Don’t Ever Give Up!
description
Transcript of Don’t Ever Give Up!
![Page 1: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/1.jpg)
Don’t Ever Give Up!
![Page 2: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/2.jpg)
X-ray Diffraction
/hcE
Typical interatomic distances in solid are of the order of an angstrom.Thus the typical wavelength of an electromagnetic probe of such distances Must be of the order of an angstrom.
Upon substituting this value for the wavelength into the energy equation,We find that E is of the order of 12 thousand eV, which is a typical X-rayEnergy. Thus X-ray diffraction of crystals is a standard probe.
![Page 3: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/3.jpg)
Wavelength vs particle energy
![Page 4: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/4.jpg)
Bragg Diffraction: Bragg’s Law
![Page 5: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/5.jpg)
Bragg’s Law
The integer n is known as the order of the corresponding Reflection. The composition of the basis determines the relativeIntensity of the various orders of diffraction.
![Page 6: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/6.jpg)
Many sets of lattice planes produce Bragg diffraction
![Page 7: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/7.jpg)
Bragg Spectrometer
![Page 8: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/8.jpg)
Characteristic X-Rays
![Page 9: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/9.jpg)
Brehmsstrahlung X-Rays
![Page 10: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/10.jpg)
Bragg Peaks
![Page 11: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/11.jpg)
X-Ray Diffraction Recording
![Page 12: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/12.jpg)
von Laue Formulation of X-Ray Diffraction
![Page 13: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/13.jpg)
Condition for Constructive Interference
![Page 14: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/14.jpg)
Bragg Scattering
=K
![Page 15: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/15.jpg)
The Laue Condition
![Page 16: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/16.jpg)
Ewald Construction
![Page 17: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/17.jpg)
Crystal and reciprocal lattice in one dimension
![Page 18: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/18.jpg)
First Brillouin Zone: Two Dimensional Oblique Lattice
![Page 19: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/19.jpg)
Primitive Lattice Vectors: BCC Lattice
![Page 20: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/20.jpg)
First Brillouin Zone: BCC
![Page 21: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/21.jpg)
Primitive Lattice Vectors: FCC
![Page 22: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/22.jpg)
Brillouin Zones: FCC
![Page 23: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/23.jpg)
Near Neighbors and Bragg Lines: Square
![Page 24: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/24.jpg)
First Four Brillouin Zones: Square Lattice
![Page 25: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/25.jpg)
All Brillouin Zones: Square Lattice
![Page 26: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/26.jpg)
First Brillouin Zone BCC
![Page 27: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/27.jpg)
First Brillouin Zone FCC
![Page 28: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/28.jpg)
![Page 29: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/29.jpg)
Experimental Atomic Form Factors
![Page 30: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/30.jpg)
Reciprocal Lattice 1
![Page 31: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/31.jpg)
Reciprocal Lattice 2
![Page 32: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/32.jpg)
Reciprocal Lattice 3
![Page 33: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/33.jpg)
Reciprocal Lattice 5
![Page 34: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/34.jpg)
Real and Reciprocal Lattices
![Page 35: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/35.jpg)
von Laue Formulation of X-Ray Diffraction by Crystal
![Page 36: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/36.jpg)
Reciprocal Lattice Vectors
• The reciprocal lattice is defined as the set of all wave vectors K that yield plane waves with the periodicity of a given Bravais lattice.
• Let R denotes the Bravais lattice points;consider a plane wave exp(ik.r). This will have the periodicity of the lattice if the wave vector k=K, such that
exp(iK.(r+R)=exp(iK.r)
for any r and all R Bravais lattice.
![Page 37: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/37.jpg)
Reciprocal Lattice Vectors
• Thus the reciprocal lattice vectors K must satisfy
• exp(iK.R)=1
![Page 38: Don’t Ever Give Up!](https://reader035.fdocuments.in/reader035/viewer/2022081506/56815214550346895dc053ad/html5/thumbnails/38.jpg)
Brillouin construction