# Nanoscale Mapping of Heterogeneous Strain and Defects in Individual Magnetic Nanocrystals

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## Abstract

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## 1. Introduction

## 2. Discussion and Conclusions

## 3. Materials and Methods

#### 3.1. Sample Growth

#### 3.2. CXD Experiments and BCDI Data Reconstructions

#### 3.3. Classical Potential Simulations

#### 3.4. Landau–Lifshitz–Gilbert (LLG) Simulation

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

BCDI | Bragg coherent X-ray diffractive imaging |

CXD | Coherent X-ray diffraction |

SEM | Scanning electron microscopy |

XRD | X-ray diffraction |

NP | Nanoparticle |

EF-TEM | Energy-filtered transmission electron microscopy |

HR-TEM | High-resolution transmission electron microscopy |

PRTF | Phase retrieval transfer function |

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**Figure 1.**Schematic of the experimental set-up and sample. (

**a**) Scanning electron microscopy (SEM) image showing a single isolated Ni nanoparticle (identified by the arrow) in an ensemble of Ni nano-objects. A monochromatic X-ray beam of wave vector ${\widehat{k}}_{in}$ focused by Kirkpatrick–Baez (KB) mirrors (not shown is sketch impinges on the sample. By rotating the sample through the Bragg condition in increments of about 0.006 degrees, coherent X-ray diffraction (CXD) patterns in the vicinity of the (111) reciprocal lattice point are recorded with a two-dimensional pixelated detector. Two typical diffraction patterns (out of the hundreds of patterns collected) are shown here in (i,ii)).

**Figure 2.**Reconstructed projections of the displacement and strain. (

**a**,

**b**) 3D isosurface projections of the displacement field ${\mathbf{u}}_{111}$ and shape morphology of the nanoparticle. (

**c**–

**f**) 2D projections that are extracted from the central slices of the reconstructions, showing strain inhomogeneity of the core and heterogeneity within the shell of the nanoparticle. The strain in (

**c**–

**f**) with non-uniform structure without symmetry within the core; while the strain within the shell is diverse when comparing the components in the three orthogonal directions as shown in (

**d**–

**h**). Line plots showing smooth variation and inhomogeneous strain within the core layer of the nanoparticle (Ni) and large phase jumps in the NiO shell region depicting the presence of singularities such as defects and dislocations. In (

**g**), the phase is plotted from the central slices of the 3D reconstructed particle, 30 nm and 60 nm away from the central slices of the 3D particle, respectively. In (

**h**), the plot was extracted from the one end of the particle to the other end of the particle, that is, from the shell–core–shell for the entire particle for the central slice linecut.

**Figure 3.**Edge dislocation result and simulation. (

**a**) Reconstructed stress field in the vicinity of an edge dislocation within the nanoparticle shell region (magnified 3X) is compared with simulated stress (

**b**) Stress due to an edge dislocation. (

**c**) The overall region of the reconstructed core–shell structure.

**Figure 4.**Resolution estimation by phase retrieval transfer function (PRTF). The phase retrieval transfer function is a tool that provides an accurate resolution measure. It takes a value of 1 where the iterative algorithm produced perfect convergence consistently, and a value near 0 where the algorithm continually failed to converge. Dashed line on the graph shows 50% cutoff frequency which is used to estimate the threshold of resolution reliability, which for our Bragg coherent diffraction imaging (BCDI) experiment is approximately 30 nm in Figure 2 and Figure 3.

**Figure 5.**(

**a**) The simulated distribution of magnetization within a single Ni nanoparticle. The arrows represent the distribution of the magnetization, and the color denotes the magnitude of the component ${m}_{z}$. (

**b**) The distribution of the displacement along (001) axis.

Dislocation | $\tilde{\mathit{b}}\mathbf{=}\mathit{n}\mathit{b}$ | Dislocation | Source Size | Critical Shear | Stacking Fault |
---|---|---|---|---|---|

($\mathit{b}\mathbf{=}$ 0.22 nm) | Type | Stress | Energy | ||

(i) | 28b | full | 43 nm | ${\sigma}_{f}$ = 12.32 GPa | - |

(ii) | 28b | full | 43 nm | ${\sigma}_{f}$ = 12.32 GPa | - |

(iii) | 27b | full | 42 nm | ${\sigma}_{f}$ = 12.16 GPa | - |

(iv) | 19b | partial | 30 nm | ${\sigma}_{p}$ = 11.98 GPa | 1421 mJ/m${}^{2}$ |

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**MDPI and ACS Style**

Shi, X.; Harder, R.; Liu, Z.; Shpyrko, O.; Fullerton, E.; Kiefer, B.; Fohtung, E. Nanoscale Mapping of Heterogeneous Strain and Defects in Individual Magnetic Nanocrystals. *Crystals* **2020**, *10*, 658.
https://doi.org/10.3390/cryst10080658

**AMA Style**

Shi X, Harder R, Liu Z, Shpyrko O, Fullerton E, Kiefer B, Fohtung E. Nanoscale Mapping of Heterogeneous Strain and Defects in Individual Magnetic Nanocrystals. *Crystals*. 2020; 10(8):658.
https://doi.org/10.3390/cryst10080658

**Chicago/Turabian Style**

Shi, Xiaowen, Ross Harder, Zhen Liu, Oleg Shpyrko, Eric Fullerton, Boris Kiefer, and Edwin Fohtung. 2020. "Nanoscale Mapping of Heterogeneous Strain and Defects in Individual Magnetic Nanocrystals" *Crystals* 10, no. 8: 658.
https://doi.org/10.3390/cryst10080658