Abstract
The determination of foil thickness by stereomicroscopy technique is discussed. The calculation of the foil thickness is performed in a general position of the foil in an electron microscope for a general choice of the marker position. In this case the crystallographic orientation of the foil normal has to be known. But there exists a special case (markers lie in the diffraction plane) where it is not necessary to know the orientation of the foil normal. The relative error in determining the foil thickness is about 10%.
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Abbreviations
- B :
-
direction in the foil parallel with the primary beam in the first micrograph
- d :
-
vector describing a common straight line ofδ andγ 1 (δ ∩ γ 1)
- F :
-
direction in the foil parallel with the primary beam in the second micrograph
- g :
-
diffraction vector
- M :
-
magnification
- n :
-
foil normal
- o :
-
vector defined byn ×B
- p 1 :
-
first coordinate ofX in the first micrograph
- p 2 :
-
first coordinate ofX in the second micrograph
- p 1i ,P 2i :
-
quantitiesP 1,P 2 corresponding to thei-th markers on the top surface
- t B :
-
foil thickness measured in theB direction
- \(\hat t_B\) :
-
auxiliary quantity
- \(\hat t_{Bi}\) :
-
\(\hat t_B\) corresponding to thei-th markers on the top surface
- t d :
-
foil thickness measured in thed direction
- t F :
-
foil thickness in general
- t n :
-
foil thickness measured in then direction
- X 1 :
-
point inλ B characterizing one of the markers
- X 2 :
-
point inλ T characterizing one of the markers
- X 2i :
-
X 2 corresponding to thei-th markers on the top surface
- X g :
-
magnitude ofX g
- X gi :
-
magnitude ofX gi
- X Γ :
-
magnitude ofX Γ
- X :
-
vector connecting pointX 1 withX 2 (X ≡X 2−X 1
- X g :
-
component ofX perpendicular to the planeγ 1
- X gi :
-
X gi corresponding to thei-th markers on the top surface
- X Γ :
-
component ofX lying in the planeγ 1
- z :
-
distance betweenγ 1 ∩λ T and the end point ofX Γ divided by cosα
- α :
-
angle betweenγ 1 ∩Ν andγ 1 ∩λ B
- Β :
-
angle betweeng andδ ∩λ T
- γ 1,γ 2 :
-
reflection planes
- δ :
-
plane containingn andg
- δm :
-
measure error
- δp :
-
difference betweenp 2 andp 1 (δp=p 2−p 1)
- δP :
-
accuracy of length measurement
- (δt B )max :
-
maximum error oft B
- \((\Delta \hat t_B )_{\max }\) :
-
maximum error of\(\hat t_B\)
- δδ :
-
accuracy of angle measurement
- η :
-
angle characterizing the deviation from the foil position when symmetrical tilting is achieved
- θ :
-
angle of tilt betweenB andF (between stereomicrographs)
- λ T :
-
plane describing approximately the top surface of the foil
- λ b :
-
plane describing approximately the bottom surface of the foil
- Ν :
-
screen plane
- ξ :
-
angle betweenγ 1∩Ν andX Γ
- π :
-
plane containingn andB
- ϕ :
-
angle of tilting from starting (after inserting the foil into the microscope) to working position (position during image observation)
- ∩:
-
intersection of two planes (common straight line)
References
Nankivell J. F.: Brit. J. Appl. Phys.13 (1962) 129.
Loretto M. H., Smallman R. E.: Defect Analysis in Electron Microscopy. Chapman and Hall. London, 1975, p. 61.
Vingsbo O.:in Proc. 7th Int. Congress on “Microscopie électronique” Grenoble, 1970, p. 325.
von Heimendahl M.: Micron4 (1973) 111.
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Dlouhý, A., Pešička, J. Estimate of foil thickness by stereomicroscopy technique. Czech J Phys 40, 539–555 (1990). https://doi.org/10.1007/BF01599778
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DOI: https://doi.org/10.1007/BF01599778