Tem

Front 1

What information about the beam that passes through the specimen does electron holography give that other imaging methods don't give?

What properties of the specimen can be measured from the measurement of this information (6 things)?

Back 1

Electron holography can give the phase information.

This allows measurement of the specimen's:

• thickness
• temperature
• composition
• strain fields
• electric fields
• magnetic fields

Front 2

How & why is the mean inner potential different from the refractive index of the specimen in terms of the speed of the interrogating beam?

Back 2

With the mean inner potential, the phase is sped up, not slowed down, as the beam passes from a vacuum into the specimen.

This is because

• the electron in the beam travels at ~70% the speed of light at 300kV
• the lens-effect of the specimen accelerates the electrons.

Front 3

What is the lens-effect of the specimen?

Back 3

Squeezing of the microscope's electron beam by Coulomb electro-static charges between the electrons and the specimen's atomic nuclei.

Front 4

What is the difference between interferometry and holography in terms of

• their method of interference?
• information obtained about the specimen?

Back 4

Interferometry:

• interferes an object wave with an interference wave
• yields relative property measurements

Holography:

• interferes an object wave with a reference wave
• yields absolute property measurements

Front 5

What three steps are required to obtain information about a specimen via electron holography?

Back 5

1. Create an interferogram/hologram by interfering an object wave with an interference/reference wave using standard optical methods.

2. Record the interferogram using a CCD or film to get the object information

3. Reconstruct the interferogram using optical/digital methods to get the object's amplitude & phase information.

Front 6

What are optical and digital methods to reconstruct an interferogram when doing electron holography?

Back 6

Optical means using another interference beam to re-illuminate interferogram.

Digital means use the Fourier transform.

Front 7

How many holograms must be collected to measure two properties of a specimen?

What is the wavelength requirement of these holograms?

Back 7

Two holograms must be collected such that a system of independent linear equations can be produced.

The wavelength of the holograms must be different (for linear independence).

Front 8

What are three methods of producing contrast in TEM images of the specimen?

Back 8

Scattering contrast

Diffraction contrast

Phase contrast

Front 9

Briefly describe scattering contrast.

Back 9

• Part of e- beam is scattered due to interaction with specimen when it is transmitted.
• Contrast occurs when small bore of objective aperture is located at the objective lens' centre to block the e- scattered at large angles.
• Image is formed by electrons transmitted through the small bore.

Front 10

Briefly describe diffraction contrast.

Back 10

• Electrons can be elastically scattered when e- beam hits crystalline specimen.
• Some will interfere with each other & enhance their signal intensities (Bragg Diffraction).
• The objective movable aperture can be adjusted to remove scattered electrons creating diffraction contrast (bright or dark field).

Front 11

How are bright field images made in TEM?

Back 11

Via diffraction contrast:

Adjust the movable objective aperture to remove scattered electrons.

This results in a weaker beam intensity at reflection locations on image, increasing signal intensity contrast.

Front 12

How are dark field images made in TEM?

Back 12

Via diffraction contrast:

Adjust the movable objective aperture to exclusively collect scattered electrons.

Front 13

What is Bragg Diffraction?

Back 13

Scattered electrons that interfere with each other & enhance their signal intensities.

(waves are superpositioned or added or whatever.)

Front 14

Briefly describe phase contrast.

What can happen if the scattered electrons cause Bragg diffraction in this case?

Back 14

Need:

• aperture that allows both transmitted & scattered e- beams
• a thin-sectioned specimen

Contrast occurs when specimen hit with parallel e- beam: small difference in phase b/w two types of e- beams causes contrast.

If Bragg reflection is present, a lattice image can occur.

Front 15

What apertures & supporting equipment are used for:

1. Scattering contrast
2. Diffraction contrast
3. Phase contrast

Back 15

1. Small bore of objective aperture at center of objective lens

2. Objective movable aperture adjusted to exclude or exclusively collect elastically scattered electrons

3. Aperture allowing both transmitted & scattered electrons, & thin-sectioned specimen

Front 16

Describe briefly the workings of a CCD (charged couple device) detector.

