Microscopy: Overview of Different Methods

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Microscopy Overview of Different Methods

• Peter N. Kalu
• FAMU-FSU College of Engineering

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(MACRO)TEXTURE

• Review
• Recall that X-ray texture (macrotexture)
• Provides an overview of the crystallographic
  texture of material - only texture information is
  obtained.
• Provides the volume fraction of the specimen,
  which has a particular orientation.
• Does not tell how grains are distributed in the
  material.

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• Lack of a direct connection between the study of
  texture and microstructure.
• Parallel but separate investigations are needed
  in order to obtain microstructural data.

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MICROTEXTURE

• Microtexture technique provides concurrently the
  spatial location and the orientation of
  individual grains in a sample.
• This technique can be referred to as the modern
  approach to texture investigation.
• Until recently, the orientation of individual
  crystals can only be determined by Selected Area
  Diffraction Pattern (SADP) technique on TEM -
  very tedious.

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• Phenomena that can be investigated using
  microtexture technique
• Effect of property variation as a function of
  orientation
• Misorientation between neighboring grains or
  distribution of grain boundary geometry, which
  can result in the grain boundary/property
  relationship.
• Correlations between geometrical and
  orientational parameters of the grains
• Orientation variations within individual grains
• Phase relationships
• Direct ODF measurement

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• Macrotexture or Microtexture analyses techniques
  rely on the diffraction of radiation by a crystal
  lattice.
• The exploring radiation can be used as an
  experimental tool for microtexture measurement
  only if the probe size is smaller than the
  microstructural unit.

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• Diffraction
• Crystal structure analysis is usually based on
  diffraction phenomena caused by the interaction
  of matter with X-rays, electrons, or neutrons.
• Therefore, when either X-rays or electrons
  interact with crystalline material, they are
• (a) Subject to diffraction have similar wave
  properties.
• (b) Monochromatic radiation) - produce a series
  of strongly diffracted beams leaving the
  crystal in defined and predicted directions.

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• The resultant diffraction pattern is given by
  Braggs Law, and this is given by
  .. 1
• where, d Interplanar spacing
• ? Grazing angle of incidence
  (Bragg angle)
• n Integer (0, 1, 2, 3 .. )
• ? Wavelength of the incident electrons
• Note
• With diffraction, we use Reciprocal lattice in
  which sets of lattice planes are represented
  simply by a set of points in reciprocal space.

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• The Reciprocal Lattice
• Very useful in metric calculations
• Let a, b, c be the elementary translations of a
  space lattice (direct lattice)
• A second lattice, reciprocal to the first one, is
  defined by translations a, b, c, which satisfy
  the following conditions
• a. b a. c b. a b. c c . a c .
  b 0
• and
• a. a b. b c. c 1
• Equation 2a suggests that a is normal to the
  plane (b,c),
• b is normal to the plane (a,c), and
• c is normal to the plane (a,b),

(2a)
(2b)
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• The magnitude and sense of a, b, c are fixed
  by (2b)
• According to (2a), a may be written as
• a p (b c)
• where p is a constant.
• The value of p is obtained by if the scalar
  product of both sides of (3a) by a is taken
• a . a 1 p (b c . a) pV
• Therefore, p 1/V, and equation (3a) can be
  written as
• a (b c)1/V

(3a)
(3b)
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• Table 1. The Characteristics of Light and Various
  Radiations Used for Texture Measurement by
  Diffraction.
• Electrons are the only radiation in which their
  penetration depth and interaction volume is small
  enough to allow diffraction from individual
  grains (very small volume). Hence, only
  electrons can be used for MICROTEXTURE

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• Microtexture technique can either be TEM-based or
  SEM-based.
• Until mid-1980, the TEM-based was the major
  microtexture technique, although an SEM-based
  Selected Area Channeling technique was available.
• Modern SEM-based technique known as can now be
  classified into two
• manual
• automated

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Principles of Electron Microscopy
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MICROSCOPY

• Introduction
• Several new microscopy-based microcharacterization
  techniques have been developed over the last
  four decades, which have significantly extended
  the ability to study the microstructure of
  materials.
• In addition to Optical Metallography, there is a
  range of Electron Optical techniques.
• Electron microscope (developed in 1931) was
  initially used for the study of biological
  systems, but thin foil techniques in the
  mid-1950s enabled microstructural investigations
  to be undertaken on metals and alloys.

