X-rays The electric field E(r,t) is given as a cosine function.

Post on 27-Dec-2015

221 views 2 download

Tags:

Transcript of X-rays The electric field E(r,t) is given as a cosine function.

X-rays X-rays

)cos(),( tkrtrE

The electric field E(r,t) is given as a cosine function.

X-rays X-rays

In formal derivations the vector potential A is used.

The electric field E(r,t) is directly related to the vector potential A(r,t).

),(),( trAtrE t

Interaction of x-rays with matter 1Interaction of x-rays with matter 1

The photon moves towards the atom

Interaction of x-rays with matter 1Interaction of x-rays with matter 1

The photon meets an electron and is annihilated

Interaction of x-rays with matter 1Interaction of x-rays with matter 1

The electron gains the energy of the photon and is turned into a blue electron.

Interaction of x-rays with matter 1Interaction of x-rays with matter 1

The blue electron (feeling lonely) leaves the atomand scatters of neighbors (cf. EXAFS) or escapes from the sample (cf. XPS)

Interaction of x-rays with matter 1Interaction of x-rays with matter 1

The probability of photon annihilation determines the intensity of the transmitted photon beam

I0I

Ek

Interaction of x-rays with matter 2Interaction of x-rays with matter 2

The photon moves towards the atom

Interaction of x-rays with matter 2Interaction of x-rays with matter 2

The photon meets an electron and is scattered

Interaction of x-rays with matter 2Interaction of x-rays with matter 2

The photon leaves the atom under a different angle.(Interference between scattering events yields XRD)

I(,k,q)

I’(’,k’,q’)

I”(Ek,k”,)

Energy Spectroscopy

Direction Structure

Polarization Magnetism

Interaction of x-rays with matterInteraction of x-rays with matter

HINT(1) describes the interaction of the vector field A on

the momentum operator p of an electron, or in other words the electric field E acting on the electron moments.

The momentum operator p is given as the electron charge q times the displacement operator r.

Interaction of x-rays with matterInteraction of x-rays with matter

ApHT mce

INT )1(1

Interaction of x-rays with matter 1Interaction of x-rays with matter 1

The photon meets the electron and is annihilated

A

p=q•r

HINT(1) describes the interaction of the vector field A on

the momentum operator p of an electron, or in other words the electric field E acting on the electron moments.

The momentum operator p is given as the electron charge q times the displacement operator r.

Interaction of x-rays with matterInteraction of x-rays with matter

ApHT mce

INT )1(1

HINT(2) describes the second order interaction of the

vector field A.

This gives rise to the elastic scattering of the x-rays by the electrons.

This is the basis for x-ray diffraction (XRD) and small angle x-ray scattering (SAXS)

Interaction of x-rays with matterInteraction of x-rays with matter

2

2)2( 2

2AH

mce

INT

Interaction of x-rays with matterInteraction of x-rays with matter

• XAFS studies photoelectric absorption

• Elastic scattering (Thompson)

• Inelastic scattering

• (Compton)100 1k 10k 100k 1M

1

10

100

Photonuclear

Electron-

positron

Photoelectric

Thompson

Compton

Inte

nsi

ty (

log

)

Energy (eV)

Mn

if EEiffXAS TI

2

1~

Excitation of core electrons to empty states.

Spectrum given by the Fermi Golden RuleFermi Golden Rule

X-ray absorption and X-ray photoemissionX-ray absorption and X-ray photoemission

I(FIXED)

X-ray absorption and X-ray photoemissionX-ray absorption and X-ray photoemission

X-ray absorption and X-ray photoemissionX-ray absorption and X-ray photoemission

X-ray emission: core hole decayX-ray emission: core hole decay

Basis for X-ray Fluorescence (XRF) and Energy Dispersive X-ray analysis (EDX)

Interaction of x-rays with matterInteraction of x-rays with matter

ApH mce

INT )1(

2

2)2( 2

2AH

mce

INT

Photoelectric effect:(annihilation of photon)XAS, XPSXES, XRF, EDX

X-ray scattering:(photon-in photon-out)XRD, SAXS

Interaction of x-rays with matterInteraction of x-rays with matter

X-ray scattering:- with Hint(2)

- with Hint(1) via a (virtual) intermediate state

= Resonant X-ray scattering

)1(2/1

)1()2(2 INTiHEINTINT HHHTi

Interaction of x-rays with matter 3Interaction of x-rays with matter 3

The photon moves towards the atom

Interaction of x-rays with matter 3Interaction of x-rays with matter 3

The photon meets an electron and is annihilated

Interaction of x-rays with matter 3Interaction of x-rays with matter 3

The electron gains the energy of the photon and is turned into a virtual blue electron.

Interaction of x-rays with matter 3Interaction of x-rays with matter 3

The virtual blue electron loses a photon with exactly the same energy as gained

Interaction of x-rays with matter 3Interaction of x-rays with matter 3

The photon leaves the atom

Resonant X-ray scatteringResonant X-ray scattering

Combination of XAS and XES [only Hint(1)]- RXES- Resonant Inelastic X-ray Scattering (RIXS) (also called Resonant X-ray Raman Spectroscopy)

Combination of Hint(1) and Hint(2)

- Resonant XRD (also called: anomalous)- Multi-wavelength anomalous Diffraction (MAD)- Resonant SAXS (ASAXS)- TEDDI