Minor revisions: October 2015 by Peter Krieger
Revised: September 1995 by B.W. Statt
Transmission Electron Microscope
The transmission electron microscope (TEM) is a common tool used by
researchers in many fields to study samples on length scales less than an optical
wavelength. Until recently is was the only method available for imaging on these
length scales. It is widely used in biology and materials science. In both cases
real space images are taken and in the latter case diffraction is also performed.
This lab concerns itself mostly with diffraction although there is the opportunity to
image magnetic domains of nickel.
As a historical note the first electron microscope in North America was
built at U of T around 1940. Shortly after that some of those involved were
attracted to RCA who then went on to produce commercial units.
The appendix describes in detail how scattering takes place in the sample
and how this can be used to determine the crystal structure of your samples. It is
important that you master this material in order to understand how the TEM is
used in diffraction work. To put it simply though, Bragg's Law is responsible for
the diffraction rings observed on the fluorescent screen of the TEM.
1. In this experiment, the diffraction pattern from the small grain Au sample will
be used to calibrate the diffraction pattern photographs of other samples.
The lattice structure of Au is f.c.c. and the lattice constant is 4.08Å.
Take a photograph of the ring diffraction pattern from the sample using a
suitable accelerating voltage and suitable lens currents. Make sure the
diffraction pattern is large enough to be able to measure the ring diameters
easily. Using the relationship between the interplanar distance d hkl and the
ring diameter D
d hkl  n 
where K is the camera constant and n is an integer, do the following:
Find an approximate value of the camera constant K for the
Label each ring with the Miller indices h, k and l of the set of planes
that produced it.
Once you have correctly carried out steps I) and II), you should
have an accurate value of dhkl corresponding to each ring of the
pattern. Using these values of dhkl, start over and calculate the
exact value of the camera constant K for each ring. Plot the value
of K as a function of distance from the centre of the diffraction
Parts (I) and (ii) above will necessarily involve some trial and error fitting of
dhkl, n and K values. The graph obtained in part (iii) can be used to get the
camera constant K for any diffraction photograph taken under the same
conditions (i.e. lens currents, accelerating voltages and aperture settings
all the same).
2. Take a photograph of the ring diffraction pattern from the Al sample using the
same settings as in section (1) part (iii). Using the calibration curve of section
(1), you can now analyze the Al diffraction pattern.
Determine the lattice structure, find the lattice constant a, and label the
diffraction rings with the Miller indices of the corresponding lattice planes.
3. Now find the lattice spacing and crystal structure of the "unknown" sample.
4. Now that you are familiar with "powder diffraction" patterns you should now
grow an epitaxially oriented film and observe it's diffraction pattern. An
epitaxial film can be grown by depositing nickel onto a cleaved surface of a
crystal. In this case NaCl is used. Using the evaporator you can deposit a
thin film of say 300 Å onto the crystal. Then the film is lifted from the crystal
in water and then put onto the usual Cu mesh TEM holder. From the
diffraction pattern determine which crystal plane has been grown.
5. If time permits you may want to have a look at domain structures in nickel.
The Curie point of pure nickel is at a temperature of T c = 627 K. Again, this is
a temperature which is easily attainable with the heating stage of the Hitachi
EM III electron microscope. It is possible to photograph the decay of the
magnetic domains in a selected field of view as the temperature is raised
through the curie temperature Tc. The thermocouple used is not very well
thermally connected to the nickel specimen on the heating stage, so that the
temperature should be changed as slowly as possible to give the
thermocouple some chance of representing the temperature of the nickel.
You can estimate the value for T c from the point at which the magnetic
domains vanish. Explain how the domain walls are rendered visible by the
It is advisable to notify Mr. Rob Smidrovskis the day before you want to
use the TEM so that he can warm it up early in the morning before you get in.
This can save you an hour or two!
To evacuate and turn on the microscope
Turn the fore pump valve to 'L'. This allows the fore pump to pump on the
selector valve and the main valve.
Turn on the fore pump. Switches are on the power supply cabinet and on
the mechanical pump.
Turn the main valve to 'D'. This allows the fore pump to pump out the
diffusion pump enclosures. Note that the diffusion pumps are not yet open
to the microscope itself.
Turn the selector valve to 'C'. This allows the fore pump to pump the
camera chamber, and hence the interior of the microscope, since the
camera chamber air lock is open.
Turn on the water supply. This provides cooling water for the diffusion
Turn the diffusion pump on. This switch is on the power supply cabinet.
This turns on the heaters in the diffusion pumps.
Allow 30 minutes for the diffusion pump oil to heat up. Turn the selector
valve to 'P' or 'S'. This cuts the fore pump off from the microscope body.
The plate reservoir and specimen chamber are not connected to the
microscope body in normal operation.
Then turn the main valve to 'H'. This causes the diffusion pumps to open
to the microscope body and pump the microscope interior down to a high
vacuum. The fore pump now pumps on the back of the diffusion pumps.
