1. Submitted By:- Nardev Kumar Bajaj Roll NO-12025138 Group-C
X-ray diffraction
Submitted To:-
Dr.Mandeep Singh
Submitted By:-
Nardev Kumar Bajaj
Roll NO
Group-C

2. Contents Introduction to X-rays Bragg’s law Scherrer law XRD
Definition
Working
Why XRD
Applications
References

3. Introduction to X-rays
X-rays were discovered by German Physicist Rontgen In 1895 and was awarded by the noble prize in 1901
X-rays are electromagnetic radiations of exactly the same nature as light but of very shorter wavelength(10nm)

4. Bragg’s Law
nʎ =2dsinɵ
English physicists Sir W.H. Bragg and his son Sir W.L. Bragg developed a relationship in 1913 to explain why the cleavage faces of crystals appear to reflect X-ray beams at certain angles of incidence (theta, ɵ). The variable d is the distance between atomic layers in a crystal, and the variable lambda ʎ is the wavelength of the incident X-ray beam; n is an integer. This observation is an example of X-ray wave interference commonly known as X-ray diffraction (XRD), and was direct evidence for the periodic atomic structure of crystals postulated for several centuries

5. Scherrer’s Formula
It is formula that relates the size of sub micrometer particles or crystallites in a solid to the broadening of a peak in a diffraction pattern. It is named after Paul scherrer, it is used in the determination of size of particles of a crystals in form of powder
t = thickness of crystallite
K = constant dependent on crystallite shape (0.89)
ʎ= x-ray wavelength
B = FWHM (full width at half max) or integral breadth
ɵB= Bragg Angle

6. What is XRD?
X-ray diffraction is a rapid analytical technique primarily used for phase identification of a crystalline material and can provide information on unit cell dimensions. The analyzed material is finely ground, homogenized and average bulk composition is determined.
The atomic plane of 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

7. Principle
X-ray are diffracted and order of this diffraction is measured in form of graph.
Diffraction occurs as a result of the interaction of radiation with electron of atom.

8. Block Diagram of Powder X-ray diffraction

9. A Modern Automated X-ray Diffractometer
Detector 2ɵ
X-ray tube ɵ
Sample stage

10. Basic Features of Typical XRD Experiment
1) Production
2) Diffraction
3) Detection

11. Working of X-RAY Diffractometer
X-ray diffractometer consist of three basic elements : an X-ray tube, a sample holder and an X-ray detector
X-rays are generated in a cathode ray tube by heating filament to produce electrons and are directed towards the target by applying a voltage,most commonly copper is used as target in single crystaldiffraction
These x-rays are collimated and directed onto the sample. As the sample and detector are rotated ,the intensity of the reflected x-rays is recorded.
When the geometry of the incident x-rays impinging

12. the sample satisfy Bragg equation, constructive interference occurs.
A detector records and processes this X-rays signal and converts the signal to a count rate which is the output to a device such as printer or computer monitor.

13. Bruker’s X-ray diffraction D8-discover instrument

14. XRD Pattern of NaCl Powder
Miller indices: The peak is due to X-ray
diffraction from the {220}
planes
Diffraction angle 2ɵ (degrees)

15. Peak Positions
d-spacings and lattice parameters ʎ=2dhklsinɵhkl Fix ʎ (Cu kα) = 1.54Å dhkl= 1.54Å/2 sinɵhkl (Most accurate d-spacings are those calculated from high-angle peaks) For a simple cubic (a = b = c =a0) a0=dhkl/(h2+k2+l2)1/2 e.g., for NaCl, 2ɵ220=46o,ɵ220=23o d220=1.9707Å, a0=5.5739Å

16. Why XRD? • Measure the average spacings between
layers or rows of atoms
• Determine the orientation of a single
crystal or grain
• Find the crystal structure of an unknown
material
• Measure the size, shape and internal
stress of small crystalline regions

17. Applications
• XRD is a nondestructive technique • To identify crystalline phases and orientation • To determine structural properties: Lattice parameters (10-4Å), strain, grain size, expitaxy, phase composition, preferred orientation (Laue) order-disorder transformation, thermal expansion • To measure thickness of thin films and multi-layers • To determine atomic arrangement

18. References www.Wikipedia.com www.slideshare.com
Notes by dr. Mandeep Singh

19. Thank you