Particle size Effect of Particle Size in X-ray diffraction a The width of the peaks in a powder pattern contain information about the crystallite size in Scherrer the sample (and also the presence of Equation microstar K Scherrer equation t=0.9 Bcos e t-mean size of crystallites .K-constant, roughly 1: depends on shape of tcos e sB-width of reflection in radian 20→ 20→ NanocrystalX- ray Diffraction Types of Diffraction Experiment IX-ray Routinely used to provide structural information on Used with both powder an crystal samples X-rays p Can also be used to examine liquids and glasses sElectron diffraction arily used for phase identification, and unit cell rmination on small crystallites in the electron microscope also used for gas phase samples seful source of structural information on crystalline Also useful for spectroscopy and structure of liquids/glasses good for looking at light atoms HRTEM Image and ED Pattern of Low Energy Electron Diffraction (LEED Tetrapod Cds Nanocrystals Provides information about surface This is a LEED pattern from diffraction pattern would show 入11 Particle size The width of the peaks in a powder pattern contain information about the crystallite size in the sample (and also the presence of microstrain) Scherrer equation t ¾ mean size of crystallites K ¾ constant, roughly 1: depends on shape of crystallites B ¾ width of reflection in radian q l = Bcos K t Effect of Particle Size in X-ray Diffraction Scherrer Equation 2q ® B 2q2 2q1 2qB Smaller Crystallite Relative Intensity 2q® B 2q2 2q1 2qB Larger Crystallite Relative Intensity B B cos 0.9 t q l = B t cos 0.9 B q l = or Nanocrystal X-ray Diffraction Types of Diffraction Experiment X-ray -Routinely used to provide structural information on compounds and to identify samples -Used with both powder and single crystal samples -X-rays produced in the home lab or using synchrotrons -Can also be used to examine liquids and glasses Electron diffraction –primarily used for phase identification, and unit cell determination on small crystallites in the electron microscope -also used for gas phase samples Neutrons –useful source of structural information on crystalline materials, but expensive -Also useful for spectroscopy and structure of liquids/glasses -good for looking at light atoms –sensitive to magnetic moments HRTEM Image and ED Pattern of Tetrapod CdS Nanocrystals Low Energy Electron Diffraction (LEED) Provides information about surfaces This is a LEED pattern from a surface of Si. A bulk X-ray diffraction pattern would show only the strong spots on defining the hexagonal pattern. The additional fainter spots contain important information about the way in which Si atoms re-arrange themselves at the surface of Si, i.e. the surface has a slightly different structure from the bulk. These measurements are very important to device manufacturers, since the surface of silicon is used in so many technological applications