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

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)

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)

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) http://pwatlas.mt.umist.ac.uk/internetmicroscope/micrographs/diffraction/decr4-a-big.jpg

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 60 000 diffraction spectra of known crystalline substances Geometric arrangement of X-ray diffractometer (Leng, 2013)

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)

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)

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)

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

References BRANDON, D. & KAPLAN, W. D. 2013. Microstructural Characterization of Materials, Wiley. FITZPATRICK, E. & LABORATORY, N. P. 2005. Determination of Residual Stresses by X-ray Diffraction, National Physical Laboratory. LENG, Y. 2013. Materials Characterization: Introduction to Microscopic and Spectroscopic Methods, Wiley.