Before turning on the electron beam, make sure that the vacuum indicator
is in the green region.
To change samples
As the microscope can be easily damaged during this procedure, please consult
your TA, professor or Mr. Rob Smidrovskis if you have not changed a sample
If the filament current is on it must be turned off. Turn the high voltage
knob to the voltage setting with filament off (i.e. NOT the 'F' position).
Turn the selector valve to 'S' . This opens a path from the fore pump valve
to the specimen chamber.
Use the sample transport device to pick up the sample from the
microscope specimen stage, and bring the sample and holder into the
specimen chamber. The sample holder chamber should be lined up with
the round window of the specimen chamber. In this position the specimen
chamber is isolated from the microscope interior.
Turn the form pump valve to 'A'.
The plexiglass window of the specimen chamber can now be removed
and the samples changed.
Replace the specimen chamber window and turn the fore pump valve to
'L'. This allows the fore pump to pump out the specimen chamber.
When the fore pump has stopped gurgling, use the sample transport
device to place the new sample in the microscope specimen stage.
Make sure the transport device is returned to its original position in the
sample chamber. Otherwise the mechanism will interfere with the electron
This allows air into the specimen
To turn off the microscope
Turn the main valve to 'D'. This cuts off the diffusion pump and fore pump
from the microscope interior.
Turn the diffusion pump switch on the power supply cabinet. This turns off
the heaters in the diffusion pumps.
Allow 30 minutes for the diffusion pump oil to cool down. Then turn the
main valve to 'OFF', the selector valve to 'OFF' and pull the locking pin of
the fore pump valve and turn it to 'S'.
Turn off the vacuum gauges, the fore pumps and the main power
To operate the microscope
Consult the manuals, your TA, professor or Mr. Rob Smidrovskis for
instructions on how to operate the controls of the microscope. The following
diagram illustrates the basic operation of the microscope by analogy to an optical
Scattering from Crystals and the Reciprocal Lattice
The most common method of obtaining information about atomic
arrangements in solids, liquids and gases is to scatter particles from the material
under study and observe the diffraction pattern produced by the scattered
particles. The particles used can be photons as in x-ray diffraction, electrons as
in electron diffraction using an electron microscope, or neutrons in neutron
scattering experiments. The basic idea of all of these methods is exactly the
same. Incident radiation is aimed at the sample, the sample scatters the
radiation, and the scattered radiation pattern is recorded using a recording device
such as photographic film.
For the purposes of this experiment, only the diffraction pattern produced
by crystalline materials will be considered.
The particles used as a probe can always be treated as free particles.
Hence the wave functions k (r ) of the particles are just plane waves.
k (r )  Aei k r
where k is the particle wave vector.
Recall that the particle momentum is  k , the wavelength  is
energy is
 2k 2
, and the
To a good approximation, the scattering of the probe particles by atoms of
a crystal is elastic. Therefore if k is the wave vector of an incident particle and
k  the wave vector of the particle after scattering, the condition k  k  must
The scattering of a particle from state k (r ) to the state k (r ) by a
crystal can be represented by the vector diagram in k -space shown in figure 2.
The sphere is the focus of all scattered vectors k which satisfy the
condition k  k . This sphere is known as the Ewald sphere. The difference
vector G turns out to be the important quantity in interpreting the diffraction
patterns produced by a crystal. The angle  is the scattering angle (i.e. the
'grazing' angle between the vectors k or k , representing the incident or
scattered beam directions, and the 'scattering plane' of atoms in the crystal).
The crystal lattice can be represented by a set of N vectors in real space.
These are denoted by R l for l = 1 to N. R l is the vector from some origin to the
lth lattice site. The vectors are of the form
Rl  na  mb  pc
where n, m and p are integers and the vectors a , b and c are the basis vectors
of the lattice site.
Now we suppose a plane wave of the form ei k r representing a particle in
the state k (r ) is incident upon the lattice. The phase of the wave at the l th
lattice site is k  R l . A detector is placed at some position r very far from the
crystal compared to the interatomic spacing. If k is the wave vector of the wave
scattered in the direction of r from the lth crystal lattice site, the phase of the
scattered wave at r will be k  Rl  k  (r  Rl ) . That is, the total phase at r is the
phase at the lth lattice site plus the phase change of the wave in travelling from
R l to r .
The total scattered amplitude at r is the sum of the scattered wave
contributions from each lattice site R l .
A(r )   e i(k  R l  k  ( r  R l ))  e i k  r  e i( k  k )  R l  e i k  r  e iG  R l
where G  k  k  .
The scattering amplitude from the crystal depends directly on the lattice
sum  l ei G  R l . In general, this sum is equal to zero, since for arbitrary G it is just
the superposition of waves with random relative phases. However, if the vector
G is chosen such that
G  R l  2n
where n is an integer, then this sum is equal to N. Therefore, there will be a very
bright spot in the corresponding scattering direction.
