Presentation on theme: "Dont Ever Give Up!. X-ray Diffraction Typical interatomic distances in solid are of the order of an angstrom. Thus the typical wavelength of an electromagnetic."— Presentation transcript:
Dont Ever Give Up!
X-ray Diffraction 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: Braggs Law
Braggs 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
X-Ray Diffraction Recording
von Laue Formulation of X-Ray Diffraction
Condition for Constructive Interference
Bragg Scattering =K=K
The Laue Condition
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