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• Typical Information from Electron Microscope
• Chemical composition of materials can be obtained
  using electron microprobes to produce
  characteristic X-ray emissions and electron
  energy losses.
• Imaging (surface) can be characterized using
  secondary electrons, backscattered electrons,
  photo-electron, Auger electrons and ion
  scattering.
• Crystallography or crystal structure information
  can be obtained from backscattered electrons
  (diffraction of photons or electrons).
• The various studies of materials exploit at
  least one of the above information, as well as
  the excellent spatial resolution of electron
  microscopes.

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Figure 1. Summary of the various signals obtained
by interaction of electrons with matter in an
electron microscope
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Comparison between Optical and Electron
Microscopy

• In many ways, electron microscopes (Scanning and
  Transmission) are analogous to light microscopes.
  
• Fundamentally and functionally, electron
  microscopes (EM) and optical microscopes (OM) are
  identical.
• That is, both types of microscopes serve to
  magnify minute objects normally invisible to the
  naked eyes.
• Basically, component terminology of an EM is
  similar to that of an OM. Both microscopes
  consist the following (see Figures 2 and 3)

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• Figure 2. A simple optical, transmission
  microscope system comprising a
  condenser and objective lens.

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• Figure 3. Comparison of image formation.

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• (a) Source of Illumination as light source
• Electron Gun produces an electron beam by
  thermionic or field emission - EM
• Lamp produces light beam (including uv rays) - OM
• (b) Condenser Lens system projects a near
  parallel radiation on to the specimen
• Electro-magnets of variable focal length are the
  lenses in EM.
• Curved transparent substance - OM
• (c) Series of Imaging Lenses form the Image of
  the specimen

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• Although (a) to (c) above address the basic
  differences between the two types of microscopes,
  a detailed comparison is provided in Table 1.

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ELECTRON MICROSCOPES
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• ELECTRON SOURCES
• Electron sources in electron beam instruments are
  required to provide either
• a large total current beam of about 50 ?m
  diameter - low magnification TEM, or
• a high intensity probe of electrons as small as
  0.5 nm in diameter - SEM
• There are three different types of electron
  source available

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• There are three different types of electron
  source available
• a) Thermionic tungsten hairpin filament
• This is usually heated to about 2800 K by
  direct resistance heating. The surrounding
  grid, known as the Wehnelt cylinder, and the
  anode, which is at earth potential, act as an
  electrostatic lens.
• For an operating condition of 100 kV, the
  brightness is about
• 3 x 105 A cm-2 sr-1.

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(a)
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(b)
Figure 4. Schematic diagram of a conventional
tungsten thermionic source. (a) the filament F
and Wehnelt cylinder (b) schematic ray path
showing focusing action.
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• b) Lanthanum hexaboride crystal (LaB6)
• The only difference between the conventional
  assembly illustrated in Figure 4 and a modern
  LaB6 assembly is that extra pumping holes are
  present in the Wehnelt cap to ensure a better
  pumping speed near the tip.
• Higher current (greater than the tungsten) is
  obtainable in small probes.
• The brightness of a LaB6 can be as high as 107 A
  cm-2 sr-1 at 100kV.

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• c) Field emission source
• This is usually a lt111gt orientation crystal of
  tungsten, and a Wehnelt cylinder, which is raised
  to an extraction potential up to about 4 kV in
  order to cause emission from the tip of the
  crystal.
• There is a requirement of high vacuum for this
  source.
• The brightness of cold or thermal emission source
  can be about 104 times of a conventional tungsten
  filament.
• The high brightness of this source make them
  preferable for scanning instruments.

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ELECTRON LENSES AND OPTICS
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• Electron lenses in microscopes are generally
  electromagnetic.
• There are three types of magnetic lenses in uses
  (refer to Figure 5)
• (a) a multi-layer coil i.e., an air-core
  solenoid coil
• (b) a coil enclosed by soft iron plates (in
  order to reduce leakage flux) containing a gap
  (in order to concentrate the induction field)
  and
• (c) a coil enclosed by soft iron plates
  containing a gap and internal soft iron pole
  pieces (in order to ensure a high intensity
  magnetic field)

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• Figure 5. Types of magnetic electron lenses.

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• Almost all modern electron microscopes use pole
  pieces for high resolving power and high
  magnification.
• The function of such an electron lens is more or
  less the same as that of horse-shoe magnets
  symmetrically arranged about an axis.
• Accordingly, all the parallel electron beams
  incident to the curved magnetic field converge at
  one point.

