In depth understanding of working principle of Transmission Electron Microscope, Electron Diffraction, Indexing of SAED pattern.

1. Transmission Electron Microscopy and Electron Diffraction

2. The Philips CM200 transmission electron microscope Accelerating voltages is 200 kV Can achieve resolution upto 2 Angstroms .

5. LM, resolving power ~0.25µm, maximum (useful) magnification is about 250µm/0.25µm = 1000X. Any magnification above this value represents empty magnification TEM at 60,000 volts has a resolving power of about 0.0025 nm. Maximum useful magnification of about 100 million times!!!

6. COMPARISION OF LIGHT AND ELECTRON MICROSCOPE Optical glass lens, Small depth of Field, lower magnification, do not Require vacuum, Low price. Magnetic lens, Large depth of field, Higher magnification and better Resolution, Operates in HIGH vacuum, Price tag. LIGHT MICROSCOPE ELECTRON MICROSCOPE

8. SPECIMEN INTERACTION IN ELECTRON MICROSCOPY SPECIMEN INTERACTION VOLUME FOR VARIOUS REACTIONS REACTIONS ON THE TOP SIDE ARE UTILIZED FOR EXAMINING THICK OR BULK SPECIMENS (SEM) RECTIONS ON THE BOTTOM SIDE ARE EXAMINED IN THIN OR FOIL SPECIMEN (TEM ) VARIOUS REACTIONS CAN OCCUR WHEN ENERGETIC ELECTRONS STRIKE THE SAMPLE

10. Transmission Electron Microscopy TEM is a unique tool in characterization of materials crystal structure and microstructure simultaneously by diffraction and imaging techniques.

11. TEM is analogous to a Slide Projector

14. The acceleration voltage of up to date routine instruments is 120 to 200 kV. Medium-voltage instruments work at 200-500 kV to provide a better transmission and resolution, and in high voltage electron microscopy (HVEM) the acceleration voltage is in the range 500 kV to 3 MV. Acceleration voltage determines the velocity, wavelength and hence the resolution (ability to distinguish the neighbouring microstructural features) of the microscope

17. BRIGHT FIELD IMAGING ALLOWING TRNSMITTED BEAM

18. DARK FIELD IMAGING ALLOWING DIFFRACTED BEAM

19. Bright-field TEM micrographs of the as-prepared ZnO powders after annealing for 1 h at various temperatures: a 300 . C, b 400 . C and c 500 . C, respectively.

21. Some fancy Diffraction Patterns

22. BASIC DESIGN OF TRANSMISSION ELECTRON MICROSCOPE Evacuated metal cylinder within which are aligned, one under another: 1. Tungsten filament (the cathode) 2. A Metal plate with central aperture (the anode) 3. A number of magnetic lenses 4. A Fluorescent screen 5. A photographic plate

23. DESIGN OF TRANSMISSION ELECTRON MICROSCOPE A simplified ray diagram of a TEM consists of an electron source, condenser lens with aperture, specimen, objective lens with aperture, projector lens and fluorescent screen .

24. In actuality a modern TEM consists of many more components including a dual condenser system, stigmators, deflector coils, and a combination of intermediate and dual projector lens

30. FEG requires a different gun design as well as much better vacuum in the gun area (~10e-8 Pa instead of the ~10e-5 Pa). Consists of a small single-crystal tungsten needle that is put in a strong extraction voltage (2-5 kV). In the case of a cold FEG, the needle is so sharp that electrons are extracted directly from the tip. For the Schottky FEG a broader tip is used which has a surface layer of zirconia (ZrO2). The zirconia lowers the work function of the tungsten and can use the broader tip . Unlike the thermionic gun, the FEG does not produce a small cross-over directly below the emitter, but the electron trajectories seemingly originate inside the tip itself, forming a virtual source of electrons for the microscope.

32. Magnetic Lenses Electron Optics Elements

33. MAGNETIC LENSES 1.Coil of several thousand turns of wire through which a current of less than or equal to one amp is passed --- creates a magnetic field. 2.. Electrons are deflected by magnetic field 3. To concentrate field further a soft iron pole piece is inserted into the bore of the objective lens. 5. To focus an electron beam onto a given plane the current through the coils must be set to a precise value. . current – beam focus closer to lens current – beam focus further from lens

34. Depth of Field: the range of distance at the specimen parallel to the illuminating beam in which the object appears to be in focus. Depth of Focus: the range of distance at the image plane (i.e. the eyepiece, camera, or photographic plate) in which a well focussed object appears to be in focus.

35. Illuminates the specimen. Relatively weak lens. Longer focal length than objective or projector lens. May bring electron beam into focus directly upon specimen, above the specimen (over focusing) or below the specimen (under focusing). CONDENSER LENS

36. As magnification increases the condenser lens must be adjusted to properly illuminate the specimen. When the lens is brought to its smallest spot the beam is said to be at the crossover point

37. Holey Formvar is used to critically adjust the stigmation of a TEM. When the beam is under or over focused on the specimen a Fresnel fringe becomes visible due to the effects of diffraction around the edges of the hole. When this Fresnel fringe is evenly distributed then the beam is said to be stigmated

40. Total magnification in the TEM is a combination of the magnification from the objective lens times the magnification of the intermediate lens times the magnification of the projector lens. Each of which is capable of approximately 100X. M ob X M int X M proj = Total Mag

41. In older TEMs functions such as gun and beam alignment were accomplished by physically moving components in the column. Today they are achieved by use of electromagnetic deflection coils that are positioned throughout the column Deflection Coils

42. Using the deflection coils the beam can be shifted so that the focused beam is centered in the back focal plane of the lens and tilted so that the beam is centered on the specimen.

