Electron Diffraction
Name Lastname
DD.MM.YYYY
Department of Physics, Bilkent University, Bilkent, Ankara
Abstract—The abstract summarizes the experiment you have performed and its major results in a few sentences. Do not go
into detail here. Example: We investigated the diffraction of electrons through a polycrystalline graphite layer onto a fluorescent screen,
thereby demonstrating the wavelike behavior of electrons. Using basic diffraction theory, the lattice constants of graphite are calculated and
found as d1= . . . and d2= . . . which are somewhat good agreement with reference values. The reasons behind the errors are also discussed.
INTRODUCTION
The introduction part should be at most one
page. (Figures are exception)
You should state a brief overview of the
background of your experiment as if a freshman
level student is the reader.
The equations (if any) should be derived - as in
this example - and numbered and satated in the
introduction. You should give reference to the
equations in later parts of the report. Do not
write the same equation over and over again.
Write the equation by yourself with and
equation editor.
In 1914, Lois De Broglie developed the theory on
the wave-like properties of particles which relates
the momentum and wavelength of a particle
(1)
  h p,
The constructive diffraction of waves reflected
from adjacent layers of a single crystal are given by
Bragg condition,
(4)
2d sin   n
where d is lattice spacing, θ is incidence angle, and
n is the order of diffraction.
For polycrystalline materials, reflected beam is
spread out in the shape of a cone and forms the
refraction pattern. Geometrically,
(5)
sin 2  r R
where α is the angle of deviation and R is the radius
of the glass bulb. The angle of deviation is twice as
the Bragg angle θ. Also by considering small angle
approximations, we get the following formula.
(6)
sin   sin 2  2 sin 
Using (3-6) the relation between Ua and θ is given
by
nh
 2d sin 
2MeVa 0.5
34
where h=6.626. 10 Js is the Planck’s constant.
[reference] In this experiment, we apply this theory
to electrons to investigate their wave-like behavior.
For this purpose, we study the diffraction of
accelerated electrons through a polycrystalline
graphite sample, since diffraction is a wave-like
phenomenon. The experiment setup consists of an
electron diffraction tube and high voltage power
supplies as shown in Fig. 1
Under an accelerating potential Ua, the electrons
gain a kinetic energy given by
p2
 eV a
2M
(2)
19
31
where, e=1.602.10
C and M=9.109.10
kg.
Using Eq.s (1) and (2) the wavelength can be
found as

h
2MeU a 0.5
 1500kV 

 
 Ua 
0.5
pm (3)
(7)
Referring to (7) and the radius of our glass bulb
used in the experiment which is 63.5 mm we find
the following formula for the lattice constants.
d1, 2
 1500kV 

 
V
a


0.5
1
pm
2 sin 1, 2
(8)
This is the most important part of the report
presenting what you have done. Give your findings,
perform the analysis as described in your manual
(and procedure part of the preliminary work), plot
figures, and make calculations. If you are asked to
plot some of your data then do not present it in a
table.
Important note about figure size: If the features in the
figure get too small when sized to report format, then
plot the figures on a separate page in an adequate size.
Here is an example
Fig. 1. A photo of the experimental setup.
Figure caption should be placed under the figure.
EXPERIMENT
Describe what you specifically did while you
were performing the experiment.
The diameters were measured by a plastic ruler
several times from inner to outer boundaries and
outer to inner boundaries through the center. Then
the average of these measurements was taken as
data which is shown on Table 1 and Fig 3. the two
radii are because of the two lattice constants of
graphite which are 211pm and 126pm.
The experimental setup is shown on Fig.2. Here the
ports G1 , G2 , G4 used for aligning the electrons
G3 is used for
accelerating the electrons. A grid voltage with a
range of 2.5-10 kV was applied for acceleration, the
Wehnelt cylinder potential, G1 arranged to -25V,
G 2 to 250V and G 4 to 250 V. After turning on the
power supplies, the electrons were emitted from
indirectly heated surface and accelerated through
the grid and hit the polycrystalline graphite then
diffracted. The diffraction pattern can be observed
on the fluorescent surface on the tube. By
measuring the diameter of the circles on the
diffraction pattern and using
Ua, the lattice
parameters can be calculated using (7).
Table 1. Table captions are placed at the top of the table
Ua (kV)
2
2.5
3.0
d1 (mm)
θ1
d2 (mm)
θ2
0.10
0.09
2
0.08
 (rad)
into a uniform beam and
1
0.07
0.06
0.05
0.04
0.03
3
4
5
6
7
8
9
10 11
Va (kV)
Fig. 3. Bragg diffraction angle as a function of accelerating
potential. Figure fonts should be as large as they easily be
read. You can use font size of 36 for tick labels and size 48
for axes titles in origin.
Fig. 2. Schematic of the experimental setup and Bragg
diffraction angle, α.
ANALYSIS
Using
equation
8,
we
find
that
d1  219  18 pm and d 2  116  3 pm.
The calculated lattice constants are plotted in Fig.4
diffraction by electrons can be utilized to infer the
crystal structure of materials. We applied this
technique to obtain the lattice spacings of graphite
and found d1 and d2 as 219±18 pm and 116±3 pm.
Our results are in somewhat good agreement with
reference values given. We discussed the possible
reasons for the errors. (refer to your analysis’ as
such. Do not repeat same things here)
Figure 4: This figure represents what you should
do as an example. It clearly illustrates the results
and the calculations - which you should do - in
one figure.
As you can see data for d1 is not very consistent.
Even so you should plot it.
ERROR ANALYSIS: (title is not necessary)
Find exact values of d1 and d2. (You have already
done it in the preliminary in this case). Calculate
a simple error percentage. Then comment on the
result.
(THIS PART IS LEFT INTENTIONALLY
BLANK.You should further extend conclusion
here)
The electron diffraction is a well established as a
characterization tool in many branches of science
such as solid state physics in crystallography, and
in biology for structural analysis of organic
substance (proteins, bacteria etc.)
REFERENCES
Give all your references which you addressed in
the experiment. It is very easy to find your
sources via google. Also refer your references in
the text.
Use the format below.
For example in this report exact value of d1 is
stated as 211pm and is found as 219±18 pm. This
concludes the good agreement. And yet is still
has some error around 4%. Comment on this.
For the data d2 we have more severe error. First
of all exact d2 does not fall in the range of found
d2. Also the error is about 9%. Comment on this
result also. Even the error amount seems small
this is not a good agreement. Compare it with d 1
what went wrong in this case.
Remember here you are not expected to get the
Nobel Prize. You will not be grades by the
amount of your error. Grading is done by your
level of understanding of your data. Therefore
good explanation of a huge error may get the
higher credit whereas a poor explanation of a
good result may get lower credit.
(THIS PART IS LEFT INTENTIONALLY
BLANK: You should discuss your results,
observations regarding your experiment, and
comment on figures.)
Give the answers of the questions here not in the
conclusion.
CONCLUSION
We confirm that electrons have a wave-particle
duality in their nature and can be diffracted as light
in slit-like conditions (e.g. a crystal). The ability of
[1] Journal Reference format is: Author(s) Name, Publication
Title, Journal Title, Volume, Page Number, (Year).
[2] Web Reference format is: http://www... (full address/path)
[2] Electron Diffraction Experiment User Manual, PHYWE.
[6] S Subramaniam, M Gerstein, D Oesterhelt, and R Henderson
(1993). "Electron diffraction analysis of structural changes in the
photocycle of bacteriorhodopsin," EMBO Journal 12: 1-8
(2000).