1. Lecture 21 (12/11/2006) X-Ray Diffraction (XRD) Theory and Analytical Technique

2. X-Ray Analysis  X-rays discovered in 1895  Fundamental to understanding of crystal structure and symmetry  Powder diffraction analyses are a simple and inexpensive method for identifying minerals, especially fine-grained minerals

3. X-ray Generation X-rays – High energy*, highly penetrative electromagnetic radiation *E = hc/λ λ (X-rays) = 0.02-100Å (~1) λ (visible light) = 4000-7200Å λ (visible light) = 4000-7200Å X-ray Vacuum Tube Cathode (W)– electron generator Anode (Mo, Cu, Fe, Co, Cr) – electron target, X-ray generator

4. X-ray Spectra  Continuous spectra (white radiation)– range of X-ray wavelengths generated by the absorption (stopping) of electrons by the target  Characteristic X-rays – particular wavelengths created by dislodgement of inner shell electrons of the target metal; x-rays generated when outer shell electrons collapse into vacant inner shells  K peaks created by collapse from L to K shell; K peaks created by collapse from M to K shell KKKK KKKK X

5. X-ray Diffraction (Bragg Law) nλ = 2d sinθ Defines the spacing (d) of atomic planes and incident angle (θ) at which X-rays of a particular wavelength will reflect in phase (i.e., diffract) GE+EH = nλ θ’θ’θ’θ’ ≠ nλ ≠ nλ

6. Powder Diffraction Method  Requires random orientation of very fine crystals  Incident beam of a certain X-ray wavelength will diffract from atomic planes oriented at the appropriate θ angles for the characteristic d spacing  Random orientation of crystals will produce more intense diffraction peaks for particular angles that correspond to characteristic atomic planes

7. Powder Diffraction Plots θ = arcsin (nλ / 2d) λ(Cu) = 1.54Å d - Qtz [101] = 3.342 θ = 13.32° ; 2θ = 26.64° Quartz

8. X-Ray Powder Diffraction Records 70,000 experimental patterns

9. Utility of XRD in Chemical ID

10. (diagram after Smilth, 1975) Silver Bay anorthosites and Duluth Complex Anorthositic Series analyzed by Miller (1986) Leveaux Porphyritic Diorite (LPD) analysed by Albers (2006) XRD Structural State Analyses Silver Bay anorthosites Duluth Complex Anorthositic Series LPD

11. Last Lecture 12/13/06 Final Review: Optical Mineralogy Trivia