Estimate of foil thickness by stereomicroscopy technique |
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Authors: | A Dlouhý J Pe?i?ka |
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Institution: | (1) Institute of Physical Metallurgy, Czechosl. Acad. Sci., i kova 22, 616 22 Brno, Czechoslovakia;(2) Present address: Faculty of Mathematics and Physics, Charles University, Prague, Ke Karlovu 5, 121 16 Praha 2, Czechoslovakia |
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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%.List of symbols
B
direction in the foil parallel with the primary beam in the first micrograph
-
d
vector describing a common straight line of and
1 (
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
-
auxiliary quantity
-
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 in
B
characterizing one of the markers
-
X
2
point in
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
magnitude ofX
-
X
vector connecting pointX
1 withX
2 (X X
2–X
1
-
X
g
component ofX perpendicular to the plane
1
-
X
gi
X
gi
corresponding to thei-th markers on the top surface
-
X
component ofX lying in the plane
1
-
z
distance between
1 ![cap](/content/m74230685v87357u/xxlarge8745.gif)
T
and the end point ofX
divided by cos
Greek symbols
angle between
1 ![cap](/content/m74230685v87357u/xxlarge8745.gif) and
1 ![cap](/content/m74230685v87357u/xxlarge8745.gif)
B
-
angle betweeng and ![cap](/content/m74230685v87357u/xxlarge8745.gif)
T
-
1,
2
reflection planes
-
plane containingn andg
-
m
measure error
-
p
difference betweenp
2 andp
1 ( p=p
2–p
1)
-
P
accuracy of length measurement
- ( t
B
)max
maximum error oft
B
-
maximum error of
-
![delta](/content/m74230685v87357u/xxlarge948.gif)
accuracy of angle measurement
-
angle characterizing the deviation from the foil position when symmetrical tilting is achieved
-
angle of tilt betweenB andF (between stereomicrographs)
-
T
plane describing approximately the top surface of the foil
-
b
plane describing approximately the bottom surface of the foil
-
screen plane
-
angle between
1![cap](/content/m74230685v87357u/xxlarge8745.gif) andX
-
plane containingn andB
-
angle of tilting from starting (after inserting the foil into the microscope) to working position (position during image observation)
Special symbol
intersection of two planes (common straight line) |
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Keywords: | |
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