Transcript Don’t Ever Give Up! X-ray Diffraction E  hc /  Typical interatomic distances in solid are of the order of an.

Don’t Ever Give Up!
X-ray Diffraction
E  hc / 
Typical interatomic distances in solid are of the order of an angstrom.
Thus the typical wavelength of an electromagnetic probe of such distances
Must be of the order of an angstrom.
Upon substituting this value for the wavelength into the energy equation,
We find that E is of the order of 12 thousand eV, which is a typical X-ray
Energy. Thus X-ray diffraction of crystals is a standard probe.
Wavelength vs particle energy
Bragg Diffraction: Bragg’s Law
Bragg’s Law
The integer n is known as the order of the corresponding
Reflection. The composition of the basis determines the relative
Intensity of the various orders of diffraction.
Many sets of lattice planes produce
Bragg diffraction
Bragg Spectrometer
Characteristic X-Rays
Brehmsstrahlung X-Rays
Bragg Peaks
X-Ray Diffraction Recording
von Laue Formulation of X-Ray
Diffraction
Condition for Constructive
Interference
Bragg Scattering
=K
The Laue Condition
Ewald Construction
Crystal and reciprocal lattice in one
dimension
First Brillouin Zone: Two
Dimensional Oblique Lattice
Primitive Lattice Vectors: BCC
Lattice
First Brillouin Zone: BCC
Primitive Lattice Vectors: FCC
Brillouin Zones: FCC
Near Neighbors and Bragg Lines:
Square
First Four Brillouin Zones: Square
Lattice
All Brillouin Zones: Square Lattice
First Brillouin Zone BCC
First Brillouin Zone FCC
Experimental Atomic Form Factors
Reciprocal Lattice 1
Reciprocal Lattice 2
Reciprocal Lattice 3
Reciprocal Lattice 5
Real and Reciprocal Lattices
von Laue Formulation of X-Ray
Diffraction by Crystal
Reciprocal Lattice Vectors
• The reciprocal lattice is defined as the set of all
wave vectors K that yield plane waves with the
periodicity of a given Bravais lattice.
• Let R denotes the Bravais lattice points;consider
a plane wave exp(ik.r). This will have the
periodicity of the lattice if the wave vector k=K,
such that
exp(iK.(r+R)=exp(iK.r)
for any r and all R Bravais lattice.
Reciprocal Lattice Vectors
• Thus the reciprocal lattice vectors K must
satisfy
• exp(iK.R)=1
Brillouin construction