Characterization of Materials

2. Characterization of Materials M. Shafiee Afarani Associate Professor of Materials Science and Engineering at University of Sistan and Balouchestan

3. References • Elements of X-ray Diffraction by B. D. Cullity • Materials Characterization: Introduction to Microscopic and Spectroscopic Methods by:Yang Leng • X-Ray Diffraction Crystallography, Introduction, Examples and Solved Problems , Yoshio Waseda, EiichiroMatsubara , Kozo Shinoda • Introduction to X– ray Powder Diffractometry by: R. Jekins and R. L. Snyder • Electron Microscopy and Analysis by: P. J. Goodhew, J. Homphreys and R. Beanland • Microstructural Characterization of Materials by: D. G. Brandon and D. W. Kaplan • Characterization of Materials by: E. N. Kaufmann • Introduction of Thermal Analysis by: M. E. Brown

4. Lecture notes of H. Garmestani • Lecture notes of R. J. Matyi • http://lecturer.eng.chula.ac.th/fchvpv/MatCharac.html • http://ocw.mit.edu/OcwWeb/Materials-Science-and-Engineering/3-012Fall-2005/CourseHome/index.htm • Lecture notes of B. Huey http://www.ims.uconn.edu/~bhuey/

5. Introduction • Terminology Analysis Characterization • Why it is important?

6. Relation between Raw materials, Processing, Microstructure (nature and distribution of internal structure), Structure and Properties: • Chemical (corrosion / oxidation resistance…) • Mechanical (strength, ductility…) • Electrical • Magnetic • Optical • Thermal • etc.

7. Input Sample Output Detector Electron Ion Electromagnetic rays Heat etc.

8. Characterization Methods • Elemental Analyses (AAS, FES, OES, ICP, XRF, …) • Phase (structure) Analyses (XRD) • Microstructure Analyses (Optical Microscopy, Electron Microscopy) • Surface Analyses (STM, AFM, AES, XPS, SIMS, …) • Thermal Analyses (TGA, DTG, DTA, Dilatometery, DSC, …) • Other Methods (Hardness, electric and magnetic properties and …)

9. X-Ray Diffraction (XRD) • Why X-ray? • Crystal structure • Range of d spaces

10. Discovery of X-Rays November 1895, Würzburg Wilhelm Conrad Röntgen

12. Characteristics of X-rays • X-rays (like all radiation) can be viewed as waves or particles • transverse electromagnetic wave -- electric field is important (interacts with electrons), but the magnetic field is not important • the wavelength l is very short (from ~0.1 nm to ~1.0 nm) • X-rays behave just like any other E-M radiation - polarization • - refraction (n less than unity by 10-6)

13. Characteristics of X-rays • Particles -- X-rays can be thought of as photons with discrete energies elastic (coherent) interaction -- responsible for diffraction inelastic interaction -- X-ray photon loses energy electron hn1 hn2hn1 coherent interaction -- incident E-field causes the electron to oscillate in phase with the in-coming wave  acceleration causes the electron to re-radiate the X-rays 2q hn1 electron electron before after

14. Generation of X-rays • Accelerated charged particle • The thermionic emission (Edison effect)

15. Generation of X-rays

16. hn1 Origin of the bremsstrahlung (a.k.a. continuous spectrum, white radiation) hn2 incident electrons hn3 hn4

17. Properties of the continuous spectrum • Smooth, monotonic function of intensity vs. wavelength • lSWL = 12,398/V (l in Ångstroms, V in volts) • Wavelength of intensity maximum about 1.5 to 2 times the value of lSWL • The total intensity of the continuous spectrum given by • Where does the equation come from? It is empirical. • (so the intensity is maximized for large Z such as tungsten)

18. Relation of eV to l For Photons c = ln K.E. = hn =hc/l For electrons K.E. = eV Equating the two the maximum photon energy (minimum l) can be found l = hc/eV, putting in the constants: l(Angstroms) = 12398/V(volts)

19. Origin of the characteristic spectrum • The characteristic spectrum arises when an incoming electron knocks out an inner shell electron • K, L, M shells correspond to principal quantum numbers n = 1, 2, 3, … • Let a K-shell electron be knocked out -- the vacancy can be filled by an electron from the L-shell (Ka X-ray) or the M-shell (Kb X-ray) • The vacancy may also be filled by the Auger effect

