Transcript Fourier transform (see Cowley Sect. 2.2)

Fourier transform (see Cowley Sect. 2.2)
Fourier transform (see Cowley Sect. 2.2)
Fourier transform (see Cowley Sect. 2.2)
Fourier transform (see Cowley Sect. 2.2)
Fourier transform
Fourier transform
Fourier transform
Fourier transform
Scattering of x-rays by single electron (Thomson)
(see Cowley sect. 4.1)
Scattering of x-rays by single electron (Thomson)
(see Cowley sect. 4.1)
Scattering of x-rays by single electron (Thomson)
Scattering of x-rays by single electron (Thomson)
Scattering of x-rays by single atom
For n electrons in an atom, time-averaged
electron density is
Scattering of x-rays by single atom
For n electrons in an atom, time-averaged
electron density is
Can define an atomic scattering factor
Scattering of x-rays by single atom
For n electrons in an atom, time-averaged
electron density is
Can define an atomic scattering factor
For spherical atoms
Scattering of x-rays by single atom
Need to find (r) …. A QM problem
But soln for f() looks like this
(in electron scattering units)
Dispersion - anomalous scattering
Have assumed radiation frequency >> resonant
frequency of electrons in atom … frequently
not true
Dispersion - anomalous scattering
Have assumed radiation frequency >> resonant
frequency of electrons in atom … frequently
not true
Need to correct scattering factors
f = fo + f' + i f"
Dispersion - anomalous scattering
Need to correct scattering factors
f = fo + f' + i f"
5
f"
1
f'
2
K
Atom assemblies
(see Cowley sect. 5.1)
Atom assemblies
(see Cowley sect. 5.1)
For this electron density, there is a Fourier transform
F(u) is a fcn in reciprocal space
Atom assemblies
(see Cowley sect. 5.1)
Atom assemblies
Atom assemblies
For single slit, width a & g(x) = 1
If scatterer is a box a, b, c
Atom assemblies
For single slit, width a & g(x) = 1
If scatterer is a box a, b, c
For periodic array of zero-wiidth slits
Atom assemblies
This requires ua = h, an integer. Then
Finally
Atom assemblies
This requires ua = h, an integer. Then
Finally