Finite strain logarithmic hyperelasto-plasticity with softening: a strongly non-local implicit gradient framework

2004 ◽  
Vol 193 (30-32) ◽  
pp. 3377-3401 ◽  
Author(s):  
M.G.D. Geers
Keyword(s):  
Finite Strain ◽  
Non Local

Strongly non-local gradient-enhanced finite strain elastoplasticity

2003 ◽  
Vol 56 (14) ◽  
pp. 2039-2068 ◽  
Author(s):  
M. G. D. Geers ◽  
R. L. J. M. Ubachs ◽  
R. A. B. Engelen
Keyword(s):  
Finite Strain ◽  
Non Local ◽  
Local Gradient

Toward High-Resolution Low-Voltage SEM

1988 ◽  
Vol 46 ◽  
pp. 218-219
Author(s):  
Zhifeng Shao
Keyword(s):  
Low Voltage ◽  
Spherical Aberration ◽  
Chromatic Aberration ◽  
Limiting Factor ◽  
Operating Voltage ◽  
Probe Radius ◽  
Non Local ◽  
Electron Microscopes ◽  
Image Position ◽  
Scanning Electron Microscopes

Recently, low voltage (≤5kV) scanning electron microscopes have become popular because of their unprecedented advantages, such as minimized charging effects and smaller specimen damage, etc. Perhaps the most important advantage of LVSEM is that they may be able to provide ultrahigh resolution since the interaction volume decreases when electron energy is reduced. It is obvious that no matter how low the operating voltage is, the resolution is always poorer than the probe radius. To achieve 10Å resolution at 5kV (including non-local effects), we would require a probe radius of 5∽6 Å. At low voltages, we can no longer ignore the effects of chromatic aberration because of the increased ratio δV/V. The 3rd order spherical aberration is another major limiting factor. The optimized aperture should be calculated as

Chromatic aberration and low-voltage SEM

1987 ◽  
Vol 45 ◽  
pp. 546-547
Author(s):  
Zhifeng Shao ◽  
A.V. Crewe
Keyword(s):  
Electron Energy ◽  
Low Voltage ◽  
Spherical Aberration ◽  
Chromatic Aberration ◽  
Primary Electron ◽  
Probe Size ◽  
Non Local ◽  
Optical Treatment ◽  
Electron Microscopes ◽  
Scanning Electron Microscopes

For scanning electron microscopes, it is plausible that by lowering the primary electron energy, one can decrease the volume of interaction and improve resolution. As shown by Crewe /1/, at V0 =5kV a 10Å resolution (including non-local effects) is possible. To achieve this, we would need a probe size about 5Å. However, at low voltages, the chromatic aberration becomes the major concern even for field emission sources. In this case, δV/V = 0.1 V/5kV = 2x10-5. As a rough estimate, it has been shown that /2/ the chromatic aberration δC should be less than ⅓ of δ0 the probe size determined by diffraction and spherical aberration in order to neglect its effect. But this did not take into account the distribution of electron energy. We will show that by using a wave optical treatment, the tolerance on the chromatic aberration is much larger than we expected.

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