TEM Flashcards
reasons to index a diffraction pattern and the utility of knowing directions
- crystal structure information including crystallinity, lattice parameters, symmetry, grain size, fabric
- directions give proper phase identification and can give clues to thermodynamic origins
how to obtain highest practical resolution
highest acceleration voltage with the smallest spherical aberration coefficient
do the laue equations or braggs law better describe electron diffraction?
we typically use Braggs law to describe a special condition of the Laue equations which describe the process of elastic scattering in transmission. Braggs law does not properly represent electron diffraction because it assumes scattering at a glancing angle. Laue’s equations take into account the the agnle of incidence and angle of the diffracted beam
how to get thickness from an EELS spectrum
log of the total intensity in the low loss region divided by the intensity of the zero loss peak multiplied, multiplied by the mean free path (
Bragg’s law
2 d sin (theta) = n lambda
3 systems of a TEM
illumination (gun and condenser lenses), image forming system (objective lenses), imaging recording lenses (projector lenses)
astigmatism
nonuniformity of lens distorts probe into an ellipse
occurs when electrons are affected by a non-uniform magnetic field as they spiral
spherical aberrations
inability of the lens to focus electron beam in the same image plane, smears out point into a disc. electrons that pass through the lens further from the center are refracted more than those passing through the center
chromatic aberrations
energy spread of beam and as electrons scatter into sample, close to the focal length of the lens, caused by gun and sample, only relevant after 5th order Cs correction. slower electrons are diffracted more strongly than nominal electrons
electromagnetic radiation of different energies converging at different focal planes
eucentric position
horizontal center of the objective lens, point where the sample should not translate while tilting in alpha
where are diffraction patterns formed?
back focal plane of the objective lens
selected area electron diffraction
a field-limiting aperture that is placed into the image plane of the objective lens to create a virtual aperture above the sample
imaging type in TEM mode
bright field imaging in TEM mode does not allow for constructive interference, giving us amplitude contrast
diffraction vs imaging mode in TEM mode
in diffraction mode, the BFP of the objective lens is the object plane of the intermediate lens
in image mode, the image plane of the objective lens is the object plane of the intermediate lens
relationship between camera length and DP
Rd=lambdaL
diffraction pattern
records the distribution of scattered electrons around the forward scattered beam, gives d-spacings of cell
atomic scattering factor
measure of the scattering amplitude of electrons scattered from isolated atom, depends on scattering angle, lambda, and atomic number
structure factor
tells us if to expect reflections in our DP based on the symmetry of the unit cell, measure of the amplitude scattered by the unit cell of a crystal. amplitude of scattering is impacted by the type, position, and atomic planes of the atom
fluorescence yield
ratio of x-ray emissions to inner shell ionization events
plasmons
incident electrons cause oscillations in the free electron gas
phonons
shaking of the lattice as a result of striking by incident electrons causes lattice to heat up due to vibrations
3 types of beam damage
- radiolysis: breaking of chemical bonds
- knock-on damage: displacement of atoms from their preferred lattice positions, resulting in point defects
- heating due to phonons
dead time
how long detector is shut off to evaluate the charge pulse
Cliff-Lorimer method
concentration of element A (in wt%) over element B is equal to the sensitivity factor of the elements times the intensity of element A over element B
contributions to the sensitivity factor in EDS
ZAF: atomic number, absorption of x-rays, fluorescence of x-rays
in TEM, only need to correct for Z bc of thin foil criterion
electron energy loss spectroscopy
uses the amount of energy lost by incident electrons to probe the structure, bonding, oxidation state, nearest neighbor environment of sample
how to form an amplitude contrast image
insert a field-limiting aperture around an image forming beam, use the forward scattered beam to exclude all diffracted beams and form a bright field image. putting the aperture around a diffracted beam will give you a dark field image of everything oriented in a certain direction
when are lenses used?
