X - Rays & Crystals

1. X - Rays & Crystals Characterizing Mineral Chemistry & Structure J.D. Price

2. Light - electromagnetic spectrum Wave behavior vs. particle behavior If atoms are on the 10-10 m scale, we need to use sufficiently small wavelengths to explore this realm if we want to learn something about atoms and lattices.

3. Diffraction E.B. Watson

4. Diffraction of light wave property E.B. Watson

5. E.B. Watson Where intersections of the diffracted wave fronts occur, there is constructive interference

6. Scale - grating and  The difference is only of scale. We can use optical wavelengths for the grid on the left, because they are appropriately spaced for those wavelengths. With small wavelengths, lattices diffract.

7. Crystal diffractometry Crystalline structure diffracts x-rays (XRD) X-ray source with known  Crystal with unknown d spacing Bragg equation: = 2d sin 

8. Modern diffractometer

9. Diffraction lines are generated by any plane within the crystal geometry. That of course means the root planes to the unit cell, but it also includes all of the possible diagonals. Miller indices are used to label to the lines resulting from the planes (you know all about indexing). In a powdered sample, grains typically orient in a myriad of directions*, such that many diffraction lines are simultaneously generated *exception - sheet silicates

10. Powder diffraction plot The resulting information is structural! (011) =3.259Å (100) 4.1341Å (110) 2.3868Å This is the diffraction patter for quartz (mindat.org). Peaks correspond to specific lattice planes. Their relative intensity is diagnostic.

11. Polymorphs This is great for polymorphs. Calcite (top) and aragonite (bottom) have the same composition, but different structures as evidenced from their diffraction patterns.

12. Chemical analysis Most minerals are sized between 0.1 - 100’s of mm. The rather ordinary rock slab on the left is composed of small (1-5mm) grains of quartz and feldspar. The feldspar below is large (15 mm) but is concentrically zoned.

13. Feldspars are solid-solutions and exhibit a range of compositions. How might we determine the composition of the minerals in our rocks? What is unique about each element? M T T

14. Photoelectric characteristic 1. To obtain composition, we need a measurable characteristic for each element. Fluorescence: electromagnetic radiation results from moving electrons closer to the nucleus Ephoton = EH - EL = h f = h c /  • Electron structure is element specific. In other words, Ephoton is the result of a specific jump in a specific element.

15. Fluorescence Visible light is produced by energies in U.V. light. Photo by Elizabeth Frank

16. Energy levels Examples of transition levels in Barium K 37.44 keV LI 5.99 keV LII 5.63 keV LIII 5.25 keV So LII to K (K 1) is… 31.81 keV Heavier atoms have many energy levels

17. Calculating the wavelength • So LIIto K is 31.81 keV or 31,810 eV • The wavelength of the photon produced by this jump is •  h c / E • h = 6.626 × 10-34 m2 kg/s • c = 3 × 108 m/s • E = 31,810 eV × 1.602 × 10-19 J/ eV = 5.096 × 10-15 J • So  = 3.900 × 10-11 m

18. Focus! 2. To get analysis at micron scale, we need high energies (keV) focused on small area Raymond Castaing formulated the technique for microanalysis and built the first working unit by 1951. Electrons are charged particles that can be focused and redirected using a magnets Lower energy example: the CRT

19. Count 3. Fluoresced x-rays need to be collected and counted. X-ray source with known  Recall that crystalline structure diffracts x-rays (XRD) Crystal with unknown d spacing Bragg equation: = 2d sin 

20. Castaing’s machine: focused electron beam that produces x-rays in an unknown, that may be counted at known diffraction angles. Wavelength dispersive spectrometry (WDS) Bragg equation: = 2d sin 

21. Maximizing counts Crystal The intensity of x-rays is much smaller relative to those generated from a tube (as in XRD) The Rowland Circle Detector Inbound X-rays The EMP wavelength spectrometer uses crystals with curved lattices and ground curvature to reduce lost x-rays

22. Example of a modern EM probe • Locate the following: • Cathode and anode • Beam • Magnets • Sample • Crystal • Detector

23. The Cameca SX100 • Five spectrometers • Each with 2-4 crystals The new RPI facility Cameca SX 100 EMP Rontec EDS detection Gatan mono CL

24. Electron-sample interactions Electron forces jump Char. photon produced Glancing background phn Produced photon adsorbed - may produce Auger e- Electron bounces off atom (high E): backscattered Electron knocks out another e- (low E): secondary

25. Analysis volume EMPA does not analyze surfaces (thin film), but penetrates a small volume of the sample. The collectable products of electron collision origin originate from specific volumes under the surface.

26. Useful interactions Secondary electrons emitted from the first 50 nm Images surface topography Backscattered electron intensity are a function of atomic density Images relative composition

27. Characteristic x-ray emission Ti

28. Nonunique nature of emission volume The x-ray volume changes as a function of a number variables. A sample with higher average atomic density will have a shallower but wider volume than one with a lower density. A beam with higher energy (keV) will produce a larger volume than one with a lower E0.

29. Sample effects Z From the excitation volume behavior, it is clear atomic density (Z) makes a difference in the emitted intensities. Some of the x-rays are absorbed into atoms within and adjacent to the excitation volume. Some of the x-rays promote electron jumps in atoms within and adjacent to the excitation volume. A F Raw data are corrected for ZAF influences. The total correction produces a rather long equation that may be satisfied only through iteration. The microprobe advanced as a tool because of the microprocessor

30. Standardization The number of x-rays counted at the appropriate diffraction angle is proportional to the concentration of the fluorescing element. But the excitation volume is not unique. Standard analyzed by other means Your sample with unknown composition Quantification requires comparison to a well-characterized standard.

31. EDS • Castaing’s micro WDS machine was a breakthrough. By 1960, advances in semiconduction permitted the construction of a new detector that could collect all of the emitted x-ray energies (pulses and background) within a few seconds. • Energy Dispersive Spectrometry (EDS) • Measures charges in semiconductor [Si(Li)] • Makes histogram of measured charges • Extremely fast • Very inexpensive • Lower accuracy relative to WDS

32. Energy spectrum Si K&  K K Al K&  K K EDS spectrum for a 15kV beam on a gemmy crystal from the Adirondacks (M. Lupulescu, NYSM).

34. EMPA traverses of spinel using WDS Formula for the spinel Nom: Mg Al2O4 Act: Mg1-3x Al2+2x O4

36. EMPA is a powerful tool for compositional analysis at the micrometer scale • High voltage electron beam can be focused on one micrometer area • Composition is determined by characteristic x-rays from excited atoms • WDS • Characteristic x-rays are focused through diffraction • Permits better resolution • EDS • All x-rays are counted simultaneously • Permits faster analysis / identification

37. Limitations • Good standards are essential • Quantification is dependant on accurate correction for ZAF effects • User needs to be aware of excitation volume • Results • Accurate assessment of mineral stoichiometry • WDS provides trace element compositions • May assess inhomogeneity at small scales