20. There is a minimum energy required to remove an electron from an atom (“K-excitation” energy, etc.) When this occurs, the energy of the atom is increased As an inner-shell vacancy is filled by electrons from outer shells, the characteristic X-ray spectrum is emitted Energies of the emitted X-rays depends on the electron energy levels of the atom, so they are “characteristic” of a particular element

21. X-ray emission spectrum Ka1 Ka2 • Not all transitions allowed • Must conserve angular momentum • n is the principal quantum number • l is the electron orbital angular momentum, l = 0 for s, l = 1 for p, l = 2 for d, etc. • j is the total angular momentum • the spin quantum number is always 1/2 for a hole • Dl = ± 1, Dj = 0, ± 1 (selection rule) • Both Ka1 and Ka2 are 1s to 2p • transitions, but the energy difference is due to a difference in angular momentum.

22. Properties of the characteristic spectrum • There is a minimum energy input needed to observe a particular line (“K-excitation energy”) • The intensities of the various emissions are determined by quantum mechanical transition probabilities (example: probability of Ka1 = 2 probability of Ka2) • The characteristic spectrum will be superimposed on top of the continuous spectrum • Since the energy levels are very sharp, the energy breadth of the characteristic line is very narrow • By the uncertainty principle (DE×Dt ), if the energy levels are very sharp (DE small), then the uncertainty in the length of time for the transition (Dt) will be large  the X-ray production process is uncorrelated in time

24. Properties of the characteristic spectrum • Common characteristic lines: • Cu Ka -- 1.541Å (8.05 keV) Cu Ka1 -- 1.54056Å Cu Ka2 -- 1.54439Å Cu Kb -- 1.392Å • Mo Ka -- 0.7107Å (17.44 keV) • Cr Ka -- 2.291Å (5.41 keV) • I =Bi(Vapplied - VK)n where n  1.5 to 2 weighted average: 1.5418Å

25. Mosely’s Law C, s constants (H.G. Mosely, 1887-1915)

26. Goal: only one characteristic beam For Cu, VK= 9 kV So: V=36 kVIn Real instruments V=30-40 kV

27. X-ray absorption • Just like an incident electron, X-ray photons can initiate electronic transitions • Decrease in intensity  distance traversed by the X-ray beam • Beer’s law where m is the linear absorption coefficient • Problem: m depends on the density of the absorbing material, but the ratio m/r does not (mass absorption coefficient) and for a mixture (or alloy): weight fractions

28. Properties of the absorption coefficient • There is a sharp discontinuity in the dependence of the absorption coefficient on energy (wavelength) at the energy corresponding to the energy required to eject an inner-shell electron • The discontinuity is known as an absorption edge • Away from an absorption edge, each “branch” of the absorption curve is given by: E l

29. We see many absorption edges…

30. Absorption and X-ray filters • Using an absorber as an X-ray filter can reduce undesirable wavelength contamination in a diffraction experiment

31. X-ray fluorescence • Fluorescence is the opposite of absorption -- when energy is absorbed, a vacancy is produced in an electron shell • Other electrons fill that vacancy, producing radiation • Absorption at an edge generates high fluorescence • Fluorescence can be a source of background in a diffraction experiment Cu Ka - l = 1.54Å Cu-radiation fluoresces Fe Ka - l = 1.94Å iron, but Cr-radiation Co Ka - l = 1.79Å does not Cr Ka - l = 2.29Å Mo Ka - l = 0.71Å • Fluorescent radiation is characteristic to specific elements and is widely used for chemical analysis

32. X-ray sources • all conventional (laboratory) X-ray sources have the following characteristics: • a source of electrons • a source of accelerating voltage • a metal target • gas tube -- the original X-ray tube; very difficult to operate (applied voltage and tube current are not independent and vary with gas pressure)  now obsolete • filament tube -- most common type of laboratory X-ray source

33. The electron (Coolidge) X-ray tube • The most widely-used laboratory X-ray source • Major components are a water-cooled target (anode) and a tungsten filament (cathode) that emits electrons by thermionic emission • A high potential (up to 60 kV) is maintained between the filament and the anode, accelerating the electrons into the the anode and generating X-rays • Cooling water is circulated through the anode to keep it from melting (>99% of input power generates heat) • Interior of the tube is evacuated for the electron beam; thin beryllium windows transmit the X-rays