Back 16

• CCD is a semi-conductor type device.
• Electrodes on oxide film on silicon substrate surface, each has voltage applied to maintain charge.
• Scintillated light creates charge on device via photo-electric effect.
• Individual electrode voltages varied to move charge to neighbouring electrode via an interline or one of two frame transfer methods to facilitate sequential charge readings.

Front 17

What three aspects of the CCD camera determines its performance?

Back 17

1. Number of pixels

2. Size of pixels

3. Sensitivity

Front 18

Where is the CCD placed to obtain

• a wide field of view?
• a high resolution image?

Back 18

Wide field: place CCD above fluorescent screen.

High resolution: place CCD below fluorescent screen.

remember: high=below, wide=above (counter-intuitive)

Front 19

Why is mapping the elements by energy dispersive x-ray (EDX) not as good as by electron energy loss spectrometry (EELS)?

Back 19

EELS is better because it:

• causes less beam damage to specimen
• process is more stable (specimen less likely to move/drift & microscope conditions/properties unlikely to change)
• is faster at mapping

Front 20

Describe the point spread function (PSF).

What does it do?

Back 20

PSF is the number of points representing atoms/molecules in the specimen contributing to one point in the image.

It limits microscope resolution by changing a point in an image to a disc on the observation plane because of blurring (from focusing defects like spherical aberration).

Front 21

What is required of the PSF to obtain a true, interpretable image of specimen features?

Back 21

PSF must be less than or equal to an atom (or the features imaged by the microscope) for a true image.

Front 22

Mathematically, how is the PSF, h(r), treated in reciprocal space?

What common term is then used for this information-limiting function?

Back 22

PSF convoluted via the Fourier transform & becomes H(r) in reciprocal space.

It is multiplied in reciprocal space with the specimen function F(r). This saves having to integrate the products of the two in regular space.

It is then called the contrast transfer function, which limits information of specimen transferred to the image.

Front 23

What three important terms must be considered for transfer of specimen information to the image?

Back 23

1. Wavelength

2. Aberrations (spherical)

3. Defocus (∆f)

Front 24

What must be considered when comparing two high-resolution images such as lattice images?

Back 24

Consider that they should be imaged under similar conditions:

• same electron accelerating voltage
• same wavelength
• similar aberration corrections
• same equipment/apparatus used to image

Front 25

What imaging condition is used to define the highest resolution image possible by EM in terms of specimen defocus and reciprocal lattice point?

Where is this point in the graph of contrast transfer function or instrumental resolution limit vs. reciprocal space frequency, u?

Back 25

Highest-resolution is found using Scherzer defocus, ∆fsch= -1.2√(Csλ), which maximizes point resolution of microscope in terms of the reciprocal lattice point: rsch=0.66λ^(3/4)Cs^(1/4)

In the graph this point is where the CTF first crosses the abscissa.

Front 26

What function ultimately limits specimen information transferred by the EM that damps out all the high frequencies?

What three general terms define this limit?

Back 26

Envelope damping function, Teff(u).

Defined by product of

• objective lens transfer function T(u)
• chromatic aberration envelope Ec
• spatial coherence envelope Ea

Front 27

What are the three machine factors that the chromatic aberration envelope function, Ec, depends on?

Back 27

Instabilities in the

• high-voltage (accelerator) supply ∆Vacc/Vacc
• objective lens current ∆Iobj/Iobj
• e-gun intrinsic energy spread ∆E/Vacc

Front 28

What is the mathematical relationship between the machine factors of the chromatic aberration envelope function & the microscope stability?

Back 28

They're related in the defocus spread due to the aberration:

δ =Cc[4( ∆Iobj/Iobj)^2+(∆E/Vacc)^2+(∆Vacc/Vacc)^2]^1/2

which is expressed in the chromatic aberration envelope function Ec(u):

Ec(u)=exp[-0.5(πλδ)^2u^4]

Front 29

What is the atomic scattering factor f(θ)?

What two components of electron scattering are involved?

Back 29

f(θ) is a measure of the amplitude of an electron wave scattered from an isolated atom.

Components:

Z: elastic nuclear scattering

fx: elastic electron-cloud scattering

Front 30

How does f(θ) vary with

1. wavelength?
2. scattering angle?
3. atomic number?

