Mineralogy, Diffraction

1. Mineralogy, Diffraction Carleton College

2. X-rays: History • Nature of x-rays

5. History: Wilhelm Conrad Roentgen • Roentgen was born on March 27, 1845 in Lennep (Germany). • He was educated in Utrect and Zurich and became professor of physics at Strassburg (1876), Giessen (1879), Würzburg (1888), and Munich (1899).

6. History: Wilhelm Conrad Roentgen • He received the Nobel Prize in 1901. Roentgen refused to patent his discoveries and rejected all commercial offers relating to them. • In his later years, he was embittered by the suggestion that he had taken credit for his laboratory assistant's discovery, and withdrew from public life. • Roentgen died on February 10, 1923 of carcinoma of the rectum, and was buried beside his wife in the family grave in Giessen.

7. History: Wilhelm Conrad Roentgen • Roentgen was working in his laboratory at the Physical Institute of the University of Würzburg, Germany, experimenting with a Crookes tube.

8. History: Wilhelm Conrad Roentgen • This tube is a glass bulb with positive and negative electrodes, evacuated of air, which displays a fluorescent glow when a high voltage current is • passed though it. When he shielded the tube with heavy black cardboard, he found that a greenish fluorescent light could be seen from a platinum screen 9 feet away.

9. History: Wilhelm Conrad Roentgen • He concluded that a new type of ray emitted from the tube, passed through the covering, and casted shadows of solid objects. The rays passes through most substances, including the soft tissues of the body, but left the bones and most metals visible.

10. History: Wilhelm Conrad Roentgen

11. History: Wilhelm Conrad Roentgen • One of his earliest photographic plate from his experiments was a film of his wife, Bertha's hand with a ring, was produced on Friday, November 8, 1895.

12. X-ray production • X-rays are produced when an electron “boiled” from filament are caused to strike a target of atoms by the force of a high voltage field. Which is seen in the next slide

13. X-ray production

14. X-ray production • Deceleration of electrons as they approach atoms in the target creates a “white” background of x-rays called the Brehmstrallen radiation.

15. X-ray production • X-rays are produced when there is a sudden deceleration of electrons. In practice, X-rays are produced when an extremely high voltage (15-60 • Kv) is applied to a filament (typically a tungsten cathode) in a vacuum. The electrons are then accelerated into a metal target (typically a copper • anode). The result is two particular types of X-radiation.

16. X-ray production • The first type is known as white radiation and consists of a broad, continuous spectrum containing many wavelengths of radiation. It is a result of the very rapid deceleration of electrons as they encounter the strong electric fields of target metal. As the electrons collide they lose energy (often designated delta-E) and that energy goes into making X-ray photons. That energy, delta-E is related to the frequency of the X-ray radiation by Planck's Constant,

17. X-ray production • ∆E = hv • Where h= plank’s constant • V=frequency of the x-ray • remember that v = c/l • C=speed of light, l=wavelength • therefore, ∆E=hc/ l

18. X-ray production

19. X-ray production • White radiation

20. X-ray production • Superimposed on this background are peaks of intense x-rays that have wavelengths that depend on the atoms involved. • These peaks of characteristic wavelengths are produced when an atom losses an electron from an inner orbital.

21. X-ray production • The peaks are labeled • Ka, Kb, La, Lb, etc • depending on the specific energy levels involved.

22. X-ray production • Laboratory production of X-rays

23. X-ray production • Target metal = anode (pure element) • Filament = cathode

24. X-ray Diffraction Experiments • Space group • Unit Cell

25. What is Diffraction? • Diffraction, generally defined as a departure of a ray from the path expected from reflection and refraction.

26. What is Diffraction? • Sets of narrow slits and ruled gratings were observed to produce diffraction patterns when the spacing of the slits is similar to the wavelength of light used.

27. What is Diffraction? • Because all of the slits in a diffracting grating are illuminated by the same source of light, the set of slits may be considered to be a set of light source all in phase with one another. • Light rays traveling perpendicular to the grating will remain in phase.

