The Braggs were awarded the Nobel Prize in 1915 for determining crystal structures including NaCl, ZnS, and diamond using X-ray diffraction. Bragg's law describes the angle at which X-rays of a particular wavelength diffract from a crystalline surface as 2dsinθ=nλ, relating inter-plane distance (d), wavelength (λ), diffraction order (n), and scattering angle (θ). Powder X-ray diffraction works by scattering X-rays in a sphere around a sample containing many randomly oriented crystallites, producing a Debye diffraction cone at each Bragg angle.

1. BRAGG S LAW
The Braggs were awarded the Nobel Prize in physics in 1915 for their work in determining
crystal structures beginning with NaCl, ZnS and diamond.
Bragg's law was used to explain the interference pattern of X-rays scattered by crystals, diffraction has been
developed to study the structure of all states of matter with any beam, e.g., ions, electrons, neutrons, and protons.
The relationship describing the angle at which a beam of X-rays of a particular wavelength diffracts from a
crystalline surface is known as Bragg’s Law.
2dsinθ= nλ
λ = wavelength of the x-ray
θ= scattering angle
n = integer representing the order of the
diffraction peak.
d = inter-plane distance of (i.e
atoms, ions, molecules)

2. CONSTRUCTIVE AND DESTRUCTIVE
INTERFERENCE OF WAVES

3. POWDER X-RAY DIFFRACTION
 In this method Samples can be powder, sintered pellets, coatings on substrates which contains tens of
thousands of randomly oriented crystallites. Every diffraction peak is the product of X-rays scattering
from an equal number of crystallites:

X-rays are scattered in a sphere around the sample. A cone along the sphere corresponds to a single Bragg
angle 2θ and the tens of thousands of randomly oriented crystallites in an ideal sample
produce a Debye diffraction cone.

4. NOT EFFICIENT
X-Ray Powder Diffraction (XRPD) is a inefficient measurement technique:
 Only a small fraction of crystallites in the sample actually contribute to the observed diffraction
pattern and other crystallites are not oriented properly to produce diffraction from any planes of
atoms.
 Only a small fraction of the scattered X-rays are observed by the detector A point detector
scanning in an arc around the sample only observes one point on each Debye diffraction cone.
Single Crystal X-ray Diffraction
Powder X-ray Diffraction

5. APPLICATIONS OF XRD

XRD is a nondestructive technique.

.
Used to identify crystalline phases and orientation.

Used to determine structural properties, lattice parameters (10-4Å), strain, grain size,
expitaxy, phase composition, preferred orientation and thermal expansions.

Used to measure thickness of thin films and multi-layers.
 Used to determine atomic arrangement.