X-Ray Diffraction

λ

(i)

Maxima and minima reinforce

(ii)

Constructive interference

(iii)

Maxima and minima cancel

(iv)

Destructive interference

(v)

X-Ray Diffraction (XRD)

• An experimental technique used to determine the arrangement of atoms in a crystalline solid

• X-rays are scattered by atoms in the crystal, producing a diffraction pattern

• The diffraction pattern reveals the crystal's structure and lattice spacing

Diffraction

• The bending and spreading of waves when they encounter an obstacle or pass through a narrow opening

• In crystallography, X-rays do this thing when they interact with regularly spaced atomic planes

Crystal Plane

• An imaginary flat surface passing through repeating rows of atoms in a crystal

• They act like reflecting surfaces for X-rays

Interplanar Spacing (d)

• The perpendicular distance between two adjacent parallel crystal planes

• Represented by d in Bragg's Law

• Determines the angles at which diffraction occurs

Incident X-Ray

The incoming X-ray beam that strikes the crystal surface before diffraction occurs

Diffracted X-Ray

The X-ray beam that leaves the crystal after interacting with its atomic planes

Constructive Interference

• Occurs when two X-ray waves combine in phase

• Their amplitudes add together, producing a strong diffraction peak

• This is the condition required for Bragg diffraction

Destructive Interference

• Occurs when two X-ray waves combine out of phase

• Their amplitudes cancel each other

• Produces little or no detected intensity

Path Difference

• The difference in distance traveled by two reflected X-ray beams

• Determines whether interference is constructive or destructive

Incident Beam

(1)

Diffracted Beam

(2)

d

(3)

θ

(4)

Constructive Interference

(5)

Destructive Interference

(6)

Bragg's Law

• The mathematical condition for constructive X-ray diffraction

• Relates wavelength, crystal-plane spacing, and diffraction angle

nλ = 2d(sin(θ))

Provide the Bragg’s Law formula

Bragg Angle (θ)

• The angle between the incident X-ray beam and the crystal plane

• Determines whether constructive interference occurs

Order of Diffraction (n)

• A positive integer representing the diffraction order

• Usually:

  • n = 1

  • n = 2

  • n = 3

X-Ray Wavelength (λ)

• The wavelength of the incident X-rays used in diffraction experiments

• Typically comparable to atomic spacing

X-Ray Diffractometer

• An instrument used to collect X-ray diffraction data from crystalline materials

• Measures diffraction angles and intensities

Detector

• Measures the intensity of diffracted X-rays

• Produces the diffraction pattern used for analysis

X-Ray Source

Produces monochromatic X-rays directed at the crystal

X-ray Source

(१)

Collimator to focus beam

(२)

X-ray diffraction

(३)

Crystalline material

(४)

Imaging surface

(५)

Diffracted x-rays

(६)

X-ray beam

(७)

X-ray diffraction pattern

(८)

Rosalind Franklin

• British chemist and X-ray crystallographer

• Produced high-quality X-ray diffraction images of DNA

• Her work played a crucial role in discovering DNA's double-helix structure

DNA X-ray diffraction image