CYL729: Materials Characterization

1. CYL729: Materials Characterization Diffraction Microscopy Thermal Analysis A. Ramanan Department of Chemistry aramanan@chemistry.iitd.ac.in

2. Reference Books George M. Crankovic (Editor)

3. Electro-magnetic Spectrum

4. History of X-rays • 1885-1895 Wm. Crookes sought unsuccessfully the cause of repeated fogging of photographic plates stored near his cathode ray tubes. • X-rays discovered in 1895 by Roentgen, using ~40 keV electrons (1st Nobel Prize in Physics 1901) • 1909 Barkla and Sadler discovered characteristic X-rays, in studying fluorescence spectra (though Barkla incorrectly understood origin) (Barkla got 1917 Nobel Prize) • 1909 Kaye excited pure element spectra by electron bombardment

5. n l = 2d sin q History of X-rays - cont’d • 1912 von Laue, Friedrich and Knipping observe X-ray diffraction (Nobel Prize to von Laue in 1914) • 1912-13 Beatty demonstrated that electrons directly produced two radiations: (a) independent radiation, Bremsstrahlung, and (b) characteristic radiation only when the electrons had high enough energy to ionize inner electron shells. • 1913 WH + WL Bragg build X-ray spectrometer, using NaCl to resolve Pt X-rays. Braggs’ Law. (Nobel Prize 1915)

6. History of X-rays - cont’d • 1913 Moseley constructed an x-ray spectrometer covering Zn to Ca (later to Al), using an x-ray tube with changeable targets, a potassium ferrocyanide crystal, slits and photographic plates • 1914, figure at right is the first electron probe analysis of a man-made alloy T. Mulvey Fig 1.5 (in Scott & Love, 1983). Note impurity lines in Co and Ni spectra

7. l Z History of X-rays - cont’d • Moseley found that wavelength of characteristic X-rays varied systematically (inversely) with atomic number • Using wavelengths, Moseley developed the concept of atomic number and how elements were arranged in the periodic table. • The next year, he was killed in Turkey in WWI. “In view of what he might still have accomplished (he was only 27 when he died), his death might well have been the most costly single death of the war to mankind generally,” says Isaac Asimov (Biographical Encyclopedia of Science &Technology).

8. Historical Summary of X-rays • 1859 Kirchhoff and Bunsen showed patterns of lines given off by incandescent solid or liquid are characteristic of that substance • 1904 Barkla showed each element could emit ≥1 characteristic groups (K,L,M) of X-rays when a specimen was bombarded with beam of x-rays • 1909 Kaye showed same happened with bombardment of cathode rays (electrons) • 1913 Moseley found systematic variation of wavelength of characteristic X-rays of different elements • 1922 Mineral analysis using X-ray spectra (Hadding) • 1923 Hf discovered by von Hevesy (gap in Moseley plot at Z=72). Proposed XRF (secondary X-ray fluorescence) • 1923 Manne Siegbahn published The Spectroscopy of X-rays in which he shows that the Bragg equation must be revised to take refraction into account, and he lays out the “Siegbahn notation” for X-rays • 1931 Johann developed bent crystal spectrometer (higher efficiency)

9. Summary of X-ray Properties • X-rays are considered both particles and waves, i.e., consisting of small packets of electromagnetic waves, or photons. • X-rays produced by accelerating HV electrons in a vacuum and colliding them with a target. • The resulting spectrum contains (1) continuous background (Bremsstrahlung;“white X-rays”), (2) occurrence of sharp lines (characteristic X-rays), and (3) a cutoff of continuum at a short wavelength. • X-rays have no mass, no charge (vs. electrons)

10. X-ray Crystallography DIFFRACTION

11. What is a Unit Cell?

12. Unit cell can be chosen in different ways!

13. Unit Cells? White and black birds by the artist, M. C. Escher.

14. A unit cell chosen such that it contains minimum volume but exhibit maximum symmetry

15. Translational vector {R = n1a1 + n2a2 + n3a3}

16. Crystal Structure Ideal Crystal: Contain periodical array of atoms/ions Represented by a simple lattice of points A group of atoms attached to each lattice points Basis LATTICE= An infinite array of points in space, in which each point has identical surroundings to all others. CRYSTAL STRUCTURE= The periodic arrangement of atoms in the crystal. It can be described by associating with each lattice point a group of atoms called theMOTIF (BASIS)

17. 7 Crystal Systems Lattice parameters: a, b, c; a, b, g

18. Bravais Lattice: an infinite array of discrete points with an arrangement and orientation that appears exactly the same from whichever of the points the array is viewed.