Back 30

1. decreases with decreasing wavelength
2. decreases with increasing scattering angle
3. increases (for any θ) with increasing Z

Front 31

Describe the concept of the mean free path of the electron passing through the specimen.

What is it's typical length scale?

Back 31

• Represents the average distance an electron travels b/w interactions with atoms (in general)
• The mean distance traveled through specimen before elastic scattering occurs

Typical length scale:

Light elements: 100s of nm

Heavy elements: 10s of nm

Front 32

How does the mean free path vary with

1. atomic number?
2. electron acceleration energy?

Back 32

1. The mean free path decreases with increasing atomic number.
2. The mean free path decreases with increasing electron acceleration energy because of a decrease in scattering cross-section to which it is proportional.

Front 33

For the mean free path,

1. what is the preferred specimen thickness?
2. why is it this thickness preferred for reducing multiple elastic scattering of electrons?
3. why is it difficult to see light elements like H?

Back 33

1. The thinner the better - less than 100nm

2. Preferred because very few high-angle elastic scattering events occur - most will have single-scattering or will not be scattered. This is preferred to more easily interpret the image.

3. Difficult to see because light elements often don't scatter the beam at all.

Front 34

Give a typical approximate size scale of an electron scattering cross-section

1. elastic

2. inelastic

Back 34

1. elastic scattering cross-sections: ~10-22 m2

• 100keV, transition metals, typical for small-angle

2. inelastic cross-sections: ~10^-22 m^2 to ~10^-26 m^2

• depending on scattering type & material type

Front 35

What is the structure factor, F(θ), in terms of amplitude & phase of elastically scattered electrons?

What's the angle input θ?

Back 35

F(θ) is a measure of the amplitude scattered from a unit cell of the crystal structure of a specimen.

The sum of f(θ) of all atoms in unit cell, multiplied the phase factor fx.

ΣF(θ)=fx [exp (-2πi (hxi+kyi+lzi) ]

Angle input is the scattering angle θ, between incident & scattered electron beams.

Front 36

What is the phase factor in the structure factor?

Back 36

Accounts for atoms on different, parallel atomic planes,

with the same miller indices,

which emit waves of differing phases.

Front 37

How is the amplitude of scattering influenced by the specimen? (4 things)

In other words, which specimen properties influence the structure factor F(θ)?

Back 37

Amplitude of scattering depends on:

• atom type
• atomic scattering factor f(θ)
• atom's spatial location within unit cell
• atomic planes comprising crystal structure

Front 38

Give two reasons why quasiparticle properties can be determined using inelastically scattered electrons.

Back 38

Energy loss process:

Electrons creating quasiparticles experience energy loss characteristic of the formed quasiparticles.

Energy gain process:

Pre-existing quasiparticles lend their scattering phase to electrons that inelastically scatter off of them.

Front 39

Experimentally, state two conditions in terms of energy and angle that can be used to make property measurements of quasiparticles existing close to the zero loss electrons.

Back 39

Intensity must be separated using a sufficiently high scattering angle.

An energy window must be used so the energy loss peak can be filtered.

Front 40

What is a systematic row of diffraction?

Back 40

A series of periodically spaced Bragg diffractions.

Have corresponding diffraction vectors which are the distance from the origin of the incident beam to the diffraction spot.

Front 41

What is dynamic diffraction?

How does it vary with specimen thickness?

Back 41

• The mixing of diffraction intensities
• Increases with increasing specimen thickness.
• Intensity of the direct beam is transferred to diffracted beams & back to the direct beam after mixing.

Front 42

How is a two-dimensional diffraction pattern generated from a crystal?

Back 42

By the electron beam's incidence with non-parallel atomic planes within the crystal.

Front 43

What is reciprocal space?

Back 43

• Diffraction space; the inverse of real space
• Conceptual geometrical mathematical construction

Front 44

What is the Ewald sphere and how does it vary with

• wavelength?
• electron accelerating energy?

How do diffracted electron beams that pass through the Ewald sphere appear?

Back 44

• A sphere of radius 1/λ representing the in-focus diffraction condition.
• Increases with decreasing wavelength
• Increases with increasing electron accelerating energy
• Diffracted electron beams pass through Ewald sphere and appear as spots

Front 45

What is the excitation or deviation parameter?

