Fourier transform (see Cowley Sect. 2.2)

Slides:



Advertisements
Similar presentations
Scattering from imperfect crystals (see Cowley Sect. 7.1) Two types average lattice exists (point defects, dislocations, thermal vibrations) no average.
Advertisements

Diffraction See Chapter 10 of Hecht.
Solid State Physics 2. X-ray Diffraction 4/15/2017.
A Brief Description of the Crystallographic Experiment
1.X-Ray Scattering 2.De Broglie Waves 3.Electron Scattering 4.Wave Motion 5.Waves or Particles? 6.Uncertainty Principle 7.Probability, Wave Functions,
Form Factors and Transverse Charge Densities Siddharth Venkat UW REU 2010.
V. Fourier transform 5-1. Definition of Fourier Transform * The Fourier transform of a function f(x) is defined as The inverse Fourier transform,
Lecture 12 Convolutions and summary of course Remember Phils Problems and your notes = everything Today Convolutions.
Diffraction from point scatterers Wave: cos(kx +  t)Wave: cos(kx +  t) + cos(kx’ +  t) max min.
Lesson 5 Conditioning the x-ray beam
Physics 452 Quantum mechanics II Winter 2011 Karine Chesnel.
Introduction to Patterson Function and its Applications
Edge ECE measurements with the AUG CTS receiver and the effects of ELMs during H-mode Morten Stejner.
Bragg Planes How to do a Fourier transform on paper with no calculations at all.
Diffraction: Real Sample (From Chapter 5 of Textbook 2, Chapter 9 of reference 1,) Different sizes, strains, amorphous, ordering  Diffraction peaks.
A. Magerl Crystallography and Structural Physics University of Erlangen-Nürnberg Neutrons versus X-rays Novosibirsk 10. Oct
Physics of wave packets K.Ishikawa Hokkaido University January Collaborators:Tobita,Shimomura, Futamura,Hotta.
PHYS 222 SI Exam Review. What to do to prepare Review all clicker questions, but more importantly know WHY Review quizzes Make sure you know what all.
Pattersons The “third space” of crystallography. The “phase problem”
The Structure and Dynamics of Solids
Atomic structure model
The Muppet’s Guide to: The Structure and Dynamics of Solids Material Characterisation.
Modulation Transfer Function (MTF)
Electromagnetism Around 1800 classical physics knew: - 1/r 2 Force law of attraction between positive & negative charges. - v ×B Force law for a moving.
QM2 Concept Test 13.6 Choose all of the following statements that are correct about electromagnetic radiation and transitions between two energy.
QM2 Concept Test 6.1 Choose all of the following statements that are correct about the free electron gas model. 1)The free electron gas model takes into.
Hydrogen atom energy levels deBroglie and Bohr: 1. Wavelength comes from speed: 2. Integer wavelengths fit in orbit of size r 3. F = ma:
Measuring Wealth and Wealth Inequality
The Marks of an Obedient Disciple-maker
Introduction to Deep Learning
IB CHEMISTRY Topic 4 Bonding Higher level.
Chemistry 130 Dr. John F. C. Turner 409 Buehler Hall
Navigating Your Casio Calculator
THEORY OF METAL MACHINING
Do Now Which of the following approaches do you think would be most effective in dealing with school violence? Assign violent students a “big brother/sister”
Chemistry The Study of Matter
Monday.
Review Questions for 1st year chemistry
Imperialism Mr. Marshall
Clarkson University Google IgniteCS
Induced emf A current can be produced by a changing magnetic field
Innovation and electricity generation of wind AND solar PV in China
Data Mining, Neural Network and Genetic Programming
Name the Parent Function
Properties of the power spectral density (1/4)
Seminar on X-ray Diffraction
Shapes in real space ––> reciprocal space
Concept test 15.1 Suppose at time
Chapter 4 The Nuclear Atom.
Concept test 15.1 Suppose at time
Discrete Fourier Transform
QM2 Concept Test 2.1 Which one of the following pictures represents the surface of constant
Periodic systems. (See Roe Sect 5.5) Repeat periods of Å
Non-particulate 2-phase systems.
Waves The first term is the wave and the second term is the envelope.
CHAPTER 5 Wave Properties of Matter and Quantum Mechanics I
Fourier transforms and
Fourier transform (see Cowley Sect. 2.2)
Scattering Theory - Invariant
.., - I ':\ ' !' #
Scattering by free charges
Diffraction T. Ishikawa Part 1 Kinematical Theory 1/11/2019 JASS02.
Chapter 13 An Introduction to Ultraviolet/Visible Molecular Absorption Spectrometry.
Wave functions (see Cowley Sect. 1.2)
Announcements 3/23/12 Prayer
The Nuclear Atom Wei-Li Chen 10/23/2012.
4 + (-5) = A. Start at zero B. Move ______ spaces ___________ to get to the first number. C. From there, move _____ spaces __________ D. My final answer.
QM2 Concept test 3.1 Choose all of the following statements that are correct about bosons. (1) The spin of a boson is an integer. (2) The overall wavefunction.
Matter is made of atoms. Matter is made of atoms.
CHAPTER 5 Wave Properties of Matter and Quantum Mechanics I
Presentation transcript:

Fourier transform (see Cowley Sect. 2.2)

Fourier transform (see Cowley Sect. 2.2)

Fourier transform (see Cowley Sect. 2.2)

Fourier transform (see Cowley Sect. 2.2)

Fourier transform

Fourier transform

Fourier transform

Fourier transform

Scattering of x-rays by single electron (Thomson) (see Cowley sect. 4.1)

Scattering of x-rays by single electron (Thomson) (see Cowley sect. 4.1)

Scattering of x-rays by single electron (Thomson)

Scattering of x-rays by single electron (Thomson)

Scattering of x-rays by single atom For n electrons in an atom, time-averaged electron density is

Scattering of x-rays by single atom For n electrons in an atom, time-averaged electron density is Can define an atomic scattering factor

Scattering of x-rays by single atom For n electrons in an atom, time-averaged electron density is Can define an atomic scattering factor For spherical atoms

Scattering of x-rays by single atom Need to find (r) …. A QM problem But soln for f() looks like this (in electron scattering units)

Dispersion - anomalous scattering Have assumed radiation frequency >> resonant frequency of electrons in atom … frequently not true

Dispersion - anomalous scattering Have assumed radiation frequency >> resonant frequency of electrons in atom … frequently not true Need to correct scattering factors f = fo + f' + i f"

Dispersion - anomalous scattering Need to correct scattering factors f = fo + f' + i f" 5 f" 1 2 K f'

Atom assemblies (see Cowley sect. 5.1)

For this electron density, there is a Fourier transform Atom assemblies (see Cowley sect. 5.1) For this electron density, there is a Fourier transform F(u) is a fcn in reciprocal space

Atom assemblies (see Cowley sect. 5.1)

Atom assemblies

Atom assemblies For single slit, width a & g(x) = 1 If scatterer is a box a, b, c

Atom assemblies For single slit, width a & g(x) = 1 If scatterer is a box a, b, c For periodic array of zero-wiidth slits

Atom assemblies This requires ua = h, an integer. Then Finally

Atom assemblies This requires ua = h, an integer. Then Finally