19. 14 Bravais lattices

20. Unit cell symmetries - cubic • 3 C4 - passes through pairs of opposite face centers, parallel to cell axes • 4 C3 - passes through cubic diagonals A cube need not have C4 !!

21. Copper metal is face-centered cubic Identical atoms at corners and at face centers Lattice type F also Ag, Au, Al, Ni... -Iron is body-centered cubic Identical atoms at corners and body center (nothing at face centers) Lattice type I Also Nb, Ta, Ba, Mo...

22. body-centered cubic (bcc) Hexagonal closed packed (hcp) face-centered cubic (fcc) periodic table

23. Caesium Chloride (CsCl) is primitive cubic Different atoms at corners and body center. NOT body centered, therefore. Lattice type P Also CuZn, CsBr, LiAg Sodium Chloride (NaCl) - Na is much smaller than Cs Face Centered Cubic Rocksalt structure Lattice type F Also NaF, KBr, MgO….

24. Diamond Structure: two sets of FCC Lattices Z = 8 C atoms per unit cell

25. Tetragonal: P, I one C4 Yellow and green colors represents same atoms but different depths. Why not F tetragonal?

26. Example 2- C CaC2 - has a rocksalt-like structure but with non-spherical carbides C Carbide ions are aligned parallel to c  c > a,b  tetragonal symmetry

27. C F Orthorhombic: P, I, F, C

28. Side centering Side centered unit cell Notation: A-centered if atom in bc plane B-centered if atom in ac plane C-centered if atom in ab plane

29. Trigonal: P : 3-fold rotation

30. Hexagonal Monoclinic Triclinic

31. Unit cell contentsCounting the number of atoms within the unit cell Many atoms are shared between unit cells

32. Atoms Shared Between: Each atom counts: corner 8 cells 1/8 face center 2 cells 1/2 body center 1 cell 1 edge center 4 cells 1/4 lattice typecell contents P 1 [=8 x 1/8] I 2 [=(8 x 1/8) + (1 x 1)] F 4 [=(8 x 1/8) + (6 x 1/2)] C2 [=(8 x 1/8) + (2 x 1/2)]

33. e.g. NaCl Na at corners: (8  1/8) = 1 Na at face centres (6  1/2) = 3 Cl at edge centres (12  1/4) = 3 Cl at body centre = 1 Unit cell contents are 4(Na+Cl-)

34. Fractional Coordinates (0,0,0) (0, ½, ½) (½, ½, 0) (½, 0, ½)

35. Cs (0,0,0) Cl (½, ½, ½)

36. Density Calculation n: number of atoms/unit cell A: atomic mass VC: volume of the unit cell NA: Avogadro’s number (6.023x1023 atoms/mole) Calculate the density of copper. RCu =0.128nm, Crystal structure: FCC, ACu= 63.5 g/mole n = 4 atoms/cell, 8.94 g/cm3 in the literature

38. Miller Indices describe which plane of atom is interacting with the x-rays

39. How to Identify Miller indices (hkl)? [001] direction: [hkl] family of directions: <hkl> planes: (hkl) family of planes: {hkl} c b a [010] [001] to identify planes: Step 1 : Identify the intercepts on the x- , y- and z- axes. Step 2 : Specify the intercepts in fractional coordinates Step 3 : Take the reciprocals of the fractional intercepts

40. Miller indices (hkl) to identify planes: Step 1 : Identify the intercepts on the x- , y- and z- axes (a/2, ∞, ∞) Step 2 : Specify the intercepts in fractional co-ordinates (a/2a, ∞, ∞) = (1/2,0,0) Step 3 : Take the reciprocals of the fractional intercepts (2, 0, 0) e.g.: cubic system: (210) (100) (110) (111)

41. Miller Indices

42. Miller Indices

43. Crystallographic Directions And Planes Lattice Directions Individual directions:[uvw] Symmetry-related directions:<uvw> Miller Indices: 1. Find the intercepts on the axes in terms of the lattice constant a, b, c 2. Take the reciprocals of these numbers, reduce to the three integers having the same ratio (hkl) Set of symmetry-related planes: {hkl}

44. (100) (111) (200) (110)

46. In cubic system, [hkl] direction perpendicular to (hkl) plane

47. Wilhelm Conrad Röntgen Wilhelm Conrad Röntgen discovered 1895 the X-rays. 1901 he was honoured by the Noble prize for physics. In 1995 the German Post edited a stamp, dedicated to W.C. Röntgen.

48. The Principles of an X-ray Tube X-Ray Cathode Fast electrons Anode focus

49. The Principle of Generation of X-ray Ejected electron (slowed down and changed direction) nucleus Fast incident electron electrons Atom of the anodematerial X-ray

50. The Principle of Generation the Characteristic Radiation Emission Photoelectron M K L K Electron L K