28. What is Diffraction? • Light rays traveling at an angle Ø to the will not be in phase, except for a special angles such that S sin Ø = nl, where S is the spacing of the slits, l is the wavelength of light and n is an integer. • We may use this expression to find l for a laser or S for a diffraction grating.

29. Diffraction • Because of spacing of planes of atoms in crystals is similar to the wavelength of x-rays… • Diffraction of X-rays by Crystals is possible.

30. Diffraction • Atoms in a crystal behave like little x-ray sources.

31. Diffraction • X-ray “reflections”

32. Diffraction • The figure to the left illustrates a modern X-ray diffraction pattern of the mineral vesuvianite (type locality is Mt. Vesuvius). The diffraction pattern is recorded on photographic film as a series of spots (this is actually a negative). The spots do not represent atoms. They do represent layers, or planes of atoms within the crystal structure. The spacing of the spots is proportional to the distance between the different diffracting layers in the crystal. Can you recognize any symmetry in this diffraction pattern? If you look carefully you should be able to convince yourself that the center of the pattern corresponds to a fourfold rotation axis perpendicular to the plane of the page. You should also be able to recognize that the axes a1 and a2 represent mirror planes. The symmetry of the crystal is reflected in the symmetry of the X-ray pattern. Although the symmetry elements are not sufficient to identify the mineral, you will soon be able to recognize that the symmetry observed implies that this mineral belongs to the tetragonal crystal system. The symmetry, together with a measurement of the separation of the spots would be sufficient to identify this diffraction pattern as belonging to the mineral vesuvianite.

33. Bragg’s equation • nl = 2dsin Ø

34. Diffraction • Diffraction of x-rays by crystals is possible because the spacing of planes of atoms in crystals is similar to the wavelength of x-rays.

35. Powder Diffraction • X-ray diffraction by mineral powders is one of the mineral identification and characterization techniques most used by geologists.

36. Powder Diffraction • Powder diffraction experiment requires only as small quantity of a mineral. • 10-500mg • Sample preparation is very simple and fast • Reliable accurate results are obtained in a relatively short time, 10 minutes to 2 hours.

37. Powder Diffraction • The principle behind PD experiment is the random orientation of crystals in a mineral powder.

38. Powder Diffraction • If the powdered crystals are randomly oriented, then for all sets of planes (hkl) some of the crystals in the powder will be in the correct orientation (usually horizontal) with respect to the x-ray source to satisfy Bragg’s law.

39. Powder Diffraction • In other words, at least a few of the mineral grains will diffract for each of the planes (hkl) during a scan through 2 Ø angle. • The more the finely ground the powder, the more likely that all orientations are presented in abundance.

40. Powder Diffraction • The ideal powder size is 5-10 microns.

41. Powder Diffraction • Here at Carleton, we have an automated powder diffractometer that yields digital computer output.

42. Powder Diffraction • Unknown minerals my be identified from powder diffraction data using ICDD Powder Diffraction File.

43. Powder Diffraction • Intensity and 2 Ø or dhkl values are used in the search. • Computer searches of the file may lead to a unique match with a known powder diffraction patter.

44. Powder Diffraction • Because of the chemical composition of most minerals is variable and some aspects of a mineral structure may depend on its history, the obtained diffraction pattern may not exactly match the standard data for a given mineral • This makes identification more challenging

45. Powder Diffraction • Once a mineral has been identified, the Powder Diffraction File data card my be used to index the observed diffraction peaks. • Miller indices, 2 Ø, d values, may be used to determine the Unit Cell Parameters of the sample.

46. Diffraction Summary • Diffraction pattern is like a finger print of the crystal structure • d-values reflect the unit cell parameters • intensities reflect the atoms/molecules

47. Sample preparation for PD • Sample preparation procedures are critical inn being able to obtain accurate and reproducible XRD results.

48. Sample preparation for PD • Care should be exercise in order to avoid introducing errors resulting from factors such as: • non-representative sampling • contamination • material loss

49. Sample preparation for PD • alteration of composition due to • Over grinding, • hydration • dehydration • oxidation

50. Sample preparation for PD • Sample height displacement • non-uniformity of the sample surface