in TEM mode you use objective lenses to form an image. in STEM we use solid state detectors
camera length
current of intermediate/projector lenses, “length” between sample to image plane
short length = high angle = more signal
utility of EELS vs EDS
EELS collects all forward scattered electrons
EDS has fluoresence yield to contend with
X-rays are scattered isotropically but we can only collect 2.0 sr
what defines the resolution of the microscope
Cs and acceleration voltage
what does the distance between spots on a diffraction pattern represent
close spots=large d-spacing (reciprocal space)
high spatial frequency = large distances from optic axis in diffraction pattern
objective lens transfer function
T(u)=A(u)*E(U) 2sin(X(u))
when T is negative, you get positive phase contrast and atoms appear dark against light background
when T is large, we have constant contrast such that we resolve small distances in real space
Scherzer defocus
balance Cs with negative value of delta F optimizes the contrast transfer function
at this value, all beams have constant phase out to first crossover of zero axis
this point is defined as the instrumental resolution limit where you can use intuition to interpret images
envelope damping function
T_eff=T(u)E_cE_a
E_c: envelope function for chromatic aberrations
E_a: spatial coherence envelope
envelope function imposes a virtual aperture in BFP in obj lens regardless of defocus value
information limit
resolution limit of microscope
instrumental vs information limit
instrumental limit is defined by the scherzer defocus value, the value where the beams will have nearly constant phase out to the first crossover of the zero axis. this is the limit where we can use intuitive arguments to interpret what we see. just because we can see detail does not mean that we can gain useful information from it.
the information limit is the highest spatial frequency transferred to the image with statistical significance
deriving braggs law
he rays of the incident beam are always in phase and parallel up to the point at which the top beam strikes the top layer at atom z (Fig. 1). The second beam continues to the next layer where it is scattered by atom B. The second beam must travel the extra distance AB + BC if the two beams are to continue traveling adjacent and parallel. This extra distance must be an integral (n) multiple of the wavelength (lambda) for the phases of the two beams to be the same.Recognizing d as the hypotenuse of the right triangle Abz, we can use trigonometry to relate d and theta to the distance (AB + BC). The distance AB is opposite theta so,
(eq 3) AB = d sintheta .
Because AB = BC eq. (2) becomes,
(eq 4) nlambda = 2AB
Substituting eq. (3) in eq. (4) we have,
(eq 1) nlambda = 2 d sintheta
components of an EELS spectrum
zero loss peak (ZLP): elastically scattered or unscattered electrons, lost no energy interacting with the sample
low-loss region: first 50 eV, contains electron information from the weakly bound conduction and valence band electrons
high-loss region: elemental information from tightly bound, core-shell electrons, detailed bonding and atomic distribution information
components of an EELS spectrometer
entrance aperture (select electrons), focusing coils, magnetically isolated drift tube, magnetic prism (separates electrons based on amount of energy lost, more loss=higher deflection angle), detector
why do you have to focus an EELS spectrometer?
the spectrometer is also a lens. you must minimize the the aberrations and astigmatism. you must focus the electrons because off-axis electrons experience a different magnetic field to on-axis electrons. the path length of off-axis electrons through the magnet varies
energy resolution of EELS
the FWHM of the focused ZLP, 0.3 eV in our microscope, based on the gun. best resolution requires small projector crossover and a small entrance aperture
electron gun
cold FEG, an electrostatic field is applied to a 100nm diameter W wire to induce quantum mechanical tunneling of high-energy electrons. FEGs have better brightness, longevity, and resolution.
condenser lens
focus electrons onto the specimen
condenser aperture
limits spherical aberrations by
objective lens
main magnifying lens. forms images and diffraction patterns that are magnified by other lenses
objective aperture
control the resolution of the image formed by the lens, the depth of focus, image contrast,
intermediate lens
selects its object plane as either the image plane or the BFP of the objective lens. can adjust the magnification and focus of the diffraction pattern
1st Int lens = diffraction focus
projector lens
magnify the electron image and form the final image on the viewing screen
electron tunneling
quantum phenomenon where a particle is able to penetrate through a potential energy barrier that is higher in energy than the particles kinetic energy
under/over focused
image forms below the image plane / image forms above the image plane
fresnel fringes
phase-contrast effect that occurs when the edge of an object is out of focus under coherent illumination
underfocused = bright fringe
overfocused = dark fringe
DeBroglie formula
wavelength of an electron is a function of acceleration voltage
mean free path
length traveled by electron between scattering events
brightness knob adjusts what?
convergence angle (alpha), lens strength
What is a cross section and in what units is it measured?
A cross section is measured in area and is the probability that a scattering event will occur
Distinguish between total, atomic, and differential cross sections.
