TEM - Electron Diffraction

What can we find using electron diffraction

whether the specimen is crystalline or amorphous

whether the specimen is single-crystal or polycrystalline

identity of the crystal structure

orientation of specimen w.r.t beam

character defects

Angular distribution of electron scattering

Can be viewed as electron diffraction pattern

spatial distribution of electron scattering

can be observed as contrast in images of specimen

Center spot in diffraction pattern

correctors to a direct beam (forward scattered electrons)

Any spot deviated from central spot in diffraction pattern

Corresponds to a specific crystalline plane where many electrons are scattered within a crystalline specimen

elastic scattering

scattering without losing energy

Inelastic scattering

scattering with the loss of some energy at a relatively low angle

Electron-electron interaction

scattering through interaction with the electron cloud…due to Coulombic interaction and results in low scattering angles (mostly inelatic)

Electron-nucleus interaction

scattering by the nucleus…due to Coulumbic attraction and results in higher scattering angles

Atomic scattering factor

The amplitude of radiation scattered by a single atom. It varies with atomic number and with the angle of scattering.

What affects electron scattering factor

Heavier atoms scatter more strongly than lighter atoms at any particular angle

At higher accelerating voltage electrons are scattered less

Lower angle results in a higher scattering factor

Constructive interference

Waves reinforce one another when they are in phase..corresponds to bright spots in electron diffraction

Destructive interference

Waves cancel one another when they are out of phase

Camera constant concept

rd = Lλ

r: distance between direct beam and diffracted beam

d: interplanar spacing

L: camera length

λ: electron wavelength determined by accelerating voltage

Crystalline materials

atoms are situated in a periodic array over large distances

Glassy (amorphous) material

where long range order is absent

Structure factor of amorphous materials

Atoms are arranged almost randomly, but the first- and second-nearest neighbor spacings are well defined…will se a few characteristic peaks and then rest will wash out

Structure factor of crystalline materials

Atom positions are fixed…intensity of diffracted beams show maxima at specific angles where electrons are more strongly scattered

Electron diffraction pattern of amorphous materials

Diffuse rings

Electron diffraction pattern of single crystal materials

sharp spots of diffracted beam

Electron diffraction pattern of single crystal w/ multiple grains

sharp spots but with more since grains are in different orientations and those spots are superimposed on each other

Structure factor

a sum of the atomic scattering factors f(θ) from all the atom positions in the unit cell…describes the amplitude of electron wave scattered by a unit cell of crystal structure

Intensity and Structure Factor

The intensity of a particular reflection (hkl) is proportional to the structure factor squared

Allowed reflections for a simple BCC lattice

Fhkl =f [1 + cosπ(h+k+l)]

if h+k+l = odd integer, Fhkl = 0 (you won't see a diffraction spot)

if h+k+l = even integer, Fhkl = 2f (you'll see a diffraction spot)

Allowed reflections for a simple FCC lattice

Fhkl =f [1 + cosπ(h+k) + cosπ(k+l) + cosπ(h+l)]

if h, k, l = all odd/all even, Fhkl = 4f (you'll see a diffraction spot)

if h, k, l = mixed odd & even, Fhkl = 0 (you won't see a diffraction spot)

Formation of spot patterns

diffraction occurs from planes which are approximately parallel to the electron beam

Ewald sphere

The relationship between the reciprocal lattice and diffraction pattern

Ewald sphere construction

1. diffracting crystal represented by reciprocal lattice

2. electron beam represented by a vector of length 1/λ parallel to beam direction, terminating at origin of reciprocal lattice

3. sphere of radius 1/λ drawn

4. diffraction occurs when Ewald sphere touches a reciprocal lattice point

Visibility of spots in diffraction pattern

Thinner specimen stretches the reciprocal lattice into long rods which allows the Ewald sphere to touch more of the points on the reciprocal lattice…more/sharper spots

Thicker specimen collapses reciprocal lattice into tiny spots…more diffuse spots/few of them

Deviation parameter, s

A measure of how far the diffraction event deviates from the exact Bragg condition

Convergent beam electron diffraction

Focus the beam to a point to get a diffraction pattern consisting of large spheres

CBED non-titled incident ray

gives rise to an intensity at the exact center of the disk

CBED tilted incident ray

gives rise to off-centered intensities on the disk

CBED mode condenser aperture

the size of the disks in the diffraction pattern are controlled by the condenser aperture which controls the convergence angle of the probe

CBED mode aperture sizes

small - kossel-mollenstedt pattern

large - kossel pattern

medium - ideal situation that maximizes information scene in pattern and ensures the disks aren't overlapping

CBED features

1. discs instead of spots

2. strong kikuchi lines

3. extra details within the disc

4. HOLZ rings

Local strain measurement

Positions of HOLZ deficiency lines in the 000 disk highly depend on the state of strain in the crystal

HOLZ stands for

higher order Laue zone

Thickness dependence of CBED pattern

thinnest samples = not much detail is seen in disk

as sample gets thicker = more detail of the dynamical fringes can be seen in the center

*symmetry of pattern does not change ats crystal thickness increases

Kikuchi lines

complex patterns of pairs of bright and dark lines are superimposed on the single crystal diffraction pattern (bright = excess line, dark = deficiency line)

As crystal is tilted

i) the kikuchi lines sweep across the diffraction pattern

ii) the diffraction spots stay fixed but their intensity changes

Formation of kikuchi lines

assuming electrons are incoherently scatter then more electrons are scatter in one direction vs. another which leads to an excess (bright) and deficiency (dark)

Kikuchi maps for navigation

Narrow bands = take you to a more "distinct" zone axis

Wide bands = take you to a less common zone axis`

Why are kikuchi lines sharper in CBED

A convergent beam impinges on a much smaller region of the specimen than a region selected by a SAD aperture.Since the small region contains much less lattice distortion due to strain or defects, the Kikuchi lines in CBED are generally sharper.