Вибрані методи досліджень

1. 105-ПФіНМ Вибрані методи досліджень лекції професор Ігор Вірт 2018

2. Лекція 1 Основи кристалографії. Кристалічні структури Crystallography and Structure 2

3. Planar Density of (100) Iron Solution:  At T < 912C iron has the BCC structure. 4 3 = a R 3 atoms 2 2D repeat unit 1 a 1 atoms atoms 12.1 = 1.2 x 1019 = = Planar Density = 2 nm2 m2 4 3 R 3 area 2D repeat unit Кристалічні структури 2D repeat unit (100) Radius of iron R = 0.1241 nm Atoms: wholly contained and centered in/on plane within U.C., area of plane in U.C.

4. Zinc blende (ZnS) unit cell showing (a) ion positions. There are two ions per lattice point (note the outlined example). Compare this structure with the diamond cubic structure (Figure 3.20a). (b) The actual packing of full-size ions associated with the unit cell. [Part (b) courtesy of Accelrys, Inc.] Кристалічні структури. Напівпровідники

5. Crystallographic Planes example example abc abc z 1 1  1. Intercepts c 1/1 1/1 1/ 2. Reciprocals 1 1 0 3. Reduction 1 1 0 y b a z x 1/2   1. Intercepts c 1/½ 1/ 1/ 2. Reciprocals 2 0 0 3. Reduction 2 0 0 y b a x Кристалічні структури 4. Miller Indices (110) 4. Miller Indices (100)

6. Crystallographic Planes z c 1/2 1 3/4 1. Intercepts 1/½ 1/1 1/¾ 2. Reciprocals 2 1 4/3 y b a 3. Reduction 6 3 4 x Family of Planes {hkl} Ex: {100} = (100), (010), (001), (100), (001) (010), Кристалічні структури example a b c 4. Miller Indices (634)

7. Let us consider in-plane scattering There is more to this Click here to know more and get introduced to Laue equations describing diffraction Extra path traveled by incoming waves AY These can be in phase if  incident = scattered Extra path traveled by scattered waves XB But this is still reinforced scatteringand NOT reflection

8. X-RAY DIFFRACTION METHODS Кристалічні структури. Методи досліджень. Дифракційні методи. 8

9. X-RAY ENERGY Electromagnetic radiation described as having packets of energy, or photons. The energy of the photon is related to its frequency by the following formula: Рентгеноструктурний аналіз =Wavelength , ע = Frequency , c = Velocity of light x-ray≈ 10-10 ≈1A° E ~ 104 ev

10. Рентгеноструктурний аналіз X-ray sources with different  for doing XRD studies The high intensity nearly monochromatic K x-rays can be used as a radiation source for X-ray diffraction (XRD) studies  a monochromator can be used to further decrease the spread of wavelengths in the X-ray

11. X-ray sources with different  for doing XRD studies C.Gordon Darwin, Grandson of C. Robert Darwin developed the dynamic theory of scattering of x-rays (a tough theory!) in 1912

12. Рентгеноструктурний аналіз. Приклади Relation between dnh nk nl and dhkl e.g.

13. Рентгеноструктурний аналіз In XRD nth order reflection from (h k l) is considered as 1st order reflection from (nh nk nl) Hence, (100) planes are a subset of (200) planes All these form the (200) set

14. Рентгеноструктурний аналіз We had mentioned that Bragg’s equation is a negative statement: i.e. just because Bragg’s equation is satisfied a ‘reflection’ may not be observed. Let us consider the case of Cu K radiation ( = 1.54 Å) being diffracted from (100) planes of Mo (BCC, a = 3.15 Å = d100). But this reflection is absent in BCC Mo The missing reflection is due to the presence of additional atoms in the unit cell (which are positions at lattice points)  which we shall consider next The wave scattered from the middle plane is out of phase with the ones scattered from top and bottom planes. I.e. if the green rays are in phase (path difference of ) then the red ray will be exactly out of phase with the green rays (path difference of /2).

15. Методи рентгеноструктурного аналізу Crystal structure determination Many s (orientations) Powder specimen POWDER METHOD Monochromatic X-rays Single  LAUETECHNIQUE Panchromatic X-rays ROTATINGCRYSTALMETHOD  Varied by rotation Monochromatic X-rays Only the powder method (which is commonly used in materials science) will be considered in this text.

16. Рентгеноструктурний аналіз X-Rays to Determine Crystal Structure detector “1” incoming reflections must X-rays “2” be in phase for “1” a detectable signal! outgoing X-rays l extra “2” distance q q traveled spacing by wave “2” d between planes X-ray nl intensity q d= c 2sin (from detector) q q c • Incoming X-rays diffract from crystal planes. Measurement of critical angle, qc, allows computation of planar spacing, d. For Cubic Crystals: h, k, l are Miller Indices

17. (a) An x-ray diffractometer. (Courtesy of Scintag, Inc.) (b) A schematic of the experiment. Рентгеноструктурний аналіз. Апаратура.

18. Theory and Analytical Technique Рентгеноструктурний аналіз

19. X-Ray Analysis X-rays discovered in 1895 Fundamental to understanding of crystal structure and symmetry Powder diffraction analyses are a simple and inexpensive method for identifying minerals, especially fine-grained minerals Рентгеноструктурний аналіз

20. Bragg Diffraction Рентгеноструктурний аналіз. Дифракція Брега Following Bragg's law, each dot (or reflection), in this diffraction pattern forms from the constructive interference of X-rays passing through a crystal. The data can be used to determine the crystal's atomic structure. Diffraction from a three dimensional periodic structure such as atoms in a crystal is called Bragg Diffraction. Similar to diffraction though grating. Consequence of interference between waves reflecting from different crystal planes. Constructive interference is given by Bragg's law: Where λ is the wavelength, d is the distance between crystal planes, θ is the angle of the diffracted wave. and n is an integer known as the order of the diffracted beam.