Total cross section: number of atoms multiplied by the atomic cross section
Atomic cross section: probability that a single atom will scatter in response to an incident electron
Differential cross section: angular distribution of scattering from an atom
Why are we interested in variations in the scattering intensity and the angular distribution of electron scattering?
Variations in scattering intensity and angle provide information about your specimen, including atomic number, bonding state, valence state. Angular distribution produces dark field and bright field images in STEM
What’s the difference between forward scattering and backscattering?
Forward scattering occurs parallel to the incident beam direction and causes most signals we observe in TEM. backscattering is similar to reflection
Distinguish between coherent and incoherent scattering.
Coherent scattering assumes that electrons are in phase with one another. Incoherent scattering has no phase relationship after interacting with the specimen
Describe what distinguishes diffraction from other kinds of scattering
Diffraction is a form of elastic scattering in which any interaction between a wave and object. Scattering more appropriately applies to particles
What’s the fundamental difference between electron scattering and X-ray scattering?
Electrons are scattered more strongly than X-rays. Electrons are directly scattered while x-rays experience a field to field exchange
X-rays are scattered by electrons in a material through interaction between negatively charged electrons and the electromagnetic field of incoming x-rays
What are the primary causes of elastic scattering?
Elastic scattering can occur from either single, isolated atoms or collective scattering from many atoms together. These both occur because of Coulomb forces
What forces act on an electron as it interacts with atoms?
Coulomb forces act on electrons. Interaction within the electron cloud results in low angle scattering. Attraction by the nucleus causes high angle scattering
Howis the scattering amplitude related to the intensity of the scattered beams that we see in the microscope?
intensity only arises if the scattering amplitude is an integer number
What is the relationship between the atomic scattering factor f(y) and the structure factor F(y)?
The atomic scattering factor is a measure of the scattering amplitude of a single atom and depends on wavelength, angle, and atomic number
The structure factor is the scattering amplitude of a unit cell
The structure factor is the sum of all of the atomic scattering factors for a single unit cell multiplied by a phase factor
Why do crystalline and amorphous specimens give rise to different scattering distributions?
In an amorphous specimen, there are no atomic planes for the wave to scatter off of to produce
Amplitude of diffraction is stronger at some angles than others, so we see diffuse rings on the screen
A crystalline sample produces diffracted beams that are at a maximum at specific angles because the interplanar spacings are well defined
What are the fundamental differences between the von Laue and Bragg approaches to diffraction and what are the similarities?
Von Laue’e equations consider diffraction in three dimensions
Bragg simplifies the Laue equations so that the waves behave as if they were reflected off of planes, not transmitted
What is the relationship between the spacing of the lattice planes and the angle of scatter?
Interplanar distance times the angle of reflection is equal to the wavelength of the beam
Distinguish background, continuum and bremsstrahlung X-rays.
Background: comes from stray radiation (uncollimated e) in the column and bremsstrahlung
Continuum: arises from interactions between electrons and atomic nuclei. Decreases monotonically with increasing x-ray energy
Bremsstrahlung X-rays: produce a continuum x-ray background, no specific peaks, sudden change of nuclear charge when the beta particle is emitted or when an orbital electron is captured
‘Characteristic’ X-rays are characteristic of what?
Characteristic of the difference in energy between two electron shells, this difference is unique to the atom
What is the critical ionization energy?
The amount of energy greater than a certain value to the inner shell electron in order to ionize the atom
What is the ionization cross section?
Probability that ionization will occur when incident e interact with sample
What is the fluorescence yield?
Ratio of x-ray emission to inner shell ionization events
What is overvoltage?
Ratio of the beam energy to ionization energy
What is the difference in the angular distribution of the ionizing electrons and the emitted X-rays?
The electron that ionized the atom is deviated through an angle of <10mrad, but x-ray emission occurs uniformly over 4pi sr
Why is all the energy transferred to the atom during ionization (Ec) not recovered by the emission of the characteristic X-ray(s)?
The atom does not completely return to the ground state when the x-ray is emitted
If the electron that fills the hole in the ionized inner shell comes from an outer shell, then this process will leave a hole in the outer shell. This hole must also be filled
How can you minimize electron-beam damage to your specimen?
Going to higher voltages minimizes thermal effects and radiolysis, but induces knock on damage
Why does sputtering of atoms from the surface of the specimen take less energy than displacing atoms in the interior?
Fewer other atoms to disrupt, beam loses energy as it penetrates the specimen
What is radiolysis?
Breaking of chemical bonds due to inelastic scattering
How do you focus an image in a TEM?
Changing the strength of the lens. This happens by changing the current through a coil around a soft-iron core which changes the strength of the magnetic field
What kind of visible-light lens does the behavior of a magnetic lens resemble?
Convex (converging) glass lens on monochromatic light
What are the back and front-focal planes of a magnetic lens?
The focal plane is where the parallel rays are brought into focus. The back focal plane is after the lens and is where we select to view a diffraction pattern
What force acts on an electron in a magnetic field and how can we control this force?
The lorentz force acts on the electron in a magnetic field. We control it by adjusting the lens strength
What effect does the magnetic lens have on the trajectory of the electron with respect to the optic axis?
The magnetic field is weakest on axis and increases in strength toward the sides of the polepiece, so the more off axis electrons will be more strongly deflected
Define ‘underfocused’ and ‘overfocused.’
Underfocused: image forms below the image plane
Overfocused: image forms above the image plane
Define the eucentric plane.
The eucentric is the standard object plane for the main imaging lens. At this height, the image of an object will not move as you tilt around the primary axis of the holder. The objective lens strength is always the same when the image on the screen is in focus
Why do we use apertures in the TEM?
To limit the collection angle of hte lens and control the resolution of the image formed by the lens, the depth of field/focus, the image contrast, the collection angle of EELS, the angular resolution of the DP
What causes spherical aberration and how can we minimize it?
The lens behaves differently for off axis electrons, so the further off axis the electron, the more strongly it is bent back. This results in smearing a point into a disk
Define chromatic aberration and describe how to minimize it.
Chromatic aberration occurs because the electron beam has some amount of energy spread. It doesn’t become important unless you have a Cs corrector. You can minimize it using a monochromator, or making your specimen thinner
What causes astigmatism and how do we correct it?
Electrons sense a non-uniform magnetic field as they spiral around the optic axis because polepieces arent perfectly symmetrical. Contamination can also contribute to charging and deflect the beam
Corrected by stigmators (octapoles) that introduce a compensating field to balance the inhomogenities causing astigmatism
How do you form a parallel beam; why would you want to do this and why is it not exactly parallel?
You produce a parallel beam by focusing the 2nd condenser lens so that there is a crossover in the front focal plane of the upper objective lens
The basic principle is to have an underfocused C2 lens (=crossover occurs after the image plane)
Its not exactly parallel because the convergence angle is 0.0057
How do you form a convergent beam; why would you want to do this and why is it sometimes divergent?
You form a convergent beam by strongly exciting C1, turning off C2, and strengthen the upper polepiece to produce a large demagnification of the C1 crossover
How does the probe size change with the C1 setting and why might you want to change the size?
A strong C1 is going to lead to a more convergent probe
What is the difference between a BF image and a DF image?
A bright field image is produced by selecting only the direct beam
A dark field image is produced using only scattered electrons, or everything but the direct beam
What is the advantage of forming images using STEM rather than TEM?
Defects in imaging lenses do not affect our image resolution
What is the most important aperture in the TEM and why?
The objective aperture is the most important because its size controls the collection angle and determines the effect of the aberrations on the obj lens and directly influences the resolution
How do you change the image magnification in a TEM?
Intermediate lenses magnify the signal onto detectors to define what area of the sample is used to capture an image
Why do we need to do the magnification calibration?
TEM imaging system does not give stable and reproducible lens strengths. Strengths will change with the ambient temperature, the efficiency of the cooling system, and lens hysteresis
List the three major differences between electron diffraction and X-ray diffraction.
XRD takes minutes to hours, produces ring patterns that show every orientation in the crystal at the same time, rotate the crystal to see multiple wavelengths
Why do we usually not measure intensities of spots in TEM DPs?
Beams are diffracted many times in the specimen
What is necessary for constructive interference to occur?
Waves must scatter at the bragg angle
Why don’t you always use the smallest selected-area aperture possible when obtaining an SADP?
The act of using an aperture magnifies the image 25 x, so a 50 um aperture will select a 2 um area
How does the SAD approach work if the aperture is not actually in the specimen plane?
Inserting the SAD into the image plane of the objective lens has the effect of putting a virtual aperture in the specimen plane
What is a ‘zone axis’?
The direction which is common to all planes of the zone
Intersection of two or more planes
