Camosun College GEOS 250 Lectures: 9:30-10:20 M T Th F300 Lab: 9:30-12:20 W F300

1. Introduction to MineralogyDr. Tark HamiltonChapter 14: Lecture 27-29Analytical & Imaging Methods in Mineral Science Camosun College GEOS 250 Lectures: 9:30-10:20 M T Th F300 Lab: 9:30-12:20 W F300

2. Analytical Techniques in Mineralogy • XRD: X-Ray Diffraction of single crystals or powders in cameras or slide mounts (structure) • XRF: X-Ray Fluorescence of bulk mineral or rock powders or during Microprobe analyses (chemistry) • SEM: Scanning Electron Microscopy for surface imagery of micrometer size mineral crystals and textures • TEM: Transmission Electron Microscopy of micrometer thick mineral films & crystal slices for imagery of phase boundaries & electron diffraction patterns • EMPA: Electron Microprobe Analyses, Quantitative or qualitative chemical analyses down to 1 micron sizes of polished mineral surfaces WDA, EDA spectroscopy (major & minor elements down to ~0.1%) • SIMS: Secondary Ion Mass Spectrometry using O- or Cs+ beams of trace elements down to ppb concentrations • AFM: Based on Scanning Tunnelling Microscopy of Metals and Conductive Sulphide Minerals, used for imaging Insulators on Atomic Scale

3. Electromagnetic Spectrum 1.0 nm > Xray λ > 0.01 nm (~the size of atoms) 10 Å = 10-9 m fig_14_01

4. Generation of X-Rays • Energetic electron transmission & elastic collision preserves Kinetic Energy (most) • Inelastic ejects inner shell electrons (few) • Outer shell electrons (N O P Q) are weakly held & closely spaced in energy levels so these generate IR or Visible Light Photons • Inner Shell Electrons (K, L, M) are close to the nucleus & feel the full atomic number so they generate hard UV or X-Ray photons • Cascade from adjacent shells is most common, e.g. L  K making a Kα photon

5. Sealed Vacuum X-Ray Source Tube Usually 15 to 30 KeV Soft X-Ray Exclusion Filter Common Sources: Mo, Cu, Co, Fe, Cr, W fig_14_02

6. Continuous & Characteristic X-Ray Spectra Mo Source & Transitions to K shell W @ Energies Kα = 0.7107 Kβ = 0.6308 Absorbtion Edge fig_14_03

7. X-Ray Absorbtion Edges • As the optical excitation of a core level electron requires the binding energy EB as a minimum photon energy, exceeding this energy will coincide with an increased absorption coefficient. This leads to the formation of absorption edges, which may be indexed by their atomic subshells (K,L,M...). Beyond the absorption edge the intensity of a monochromatic X-ray passing through a medium of thickness d will follow the absorption law • I = exp (-μd) where μ = Z2 / (hv)2 • whereby μ depends the atomic number Z of the medium and decreases with increasing photon energy hv

8. Production of K L & M Characteristic X-Ray Spectra K lines transit to K Shell α is from the L shell β is from the M Shell L lines transit to L Shell α is from the M shell β is from the N Shell fig_14_04

9. X-Ray Source • Schematic Diagram of an X-ray Generator. The heated filament boils off electrons, which then accelerate toward the positively charged Cu anode. ~99% just collide and heat up the target. ~1% generate X-Rays. The photons are absorbed by shielding and collimators (not shown), except those headed along the main beam axis. (After Piccard and Carter, 1989.)

