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

2. Objective In this laboratory experiment, we will learn: 1.The principle of X-ray powder diffraction, idea of unit cell and use of Bragg equation 2.A modern chemical analysis technique to identify a known and unknown sample (fingerprinting a solid)

3. Characterization of solids Structure: 1.Single vs. Polycrystalline structure 2.Crystal structure (unit cell, dimensions) 3.Crystal defect (vs. molecular structure) 4.Impurities (concentration and distribution) 5.Surface structure (compositional inhomogeneities) How to characterize solids: Diffraction, Microscopy, Spectroscopic techniques X-ray diffraction, neutron diffraction and electron diffraction Diffraction, Microscopy, Spectroscopic techniques

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 White radiation Peak intensity ∝ rate of transition Cut off Fixed transition energy (e.g. copper metal as target): 2p  1sCu K  1.5418 Å 3p  1sCu K  1.3922 Å Moseley’s Law = K/(Z-  ) 2

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 K  lines can be filtered

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

8. Diffraction of X-rays Crystal with repeating structure Optical grating Interatomic distance ~2-3 Å, which is slightly larger than the wavelength of X-ray e.g. Cu K  n = a sin  1D optical grating: 3D crystal structure: n = a 1 sin  1 n = a 2 sin  2 n = a 3 sin  3 Laue equations

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 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 a/2, b, c/3 (213) Intersection: Miller indices:(hkl) Set of equivalent planes

12. Miller indices Examples:

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

14. X-ray Diffractometer Single crystal X-ray diffractometerPowder XRD

15. Qualitative identification of compounds Powder Diffraction File (International Centre for Diffraction Data, USA) 1.The existence of crystalline compounds or phases (not chemical composition) 2.Peak position (d-spacing) and intensity (pattern) 3.Each crystalline phase has a characteristic powder pattern which can be used as a fingerprint for identification process

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