Lecture 1
Apr. 18
The Electron Microscope
Introductory considerations
A wave and its propagation
A particle and its wave length:  = h/p = h/mv
Uncertainty and particle waves, pxx = h
Special relativity: m = mo/(1 – v2/c2)1/2
Introduction to microscopes and image formation
A lens and an image
A diffraction pattern forms at the back focal plane
Lens laws and magnification
Resolution, its limits with light, and the rationale for doing electron microscopy
Making an electron beam
1
Thermionic emission: Dermi-Dirac Distribution of electron energies: ni = exp{Ei – EF)/kT}+1
Electrons need energy = work function w = (Eo – EF)
Annode and cathode: electrostatic forces: F = (q1q2/r.r) r E = q/r2
The Wehnolt, the bias to the Wehnolt helps to shape the electron cloud
A column at ground potential
Filament size and beam coherence: the LaB6 gun
This material has a work function of ca. 3ev, compared with 4.5 for tungston
The Field emission gun, The Schottky effect and a tunnel effect combined. Table.
Vacuum requirements
Mean free paths for electrons in gases l = 1/n, where  is the scattering cross-section
Vacuum technologies: rotory pumps, diffusion pumps, cryopumps, ion-getter pumps
Implications of vacuum for the study of biological materials
Electron lenses
Electrostatic lenses: discuss principle and show a diagram
Magnetic lenses and the paths for electrons: F = q(v X B) The spiraling path of e’s
A solanoid and its lens properties
Using iron to increase curvature of the B, and thus shortening focal length
Diagram of lens and its effect
Lens aberrations and their corrections
Definition of chromatic aberration and how to deal with it, especially for e’s
Definition of spherical aberration and its impact on resolution;
Diagrams of lenses with spherical aberration.
Cs, and its impact on image blurring: o = Cs3
Miminum blurring is (opt) = 0.67Cs(-1/4)(1/4)
Ddc = 1.6Cs(1/4)(3/4)
Curvature of field
Astigmatism (Isotropic and anisotropic)
Distortion (Isotropic and anisotropic)
Coma (Isotropic and anisotropic)
Scanning microscopy
The idea of scanning microscopy
Electron scattering as a source of information about the specimen:
Elastic and inelastic scattering: inelastic forward scattering is ~all due to electron
transitions in the scattering atom, because the mass of the atom is so great compared with that of e-.
Ze
For nuclear scattering, Rn = 
where Rn = distance of closest approach of electron to the
nucleus, Z = atomic number, e = electron charge, = beam potential, = scattered angle (small
enough that = sin)
e
For electron scattering from electrons, Re = 
Scanning transmission EM: collecting the unscattered electrons
Collecting the scattered electrons
Collecting electrons scattered through high angles
Scanning EM with secondary electrons
The Photoelectron microscpe
Energy loss spectrometry
Quantifying energy loss: an EELS
Imaging with EELS
XDS
Power of the method; limitations due to dose: