PHASE-CONTRAST IMAGES
12.10.2016
JANEZ KOŠIR
CONTENTS
1. Introduction Phase-Contrast Images
2. Lattice Fringes
3. Moiré Patterns
•
•
•
•
Translational Moiré Patterns
Rotational Moiré Patterns
Mixed Moiré Fringes
Dislocations and Moiré Fringes
4. Fresnel Contrast
•
•
•
Fresnel Contrast from Voids and Gas Bubbles
Fresnel Contrast from Grain Boundaries
Fresnel Contrast from Dislocations
INTRODUCTION TO PHASE-CONTRAST IMAGES
• Phase-contrast images arise due to the differences in the phase
of electron waves scattered through a thin sample.
• This contrast mechanism is very sensitive and can detect changes
in the thickness, orientation and scattering factor of the sample.
• Its sensitivity is the reason why we can image atomic structures of
thin samples.
• These images are formed by using more than one electron beam
to image of our sample.
LATTICE FRINGES
• Fringes refer to a phase-contrast phenomenon where an image
of alternate light and dark bands is produced due to the
diffraction and interference of electron waves.
• A lattice fringe is a periodic fringe in a TEM image formed by
two electron beams traveling through the sample.
• This image will show sinusoidal intensities with a periodicity
depending on several factors.
• These fringes can tell us the spacing and orientation of the
lattice planes.
• Fringes also correspond to an array of spots in a diffraction
pattern.
MOIRÉ PATTERNS
• Moiré patterns are formed by the interference of two sets of fringes.
• There are two different types of interference between the fringes:
o Translational moiré fringes
o Rotational moiré fringes
•
If we mix these two moiré fringes together we get mixed moiré fringes.
•
Moiré fringe spacing can give us information about our crystals even if we cannot
resolve the lattice planes.
TRANSLATIONAL MOIRÉ FRINGES
• These fringes occur when two different fringes are parallel to each other but have different
spacing between the fringes.
• We can calculate the spacing of the translational moiré fringes using the following equation:
𝑑𝑡𝑚
𝑑1 𝑑2
=
𝑑1 − 𝑑2
• Translational moiré fringes are especially useful when characterizing crystal properties of thin
films.
ROTATIONAL MOIRÉ FRINGES
• These fringes occur when two different fringes have the same
spacing but are rotated at an angle.
• We can calculate the spacing of the rotational moiré fringes
using the following equation:
𝑑𝑡𝑚 =
𝑑
2 sin
𝛽
2
• Rotational moiré fringes are sometimes accommodated with an
array of dislocations which can complicate things when we want
to observe our sample.
MIXED MOIRÉ FRINGES
• These fringes occur when two different fringes have
different spacing and are also rotated at an angle.
• We can calculate the spacing of the mixed moiré fringes
using the following equation:
𝑑𝑡𝑚
𝑑1 𝑑2
=
((𝑑1 − 𝑑2 )2 + 𝑑1 𝑑2 𝛽2 )1
2
DISLOCATIONS AND MOIRÉ FRINGES
• We can use moiré fringes to locate and obtain information
about dislocations within our sample.
• The resulting images of these moiré fringes appear as a
magnified view of the projection of the dislocation.
• These images can be directly related to the Burgers vector
of the dislocation.
• This analysis works even if we have multiple terminating
dislocations.
FRESNEL CONTRAST
• An image of the Fresnel fringes is created every time we operate the TEM out of focus.
• They are created due to the abrupt changes of the inner potential in our sample.
• Because the objective lens is focused close to the sample, we say that we are operating in the
near-field or Fresnel regime.
FRESNEL CONTRAST FROM VOIDS AND GAS BUBBLES
• We can observe voids and small gas-filled cavities by
defocusing the image and observing the Fresnel contrast.
• The contrast will depend on the difference in the inner
potential of the matrix and the cavity. The most contrast is
obtained from vacuum filled cavities.
• When the image is in focus the cavities will appear invisible.
• This technique can also be applied to voids filled with a liquid
or solid (second phase).
FRESNEL CONTRAST FROM GRAIN BOUNDARIES
• To image grain boundaries using Fresnel fringes we must first orient the
boundary in the edge-on position so that we can probe the inner potential at
the grain boundary.
• The difference in the inner potential comes from the fact that real TEM
samples are usually thinner at the grain boundary which changes the inner
potential at the boundary.
• This technique can also be used to image phase boundaries.
SUMMARY
• Phase-contrast occurs whenever we have more than one beam contributing to the image.
• Fringes can tell us the spacing and orientation of the lattice planes.
• Moiré patterns are formed by the interference of two sets of fringes.
• They can tell us information about our crystal structure and the presence of any defects
• An image of the Fresnel fringes is created every time we operate the TEM out of focus.
• We can use them to image different defects within a sample such as voids and grain
boundaries.