Yat Li Department of Chemistry & Biochemistry University of California, Santa Cruz

1. CHEM 146C_Experiment #3 Identification of Crystal Structures by Powder X-ray Diffraction (PXRD) Yat Li Department of Chemistry & Biochemistry University of California, Santa Cruz

2. Objective In this laboratory experiment, we will learn: The principle of X-ray powder diffraction, idea of unit cell and use of Bragg equation A modern chemical analysis technique to identify a known and unknown sample (fingerprinting a solid)

3. Diffraction, Microscopy, Spectroscopic techniques X-ray diffraction, neutron diffraction and electron diffraction Characterization of solids How to characterize solids: Diffraction, Microscopy, Spectroscopic techniques Structure: • Single vs. Polycrystalline structure • Crystal structure (unit cell, dimensions) • Crystal defect (vs. molecular structure) • Impurities (concentration and distribution) • Surface structure (compositional inhomogeneities)

4. Generation of X-rays X-ray are produced when high energy charged particles (e.g. 30 kV) collide with matter. X-ray radiation has fixed transition energy.

5. X-ray wavelength Fixed transition energy (e.g. copper metal as target): White radiation 2p  1s Cu Ka 1.5418 Å 3p  1s Cu Kb 1.3922 Å Moseley’s Law Cut off l = K/(Z-s)2 Peak intensity ∝ rate of transition

6. Monochromatic X-ray radiation • Absorption of X-rays on passing through materials depends on the atomic number of the elements • Be is the best window, while Pb is a good shielding materials • White radiation and unwanted Kb lines can be filtered

7. Diffraction of light Diffraction of light by an optical grating AB = asinf Separation of lines should be slightly larger than the wavelength of light In phase: AB = l, 2l, 3l,…. nl nl = asinf

8. Diffraction of X-rays Crystal with repeating structure Optical grating 1D optical grating: nl = a sinf nl = a1 sinf1 3D crystal structure: Laue equations nl = a2 sinf2 nl = a3 sinf3 Interatomic distance ~2-3 Å, which is slightly larger than the wavelength of X-ray e.g. Cu Ka

9. Bragg’s Law Regard crystals as built up in layers or planes such that each acts as a semi-transparent mirror The angle of reflection is equal to the angle of incidence!

10. Lattice planes Lattice planes, are defined purely from the shape and dimensions of the unit cell. They are entirely imaginary and simply provide a reference grid to which the atoms in the crystal structure may be referred. The lattice planes are separated by the interplanar d-spacing

11. Miller indices Lattice planes are labeled by assigning three numbers known as Miller indices to each set Intersection: a/2, b, c/3 Miller indices: (213) (hkl) Set of equivalent planes • Identify that plane which is adjacent to the one that passes through the origin • Find the intersection of this plane on the three axes of the cell • Take reciprocals of these fractions

12. Miller indices Examples:

13. Debye-Scherrer method Sample: Powder Detector: Film S/2pR = 4q/360 Each set of planes (unique d-spacing) gives it’s own cone of radiation. d-spacing can be obtained.

14. X-ray Diffractometer Single crystal X-ray diffractometer Powder XRD

15. Qualitative identification of compounds • The existence of crystalline compounds or phases (not chemical composition) • Peak position (d-spacing) and intensity (pattern) • Each crystalline phase has a characteristic powder pattern which can be used as a fingerprint for identification process Powder Diffraction File (International Centre for Diffraction Data, USA)

16. Fingerprint powder pattern What factors determine the powder pattern: • The size and shape of the unit cell • The atomic number and position of the atom in the cell High symmetry (cubic) structure may have similar pattern