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ELECTRON OPTICS

• The action of a magnetic field on an electron is
  described by a well-known right hand rule where
  thumb, first and second finger are used to
  represent the terms in a vector product
• The force F which an electron of charge -e
  experiences when travelling with velocity v, due
  to a magnetic field B, is given by
• 
  (4a)

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Figure 6. Schematic diagram of the action of a
cylindrical magnetic lens on the path of
non-axial electrons.
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• and the magnitude of the force is then given by
• 
  ..(4b)
• where ? is the angle between B and v.
• If the initial velocity of an electron is divided
  into two components, vp parallel to B and vo
  perpendicular to B, then the value of vp will be
  unchanged by B (since ? will be zero) and the
  force resulting from B and vo will result in a
  circular motion of the electron about B (see
  Figures 7 and 8).

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• Figure 7. Electrons passing through magnetic lens

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• Figs. 7 8 shows the trajectory of an electron
  passing through such a magnetic field.
• Although the electron beam path in a magnetic
  lens is not the same as the light ray path in an
  optical lens, the results are similar.
• As shown in Figs. 7 8, the electron travels
  rectilinearly, crosses the axis, moves through
  the magnetic field along a spiral orbit,
  approaches the axis, crosses the axis again, and
  travels rectilinearly.

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Figure 8. Schematic diagram showing the
trajectory of an electron through a magnetic
lens.
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• The radius r of this spiral motion is given by
• .(4c)
• Since generally, in electron microscopes,
  electron beams near the axis are used for forming
  an image, a is extremely small.
• This effect is similar to the converging action
  of an optical convex lens, and if the revolution
  of the electron about the axis is omitted, the
  converging action of an electron lens can be
  considered to be identical to that of an optical
  lens.

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• A magnetic lens containing pole pieces magnetized
  to near-saturation for concentrating magnetic
  flux in a very narrow space constitutes a thin
  lens.
• The focal length f and rotation angle q are given
  as follows
• .. 5
• where, V gt Accelerating voltage
• ? specific charge of electron e/m

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• Resolution of Lens
• Resolution defines the smallest separation of two
  points in the object, which may be distinctly
  reproduced in the image.
• The resolving power for light microscopy is
  determined by diffraction aberration and can be
  defined as 1,2
• .. 6
• where ? is the wavelength of the illumination, n
  is the refractive index of the medium between the
  specimen and the lens, ? is the semi-angle
  (aperture angle) subtended by the object at the
  lens and k is a constant usually taken to be 0.61.

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• Examples
• (a) Optical Microscope
• ? 50 nm (for white light
  Illumination)
• n sin ? 0.135 (when fitted with an oil
  immersion lens)
• Therefore, it is possible to achieve a
  resolution of about 250 nm in Optical
  Microscopes.
• (b) Electron Microscope
• De Broglie relationship relates the wavelength
  of electrons, ?, to their momentum, mv (m is the
  mass and v is velocity), by h Plancks
  constant, such that

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• 7
• Since electrons are accelerated by a potential
  difference of V volts and have a kinetic energy
  K, where K is given as
• ... 8
• Therefore,
• 9

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• By considering equations (7) and (9), we have
• 
  . 10
• The energy term e.V is expressed in electron
  volts and represents that energy required to pass
  an electron through a potential difference of one
  volt ( 1 eV 1.602 x 10-19 J).

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• When the velocity of the electron approaches the
  speed of light, v c, a relativistic
  correction is required for the voltage, such that
• .. 11
• where mo is the mass of the electron at rest. It
  is important to use this correction for cases
  when V ? 105 volts. Table 2 presents a chart of
  electron wavelength in relation to applied
  voltage.

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• Table 2. Variation of Electron Wavelength with
  applied voltage

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• If diffraction aberration is considered (see
  equation (6)), the resolving power of 100 and 300
  keV electron microscopes will be about 0.0025 nm
  and 0.0017 nm respectively. These values are not
  realistic!
• The ultimate resolution of an electron microscope
  is dictated by the defects in the imaging system
  rather than by the wavelength (diffraction
  aberration) of the radiation employed.

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• Lens defects
• Chromatic aberration is related to energy losses
  within the specimen. This is generally of little
  importance except for very thick regions of thin
  foils or bulk specimens.
• Astigmatism may arise from
• intrinsic defects in the objective lens, or
• from contamination on the lens and the objective
  aperture.
• Microscope manufacturers have developed
  methods for correcting this defect
• small set of coils are used to produce uniform
  magnetic field.

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• Spherical aberration is the main factor, which
  limits the performance of electromagnetic lenses
  used in microscopes.
• It is a function of the lens design and the
  acceptance angle (?) for electrons entering the
  lens.
• This angle must be kept at a minimum, however
  this decreases the resolution limit due to
  diffraction. The best resolution is accomplished
  with a compromise value of ?, and is given by
• 12
• where cs is the coefficient of spherical
  aberration, and ?min is typically less than 3 Å
  on modern microscopes.