislocation and (

**b**) a perfect lattice dislocation with a coherent twin boundary in fcc metals. ${\epsilon}_{\mathrm{appl}}$ denotes the applied shear strain that drives the dislocation towards the twin boundary. Figures taken from Refs. [19,20] with permission.

**Figure 2.**(

**a**) Simulation box containing two grains misoriented around the [111] rotation axis for simulating the interaction between a lattice dislocation and a tilt GB. (

**b**–

**e**) Snapshots showing different steps of the interaction between a dislocation and a symmetrical $\mathsf{\Sigma}57$ tilt GB. Figure taken from Ref. [33] with permission.

**Figure 3.**Dislocation structures developing under indention of a Ni-Cu bicrystal. Atoms are color coded according to the centrosymmetry parameter; atoms corresponding to a nearly perfect structure are not shown. Since the interface between Ni and Cu is not visible due to its coherency, a mesh that schematically represents the interface is added to the plots. At an early stage of indentation (

**a**), dislocations are contained in the top Ni layer, but have traversed the interface after further indentation (

**b**). The arrow points at a stacking-fault plane widening in the Cu bottom layer due to the small stacking-fault energy in Cu. Atoms are colored according to the centrosymmetry parameter. Figure taken from Ref. [46] with permission.

**Figure 4.**Interaction of dislocations generated by indentation of an Al/Si bicrystal to the depths d indicated with the interface. Dislocations are generated in the top Si layer which is crystallographically aligned with the bottom Al layer. P1–4 denote dislocation segments. Top row: dislocations generated in the Si top layer colored according to Burgers vector: $\frac{1}{2}\langle 110\rangle $ (dark blue), $\frac{1}{6}\langle 112\rangle $ (green), $\frac{1}{3}\langle 100\rangle $ (yellow), and others (red). The gray planes indicate the surface, interface and the indent pit. Middle row: Close-up view of the penetrating dislocations and the Al interface atoms. Interface atoms are colored by height, see color bar. Bottom row: View from the Al side showing the Al interface atoms, the dislocations and the stacking faults. Insert at 54.2 Å zooms into rectangular area and demonstrates dislocation interaction, A+B=C, Equation (1). Figure taken from Ref. [22] with permission.

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**MDPI and ACS Style**

Zhang, Z.; Shao, C.; Wang, S.; Luo, X.; Zheng, K.; Urbassek, H.M.
Interaction of Dislocations and Interfaces in Crystalline Heterostructures: A Review of Atomistic Studies. *Crystals* **2019**, *9*, 584.
https://doi.org/10.3390/cryst9110584

**AMA Style**

Zhang Z, Shao C, Wang S, Luo X, Zheng K, Urbassek HM.
Interaction of Dislocations and Interfaces in Crystalline Heterostructures: A Review of Atomistic Studies. *Crystals*. 2019; 9(11):584.
https://doi.org/10.3390/cryst9110584

**Chicago/Turabian Style**

Zhang, Zhibo, Cancan Shao, Shuncheng Wang, Xing Luo, Kaihong Zheng, and Herbert M. Urbassek.
2019. "Interaction of Dislocations and Interfaces in Crystalline Heterostructures: A Review of Atomistic Studies" *Crystals* 9, no. 11: 584.
https://doi.org/10.3390/cryst9110584