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Convergent Beam Electron Diffraction (CBED)
Poster Group Z:
Martin Moran
John Roche
David Tims
Nikki Truss
Group Coordinator:
Prof. Hongzhou
Zhang
I. Basics
II. History
CBED is a technique of electron microscopy using a convergent beam
of electrons directed at a specimen to produce a diffraction pattern to
investigate the structure of a specimen. The convergence of electrons
is acquired in a transmission electron microscope, TEM, by using an
electrical or magnetic lens. The convergence semiangle, α, can be
adjusted by changing the C2 aperture. The size of the diffraction disk
depends on α. Depending on α different patterns are produced. For
small α, a Kossel-Möllenstedt pattern is produced. For large α, a
Kossel pattern is produced. In general, a Kossel-Möllenstedt pattern
contains more useful information than a Kossel pattern.
The diffraction pattern in CBED is produced by the electron beam
interacting with the atoms in the specimen. There are two kinds of
scattering from crystalline specimen: inelastic scattering which can go
in any direction and elastic scattering which can go in only one
direction. Scattering is given by Braggs Law: 2dsinθ=nλ where n is an
integer, λ is the wavelength of the incident electrons, θ is the spacing
between the planes of the atomic lattice, is the angle between the
incident beam and the scattering planes. An electron after scattering is
going in a direction which is 2θ away from the direction it had before
the scattering. At the specimen in CBED, the electrons are travelling in
a range of directions inside a cone. Electrons are scattered in all
directions in the convergent conical illumination. Each point in the
direct beam disc is one direction of illumination so each point in the
disc can be scattered by the same 2θ. Therefore the diffracted
electrons also form discs, one for each Bragg reflection.
Fig1.1 Ray diagram showing CBED pattern
formation
At a zone axis reflection, the diffraction pattern consists of a
regular net of discs. In this orientation, the reflections in the diffraction
pattern break up into zones called Laue zones. The central zone is
called the zero-order Laue zone, ZOLZ. The first ring is called the firstorder Laue zone, FOLZ, and so on. The first-order, second-order,
third-order etc. are known collectively as the higher-order Laue zones,
HOLZ. Because the narrow, dark, straight lines in the bright field disc
are associated with diffraction into a HOLZ reflection, they are known
as HOLZ lines.
Fig 1.2 CBED pattern from[111] Si
Ernst Abbe originally proposed that the ability to resolve detail in an object was limited by the
wavelength of the light used in imaging, thus limiting the useful obtainable magnification from an
optical microscope to a few micrometers. Developments into ultraviolet (UV) microscopes, led
by Köhler and Rohr, allowed for an increase in resolving power of about a factor of two, but
required more expensive quartz optical components. At this point it was believed that obtaining
an image with sub-micrometer information was simply impossible due to this wavelength
constraint. In 1891 it was recognized by that cathode rays could be focused with magnetic f
ields, allowing for simple lens designs.
In 1928, Max Knoll and a team of researchers at the Technological University of
Berlin created a device that used two magnetic lenses to achieve higher magnifications,
arguably the first electron microscope. The wave nature of electrons, which were considered
charged matter particles, had not been fully realised until the publication of the De Broglie
hypothesis in 1927. The group was unaware of this publication until 1932, where it was quickly
realized that the De Broglie wavelength of electrons was many orders of magnitude smaller
than that for light, theoretically allowing for imaging at atomic scales.
After these discoveries, in the early 1930’s, Hungarian physicist Leo Szilárd invented and
patented the modern electron microscope, however a prototype was not constructed until 1931,
when an apparatus capable of 400 times magnification was built. Two years later, in 1933, Ernst
Ruska, a German physicist, built an electron microscope that exceeded the resolution attainable
with an optical lens microscope, a major milestone in the evolution of electron microscopy. The
first practical electron microscope was constructed in 1938, at the University of Toronto, by Eli Franklin Burton and his students. By 1939
Ruska was working for Siemens, and together they produced the first commercial transmission electron microscope (TEM). It was then
installed in the Physics department of I. G Farben-Werke. Further work on the electron microscope was held back by the destruction of
a new laboratory constructed at Siemens by an air-raid, as well as the death of two of the researchers, during World War II.
