Chapter 3 A Strange Analogy between S. Timoshenko’s Beam Theory and General Relativity

2021 ◽  
pp. 47-64
Author(s):  
K. Kuroda ◽  
Y. Tomokiyo ◽  
T. Kumano ◽  
T. Eguchi

The contrast in electron microscopic images of planar faults in a crystal is characterized by a phase factor , where is the reciprocal lattice vector of the operating reflection, and the lattice displacement due to the fault under consideration. Within the two-beam theory a planar fault with an integer value of is invisible, but a detectable contrast is expected when the many-beam dynamical effect is not negligibly small. A weak fringe contrast is also expected when differs slightly from an integer owing to an additional small displacement of the lattice across the fault. These faint contrasts are termed as many-beam contrasts in the former case, and as ε fringe contrasts in the latter. In the present work stacking faults in Cu-Al alloys and antiphase boundaries (APB) in CuZn, FeCo and Fe-Al alloys were observed under such conditions as mentioned above, and the results were compared with the image profiles of the faults calculated in the systematic ten-beam approximation.


Author(s):  
M. P. Hobson ◽  
G. P. Efstathiou ◽  
A. N. Lasenby
Keyword(s):  

2012 ◽  
Vol 182 (8) ◽  
pp. 894 ◽  
Author(s):  
Vladimir N. Lukash ◽  
Elena V. Mikheeva ◽  
Vladimir N. Strokov
Keyword(s):  

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