The document discusses crystal structure and x-ray diffraction. It defines crystal structure as the periodic arrangement of atoms in 3D space, with a lattice and motif. The basic unit of the lattice is the unit cell defined by its length along the x, y, and z axes and the angles between them. Miller indices are used to describe crystal planes and are the reciprocals of the plane parameters. Bragg's law relates the diffraction angle to the wavelength and plane spacing. Ewald's sphere construction is used to visualize diffraction and relate the reciprocal lattice to the diffraction pattern.

1. 1

2. 2

3. 3

4. Crystal Structure
4
Crystal structure of a material is way in
which atoms, ions, molecules are
periodically arranged in 3-D space.
Crystal structure = lattice + motif
A lattice is a 3-D array of points in space.
Every lattice point must have identical surroundings.
Basic unit of Lattice structure is called Unit Cell

5. 5
Unit Cell
The length of the unit cell along the x,
y, and z direction
are defined as a, b, and c.
The angles between the crystallographic
axes are defined by:
= the angle betweenα b and c
= the angle betweenβ a and c
= the angle betweenγ a and b
Unit Cell - Basic structural unit or building block of Lattice

6. 6
Crystal System and Bravais Lattice

7. 7
Crystal Structure - Periodic Table

8. Now we got the basis of Crystal
structure in 3D. Lets move
toward Planes (2D) or Surface.
8

9. 9
Crystal Plane and Notation
Consider the plane in pink, which is
one of an infinite number of parallel
plane each a consistent distance (“a”)
away from the origin
The plane intersects the x-axis at point
a. It runs parallel along y and z axes.
Thus, this plane can be designated as
(1,∞,∞)

10. 10
Miller Indices are the reciprocals of theMiller Indices are the reciprocals of the
parameters of each crystal faceparameters of each crystal face
Procedure :
•Identify the coordinate intercepts
•Take reciprocals
•Clear fractions
•Cite specific planes in parentheses
Miller Indices
X Y Z
Intercept 1 ∞ ∞
Reciprocal 1/1 1/
∞
1/
∞
Clear 1 0 0
INDICES 1 0 0

11. 11
Miller Indices

12. 12
Advantage of Miller Indices
For cubic crystals, the angle, f between two planes, (h1
k1
l1
) and
(h2
k2
l2
) is given by

13. 13
Stereographic Projection of Crystal Plane
Representing
a plane normal
010
10
0
001
(north)
(south)
Projection of Planes
on to a plane

14. 14
Stereographic Projection

15. 15
Stereographic Projection

16. 16
Stereographic Projection

17. 17
Stereographic Projection

18. 18
Stereographic Projection

19. 19
Stereographic Projection

20. 20
Reciprocal Lattice
In the reciprocal lattice, sets of
parallel (hkl) atomic planes are
represented by a single point
located a distance 1/dhkl from the
lattice origin and is normal to the
planes separating the original
vector.
γ + γ* = 180°
hkl
hkl
d
d
1
=∗

21. Reciprocal Lattice in 3D
21
Reciprocal Lattice in Plane Projection
(100)
(110)
(111)

22. 22

23. 23
Electromagnetic Spectrum

24. 24
Interference

25. 25
Interference and Geometry
Slits
Interference
Pattern
Square Rectangular Square Oblique
Now If one imagine crystal Lattice instead of slit geometry, its
interference pattern is reciprocal lattice
Basically , Interference pattern is reciprocal of slit geometry

26. 26
X ray Interaction with Matter
PHOTON SCATTERING:
COHERENT
COMPTON
PHOTON DISAPPEARANCE
PHOTOELECTRIC EFFECT
PAIR PRODUCTION
PHOTODISINTEGRATION

27. 27
Diffraction and Bragg’s Law
set of
lattice
planes
d
θ θ
X-rays
d sin θ
To find dhkl , one
can fix λ and
vary θ (PXRD)
or vise versa
(Laue Method)

28. 28
Ewald’s Sphere
Explanation of Ewald’s Sphere using – Animation
http://www.doitpoms.ac.uk/tlplib/reciprocal_lattice/ewald.php

29. 29
Ewald’s Sphere
Explanation of Ewald’s Sphere using – Animation
http://www.doitpoms.ac.uk/tlplib/reciprocal_lattice/ewald.php

30. 30
Ewald’s Sphere
Explanation of Ewald’s Sphere using – Animation
http://www.doitpoms.ac.uk/tlplib/reciprocal_lattice/ewald.php

31. • http://www.doitpoms.ac.uk/tlplib/reciprocal_lattice/ewald
• animation
31
Ewald’s Sphere - Animation

32. Ewald’s Sphere + Reciprocal Lattice +
Projection = X – ray Diffraction
32
Ewald’s Sphere + Reciprocal Lattice + Projection
Live Demonstration (simulated )
http://phillips-lab.biochem.wisc.edu/software.html
XRayView : A Virtual X-Ray Crystallography Laboratory

33. 33

34. 34
X – Ray Production

35. 35
X – Ray Types
When the target material of the X-ray tube is bombarded with
electrons accelerated from the cathode filament, two types of X-
ray spectra are produced.
Bremsstrahlung X-Rays
The continuous spectra consists
of a range of wavelengths of X-
rays with minimum wavelength
and intensity

36. 36
X – Ray Types
When the target material of the X-ray tube is bombarded with
electrons accelerated from the cathode filament, two types of X-
ray spectra are produced.
Characteristic X-ray Spectra
Characteristic spectra is produced
at high voltage as a result of
specific electronic transitions
that take place within
individual atoms of the target
material.

37. 37
X – Ray Types
When the target material of the X-ray tube is bombarded with
electrons accelerated from the cathode filament, two types of X-
ray spectra are produced.
Characteristic X-ray Spectra
Characteristic spectra is produced
at high voltage as a result of
specific electronic transitions
that take place within
individual atoms of the target
material.

38. 38
X – Ray Types
When the target material of the X-ray tube is bombarded with
electrons accelerated from the cathode filament, two types of X-
ray spectra are produced.
Bremsstrahlung X-Rays
Characteristic spectra is produced
at high voltage as a result of
specific electronic transitions
that take place within
individual atoms of the target
material.

39. 39
X – Ray Tubes

40. 40
Some Diffraction Technique demands
monochromatic X-ray (not Laue
method). K line in the X-ray spectrumβ
needs to be removed.
Mass absorption coefficient
of the β-filter.
Anod
e
C
u
Co Fe Cr Mo
Filter Ni Fe Mn V Zr
Filter

41. 41
X ray Detection
Three Principle Types of X ray detection:
Photographic Films
Counters
Florescent Screens and CCDS
Photographic Films
• Film has excellent resolution.
• Inexpensive.
• Very long exposures

42. Counters:
Counters produce electrical signal from an incident X ray
radiation. Counters are for rigorous studies of intensities with
X –rays.
42
X ray Detectors
Phosphors
A thin phosphor screen converts
the incident x-rays into optical
photons, which the CCD detects.
. 1
Performance Parameter :
Phosphor - Camera Optics - CCD Efficiency and Resolution
Control Electronics - Software

43. 43
Types of X-ray Diffraction

44. 44
Acklowdegement
& Our Research Group