Features

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Features
Direct Methods for Image Processing in
HREM Direct Methods of Solving Aperiodic
Structures Searching Algorithm for Finding
Modulation waves in 4D Fourier Maps
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Deconvolution of a Single EM
far from the Scherzer defocus
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Two-Step Image Processing
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Image Processing of Bi-2212
EM image from Dr. S. Horiuchi Space group N
Bbmb 1 -1 1 a 5.42, b 5.44, c 30.5Å q
0.21b c
Phase extension
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Features
Direct Methods for Image Processing in
HREM Direct Methods of Solving Aperiodic
Structures Searching Algorithm for Finding
Modulation waves in 4D Fourier Maps
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Whats a Modulated Structure ?
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Schematic diffraction pattern of an
incommensurate modulated structure
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Conclusion
In the reciprocal space
The diffraction pattern of an incommen-surate
modulated crystal is the projection of a 4- or
higher-dimensional weighted lattice
In the direct space
An incommensurate modulated structure is the
hypersection of a 4- or higher-dimensional
periodic structure cut with the 3-dimensional
physical space
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Representation of one-dimensionally modulated
incommensurate structures
Lattice vectors in real- and reciprocal- space
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Structure-factor formula
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Modified Sayre Equations in multi-dimensional
space
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Strategy of solving incommensurate modulated
structures
i) Derive phases of main reflections
ii) Derive phases of satellite reflections
iii) Calculate the multi-dimensional Fourier map
iv) Cut the resulting Fourier map with the
3-D hyperplane (3-D physical space)
v) Parameters of the modulation functions are
measured directly on the multi-dimensional
Fourier map
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DIMS direct methods for incommensurate
structures
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Modulated atoms in g - Na2CO3 Na
O1,3
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Bi-2223
superconductor
Incommensuratemodulation revealed by the direct
method
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(PbS)1.18TiS2 composite structure 4-dimensional
average structure solved by the direct method
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Features
Direct Methods for Image Processing in
HREM Direct Methods of Solving Aperiodic
Structures Searching Algorithm for Finding
Modulation waves in 4D Fourier Maps
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MIMS automatic search in 4D Fourier maps
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MIMS searching in 3-dimensional space
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MIMS searching in 4-dimensional space
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MIMS output structure model
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4-Dimensional Structure Refinement
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Multislice Method for
conventional structures and
aperiodic crystals
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Using experimental thermal motion (B)
modulation (M) parameters
Bi-2201 Variation of dynamical-diffraction ampli
tudes with sample thickness
Setting B0
Setting B0 M0
Setting M0
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Potential Maps of Bi-2201 calculated with
dynamical-diffraction amplitudes
100Å
200Å
300Å
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Fourier sections of the superconductor Bi-2212
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2D section in a 4D Fourier map
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Contour mapping
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Contrast Adjustment