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Don’t Ever Give Up!.

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Presentation on theme: "Don’t Ever Give Up!."— Presentation transcript:

1 Don’t Ever Give Up!

2 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.

3 Wavelength vs particle energy

4 Bragg Diffraction: Bragg’s Law

5 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.

6 Many sets of lattice planes produce Bragg diffraction

7 Bragg Spectrometer

8 Characteristic X-Rays

9 Brehmsstrahlung X-Rays

10 Bragg Peaks

11 X-Ray Diffraction Recording

12 von Laue Formulation of X-Ray Diffraction

13 Condition for Constructive Interference

14 Bragg Scattering =K

15 The Laue Condition

16 Ewald Construction

17 Crystal and reciprocal lattice in one dimension

18 First Brillouin Zone: Two Dimensional Oblique Lattice

19 Primitive Lattice Vectors: BCC Lattice

20 First Brillouin Zone: BCC

21 Primitive Lattice Vectors: FCC

22 Brillouin Zones: FCC

23 Near Neighbors and Bragg Lines: Square

24 First Four Brillouin Zones: Square Lattice

25 All Brillouin Zones: Square Lattice

26 First Brillouin Zone BCC

27 First Brillouin Zone FCC


29 Experimental Atomic Form Factors

30 Reciprocal Lattice 1

31 Reciprocal Lattice 2

32 Reciprocal Lattice 3

33 Reciprocal Lattice 5

34 Real and Reciprocal Lattices
Atoms are represented by dots. Two atoms per site, connected by straight lines.

35 von Laue Formulation of X-Ray Diffraction by Crystal

36 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.

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

38 Brillouin construction

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