1. X-ray diffraction to identify phases
Mahdi Masoumi
Amirkeyvan Edalat
Keyvan Heidari

2. Introduction What? X-ray Diffractometry (XRD) for Phase Identification
How? from their crystalline structure, not from their compositions of chemical elements
When? 1912
Characteristic X-rays of anode materials
X-ray tube structure. X-ray radiation from the anode is guided by the windows of the tube to produce an X-ray beam for diffraction
X-ray spectra generated with a molybdenum target at various acceleration voltages.
(Leng, 2013)

3. completely out of phase
Bragg’s Law- θ Angle
Phenomenon of Wave Interferences
Bragg’s Law
SQ+QT=2PQ sinθ
phase difference of nλ
phase difference of nλ/2
nλ = 2d sin θ
𝑑= 𝑎 ℎ 2 + 𝑘 2 + 𝑙 2
in phase
completely out of phase
(Leng, 2013)

4. Diffraction Intensity- I
more than one atom in a unit cell>>>>>>>> intensity from certain crystallographic planes can become extinct due to interference between atoms on different planes.
Diffraction intensity may vary among planes even though the Bragg conditions are satisfied >>>>there is no guarantee to detect or see diffraction from crystallographic planes
Allowed reflections in crystals of cubic symmetry with one atom per lattice site, listed in order of the sum of the sequence of the miller indices
AL- FCC structure
(Brandon and Kaplan, 2013, Leng, 2013)

5. X-Ray Diffractometry
The XRD >>>>>>>>>>>>>X-ray diffractometer
Continuously changing the incident angle of the X-ray beam
a spectrum of diffraction intensity versus the angle between incident and diffraction beam
Comparing the spectrum with a database containing over diffraction spectra of known crystalline substances
Geometric arrangement of X-ray diffractometer
(Leng, 2013)

6. Sample Preparation originally designed for examining powder samples.
X-ray Diffractometry
often used for examining samples of crystalline aggregates other than powder.
X-ray penetration is limited because of X-ray absorption
A certain depth from the surface can only be examined
Penetration depths of Cu Kα radiation with different incident angles
(Leng, 2013)

7. makes certain peaks invisible
Distortions of Diffraction Spectra
Preferential Orientation
Crystallite Size
Residual Stress
Small crystals cause the peak to be widened due to incompletely destructive interference.
Acquired
spectrum
standard
Standard: fine powder size
coarse powder or nonpowder samples
Effects of residual stress and strain on diffraction peak position and shape: (a)no strain; (b) uniform strain; and (c) nonuniform strain.
preferential crystal orientation
makes certain peaks invisible
Change of peak line width with crystal size
(Leng, 2013)

8. Applications Crystal-Phase Identification
X-ray diffraction data from a known substance >>>>>>>>>>>PDF (Powder Diffraction File)
Most PDFs >>>>>>>>>>>>>>>CuKα radiation
Standard diffraction data >>>>>>>>>>>>>ICDD (International Center for Diffraction Data)
Quantitative Measurement
The intensity of the diffraction peaks of a particular crystalline phase in a phase mixture >>>>>> weight fraction of the particular phase in the mixture.
𝐼 𝑖 = 𝐾𝐶 𝑖 𝜇 𝑚
𝜀 𝑧 = 𝑑 𝑛 − 𝑑 0 𝑑 0
Residual Stress
(Fitzpatrick and Laboratory, 2005, Leng, 2013)

9. Limitations
Only crystalline materials, not applicable for glasses and partially crystalline materials
Phases less than about 3-5 wt.% of a sample will not be detected using a bench-top XRD.
Mixtures of phases with low symmetry will be difficult to differentiate due to the larger number of diffraction peaks

10. References
BRANDON, D. & KAPLAN, W. D Microstructural Characterization of Materials, Wiley.
FITZPATRICK, E. & LABORATORY, N. P Determination of Residual Stresses by X-ray Diffraction, National Physical Laboratory.
LENG, Y Materials Characterization: Introduction to Microscopic and Spectroscopic Methods, Wiley.