scholarly journals Estimates of first and second order shape derivatives in nonsmooth multidimensional domains and applications

2016 ◽  
Vol 270 (7) ◽  
pp. 2616-2652 ◽  
Author(s):  
Jimmy Lamboley ◽  
Arian Novruzi ◽  
Michel Pierre
Keyword(s):  
Second Order ◽  
Shape Derivatives

scholarly journals A Variational Method for Second Order Shape Derivatives

2016 ◽  
Vol 54 (2) ◽  
pp. 1056-1084 ◽  
Author(s):  
Guy Bouchitté ◽  
Ilaria Fragalà ◽  
Ilaria Lucardesi
Keyword(s):  
Variational Method ◽  
Second Order ◽  
Shape Derivatives

Disappearance Voltage Determinations Using a Convergent Beam

1971 ◽  
Vol 29 ◽  
pp. 184-185
Author(s):  
W. L. Bell
Keyword(s):  
Second Order ◽  
Objective Method ◽  
Uniform Thickness ◽  
Rocking Curve ◽  
Crystal Perfection ◽  
Kikuchi Line ◽  
Central Maximum ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

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