Dynamical Theory

PASI Santiago, Chile July 20061Eades / Dynamical theory

Dynamical Theory

(without equations)


Dynamical Theory

• This lecture aims to communicate some intuitive bases for thinking dynamically

• Some familiarity with basic ideas of diffraction (for example, Bragg’s law and the reciprocal lattice) will be assumed.


Kinematical vs Dynamical theory.

• Any sample more than a few atoms thick requires dynamical theory.

• A simple argument suggests that if the sample thickness is greater than about ξg/8, then dynamical theory is necessary


Bragg’s Law

Bragg’s Law

2d sin θ = λ

still tells us where there are diffracted beams.


Rocking Curves

How far from the Bragg angle do we get diffraction?

For thick samplesΔθ = 4/gξg ξg is the extinction distance

For thin samplesΔθ = 1/gt t is the sample thickness


ReimerTransmission Electron Microscopy


Channeling

Electrons do not travel through crystals with a uniform distribution.

When electrons are incident on a crystal close to the Bragg angle, the electrons are channeled down the atomic planes.

Indeed, Bragg reflection may be thought of as the result of electrons coupling into channeling states.


Channeling II

The channeling states are also called Bloch states or Bloch waves.

Bloch waves consist of electrons traveling parallel to the planes but the electrons are not uniformly distributed. The Bloch waves may be channeled onto the atoms or between the atoms.

Defect contrast arises because the defects scatter electrons from one Bloch state to another.


To understand dynamical diffraction it is convenient to use a new graphical construction. We replace the Ewald sphere construction with a dispersion surface construction.

For kinematical diffraction they give the same result but it is easier to extend the dispersion surface construction to describe dynamical diffraction


Constructions


End

• Dynamical diffraction explains everything.


Two-beam dynamical

Dynamical Theory

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Transcript of Dynamical Theory