1

Baski - Fall 2002 PHYS 550 Notes: X-ray Diffraction Page 1

X-ray Diffraction (XRD)

• Bragg’s Law and Ewald Construction

• Types of Scans:– Theta/2Theta (θ/2θ)– Rocking Curve– Diffraction-Space Map

• Philips Materials ResearchDiffractometer

Baski - Fall 2002 PHYS 550 Notes: X-ray Diffraction Page 2

Diffraction Condition

Ewald Construction

2 sin

2where

hkln d

k

λ θ

πλ

=

=

dk∆

ik

ik

fk

k∆

fk

Bragg’s Law

2

Baski - Fall 2002 PHYS 550 Notes: X-ray Diffraction Page 3

Theta/2Theta (Θ/2Θ) Scan (“Gonio” on MRD)

• Vary MAGNITUDE of ∆k while maintaining its orientation relative to sample normal.HOW? Usually rotate sample and detector with respect to x-ray beam.

• Resulting data of Intensity vs. 2θ shows peaks at the detector (kf) for ∆k values satisfying the diffraction condition.

• Detects periodicity of planes parallel to surface.

ikfk

k∆smaller k∆

1θ12θ

2θ22θ

Baski - Fall 2002 PHYS 550 Notes: X-ray Diffraction Page 4

Θ/2Θ Example

• Polycrystalline sample has a number of peaks due to mixture of crystal orientations.

10 20 30 40 50 60 70 80 90 1000

2000

4000

6000Polycrystalline Silicon Powder

Inte

nsity

(cou

nts/

sec)

2Θ

3

Baski - Fall 2002 PHYS 550 Notes: X-ray Diffraction Page 5

“Rocking” Curve Scan

• Vary ORIENTATION of ∆k relative to sample normal while maintaining its magnitude.How? “Rock” sample over a very small angular range.

• Resulting data of Intensity vs. Omega (ω, sample angle) shows detailed structure of diffraction peak being investigated.

ikfk

k∆

“Rock” Sample

k∆Sample normal

Baski - Fall 2002 PHYS 550 Notes: X-ray Diffraction Page 6

Rocking Curve Example

• Rocking curve of single crystal GaN around (002) diffraction peak showing its detailed structure.

16.995 17.195 17.395 17.595 17.7950

8000

16000

GaN Thin Film(002) Reflection

Inte

nsity

(Cou

nts/

s)

Omega (deg)

4

Baski - Fall 2002 PHYS 550 Notes: X-ray Diffraction Page 7

Diffraction-Space Map

• Vary Orientation and Magnitude of ∆k.

• Diffraction-Space map of GaN film on AlN buffer shows peaks of each film.

ω/2Θ

ω

GaN(002) AlN