1. III. Analytical Aspects Summary Cheetham & Day, Chapters 2, 3 Chemical Characterization of Solid-State Materials Chemical Composition: Bulk, Surface, … Inductively-Coupled Plasma-Mass Spectrometry X-ray Photoelectron Spectroscopy Scanning Electron Microscopy Electron Microprobe Electrochemistry Atomic Structure: Long-range order; short-range order; … Diffraction Nuclear Magnetic Resonance Transmission Electron Microscopy Oxidation States of Atoms Photoelectron Spectroscopy

2. III. Analytical Aspects Diffraction Cheetham & Day, Chapter 2 Reference: On-Line Tutorial: Proffen (LANL), Neder (Erlangen), Billange (Michigan St.) Interatomic Distances in solids ca. 10  10 m (= 1 Å = 0.1 nm = 100 pm). T (K) (Å) E (eV)v (m/sec) Cu K  ---1.541788042 3  10 8 Mo K  ---0.7106917450 3  10 8 Neutrons 2981.45730.0385 2.72  10 3 Electrons 5.17  10 5 1.500066.9 4.85  10 6 Hand-Outs: 1

3. III. Analytical Aspects Diffraction: Producing X-rays and Neutrons Cheetham & Day, Chapter 2 X-Rays: Light created by(i) accelerating electrical charges (ii) inducing transitions between energy states Conventional X-Ray Tube Isotropic emission (just a small fraction is used); Single wavelength; Water-cooled (high current will melt the anode); Rotating the anode allows more power (e  beam travels over anode surface) (Anode) X-Rays (W coil) 1.5 kW Tube Hand-Outs: 1

4. III. Analytical Aspects Diffraction: Producing X-rays and Neutrons Cheetham & Day, Chapter 2 When electrons hit the anode, they (i) collide with atoms & slow down - bremsstrahlung (ii) cause sharp transitions of core electrons through ionization and relaxation L(2p)  K(1s): K  1 (2p 1/2 ), K  2 (2p 3/2 ) M(3p)  K(1s): K  1 (3p 1/2 ), K  2 (3p 3/2 ) Bremsstrahlung MIN E To further control the wavelength, use a (i) monochromator: diffraction from an oriented single crystal (Ge, SiO 2 ) (ii) filter: absorption – Beer’s law, I = I 0 exp(  l)  ~ a 3 (Absorption Edge) Filter for Element Z would be Z  1 or Z  2; e.g., Ni is a filter for Cu Zr is a filter for Mo. Hand-Outs: 2

5. III. Analytical Aspects Diffraction: Producing X-rays and Neutrons Cheetham & Day, Chapter 2 Synchrotron Radiation: accelerate electrons in circular motion v =  c R E H (wavevector k) Radiates with power Energy lost per revolution is Bremsstrahlung Brightness = 10 12 -10 15 photons/sec  mm 2  mrad 2  (X-ray tubes are 10 7 ; Rotating anodes are 10 8 -10 9 ) ADVANTAGES High intensity, tunable, Intrinsically collimated, pulsed, polarized DISADVANTAGES Large facility, beam time is competitive, possible radiation damage and heating Hand-Outs: 2

6. III. Analytical Aspects Diffraction: Producing X-rays and Neutrons Cheetham & Day, Chapter 2 Synchrotron Radiation: possible applications include Spectroscopy: EXAFS (Extended X-ray Absorption Fine Structure) XANES (X-ray Absorption Near-Edge Spectroscopy) Very fast crystallography:time-resolved phenomena (100 ps – 1 week) High resolution / diffuse scattering with small samples: intermediate length scales Magnetic scattering:Magnetic ordering in Gd Inelastic scattering:Vibrational modes and amplitudes. Hand-Outs: 2

7. III. Analytical Aspects Diffraction: Producing X-rays and Neutrons Cheetham & Day, Chapter 2 Neutrons: produced in nuclear reactors create broad spectral distribution of wavelengths Spallation Sources: bombarding metal targets with 800 MeV H + ; generate pulsed neutron beams – analyzed by time-of-flight (TOF) methods.  t Hand-Outs: 2

8. III. Analytical Aspects Diffraction: A Scattering Process Cheetham & Day, Chapter 2 X-Rays are scattered by electrons. k = (2  / ) z E = (oscillating) electric field H = (oscillating) magnetic field Plane Waves:E = E 0 e i(  t + k  r) = [E 0 e i(  t + 2  z/ ) ] x;E =   =  c/ Scattering by a Single Electron: Oscillating E, so electron will oscillate (accelerate) and emit radiation in all directions q Elastic Scattering: | k i | = | k f | = 2  / Scattering Vector: q = k f  k i 2  = scattering angle NOTE: q and k have units m  1 Hand-Outs: 3

9. III. Analytical Aspects Diffraction: A Scattering Process Cheetham & Day, Chapter 2 Scattering by a Single Electron: Oscillating E, so electron will oscillate (accelerate) and emit radiation in all directions q = scattering vector 2  = scattering angle Electron is accelerated: Amplitude of scattered radiation (along k f direction): Intensity of scattered radiation: Polarization Factor Hand-Outs: 3

10. III. Analytical Aspects Diffraction: A Scattering Process Cheetham & Day, Chapter 2 Scattering by an Atom: Continuous, spherical distributions of electron density  Two scattered rays show phase difference (  ) related to the path difference (  ) traveled by the two rays D (2) D (1) With respect to 1 electron: Differential Scattering Amplitude Hand-Outs: 4

11. III. Analytical Aspects Diffraction: Atomic Scattering Factors Cheetham & Day, Chapter 2 Atomic Scattering Factor: shows constructive interference – atomic size ~ X-rays (NO Interference) Size of Atom ~ (X-rays) Interference increases with 2  Both have 10 electrons; Si 4+ more like point ion than O 2  (1)Difficult to distinguish elements with similar Z by diffraction alone (use interatomic distances); (2) Light atoms next to heavy atoms are difficult to find (large scattering angles help…) Scattering Vector: q(2  ) Phase:  = q  r Hand-Outs: 4