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Don’t Ever Give Up!

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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.

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**Wavelength vs particle energy**

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**Bragg Diffraction: Bragg’s Law**

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**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.

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**Many sets of lattice planes produce Bragg diffraction**

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Bragg Spectrometer

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**Characteristic X-Rays**

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**Brehmsstrahlung X-Rays**

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Bragg Peaks

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**X-Ray Diffraction Recording**

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**von Laue Formulation of X-Ray Diffraction**

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**Condition for Constructive Interference**

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Bragg Scattering =K

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The Laue Condition

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Ewald Construction

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**Crystal and reciprocal lattice in one dimension**

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**First Brillouin Zone: Two Dimensional Oblique Lattice**

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**Primitive Lattice Vectors: BCC Lattice**

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**First Brillouin Zone: BCC**

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**Primitive Lattice Vectors: FCC**

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Brillouin Zones: FCC

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**Near Neighbors and Bragg Lines: Square**

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**First Four Brillouin Zones: Square Lattice**

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**All Brillouin Zones: Square Lattice**

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**First Brillouin Zone BCC**

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**First Brillouin Zone FCC**

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**Experimental Atomic Form Factors**

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Reciprocal Lattice 1

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Reciprocal Lattice 2

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Reciprocal Lattice 3

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Reciprocal Lattice 5

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**Real and Reciprocal Lattices**

Atoms are represented by dots. Two atoms per site, connected by straight lines.

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**von Laue Formulation of X-Ray Diffraction by Crystal**

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**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.

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**Reciprocal Lattice Vectors**

Thus the reciprocal lattice vectors K must satisfy exp(iK.R)=1

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**Brillouin construction**

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