This document summarizes X-ray diffraction (XRD), including what it is, why it is used, common diffraction methods like Bragg's method and powder method, applications like determining crystal structure and lattice constants, and advantages like being inexpensive and convenient while determining crystal structures. The key points covered are that XRD involves X-rays interfering with atomic planes in a crystal, it is used to measure interplanar spacings and determine unknown crystal structures, common methods include Bragg's method using wavelength and angle and powder method using fixed wavelength, and applications involve crystal structure analysis and characterization.

1. A seminar talk
on
X-Ray Diffraction(XRD)
Presented by
GITA KRUSHNA SATAPATHY
Regd. no-160705120038

2. Plan of Talk
• What is XRD?
• Why XRD?
• Diffraction Methods.
• Applications of XRD.
• Advantages & Disadvantages.

3. Definition
The atomic planes of a crystal cause an incident beam of
X-rays to interfere with one another as they leave the crystal.
The phenomenon is called X-ray diffraction.
What is X-ray Diffraction ?

4. Why XRD?
 Measure the interplanar spacing between layers of
atoms.
 Determine the orientation of a single crystal or grain.
 Determine crystal structure of an unknown material.
 Measure the size, shape and internal stress of small
crystalline regions.

5. Diffraction Methods
Method Wavelength Angle Specimen
Bragg’s
Laue
Variable
Variable
Variable
Fixed
Single
Crystal
Single
Crystal
Rotating
Crystal
Fixed Variable (in
part)
Single
Crystal
Powder Fixed Variable Powder

6. Bragg’s Method
n=2dsin
n: Order of reflection
d: Plane spacing
=
: Bragg Angle
λ < 2d
 Path difference must be integral multiples of the wavelength
& in=out
in out
2
2 2 2
a
h k l 

7. Laue Method
 The diffraction spots generally
lying on an ellipse
Back-reflection method
 The diffraction spots generally
lying on an hyperbola.
Zone axis
crystal
Incident beam
Film
Reflection Zone axis
crystal
Incident beam Film
 Used to assess crystal perfection from the size and shape .
 It is the only method for the study of large and thick
specimens.
 Crystal orientation is determined from the position of the
spots.
Transmission Laue method

8. Rotating Crystal Method
 Determine the shape & size of unit cell as well as
the arrangement of atoms inside the cell.
 The Lattice constant of the crystal.
film
 Determine the crystal structure of un known material.

9. Powder Method
 Useful for determining the complex structures of metals
and alloys.
 Determine the unit cell dimensions.
 Measure the sample purity.
Incident Beam Sample
Film

10. Determination of Structure Factor
2 ( )
1
n n n
N
i hu kv lw
hkl nF f e   
 
Bravais Lattice Reflections possibly present Reflections necessarily absent
Simple All None
Body Centered (h+k+l): Even (h+k+l): Odd
Face Centered h, k, and l unmixed i.e. all
odd or all even
h, k, and l: mixed
 h,k,l : miller indices
 u,v,w : co-ordinates of the atoms in the lattice
 N : number of atoms
 fn : scattering factor
Applications of XRD

11. BCC
FCC

12. Significance of Peak Shape in XRD
 Peak position
 Peak width
 Peak intensity
 Important for
 Particle or
grain size
 Residual
strain
 Plane spacing

13. Bragg’s Law
n = 2d sin
For 1st order reflection n=1
So  = 2d sin
For cubic crystals
hkl 2 2 2
2 2
2 2 2 2
a
d
h k l
which gives rise to
sin θ
h k l 4a
which is a constant


 

 
INTERPLANAR SPACING & LATTICE
CONSTANT DETERMINATION

14. Crystallite size can be calculated using Scherer Formula
T=
Kλ
𝑩𝒄𝒐𝒔θ
 T = crystallite thickness
 λ (X-ray wavelength, Å)
 K (Scherer’s constant) ~ 0.9
 B=Full width with half maximum
 =Diffraction angle at peak position
PARTICLE SIZE DETERMINATION

15. STRAIN EFFECTS

16. Also applicable for
Phase analysis
Lattice parameter determination
Strain determination
Texture and orientation analysis
Order-disorder transformation & Thin film
characterization

17. Advantages & Disadvantages of XRD
Compared to Other Methods
Advantages
 Least expensive, the most convenient.
 Widely used method to determine crystal structures.
 The best method for phase analysis.
 X-Rays are not absorbed very much by air, so the sample
need not be in an evacuated chamber.
Disadvantages
 X-Rays do not interact very strongly with lighter
elements.
 The intensity is 𝟏𝟎 𝟖 times less than that of electron
diffraction.