Back 45

A vector in reciprocal space representing amount of deviation from exact Bragg condition.

aka small angle of rotation off of exact Bragg angle of diffraction

• Negative when G is outside Ewald sphere
• Positive when G is inside Ewald sphere

Front 46

What is diffraction's extinction distance?

How does it vary with specimen thickness?

What is a typical order of magnitude?

Back 46

• ξg is a dynamic diffraction effect dependant on Bragg angle θ & specific beam's fg. (f(θ) using θB)
• ξg = πVccosθB / λfg
• It is the sinusoidal minimum of the direct beam's intensity.
• Increases with increasing specimen thickness.
• Typical order of magnitude is ~100s nm.

Front 47

Why is the extinction distance important?

Back 47

In a wedge-shaped specimen, extinction distance appears as dark & light bands with increased specimen thickness.

• can be used to approximate the thickness of the specimen at a point in the image.

Front 48

What is double diffraction?

What do we see when this occurs?

Back 48

The re-diffraction of a beam travelling through a crystal, either through a neighbouring crystal or back through original crystal.

A diffraction pattern or spots are visible around the diffracted beam when imaged on the diffraction plane.

Front 49

How are forbidden reflections created?

Back 49

Created due to dynamical scattering events when oriented at a zone axis such that some beams have F=0, so they act like new incident beams. As a result, they're re-diffracted by certain planes.

• diffracted beams found in the diffraction pattern that should not be there because there is not a crystal plane in the specimen that could give rise to the diffracted beam.
• created by dynamic diffraction such that two diffracted beams act as a main beam creating an allowed diffracted that now coincides with the spot where the forbidden diffracted beam is found.

Front 50

How are Kikuchi lines produced?

What is their general direction of travel?

Why are their patterns useful?

Back 50

• Bragg diffracted inelastically scattered electrons mostly comprised of phonon loss electrons.
• Mostly travel close to direction of incident beam (forward).
• They are useful for knowing the orientation of the crystal and can be used to rotate from one zone axis or crystal orientation to another.

Front 51

Why do Kikuchi lines appear as lines and not spots?

Back 51

Appear as lines because:

• there is a range of k-vectors as the scattered electrons are travelling in all directions
• The beam lies on one of two Kossel cones.

Front 52

Give some advantages that CBED patterns have over SAD patterns in terms of obtaining specimen information.

(6 things)

Back 52

• CBED has better spatial resolution, is simpler & more versatile
• can scale down to single-unit cell dimensional levels of nanodiffraction
• info collected from much smaller specimen volume than SAD
• Kikuchi lines are attainable w/o thick specimen
• Kossel patterns (discs) allow thickness fringes to be obtained
• Discs also make HOLZ diffraction effects possible - enable determination of crystal orientation

Front 53

What is the difference between HOLZ lines and Kikuchi lines in terms of their production from electrons passing through the specimen?

Back 53

HOLZ lines are produced from

• Bragg diffracted elastically scattered electrons

Kikuchi lines are produced from

• Bragg diffracted inelastically scattered electrons

Front 54

What two focusing conditions are required to bring HOLZ lines into the zero-order beam?

Back 54

1. over-focus the focus probe from the specimen plane (or manually raise the specimen to defocus it).

2. the diffraction plane may need defocusing upwards a bit to see the HOLZ lines when they are passing close to the optic axis

Front 55

How can HOLZ lines be used to measure strain in crystals?

What is their dependency on Bragg's angles or the diffraction vector, g?

Back 55

The separation of the two HOLZ lines (split HOLZ line) is a measure of the strain of the atomic planes.

Split HOLZ lines are very sensitive to a change in lattice spacing, Δd, resulting in a change in the diffraction vector, Δg such that

Δg = Δd/(d2)

providing the highest resolution method to measure strain in crystals.

Front 56

How do split HOLZ lines occur?

Back 56

When atomic planes are strained or bent, Bragg diffraction of the elastically scattered electrons can occur twice:

• once when the atomic planes bend away from the beam and
• again when they bend back towards the beam.

This results in two lines or a split HOLZ line.