electron diffraction

Electron Diffraction Analyses and the Powder Diffraction File

Cyrus E. Crowder, David Crane, Justin Blanton, Charles Weth, Joe Sunzeri

ICDD, Newtown Square, PA

Electrons and Electron Diffraction X-rays and X-ray Diffraction

Particles Electromagnetic waves

λ = 2 – 10 pcm (0.02 – 0.10 Å) λ = 30 – 250 pcm (0.30 – 2.50 Å)

2θ = 0 - 2˚ 2θ = 0 - 180˚

Coulombic interactions with structure Wave/particle interactions with structure

Small beam size (few nanometers) Larger beam size (typically microns to millimeters)

High absorption coefficients - sample thickness limited to < 10 nm

Lower absorption coefficients

Significant dynamic diffraction - affects intensities, forbidden reflections may be observed

A Comparison of Electrons and X-rays

TEM Set-up for Selected Area Electron Diffraction (SAED) Pattern Collection

Incident Electron Beam

Specimen

Diffraction Pattern

Image Screen

Scattered Electrons

Electromagnetic Objective Lens

Incoming electron beam

Specimen Detector

Phosphor Screen

SEM Set-up for Electron Back-Scatter Diffraction (EBSD) Pattern* Collection

70˚ tilt

* Often called Kikuchi patterns

SAED Simulation EBSD Simulation

The PDF-4+ database software can be used to simulate kinematic SAED and EBSD patterns for any entry in the database that contains a space group and cell parameters.

Basis of electron diffraction simulated intensities:

1. PDF entries with atomic coordinates . . .

Intensities are calculated using electron diffraction scattering

factors, the user specified voltage, and the given crystal structure

2. Calculated PDF entries without atomic coordinates . . .

Intensities are calculated using pre-calculated structure factors

based on electron diffraction scattering factors for 200 keV

electrons

3. Only experimental d’s and I’s, and known space group . . .

Intensities are estimated using X-ray powder diffraction

intensities with the multiplicity factors divided out

All simulated intensities are based on kinematic scattering

only. No attempt has been made to simulate the dynamic

scattering resulting from multiple electron scattering

SAED Simulation The user interface and kinematic electron diffraction spot pattern simulation - YAlO3 0 0 1 zone

SAED Simulation Kinematic electron diffraction spot pattern simulation - YAlO3 1 1 0 zone

EBSD Simulation The user interface for kinematic electron back-scatter pattern simulation - YAlO3 2 1 1 zone

EBSD Simulation The user interface for kinematic electron back-scatter pattern simulation - YAlO3 211 zone with shortened camera length

SAED Pattern obtained for Ca3(PO4)2

The interactive menu can be used to determine the Zone, adjust the Center of View, Rotation Angle, and Camera Length to match the imported pattern.

For clarity, the Spot color is set to ‘Red’ and the Display Font color to ‘Blue’.

The 0 0 1 zone is displayed by default, but does not appear to be a good match with the experimental pattern.

Another Zone Axis, the 0 1 6, appears to have a better ratio of spacing distances.

Rotating the simulated pattern angle by 99˚ gives a better row alignment direction.

The scale of the simulated pattern matches that of the experimental pattern when a camera length of 64 cm is entered.

Finally, adjusting the center of view to 0.09, 0.08 provides a superimposed simulated pattern.

400

200

Note dynamical spots that violate extinction rules for P21/a

Phase Identification From SAED Patterns

Mn3O4 Powder Pattern

Mn3O4 Ring Pattern

Mn3O4 Ring Pattern

2 0 0

0 2 0

2 2 0

0 4 0

4 0 0 2 -2 0

-2 2 0

0 -2 0

-2 0 0

0 -4 0

-2 -2 0

-4 0 0

0 0 1 Zone

Mn3O4 Ring Pattern

0 0 1 Zone

1 0 0 Zone

Mn3O4 Ring Pattern

0 0 1 Zone

1 0 0 Zone

1 1 2

2 1 1

3 2 1

2 2 4

Mn3O4 Ring Pattern

not observed in 001 or 100 zones

3 1 2

0 0 1 Zone

1 0 0 Zone

1 1 2

2 1 1

3 2 1

2 2 4

Mn3O4 Ring Pattern

All are observed when 111 zone is added

3 1 2

1 1 1 Zone

Another Set of hree ‘observed’ zones

Mn3O4 Ring Pattern

1 1 1 Zone

2 1 0 Zone

1 0 1 Zone

Another set of three ‘observed’ zones

Mn3O4 Ring Pattern

1 1 1 Zone

2 1 0 Zone

1 0 1 Zone

1 0 3

3 1 2

Two Bragg peaks not observed among these 3 zones

Using a known camera constant, or a standard material, one can determine the diffraction angle for each of the observed spots in an SAED pattern and thus obtain a list of d-space values. (For the previous example, this list will have two significant d-spacings missing as they were not observed in the three observed zones – 1 0 1, 2 1 0, and 1 1 1)

To perform an phase identification search with a PDF-4+ database, this list of observed SAED spot d-spacings is required, along with an estimate of their relative intensities. Additionally, to restrict the search subset to a reasonable number of entries, one element present in the phase is required.

Electron Diffraction Phase ID Search

Search Results

. . .

. . .

Search Results List Sorted by GOM

Best match entry – 04-001-7621 (Mn3O4) showing line match and pattern match.

Summary

Simulations of kinematic SAED and EBSD patterns can be created for PDF-4 entries having unit cell and space group information. The user specifies the zone direction desired, the electron voltage, camera length (or constant), and plot size. Phase identification for the PDF-4 add-on software, Sieve+, has been modified to work with d-spacing lists from SAED patterns that may not include all strong lines or may include symmetry-forbidden peaks. Currently one element must be specified to make the search practical.