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In-line three-dimensional holography of nanocrystalline objects at atomic resolution.

Chen FR, Van Dyck D, Kisielowski C - Nat Commun (2016)

Bottom Line: Resolution and sensitivity of the latest generation aberration-corrected transmission electron microscopes allow the vast majority of single atoms to be imaged with sub-Ångstrom resolution and their locations determined in an image plane with a precision that exceeds the 1.9-pm wavelength of 300 kV electrons.The method is compatible with low dose rate electron microscopy, which improves on signal quality, while minimizing electron beam-induced structure modifications even for small particles or surfaces.We apply it to germanium, gold and magnesium oxide particles, and achieve a depth resolution of 1-2 Å, which is smaller than inter-atomic distances.

View Article: PubMed Central - PubMed

Affiliation: Department of Engineering and System Science, National Tsing-Hua University, 101 Kuang-Fu Road, Hsin Chu 300, Taiwan.

ABSTRACT
Resolution and sensitivity of the latest generation aberration-corrected transmission electron microscopes allow the vast majority of single atoms to be imaged with sub-Ångstrom resolution and their locations determined in an image plane with a precision that exceeds the 1.9-pm wavelength of 300 kV electrons. Such unprecedented performance allows expansion of electron microscopic investigations with atomic resolution into the third dimension. Here we report a general tomographic method to recover the three-dimensional shape of a crystalline particle from high-resolution images of a single projection without the need for sample rotation. The method is compatible with low dose rate electron microscopy, which improves on signal quality, while minimizing electron beam-induced structure modifications even for small particles or surfaces. We apply it to germanium, gold and magnesium oxide particles, and achieve a depth resolution of 1-2 Å, which is smaller than inter-atomic distances.

No MeSH data available.


Related in: MedlinePlus

Schematic representation of the exit wave function in Argand space and propagation intensity.(a) The complex values of pixels in the centre of each atomic column are represented as blue dots. The red dots correspond to pixels of the wave function if propagated across a distance Δf away from the exit surface of the sample. Black circle is called ‘mass circle' and the red dashed circle is called ‘defocus circle'. (b) The propagation intensity of one atomic column. The true position of atom at the bottom exit surface is at the position of maximum intensity (blue point).
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f1: Schematic representation of the exit wave function in Argand space and propagation intensity.(a) The complex values of pixels in the centre of each atomic column are represented as blue dots. The red dots correspond to pixels of the wave function if propagated across a distance Δf away from the exit surface of the sample. Black circle is called ‘mass circle' and the red dashed circle is called ‘defocus circle'. (b) The propagation intensity of one atomic column. The true position of atom at the bottom exit surface is at the position of maximum intensity (blue point).

Mentions: where t is the mass thickness of the sample, Ψ(r,0) is the incident wave, Φ1s(r) is the 1s eigenstate of the projected electrostatic potential of the atom column with eigenenergy E. α is a constant and Δf is the focus difference given by the distance of the image plane to the exact exit surface defined by the last atom in a column. The exit wave is complex and can be represented in an Argand plot. Figure 1a shows the Argand plot of pixels from the centre of atom columns. It is clear that the two factors (e−iEt−1) and (1−e−iαΔf) from equation describe two circles called ‘mass (Et) circle' (black circle) and ‘defocus (αΔf) circle' (red circles), respectively. It is seen that information about the column mass and its local focus are orthogonal. If the sensitivity of a microscope suffices to isolate the contrast contribution from scattering at single atoms, the ‘mass' values will be discrete and their regular spacing will give an ultimate mass calibration. Similarly, discrete focus values must be detected if the spatial resolution in beam direction is smaller than the periodic distance between successive atoms in a column.


In-line three-dimensional holography of nanocrystalline objects at atomic resolution.

Chen FR, Van Dyck D, Kisielowski C - Nat Commun (2016)

Schematic representation of the exit wave function in Argand space and propagation intensity.(a) The complex values of pixels in the centre of each atomic column are represented as blue dots. The red dots correspond to pixels of the wave function if propagated across a distance Δf away from the exit surface of the sample. Black circle is called ‘mass circle' and the red dashed circle is called ‘defocus circle'. (b) The propagation intensity of one atomic column. The true position of atom at the bottom exit surface is at the position of maximum intensity (blue point).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4759637&req=5

f1: Schematic representation of the exit wave function in Argand space and propagation intensity.(a) The complex values of pixels in the centre of each atomic column are represented as blue dots. The red dots correspond to pixels of the wave function if propagated across a distance Δf away from the exit surface of the sample. Black circle is called ‘mass circle' and the red dashed circle is called ‘defocus circle'. (b) The propagation intensity of one atomic column. The true position of atom at the bottom exit surface is at the position of maximum intensity (blue point).
Mentions: where t is the mass thickness of the sample, Ψ(r,0) is the incident wave, Φ1s(r) is the 1s eigenstate of the projected electrostatic potential of the atom column with eigenenergy E. α is a constant and Δf is the focus difference given by the distance of the image plane to the exact exit surface defined by the last atom in a column. The exit wave is complex and can be represented in an Argand plot. Figure 1a shows the Argand plot of pixels from the centre of atom columns. It is clear that the two factors (e−iEt−1) and (1−e−iαΔf) from equation describe two circles called ‘mass (Et) circle' (black circle) and ‘defocus (αΔf) circle' (red circles), respectively. It is seen that information about the column mass and its local focus are orthogonal. If the sensitivity of a microscope suffices to isolate the contrast contribution from scattering at single atoms, the ‘mass' values will be discrete and their regular spacing will give an ultimate mass calibration. Similarly, discrete focus values must be detected if the spatial resolution in beam direction is smaller than the periodic distance between successive atoms in a column.

Bottom Line: Resolution and sensitivity of the latest generation aberration-corrected transmission electron microscopes allow the vast majority of single atoms to be imaged with sub-Ångstrom resolution and their locations determined in an image plane with a precision that exceeds the 1.9-pm wavelength of 300 kV electrons.The method is compatible with low dose rate electron microscopy, which improves on signal quality, while minimizing electron beam-induced structure modifications even for small particles or surfaces.We apply it to germanium, gold and magnesium oxide particles, and achieve a depth resolution of 1-2 Å, which is smaller than inter-atomic distances.

View Article: PubMed Central - PubMed

Affiliation: Department of Engineering and System Science, National Tsing-Hua University, 101 Kuang-Fu Road, Hsin Chu 300, Taiwan.

ABSTRACT
Resolution and sensitivity of the latest generation aberration-corrected transmission electron microscopes allow the vast majority of single atoms to be imaged with sub-Ångstrom resolution and their locations determined in an image plane with a precision that exceeds the 1.9-pm wavelength of 300 kV electrons. Such unprecedented performance allows expansion of electron microscopic investigations with atomic resolution into the third dimension. Here we report a general tomographic method to recover the three-dimensional shape of a crystalline particle from high-resolution images of a single projection without the need for sample rotation. The method is compatible with low dose rate electron microscopy, which improves on signal quality, while minimizing electron beam-induced structure modifications even for small particles or surfaces. We apply it to germanium, gold and magnesium oxide particles, and achieve a depth resolution of 1-2 Å, which is smaller than inter-atomic distances.

No MeSH data available.


Related in: MedlinePlus