21. Diffraction with large SAD aperture, ring and spot patterns Poly crystalline sample Four epitaxial phases The orientation relationship between the phases can be determined with ED. Similar to XRD from polycrystalline samples.

22. The Powder Method If a monochromatic x-ray beam is directed at a single crystal, then only one or two diffracted beams may result. Рентгеноструктурний аналіз. Порошковий метод • If the sample consists of some tens of randomly orientated single crystals, the diffracted beams are seen to lie on the surface of several cones. • A sample of some hundreds of crystals (i.e. a powdered sample) show that the diffracted beams form continuous cones. A circle of film is used to record the diffraction pattern as shown. 22

23. Debye Scherrer Camera A very small amount of powdered material is sealed into a fine capillary tube made from glass that does not diffract x-rays. Рентгеноструктурний аналіз. Порошковий метод The specimen is placed in the Debye Scherrer camera and is accurately aligned to be in the centre of the camera. X-rays enter the camera through a collimator. 23

24. Рентгеноструктурний аналіз. Порошковий метод • In the powder sample there are crystallites in different ‘random’ orientations (a polycrystalline sample too has grains in different orientations) • The coherent x-ray beam is diffracted by these crystallites at various angles to the incident direction • All the diffracted beams (called ‘reflections’) from a single plane, but from different crystallites lie on a cone. • Depending on the angle there are forward and back reflection cones. Usually the source is fixed and the detector and sample are rotated Different cones for different reflections POWDER METHOD Also called Debye ring

25. Рентгеноструктурний аналіз. Порошковий метод It is ‘somewhat difficult’ to actually visualize a random assembly of crystallites giving peaks at various angels in a XRD scan. The figures below are expected to give a ‘visual feel’ for the same. [Hypothetical crystal with a = 4Å is assumed with =1.54Å. Only planes of the type xx0 (like (100,110)are considered]. For convenience the source may be stationary (and the sample and detector may rotate– but the effect is equivalent) The sample is not rotating only the source and detector move in arcs of a circle How to visualize the occurrence of peaks at various angles As the scan takes place at increasing angles, planes with suitable ‘d’, which diffract are ‘picked out’ from favourably oriented crystallites Random assemblage of crystallites in a material

26. Лекція 2 Електронна мікроскопія кристалічних структур Electron Microscopy and Structure 26

27. ANALYSIS SYNTHESIS Microscopy Spectroscopy Електронна мікроскопія кристалічних структур. Методи Areas of Application

28. Scanning Electron Microscopy (SEM) Електронна мікроскопія кристалічних структур SEM: A focused electron beam (2-10 keV) scans on the surface, several types of signals are produced and detected as a function of position on the surface. The space resolution can be as high as 1 nm. Different type signal gives different information: a. Secondary electrons: surface structure. b. Backscattered electrons: surface structure and average elemental information. b. X-rays and Auger electrons: elemental composition with different thickness-sensitivity.

29. Електронна мікроскопія. Мікроскопи. The instrument in brief

30. SEM Focusing Column Електронна мікроскопія. Мікроскопи. Steering Quadrupole 1 Thermal Field Emitter Lens 1 Steering Quadrupole 2 Lens 2 Sample Extractor Beam Acceptance Aperture Deflection Octupole Beam Blanking Plates Suppressor Assembly

31. Gold coating Електронна мікроскопія. Технологія препарування EBT2 with Au coating Graduate School of Convergence Science and Technology. Seoul National University

32. Example Електронна мікроскопія. Приклади EBT2

33. TEM Електронна мікроскопія. Мікроскопи. Transmission Electron Microscopy

34. Functional principle Електронна мікроскопія. Мікроскопи.

35. Електронна мікроскопія. Мікроскопи. TEM Control brightness, convergence binocular screen Control contrast

36. Principle Мікроскопія. Мікроскоп AFM Tip Position-sensitive photodetector Laser diode Cantilever spring Tip by measuring forces between a sharp probe (<10 nm) and surface at very short distance

37. Лекція 3 Електрофізичні характеристики матеріалів. Гальваномагнітні властивості Galvanomagnetic properties of materials 37

38. Гальваномагнітні властивості. Ефект Холла. B y z x Two types of carriers. 38

39. Гальваномагнітні властивості. Ефект Холла. Ey y z jx B x Ey tga Ex Hall effect in semiconductors 39

40. Гальваномагнітні властивості. Закон Ома у маричній формі. Semiconductor 40

41. Гальваномагнітні властивості. Ефект Холла. Hall effect in semiconductors 41

42. Гальваномагнітні властивості. Ефект Холла. Hall effect in semiconductors 42

43. Ефект Холла. Концентрація носіїв та їх рухливість Determining the concentration and mobility 1) 2) 3) 43

44. Ефект Холла. Сильні магнітні поля. Determining the concentration and mobility 44

45. Ефект Холла. Концентрація носіїв та їх рухливість z y c<<1  x z y c>>1 →/2 x tg=HB= c 45

46. Ефект Холла. Концентрація носіїв та їх рухливість. Слабкі магнітні поля. -UH - n=ND ni=Cexp(-Eg/kT) 1/T Determining the concentration and mobility + p=NA 46

47. Кванотовий ефект Холла. Quantum Hall Effects 47

48. Лекція 4 Резонансні методи досліджень матеріалів. Магнітні резонанси. Magnetic Resonances 48

49. The Electromagnetic Spectrum Магнітні резонанси. • NMR, MRI • EPR/ESR

50. Energy Differences Between Nuclear Spin States Магнітні резонанси. + + DE ' DE increasing field strength, HZ no energy difference in absence of magnetic field proportional to strength of external magnetic field