10. X-Ray K Wavelengths for Common Sources

11. X-Ray Diffraction Effects • Incident X-Ray beam of photons causes electrons in lattice atoms to resonate & emit new wave fronts of the same wavelength • Usually these new wavefronts distructively interfere • When the spacing between atoms is a regular trigonometric function of the X-Ray wavelength, constructive interference occurs • This reinforced scattering of relatively intense X-rays is termed “Diffraction” • For fixed λ, lattice d-spacings relate to the angle

12. Constructive Diffraction: 1 Atomic Row AB = nλ = c cos Φ fig_14_06

13. Constructive Interference from Atomic Lattices fig_14_05

14. Successive Diffraction Conesfrom a Row of Atoms AB = nλ = c CosΦ fig_14_07

15. Scattering from 3D Intersecting Atomic Rows Solution to 3 Laue equations = 1 line, 1 spot fig_14_08

16. The Bragg Equation: Reflections from Planes of Atoms in a Crystal Lattice nλ = 2d Sin θ , θ = 90°- Φ fig_14_09

17. Laue X-Ray Diffraction Photographof Vesuvianite 4/m 2/m 2/m Ca19 (Al,Fe,Mg)13 (Si2O7)4 (SiO4)10 (O,OH,F)10 Contact Metamorphism Impure Limestones fig_14_10

18. Precession Photograph About C-Axisof Vesuvianite 4/m 2/m 2/m fig_14_11

19. Determination of a Crystal Structure • I = k [ Σ f exp(i2π(hx+ky+lz))]2 = kF2hkl • Intensity of a diffracted beam for (hkl) • k is a combined experimental constant • f is the scattering factor for an atom, depending on Z, scattering angle θ, & thermal motion • Fhkl is the Structure Factor, depending on atom types & positions in unit cell

20. P4-Single Crystal Diffractometer 4 Circle Goniometer X-Ray Tube X-Ray Detector fig_14_12

21. Electron Density Map for Diopside on (010) from Fourier Sums & Atomic Positions 2/m cut oblique To (110) Cleavage fig_14_13

22. Derivation of Crystal Structure from Stoichiometry & Unit Cell • NaCl: Space Group 4/m 3 2/m • a = 5.64 Å, unit cell edge (V=a3) • 39.4% Na & 60.6% Cl by weight • (39.4 / 22.99) / (60.6 / 35.453) = 1.71/1.71 = 1 • ρ = 2.165 g/cm • Since density & unit cell volume are known, the number of formula units per cell are: • Z = (n D V)/M where Z is formula units, D is density, V is molar volume, M is formula weight & n is Avogadro’s number • For NaCl : Z = (6.022 x 1023 per mol) x (2.165 g/cm3) (5.64 x 10-8 cm)3 / 58.443 g/mol = 4.002 formulae per unit cell • Na+/Cl- =1.02/1.81 = 0.564, 0.41 < .564 < 0.73 FCC

23. Other Spectroscopic Techniques for Determining Crystal Structures • Neutron or Electron Diffraction: wave behaviour of particle beams • Infrared: energy absorbtion bands related to bonds, strengths & atomic masses, stretching, bending, torsion of bonds; molecular ions • Mossbauer: Distinguishes positions & valences of Iron, Fe2+ versus Fe3+, e.g. M1 versus M2 • Nuclear Magnetic Resonance: useful for Hydrogen & other elements with unpaired nuclear spins. Good for O-2 versus OH-

24. X-Ray Powder Diffraction For Randomly Oriented Crystals, All Bragg Angles are solved Simultaneously nλ = 2d sin θ Flat Plate Method Works only for small 2θ fig_14_14

25. X-Ray Powder Camera:Straumanis Method Powder Spindle Pb Beam Catcher Film Strip, Low 2θ fig_14_15

26. X-Ray Powder Diffractometer Sample & Detector Rotate Respectively by θ & 2θ fig_14_16

27. Powder Diffractometer Scan for α-Quartz 32 Peak Intensity is Scaled Relative to (101)=1, (or whatever is the strongest peak) What kind of a form is the strongest diffraction for low Quartz? fig_14_17

28. PDF file for Low Quartz from ICDD • 217,000 files Experimental & Calculated, for natural & Synthetic compounds Usually <5 peaks < 75° 2θ fig_14_18

