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研究生： 卓亞克
Roman Dronyak
論文名稱： Coherent Electron Diffractive Imaging of Nanocrystals
指導教授： 陳福榮
Chen, Fu-Rong
梁耕三
Liang, Keng S.
口試委員:
學位類別： 博士
Doctor
系所名稱： 原子科學院 - 工程與系統科學系
Department of Engineering and System Science
論文出版年： 2010
畢業學年度： 98
語文別： 英文
論文頁數： 104
中文關鍵詞： 電子繞射 、同調性 、同調繞射影像術
外文關鍵詞： Electron Diffraction, Coherence, Coherent Diffractive Imaging
相關次數： 點閱：71  下載：0 
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    • Coherent diffractive imaging (CDI) is a new technique for the structural analysis of materials at a resolution limited by the wavelength of the radiation involved. Due to the strong interaction of electrons with matter and short de Broglie wavelength of electrons, electron CDI offers, in principle, atomic-scale resolution of nano-objects in coherent diffraction experiments. In addition, for nanocrystals, coherent diffraction in Bragg geometry allows for the recovery of a three-dimensional (3D) structure of the sample using an angular range of crystal tilt within a few degrees.
    In this thesis, a detailed theoretical and experimental investigation of the electron CDI technique is presented. The well-known nanocrystals of MgO smoke were used as a test nano-object. For diffraction experiments, we used a highly coherent illumination from a field-emission gun as a source of electrons. In our data analysis, we developed an algorithm to reconstruct a complex exit wave from the electron diffraction pattern alone. Results of the two-dimensional (2D) CDI reveal a crystal lattice with 0.15 nm resolution using Bragg reflections, and characterize the crystal boundary with a resolution of about 3 nm using diffuse scattering measured in the vicinity of the Bragg peak.
    In 3D electron CDI, we, for the first time, experimentally determined the morphology of a single MgO nanocrystal using Bragg diffraction geometry. The iterative algorithm developed was applied to invert the 3D diffraction pattern about a (200) reflection of the nanoparticle measured at an angular range of 1.8º, which revealed a 3D image of the sample at about 8-nm resolution. Computer simulations verified the results of 2D and 3D reconstructions. The described technique offers a powerful way to image crystals, disordered materials and biological samples of nanometer size with atomic-scale resolution

    Contents Abstract i Acknowledgements ii Contents iii List of Figures vi List of Tables ix 1 Introduction 1 1.1 Interaction of Electrons with Matter 4 1.1.1 Optical refractive index of electrons 6 1.1.2 Projected potential of the sample 7 1.1.3 Weak-phase object approximation 8 1.1.4 Complex-valued scattering potential 9 1.2 Electron Diffraction by Crystalline Samples 11 1.2.1 Bragg’s condition of diffraction and excitation error 11 1.2.2 Scattering from a finite crystal 12 1.3 Methods of Phase Recovery 15 1.3.1 The phase problem 15 1.3.2 Gerchberg-Saxton and Fienup's algorithms 16 1.3.3 Difference map algorithm 18 1.3.4 Dynamic support 19 2 Coherent Electron Diffraction Experiments 21 2.1 Principle of Experimentation 21 2.1.1 Interpretation of crystal images and resolution in the electron microscopy 21 2.1.2 Coherence properties of the electron beam 24 2.1.3 Nano-beam electron diffraction of nanoparticles 26 2.1.4 Resolution in the electron CDI 28 2.2 General Survey of Au and TiO2 Nanocrystals 30 2.3 Electron CDI Study of MgO Nanocrystals 32 2.3.1 Sample preparation of MgO nanocrystals 32 2.3.2 Coherent diffraction from hydrated nanocrystals 34 2.3.3 Electron diffraction patterns for the exit wave reconstruction 37 3 Development of Optimization Procedure for the Phase Retrieval 40 3.1 Problem of Uniqueness of Solution in CDI 41 3.1.1 Oversampling condition for diffractive imaging 42 3.1.2 Sampling requirement for electron CDI 44 3.2 Optimization Procedure for the Phase Retrieval 46 3.2.1 Error metric and its standard deviation 47 3.2.2 Measure of reproducibility of solutions 49 3.2.3 Convergence map 52 3.3 Computer Simulation of Phase Recovery 54 3.3.1 The phase retrieval using noise-free data 54 3.3.2 The phase retrieval in the presence of noise in data 57 3.3.3 Guiding method for the phase retrieval 60 4 Two-Dimensional Electron Coherent Diffractive Imaging of MgO Nanocrystals 64 4.1 Diffuse Intensity and Shape of MgO Nanoparticles 64 4.1.1 Determination of the sample size and the oversampling ratio 65 4.1.2 Optimization procedure for the reconstruction of the shape function 67 4.2 Reconstruction of Electron Exit Wave Function 69 4.2.1 Effects of the missing data and the background scattering 69 4.2.2 Effects of incident electron beam 71 4.2.3 Reconstruction procedure 74 5 Electron Coherent Diffraction Tomography of a Nanocrystal 77 5.1 Diffraction Geometry of the Electron Diffraction Tomography 77 5.2 Experimental Arrangement and 3D Reconstruction 80 5.3 Dynamical Scattering Effects 83 6 Conclusions 86 List of Publications and Conference Participations 88 References 96

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