X-ray diffraction (XRD) is a technique used to analyze the crystal structure of materials. It works by firing X-rays at a material and measuring the angles and intensities of the X-rays that are diffracted by the material. This can be used to determine properties like the average spacing between layers of atoms in the material, the material's crystal structure, and the size and shape of crystallites in the material. Key aspects of XRD include Bragg's law, which relates the wavelength of X-rays to the diffraction pattern, and Scherrer's formula, which relates crystallite size to peak broadening in the diffraction pattern. XRD has applications in fields like residual stress analysis and materials characterization.

1. X-RAY DIFFRACTION
(XRD)
NAME : MARIUM GHULAM NABI NAME : HAFIZA HAYA NAYYER
ROLL NUMBER : PH – 10 / 2019-20 ROLL NUMBER : PH – 14 / 2021
COURSE TITLE : ADVANCED MATERIALS CHARACTERIZATION TECHNIQUES
COURSE CODE: MM-505

2. • WHAT IS XRD?
• X-RAY DIFFRACTION RESIDUAL STRESS TECHNIQUES
• BRAGG’S LAW AND SCHERRER’S LAW
• SCHEMATIC DIAGRAM OF XRD AND DIFRACTOMETER
• WORKING OF XRD AND PATTERN
• TYPES OF XRD
• X-RAYS DIFFRACTION METHODS
• APPLIICATIONS
CONTENT

3. WHAT IS
XRD?

4. • Measure the average spacing 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 the
small crystal region.
XRD TECHNIQUE

5. RESIDUAL STRESS TECHNIQUES

6. XRD RESIDUAL STRESS MEASUREMENT
TECHNIQUE
• XRD technique measures surface residual stresses to depths of up to 30μm by
measuring the material's inter-atomic spacing..
• In x-ray diffraction residual stress measurement, the strain in the crystal lattice is
measured, and the residual stress producing the strain is calculated.
• Although the term stress measurement has come into common usage, stress is an
extrinsic property that is not directly measurable. All methods of stress
determination require measurement of some intrinsic property, such as strain or
force and area, and the calculation of the associated stress.

7. BRAGG’S LAW
BRAGG’S LAW STATES THAT:
“X-RAYS REFLECTED FROM DIFFERENT PARALLEL PLANES OF
A CRYSTAL INTERFERE CONSTRUCTIVELY WHEN THE PATH
DIFFERENCE IS THE INTEGRAL MULTIPLE OF THE
WAVELENGTH”

8. • IN X-RAY DIFFRACTION AND CRSTALLOGRAPHY . IT IS A FOMULA THAT RELATES THE SIZE OF THE SUB-MICROMETRE PARTICLES
OR CRSTALLITES, IN A SOLID TO THE BROADENING OF A PEAK IN ADIFFRACTION PATTERN.
• IT IS USED IN THE DETERMINATION OF THE SIZE OF PARTICLES OF CRYSTALS IN THE FORM OF POWDER
SCHERRER’S EQUATION
• In X-Ray Diffraction and crystallography,
it is a formula that relates the size of the
sub-micrometer particles or crystallites,
in a solid to the broadening of a peak in
a diffraction pattern.
• It is used in the determination of the
size of particles of crystals in the form of
powder
SCHERRER’S FORMULA
τ=
𝒌×𝝀
β×𝒄𝒐𝒔𝜽𝑩
τ = thickness of crystallite/ crystallite size
k = constant dependent on crystallite shape
(0.89)
λ = X-ray wavelength
β = FWHM (Full Width at half maximum)
θB= Bragg angle

9. DIFFRACTOMETER
SCHEMATIC DIAGRAM OF XRD
DIFFRACTOMETER

10. WORKING
• XRD analysis is based on constructive
interference of monochromatic x-rays and a
crystalline sample
• The x-rays are generated by a cathode ray
tube, filtered to produce monochromatic
radiation, collimated to concentrate, and
directed toward the sample.
• The interaction of the incident rays with the
sample produces constructive interference
when conditions satisfy Bragg’s law.

11. XRD PATTERN
XRD PATTERN OF NaCl POWDER
XRD PATTERN

12. SINGLE CRYSTAL
X-RAY
DIFFRACTION
X-RAY POWDER
DIFFRACTION
TYPES OF XRD

13. LAUE METHOD
• Orientation
• Single crystal
• Polychromatic
beam
• Fixed angle
ROTATING CRYSTAL
METHOD
• Lattice constant
• Single crystal
• Monochromatic
beam
• Variable angle
POWDER METHOD
• Lattice
parameter
• Polycrystal
• Monochromatic
beam
• Variable angle
X-Ray Diffraction Method

14. ROTATING CRYSTAL METHOD
LAUE METHOD POWDER METHOD

15. APPLICATIONS OF XRD