It turns out that for any crystal lattice with the set of lattice vectors R l ,
there corresponds a discreet set of vectors G satisfying equation (4). These
vectors G i form a lattice in k -space in the same way as the vectors R l form the
crystal lattice in real space. This abstract lattice in wave vector space is known
as the reciprocal lattice.
If the real space lattice is a Bravais lattice with basis vectors a , b and c ,
it follows immediately that the reciprocal lattice vectors G i can be constructed
from the basis vectors u , v and w given by the formulas in equation (5).
u  2
v  2
w  2
(b  c)
a  (b  c)
(c  a )
a  (b  c)
( a  b)
a  (b  c)
Because u , v and w depend on the real space basis vectors a , b and c
in the above manner, the reciprocal lattice corresponding to a given crystal is
determined by the crystal lattice in terms of both orientation and lattice structure.
Hence the importance of the concept of a reciprocal lattice. If we know the
reciprocal lattice of a crystal we can work backwards to find both the orientation
of the crystal lattice as well as the lattice structure.
It was shown above that the peaks in the diffraction pattern produced by
radiation scattering from a crystal occur when the difference wave vector G is a
reciprocal lattice vector. The diffraction pattern produced by a crystal is then a
direct picture of a crystal's reciprocal lattice and so yields a great deal of structure
and orientation information about the crystal.
It is at this point that the Ewald sphere construction of figure 2 becomes
useful. If figure 2 is superposed over the reciprocal lattice of the scattering
crystal so that the origins of the Ewald sphere and the reciprocal lattice coincide,
the diagram in figure 3 results.
The dots are the lattice points of the reciprocal lattice and the focus of all
possible G vectors forms the Ewald sphere. Because a diffraction peak results
only when G is a reciprocal lattice vector, only those reciprocal lattice points
lying on the Ewald sphere will produce a diffraction spot in the direction of k .
This is how a spot pattern is produced by single crystal scattering.
If instead of using a single crystal, the scattering is from many crystals all
oriented randomly with respect to each other, a different diffraction pattern will
result. Scattering from a large number of randomly oriented crystals is equivalent
to scattering from a single crystal while it is rotated through all possible angles.
The reciprocal lattice in figure 3 is then also rotated through all possible angles,
keeping the point at the origin fixed. The focus of points where a given reciprocal
lattice point, say the one at A in figure 3, intersects the Ewald sphere will be a
circle perpendicular to the incident wave vector k . Thus any scattering direction
of k such that G lies on this circle will produce a diffraction peak. It follows that
the diffraction pattern produced by the reciprocal lattice point at A will be a cone
such that the angle between k and k is constant. The total diffraction pattern
from a large number of randomly oriented crystals will be a set of cones in wave
vector space. If one were to put a photographic plate to the right of figure 3, the
cones would intersect the photographic plate to form rings. This is how a ring
diffraction pattern is produced.
To see why scattering experiments using an electron microscope differ
from those using x-rays, it is necessary to look at the relative scales of the Ewald
circle and the reciprocal lattice spacing in wave vector space. From equations
(5) for the reciprocal lattice wave vectors, the spacing between reciprocal lattice
points is of the order of 2/a where a is the real space lattice constant. For a
typical metal such as Au, a is 4.08Å. The lattice constant of the reciprocal lattice
is then roughly 1Å-1 to 2Å-1.
Recall that the wave vector k is given by 2/ where  is the wavelength
of the radiation. For x-ray scattering,  is of the order of 1Å, so k is of the order
of 6Å-1 in length. Because the incident wave vector k and the scattered wave
vector k are the same length, the radius of the Ewald sphere is also of the order
of 6Å-1. The Ewald sphere and the reciprocal lattice presented in figure 3 are
therefore drawn to more or less the right proportions for x-ray scattering.
If an electron microscope is used for scattering experiments, the situation
is very different. If a 100 KeV accelerating potential is used to produce the beam
of electrons, the electron wavelength is 0.037Å. The Ewald sphere radius is then
2/0.037 161Å-1 which is two orders of magnitude larger than the typical
reciprocal lattice spacing. The Ewald sphere diagram must then be redrawn to
show the relative sizes of the sphere and the reciprocal lattice. Since in an
electron microscope the electrons observed are scattered in the extreme forward
direction, only the forward direction of the Ewald sphere is shown in figure 4.
In this diagram, the reciprocal lattice points which intersect the sphere
tend to lie only on one plane of the reciprocal lattice. The diffraction pattern
produced is an image of this plane. Because the scattering angles are so small,
the projection of this diffraction pattern on a film plate retains the spatial
relationships between reciprocal lattice points in a given plane.
The plane of the reciprocal lattice that is observed can be chosen by
selecting a crystal of the appropriate orientation.
By looking at the diffraction patterns due to several crystal orientations,
the reciprocal lattice of the material can be constructed. Using this information,
the structure of the crystal in real space can be completely specified.
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