Crystallography and Diffraction. Theory and Modern Methods of Analysis Lectures Electron Diffraction Dr. I. Abrahams Queen Mary University of London Lectures co-financed by the European Union in scope of the European Social Fund

History of electron diffraction 1927 Davisson and Germer USA, Thompson and Reid in Scotland, report electron scattering by crystals giving interference patterns. Share Nobel prize in Physics George Paget Thompson Lester Germer (right) with Clinton Joseph Davisson (left) Knoll and Ruska use the term electron microscope and present first electron images. Nobel prize in Physics for Ruska First commercial TEMs produced. Ernst Ruska Ruska’s microscope

Lectures co-financed by the European Union in scope of the European Social Fund Introduction to electron diffraction Electrons like X-rays are scattered by atoms and can be used analyse crystal structures in a similar way. There are however fundamental differences. X-rays are scattered by the electrons that make up the bulk of the atom. Electrons are charged particles and interact with the electrons surrounding atoms and also the nucleus. The elastic cross section of the electron is ca times larger than that of X-rays. Electron beams can be focussed using electromagnetic lenses. Excellent for studying small crystals, microstructure or surfaces. Disadvantages are that secondary diffraction may occur making additional spots appear on images. Samples should be very thin and able to withstand high vacuum conditions.

Lectures co-financed by the European Union in scope of the European Social Fund Electron Diffraction Techniques Electron diffraction (ED) techniques can be divided by the energy used (High or Low), the geometry (Transmission or Reflection) and the type of beam (Parallel or Convergent). ED = Electron Diffraction HEED = High Energy Electron Diffraction LEED = Low Energy Electron Diffraction THEED = Transmission High Energy Electron Diffraction RHEED = Reflection High Energy Electron Diffraction SAED = Selected Area Electron Diffraction NED = Nano Area Electron Diffraction CBED = Convergent Beam Electron Diffraction LACBED = Large Angle Convergent Beam Electron Diffraction

Lectures co-financed by the European Union in scope of the European Social Fund A TEM consists of an electron gun with a series of electrostatic or magnetic lenses and an electron detector. There are two basic modes of operation. Parallel beam or convergent beam. Parallel Beam TEM Used for TEM Imaging and diffraction Convergent Beam TEM Used for Scanning TEM (STEM) microanalysis and microdiffraction

Lectures co-financed by the European Union in scope of the European Social Fund SAED Selected Area Electron Diffraction SAED is probably the most common technique used. It uses the parallel beam method. A selected area aperture is located underneath the sample holder and can be adjusted to block parts of the beam so as to examine just selected areas of the sample. Combined with sample tilting, diffraction images of single crystallites can be obtained in various orientations. Single crystals of a few hundred nanometers in size can be examined in this way.

Lectures co-financed by the European Union in scope of the European Social Fund The atomic scattering factor for electrons f e shows a similar variation with sin  / to the X-ray scattering factor f x. f n (x m) f e x mf x x m sin  / H W The structure factor F hkl is calculated in the same way as for X-ray diffraction, but this time f is the atomic scattering factor for electrons. Scattering and structure factors I hkl  (F hkl ) 2

Lectures co-financed by the European Union in scope of the European Social Fund Samples are mounted on a sample holder that can be tilted in various orientations to allow Bragg’s Law to be satisfied. i.e. so that the reciprocal lattice points can touch the surface of Ewald’s sphere. In this way images of the reciprocal lattice can be obtained for different orientations. Single Crystal Images. When the area under illumination is a single crystal then the diffraction image corresponds to an image of the reciprocal lattice 000l image of GaN

Lectures co-financed by the European Union in scope of the European Social Fund Polycrystalline Images. In the case of polycrystalline materials, the image is a set of rings, with some spots depending on the crystallite sizes. Amorphous materials In this case the images are diffuse rings or halos Modulated structures In this case additional spots are observed corresponding to the structure modulation.

Lectures co-financed by the European Union in scope of the European Social Fund In electron diffraction of high energy electrons the Bragg angles are very small ca. 1 . This means that Bragg’s Law approximates to Where L is a constant for a microscope at a particular magnification. D is the distance on the diffraction pattern between 000 and the diffraction spot of interest.

Lectures co-financed by the European Union in scope of the European Social Fund Indexing spots is done in the same way as in the X-ray reciprocal lattice images. If the indices of the nearest spots are used one can use vector addition to get the indices of the other spots

Lectures co-financed by the European Union in scope of the European Social Fund Zone Axes If two or more sets of hkl planes intersect a common line in the lattice (called the zone axis) designated as u,v,w, then if the electron beam is directed along u.v.w they will all satisfy Bragg’s law and the zone equation: hu + kv + lw = n Where n = 0,1,…… Thus each set of planes that satisfies the zone equation gives rise to a spot on the image

Lectures co-financed by the European Union in scope of the European Social Fund Applications Applications for electron diffraction include: 1. Phase identification 2. Crystal orientation 3. Microstructure and texture and strain 4. Structure determination Examples from: J. M. Zuo in “Encyclopeadia of Inorganic Chemistry”

Lectures co-financed by the European Union in scope of the European Social Fund Phase identification in CuO nanowires

Lectures co-financed by the European Union in scope of the European Social Fund Diffraction pattern from a single CuO nanowire

Lectures co-financed by the European Union in scope of the European Social Fund Ag 50 Cu 50 thin film

Lectures co-financed by the European Union in scope of the European Social Fund Combination with TEM imaging is very powerful. HREM image of tantalum oxide with derived FT diffraction pattern