29. Applications of Powder XRD • Minerals with solid solution have variations in “d-spacings” proportionate to ionic substitutions • Some “d-spacings” are particularly sensitive as are molar volume and density as with Fe vs Mg • Fine grained minerals like clays, zeolites & Fe, Mn or Al oxy-hydroxides often occur in mixtures. Comparing patterns of pure end members & known mixtures permit calculation of compostions e.g. illite vs montmorillonite or natrolite vs thompsonite or limonite vs goethite • The Reitveld refinement method is the main tool for clay mineral structures

30. Example d-spacing Calculation • nλ = 2d sinθ or d = λ/2sinθ • λ = 1.540598 Å for Cu Kα1 • θ(100) = 10.425° for d (100) as measured • So for α-Quartz: • d(100) = 1.540598 Å / 2 • (0.18094) = 4.2570 Å • Data from table 14.18 in Klein & Dutrow (2002)

31. Variation in Vmol Å3, β Å & 2θ(1,11,0) forMonoclinic Amphiboles: Cummingtonite-Grunerite After Klein & Waldbaum (1967) fig_14_19

32. Formula Units from Crystal Structure for Unit Cell of Grunerite • Grunerite: 2/m , Fe7Si8O22(OH)2 • b = 18.44 Å, β = 102° • M = 1001.614 g/mol • ρ = 3.6 g/cm • Since density & unit cell volume are known, the number of formula units per cell are: • Z = (n D V)/M where Z is formula units, D is density, V is molar volume, M is formula weight & n is Avogadro’s number • For Grunerite: Z = (6.022 x 1023 per mol) x (3. 6 g/cm3) (925 x 10-24 cm3) / 1001.614 g/mol = 2.004 formulae per unit cell

33. XRF: X-Ray FluorescenceEmission Spectroscopy • Chemical Analyses of Inorganic Compounds, Rocks and Minerals • Mining, Ceramics, Metallurgy, Mineralogy, Petrology • Compressed powdered sample + binder or flux if fused • Polychromatic X-ray Source • Absorbtion according to Beer’s Law: • log(Io/I) = KdΔd , I-Intensities, Kd–Constant, Δd-thickness • Absorbed X-ray photons expel inner shell e- & falling e- L to K emits characteristic X-rays for each element • Spectra for 2 or more elements need to be resolved for emission lines proportions

34. XRF: X-Ray FluorescenceEmission Spectroscopy Characteristic Spectrum Spectrum for 2 Elements Molybdenum & Copper Background Spectrum fig_14_20

35. X-Ray Fluorescence Spectrometer LIF: LiF, ADP: Ammonium dihydrogen phosphate KAP: Potassium biphthalate, Known d-spacings Different elements & λ’s fig_14_21

36. XRF Spectrum of a Genuine Bank Note(Counterfeiting is not a way to get ahead) W is due to X-Ray Tube Target Metal fig_14_22

37. Schematic of Electron Microprobe ~30 KeV 10-7 Torr SEM’s have detectors for Electrons to image sample Magnetic Lenses or Energy Dispersive Spectrometer w/ Be window & SiLi detector fig_14_24

38. SEM or EMP Stage BSE: Backscattered e- s SE: Secondary e- s CL: Cathodoluminescence 25 Å < Resolution < 50 Å fig_14_25

39. Cathodoluminescence SEM Images Granite Llano Texas J.Schreiber, IU Sandstone Simon Fm Ill Rob Reed, UofTx Calcite & K-spar Quartz & Barite

40. TEM Schematic Magnetic Lenses Resolution to 0.14 Å (half a small unit cell) Where are those impurities? fig_14_27

41. EMPA & Analytical VolumeVolume is proportional to Average Z fig_14_30

42. SIMS: Secondary Ion Mass Spec Most Elements & Isotopes 1H to 92U Especially Light Elements fig_14_32

43. SHRIMP: Ion Microprobe U & Pb isotopes On a 20 μ scale Zircon growth zones fig_14_33

44. SHRIMP Analyses for Dating research.eas.ualberta.ca/rif/mc_icp_ms.html

45. AFM: Atomic Force Microscope Electro-mechanical Amplifier Of the Force Between Atoms Outgrowth of STEM for conductors Atomic Topography fig_14_34