Fig 2.1 Ernst Ruska, one of
the fathers of electron
microscopy
After the war, Ruska resumed work at Siemens, where he continued to develop the electron microscope, producing the first
microscope with 100k magnification. The fundamental structure of this microscope design, with multi-stage beam preparation optics, is
still used in modern microscopes. Once the electron microscope had been developed, a variety of techniques were invented to examine
samples. With the invention of the TEM, it was realised that diffraction of the electron beam through the sample gave more detail when it
came to analysing the sample, thus came the dawn of electron diffraction microscopy, and the foundations of CBED.
If the specimen is thick enough, a large number of scattered
electrons will be generated which travel in all directions. They are
incoherently scattered but not necessarily inelastically scattered.
These diffusely scattered electrons can then be Bragg diffracted by
the planes. The resultant pattern, the Kikuchi lines, is explained by
geometry. The Kikuchi lines consist of an excess line and a deficient
line. In the diffraction pattern, the excess is further from the direct
beam than the deficient line. The Kikuchi lines are fixed to the crystal
so they can be used to determine the orientation of the crystals
accurately.
IV. Advantages/Disadvantages
X-ray/Neutron microscopy:
CBED has become the most prominent method in microscopy due to its benefits over other
methods like x-ray microscopy. The main problems of x-ray and even neutron microscopy is
the lack of an interaction between the particles of the sample and the x-rays/neutrons
themselves.
Some problems arising from this include a minimum thickness necessary from the sample.
Without the thickness of ~100nm, the x-rays/neutrons will simply pass through the sheets.
Electron diffraction in general covers this problem due to the much stronger interaction
between electrons and atoms, as discussed in greater detail later in the poster.
Fig 1.3 Diagram showing lines formed in
CBED pattern
III. Evolution
SAD
None of these problems appear when using SAD, as expected due to its use of electrons.
However there are still many notable problems of this technique.
There exists the engineering aspect of manufacturing the aperture. There is much difficulty in
manufacturing these to compete with converging . While it is easy to make apertures of ~1μm,
it is currently difficult to reduce this size to ~1nm. The use of CBED does not require an
aperture of this size due to the convergence of the beam.
With the development of TEM, the associated technique of scanning transmission electron
microscopy (STEM) was re-investigated, but no real progress was made until the 1970s, when
the field emission gun was developed, and a high quality objective lens was added to create the
modern STEM. Using this design, Albert Crewe of the University of Chicago demonstrated the
ability to image atoms using annular dark-field imaging. Since then many modifications have been
added, and a wide range of more sophisticated techniques have been developed.
Disadvantages
One of the main disadvantages of CBED is the fact that the focused beam gives a very high
current density. This can cause atoms to be stripped from the surface of the sample. Ways of
counteracting this include cooling the specimen itself using a cooling rod and liquid nitrogen.
Following the invention of the TEM, research began into the field of electron diffraction. The
first effort was selected area electron diffraction (SAED) where a parallel beam of electrons is
incident on the sample. This technique proved excellent for analysis of the surface of a material,
however it did not provide in-depth crystallographic information that researchers still needed.
In search of better imaging techniques, convergent beam electron diffraction (CBED) was
developed, first being used in the commercial microscope developed by Ruska in 1939. It was
found that if a convergent beam of electrons, essentially beams of many angles of incidence, was
passed through a sample, then diffraction occurred at many angles, giving a 3D representation of
the material being examined. This was a revolution in electron microscopy, allowing
crystallographers and solid state physicists access to more data than ever before.
Fig 3.1 A transmission
electron microscope
constructed in 1928
Although CBED is a highly advanced technique, it is still evolving, recent researchers have
been experimenting with a technique called large angle electron diffraction (LACBED). As a larger
angle (about 2°-5° in modern TEM’s) of the convergent beam of electrons is used, more deficiency
lines become visible on the images obtained, offering more accurate measurements and
interpretations of results.
The thickness of the specimen under investigation in CBED has a major
effect on the diffraction pattern produced. Thin specimens produce
kinematical-diffraction conditions, where the diffraction discs are uniformly
bright and devoid of contrast. Thicker specimen produce diffraction patterns
of strong dynamic contrast, producing ZOLZ, HOLZ, HOLZ lines and
Kikuchi lines as well as other characteristic patterns. These patterns give
more information than those of kinematical-diffraction, so in general, when
using the CBED technique, thicker specimens are better. When specimens
are too thick, however, certain lines from the diffraction pattern disappear.
