X-Ray Crystallography

1. X-Ray Crystallography • The most important technique for mineralogy • Direct measurement of atomic arrangement • Direct measurement of what was originally deduced from crystal faces

2. X-Rays • Electromagnetic radiation – similar to visible light • l = 0.02 to 100 Å • = 0.002 to 10 nm • Visible light = 400 to 750 nm

3. Fig. 6-6 l (nm) f (hertz) }X-Rays Visible light spectrum Full range of electromagnetic radiation 1 nm = 10-9 m

4. X-Ray generation • Heat filament, which discharges electrons • Electron accelerated with 20 to 100 kV toward “target” • Target is Cu or Mo (also Co, Fe and Cr) Full spectrum of X rays Very hot – requires continuous circulation of cooling water Fig. 8-2

5. X-Ray generated Ka the most intense (highest energy) • Continuous spectrum of X-ray energy (wavelengths) are produced without electrons changing shells • Characteristic spectrum when incoming electrons dislodge electrons from outer shells • Electrons drop from either M shell (Kb) or L shell (Ka) X-rays Kb Electrons Ka Target material - Cu Fig. 8-3

6. Use of X-rays requires single wavelength • Similar to monochromatic visible light • Wavelength critical for measurement • Acts like a “ruler” • Must filter out the continuous spectrum, and leave only one of the characteristic spectrum • Typically Ka peak – most intense • Referred to as Cu – Ka radiation

7. Filtering • Use a monochrometer • Typically a thin piece of Ni or Be foil • Foil allows most Cu-Ka radiation to pass • Blocks most wavelengths except Ka Absorption edge, Ni filters out these wavelengths X-rays pass through filter l = 1.5418 Å X-rays blocked by filter

8. Detection • Variety of detectors • Scintillation counters (light flashes) • Gas proportional counters • Detectors are arranged so that X-rays reflected off of mineral surfaces can be recorded Arrangement of X-Ray diffractometer Detector X-ray generation Sample

9. X-Ray diffraction • Wavelength of X rays 1 to 2 Å • Cu Ka = 1.5418 Å • About the same length as spacing of atoms in minerals l = 1.5418 Å Typically 1 to 2 Å Called d spacing

10. X-Ray diffraction Reflects waves in phase, only if angle is such at that the additional distance pqr traveled by wave 2 is an integer number of wavelengths (here 1 wavelength) pqr = nl pq = d sin  l

11. Bragg Equation pqr = nl pq = d sin  pqr = 2pq = 2d sin  = nl l Bragg Equation Planes of atoms

12. Example • Halite – {111} planes have d spacing of 3.255 Å • Cu Ka radiation, l = 1.5418 Å • Solving Bragg equation shows •  = 13.70º for n = 1 •  = 28.27º for n = 2 •  = 45.27º for n = 3 •  = 71.30º for n = 4 When X-rays reflect off mineral at these angles, they will interfere constructively – cause a peak in energy at the detector

13. Multiple possible atomic planes {110}, {100}, {001} etc. • Orienting a single grain unlikely to reflect X-rays off of any of these planes • Better to use multiple grains with random orientations • With enough planes (1000’s), there will be enough parallel to create reflections. • Powder Diffraction method

14. Powder Diffraction • Sample crushed to small size, typically < 0.05 mm • Placed on glass slide or hollow holder • Sample placed in X-Ray diffractometer • Blasted with X-rays as sample and detector rotate from around 2º to 70º

15. Strip recorder records intensity of signal from detector Intensity of reflection Degrees 2 

16. Data reduction All peaks, d spacings relative intensity, reflecting plane 4 major peaks, d spacing • Powder diffraction files • Cards with the intensity and d spacing for all minerals

17. Take rock, sediment, mineral sample • Grind sample • Mount • Measure all d spacings • Compare with the powder diffraction files