xrd_peakintensities

xrd_peakintensities - X-ray Powder Diffraction II Peak...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
1 X-ray Powder Diffraction II ray Powder Diffraction II Peak Intensities Peak Intensities Chemistry 754 Solid State Chemistry Lecture #10 Outline Outline • Elastic scattering of X-rays by atoms • Diffraction peak intensities Structure Factors Multiplicity Lorentz and Polarization Factors Temperature Factors •N e u t r o n d i f f r a c t i o n • Electron diffraction
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 Interaction of X Interaction of X -rays with Matter rays with Matter These are the diffracted X-rays Elastic Scattering by an Electron Elastic Scattering by an Electron Charged particles (electron) scatter electromagnetic radiation (x-rays) The varying electric field of the X-ray induces an oscillation of the electron The oscillating electron then acts as a source of electromagnetic radiation In this way the x-rays are scattered in all directions JJ Thompson analyzed the scattering and found that: I = I 0 [( μ 0 /4p) 2 (e 4 /m 2 r 2 )sin 2 α ] I = I 0 (K/r 2 ) sin 2 α α is the angle between the scattering direction and the direction in which the electron is accelerated r is the distance from the scattering electron K is a constant
Background image of page 2
3 Scattering by an Atom Scattering by an Atom We can consider an atom to be a collection of electrons. The electrons around an atom scatter radiation in the manner described by Thompson. However, due to the coherence of the radiation we need to consider interference effects from different electrons within an atom . This leads to a strong anglular dependence of the scattering . We express the scattering power of an atom by its form factor (f). X-ray Form Factors ray Form Factors 0 5 10 15 20 25 0 0.1 0.2 0.3 0.4 0.5 0.6 Sin( θ )/ λ Form Factor, f Ca Ca2+ The form factor is equivalent to the atomic number at θ = 0 The form factor drops rapidly as a function of (sin θ )/ λ
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4 The Effect of Form Factors on The Effect of Form Factors on Diffraction Patterns Diffraction Patterns 0 500 1000 1500 2000 2500 3000 3500 4000 4500 52 54 56 5 2-Theta (Degrees) Intensity TbBaFe 2 O 5 - 300 K Synchrotron X-ray 10 30 50 70 90 110 130 2-Theta (Degrees) Intensity (Arb. Units) TbBaFe 2 O 5 - 70 K Neutron Data The peak intensities drop off at high angles in an X-ray diffraction pattern because the form factor decreases Neutrons are scattered from the nucleus and the form factor is not angle dependent. Intensities do not drop off at high angle. Diffraction Intensities Diffraction Intensities The integrated intensity (peak area) of each powder diffraction peak is given by the following expression: I( hkl ) = |S( )| 2 × M hkl × LP( θ ) × TF( θ ) S( ) = Structure Factor M hkl = Multiplicity LP( θ ) = Lorentz & Polarization Factors TF( θ )= Temperature factor (more correctly referred to as the displacement parameter) This does not include effects that can sometimes by problematic such as absorption, preferred orientation and extinction.
Background image of page 4
5 Structure Factor Structure Factor The structure factor reflects the interference between atoms in the basis (within the unit cell). All of the information regarding
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 06/11/2011 for the course CHEM 101 taught by Professor Stegemiller during the Spring '07 term at Ohio State.

Page1 / 13

xrd_peakintensities - X-ray Powder Diffraction II Peak...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online