Kikuchi lines disappear in very thick specimens because inelastic scattering
of the electrons dominates over elastic scattering.
V. Applications
Nanodiffraction:
Uses CBED to obtain diffraction patterns from regions of a specimen
~[1nm] or less in diameter. The electron beam is perfectly coherent with
diameters as small as 0.2nm, which allows one to obtain crystallographic
information on a near atomic scale. Specifically, the study of defects and
disorder in very small particles, structure of individual defects in thin
crystal foils and determination of local symmetry within particular parts of
a defect or a unit cell of a crystal.
Strain / Lattice Parameter Measurements
Strain occurs from changes in the lattice spacing’s of a material which
may arise from the presence of defects such as dislocations or through
local changes in the chemistry. Making use of certain fine features of the
HOLZ lines pattern, CBED can be used to measure the lattice parameter
from microscopic regions. The lines appear as a pair called "deficiency"
and "excess" lines. The angular position of these lines is sensitive to the
accelerating voltage. If the accelerating voltage of the incident electrons is
maintained constant, the changes in the angular position of these HOLZ
lines can be directly correlated to the variations in the lattice parameter.
By measuring the HOlZ line positions we can measure changes in lattice
parameters and in particular changes due to strain.
VI. Thickness Measurement
Fig 6.1 Parallel Kossel-Möllenstedt fringes in
a ZOLZ CBED pattern from pure Al taken
under two-beam conditions with (200)
strongly excited
Thickness determination is a useful application of CBED patterns. The
000 disk usually contains concentric diffuse fringes known as KosselMöllenstedt, K-M, fringes. The number of these fringes in the 000 disk
increases by one every time the thickness of the specimen increases by
one extinction distance, ξg. When the specimen thickness is less than the
extinction distance, the 000 disk is uniformly bright and no K-M fringes
appear. Extinction distance can be found using the equation:
where Vc is the volume of a unit cell, θB is the Braggs angle, λ is the
wavelength of the electrons and Fg is the structure factor of the unit cell for
reflection g.
Fig 5.1 High-resolution TEM
of atomic arrangement in a
crystal lattice.
Lattice Imaging
Using coherent nano probes with a large convergence angle, the discs in
CBED patterns which form are allowed to overlap. Lattice fringes are
revealed in this overlapping region of the pattern, which leads to STEM
lattice imaging. It is possible to locate the probe accurately by this method
at various regions within the unit cell. The CBED patterns obtained from
these areas show different site symmetries and atomic positions. A
coherent CBED pattern recorded with a very large objective aperture or
without the objective aperture, so that a gross overlap of CBED discs
occurs is called a ‘ronchigram’.
References
‘CBED Basics 2006’ – J.A. Eades
‘Transmission Electron Microscopy – D. B. Williams and C. B. Carter
‘LACBED’ – Morniroli
www.wikipedia.org
www.ammrf.org.au
‘Impact of Electron and Scanning Probe Microscopy on Materials Research’ – David G.
Rickerby
A more practical way of using this method is to tilt the specimen to two
beam conditions with only one strongly excited hkl reflection. Under these
conditions, the CBED disks contain parallel rather than concentric intensity
oscillations as shown in Fig 6.1. The central bright fringe is at the exact
Bragg condition where s=0. The deviation for the ith fringe can be obtained
from the equation: where is the angle corresponding to the fringe spacing,
is the Bragg angle for the diffracting hkl plane and d is the hkl interplanar
spacing. The specimen thickness, t, can then be calculated using the
equation:
Fig 6.2 Diagram of diffraction pattern with
two beam conditions with only one
strongly excited hkl reflection
where nk is an integer.
Thickness determination has become the most popular use for CBED
patterns, because the specimen thickness can be measured precisely at the
point of diffraction and because the method can be computerized. This
method is limited to crystalline specimens and is a bit tedious, but it is one
of the best and most accurate method of thickness determination
© School of Physics, Trinity College Dublin