electron diffraction - introduction

EM Course – Electron Diffraction

Professor Rodney Herring

Electron Diffraction - IntroductionElectron diffraction is an important method to characterize

materials.

The textbook, Transmission Electron Microscopy, dedicates 10 of its chapters to electron diffraction and it’s discussed in many of the other chapters, as well.

Every time a beam, of any kind, passes through an object, the beam diffracts by some process.

Diffraction has many forms. For example,• The beam can diffract, or scatter, off of individual atoms or

molecules or single, small structures. • If there is a periodic arrangement, the diffraction intensity will

be constructive in some orientations and destructive in other orientations.

• If there is only short range order such as in amorphous materials, the diffraction intensity will be speckled or in rings.

Examples of Electron Diffraction

• The arrangement of “spots” (square, rectangular, hexagonal) gives the crystal structure of the material.

• A lot of other crystal structure information is given by Kikuchi lines and Higher-ordered Laue Zone Lines (HOLZ), which we will discuss in some detail.

• If we open up the spots, we may see crystal structure as in the following slide.

diffracted beam or spotKikuchi linesHigher-ordered Laue Zone Lines

Examples of Electron Diffraction

Electron diffraction from atomic planes of a crystal

Kossel Images of GaAs/ InGaAs Superlattices

Electron Diffraction - Introduction

To understand electron diffraction, we’ll start from first principles, as presented in Williams and Carter.

Electron Diffraction

Electron Diffraction

Electron Scattering

Note the use of incoherent to describe scattered electrons, as used in all EM textbooks. Nothing could be further from the truth!

Inte

nsi

tye-

1/nm

32

33

34

35

36

37

e-

0.00 0.02 0.04 0.06 0.08 0.10 0.121/nm

e-

1/nm

4500

5000

5500

6000

6500

7000

e-

0.00 0.02 0.04 0.06 0.08 0.101/nm

Position 1

Position 2

High-angle diffusely-scattered electrons

Fringes Produced from Elastically and Inelastically Scattered Electrons Ge specimen

Intensityalong white line(essentially constant)

Fringes found > 18 mrad

1

1

2

~ 0.05e-

1/nm

0

50

100

150

200

250

300

e-

0.0 0.5 1.0 1.5 2.0 2.5 3.01/nm

Inte

nsi

ty

Position 1/nm

Inte

nsi

ty2

1

Contrast enhanced image

000/111

2

Interference fringes produced from elastically and inelastically scattered electrons generated from a Ge specimen.

3

1 mrad

Electron Scattering

Electron Scattering Cross Section,

=

Single atom

Electron Scattering Cross Section,

Electron Scattering Cross Section,

O.01 nm is approximately the spatial resolution of UVic’s STEHM.

Mean Free Path, This a common term and concept used in electron microscopy

Mean Free Path,

No is number of atoms is density

Regrettably, also means wavelength, which is more commonly referred to than mean free path.

Fraunhofer and Fresnel Diffraction

In the TEM we can focus the diffraction pattern so that the spots and lines are clear. This condition is considered Fraunhofer diffraction.

Diffraction From Apertures

= wavelength

Constructive Interference

Wavelength

Phase Shift Between Images

x

image 1image 2

phase shift = x/ x 2

Calculation of Temperature

Refractive index, x/

T 103.49/

for air = 103.49 p1/T + 177.4 p2/T + 86.26p3/T x (1+5748/T)

For a 1 mm translation,

x = 12.7 pixels = 67.5 pixels(measured values)

Calculation of Temperature

T 103.49/= 103.49/0.188= 550 K

x/= 12.7/67.5= 0.188

Thus an approximate value of the temperature can be obtained by this simple analysis, which provides an example of confocal holography.

Definition of Angles in TEM

EELS Spectroscopy