34. Major components of an X-ray tube

35. Aspects of X-ray tube design and operation • The electron beam produced and controlled by the current that is passed through the filament • Stable high voltage and filament current power supplies are needed (old-style transformers  high frequency supplies) • Power rating: applied potential  electron beam current (example: 50 kV and 40 mA  2 kW) • Maximum power determined by the rate of heat removal (without water, a tube can be destroyed in seconds  flow interlocks) • The anode is electrically grounded, while the filament is kept at negative kV’s (the water-cooled anode won’t short out, and the filament is protected by glass insulation

36. Aspects of X-ray tube design and operation (continued) • A new tube (about $3000) should last several thousand hours; “gassy” tubes will last much less • A new tube should be brought into operation carefully so that the release of adsorbed gases proceeds slowly • An important rule of thumb: • When turning a tube up, increase the kVfirst, and thenincrease the mA • When turning a tube down, decrease the mAfirst, and then decrease the kV • Beryllium windows are fragile and toxic: • don’t shock (mechanically or thermally) • don’t touch (and don’t taste)!

37. X-ray focus and take-off angle • The filament irradiates a roughly rectangular spot on the anode • spot focus -- the focal spot is viewed end-on • line focus -- the focal spot is viewed from the side • the take-off angle is the angle off the horizontal at which the focus is viewed (usually ~6º); a compromise between resolution and intensity

38. Rotating anode X-ray generator • The maximum power of an X-ray generator can be greatly increased if a new cooled surface is continually presented to the electron beam • Typical rotating anode generators operate from 12 kW to 18 kW (60 kV/300 mA); specialized generators will go up to 90 kW (60 kV/1500 mA)

39. Aspects of rotating anode X-ray generators • The anode (about 100 mm diameter  40 mm wide) rotates at speeds of 2400 rpm up to 6000 rpm • Exceptional dynamic balancing is required • Rotating anode resides in a high vacuum environment (better than 10-6 torr) with both rotation and water feedthroughs • Impressive water flow rates are necessary • Electron beam currents exceeding 0.3 ampere at 60 kV Rotating anode generators are expensive and require high maintenance but are the most powerful laboratory X-ray source available -- higher X-ray fluxes require a synchrotron

40. Radiation safety • X-rays are ionizing radiation and can cause injury and/or death • the Röntgen is the amount of radiation needed to create 1 electrostatic unit (2.093109 ion pairs) in 1 cm3 of dry air • the rad is the amount of radiation that will cause the absorption of 100 erg/gram in tissue • the rem (Röntgen equivalent man) is the absorbed dose corrected for the relative biological effectivenes: rem = (dose in rad RBE)

42. Radiation safety • X-rays don’t “burn” -- the effects of X-ray exposure may be delayed by hours to days • Always know where the primary beam is! • Use shielding (lead sheets or leaded plastic) for scattered radiation • Use the available tools: • survey meter • shielding • dosimeters • fail-safe interlocks • training and common sense (the best protection!) • Minimize time and maximize distance whenever possible • Other hazards -- electric shock (with H2O), Pb, Be

43. Origin of Diffraction

46. (X-ray) diffraction versus (light) reflection • The diffracted beam is composed of waves that have been scattered by all the atoms in the crystal within the irradiated volume (several microns deep) Reflection of visible light is a surface phenomenon occurring in a layer /2 thick • Diffraction of a single wavelength takes place only at a specific angle B Reflection takes place at any angle of incidence • The intensity of diffracted X-rays is extremely small compared to the incident beam The intensity of visible light reflected by a good mirror is comparable to the incident intensity

47. Basic principles of waves • An electromagnetic wave can be expressed as a cosine function • During a time t the wave travels t  c = t     so: • At z=0 the field strength is E(t,z=0) = Acos 2t or

48. Original wave at z = 0 and time t: New wave at z = 0 and time t: Basic principles of waves • Now consider a second wave with the same wavelength and amplitude but displaced a distance Z  this is a phase shift of (Z/)  2 = 

49. Superposition of waves • When two waves are moving through the same region of space they will overlap, with the resultant wave being algebraic sum of the amplitudes at each point Superposition of waves with nearly equal amplitudes and small (top) and large (bottom) differences in phase

50. Laue Equations