PHY 752 Solid State Physics

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Presentation transcript:

PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 31: X-ray and neutron diffraction in solids (some material contained in Chap. 3 of Marder’s text) Bragg law Intensity relationships Sensitivity to atomic parameters 4/13/2015 PHY 752 Spring 2015 -- Lecture 31

4/13/2015 PHY 752 Spring 2015 -- Lecture 31

X-ray and neutron diffraction in solids Comment on topics X-ray and neutron diffraction in solids Low energy electron diffraction in solids Beyond independent electron picture -- Electron-electron interactions in the Hubbard model (Chapter 26 of your text) 4/13/2015 PHY 752 Spring 2015 -- Lecture 31

In terms of wave vectors kinc Dk 2q Bragg diffraction incident beam defracted beam kscat In terms of wave vectors kinc Dk 2q 4/13/2015 PHY 752 Spring 2015 -- Lecture 31

Relationship of normal distance between diffracting planes to Bravais lattice 4/13/2015 PHY 752 Spring 2015 -- Lecture 31

Comes from Born approximation describing the interaction between scattering particle and material. Intensity profile 4/13/2015 PHY 752 Spring 2015 -- Lecture 31

Atomic structure factors For X-ray scattering; Fourier transform of electronic density (these are from crystaldiffract) 4/13/2015 PHY 752 Spring 2015 -- Lecture 31

Atomic structure factors http://www.ncnr.nist.gov/resources/n-lengths/ 4/13/2015 PHY 752 Spring 2015 -- Lecture 31

scattering length in 10-15 m 4/13/2015 PHY 752 Spring 2015 -- Lecture 31

Cu (fcc) 4/13/2015 PHY 752 Spring 2015 -- Lecture 31

X-ray powder diffraction pattern for Cu (fcc) what is lattice constant a? 3.615 Angstroms 4/13/2015 PHY 752 Spring 2015 -- Lecture 31

Fe (bcc) 4/13/2015 PHY 752 Spring 2015 -- Lecture 31

Fe (bcc) What is a ? 2.8665 Angstroms 4/13/2015 PHY 752 Spring 2015 -- Lecture 31

NaCl 4/13/2015 PHY 752 Spring 2015 -- Lecture 31

NaCl a=5.6573 Angstroms 4/13/2015 PHY 752 Spring 2015 -- Lecture 31

Comparison of X-ray and Neutron diffraction time of flight path length 4/13/2015 PHY 752 Spring 2015 -- Lecture 31

X-ray Neutron 4/13/2015 PHY 752 Spring 2015 -- Lecture 31

4/13/2015 PHY 752 Spring 2015 -- Lecture 31

X-ray 4/13/2015 PHY 752 Spring 2015 -- Lecture 31

Properties of scattering particles from pg. 61 of Marder’s text 4/13/2015 PHY 752 Spring 2015 -- Lecture 31