46. The de Broglie wavelength of electron is given by or Diffraction intensity in a given direction is the sum over contribution from all location of the specimen taking into account their relative phases. Bragg’s conditions for constructive interference: In vector form: The scattering vector(not necessarily a Lattice vector) = Reciprocal lattice vector

48. ELECTRON DIFFRACTION UNDER THE CONDITION OF TEM • Consider a row of N unit cell along the z-axis • The topmost unit cell scattered with amplitude F 0 [s] • S=s-s 0 is the scattering vector • Scattered wave from the next unit cell below is Where c is the lattice vector along the z-axis Final scattered wave intensity is given by Where I 0 [s] = It has sharp maximum for S.c = l an integer Lattice factor

49. EXCITATION ERROR Assume that the diffraction condition is not exactly satisfied : Where s is the excitation error g is a lattice translation of the REL, satisfying the 3rd Laue equation : s is not a lattice translation of the REL, and we assume that This yields, the diffraction intensity TEM thin foil: Small extension in the z-direction, large extension in the x And y direction. Thus 1 st and 2 nd Laue equation satisfies exactly, Excitation error only have z-component, thus

50. This yields following expression of intensity First minimum of I occurs at ± 1/t. Thus diffraction Occurs although S is not a RLV. I[s] >0 is represented by ‘rods’ parallel to z* in every REL point (REL rods). Since s is small And the scalar product, N.c.s =

52. Ewald Construction for Electron Diffraction in TEM 1. Replace REL points by REL rods! 2. Direction of the rods: normal to the plane of the foil (parallel to z *) 3. Length of the rods: ± 1/ t Special Ewald construction for diffraction of electrons at thin foils: • special conditions: 1. Very small wavelength (compared to X-ray diffraction, for example)  Ewald sphere has a very large radius 1/  2. REL points  “rods” normal to the TEM foil

53. Specimen, transmitted and diffracted beam forming the diffraction pattern. Also see the Ewald sphere construction in Reciprocal Space.

54. CONSEQUENCES: 1. Even for a “sharp” wavelength,  const., a TEM foil generates diffracted beams, irrespective of the orientation of the foil versus the primary beam! 2. Very small Bragg angles ( 1°) 3. Reflecting planes are approximately parallel to the primary beam 4. = Reduces the Bragg condition to 5. Ewald sphere “flat” in the angular region of ±1° around the direction of the primary beam 6. Curvature of the sphere is negligible compared to length ±1/ t of the REL rods Consequence: Example: Diffraction pattern of f.c.c lattice in <hkl> direction (hkl) plane of b.c.c lattice and vise versa.

55. In this case incident beam direction B [100] in an Aluminum (f,c.c), single crystal specimen. Transmitted beam is marked as T and the arrangement of the diffracted beams D around the transmitted beam is the characteristic of the four fold symmetry of the [100] cube axis of Aluminum. EXAMPLE OF DIFFRACTION PATTERN

56. SINGLE CRYSTAL DIFFRACTION PATTERN Single crystal are most ordered (lattice type such as f.c.c, b.c.c, s.c etc.) among the three structures. Electron beam passing through a single crystal will produce a pattern of spots. Type of crystal structure (f.c.c., b.c.c.) and the &quot;lattice parameter&quot; ( i.e. , the distance between adjacent planes) can be determined . Also, the orientation of the single crystal can be determined: if the single crystal is turned or flipped, the spot diffraction pattern will rotate around the centre beam spot in a predictable way.

73. Camera Length INDEXING DIFFRACTION PATTERNS is the distance between and screen and the crystal (without imaging lens). With imaging lenses effective L is considered. From the figure: Using the reduced Bragg condition: and the above relation we have,

76. INDEXING DIFFRACTION PATTERNS General Method: 1. Measure R of the fundamental reflection. 2. Calculate the corresponding plane spacing d hkl . 3. Index the reflections with (hkl). In a good approximation primary beam is parallel to the reflecting planes. That is primary beam corresponds to the zone axis of the reflecting plane. Addition Rule: If a zone includes the plane h i and k i , then it also includes the plane (h i + k i ). For the diffraction pattern of a single crystal this implies that after indexing two non-collinear fundamental reflections, the indices of the entire pattern follow from vector addition.

79. DETERMINATION OF BEAM DIRECTION The zone axis [uvw]=Z=B can be determined by using the relations , u=k1l2-k2l1 v=l1h2-l2h1 w=h1k2-h2k1 Where the spot (h1l1k1) is positioned counter clockwise around the central spot relative to the spot (h2k2l2). If the spots are expressed in terms of reciprocal lattice vector g1 and g2 then B= g1 g2