Basic properties of X- rays and neutrons
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- Wilfrid Mathews
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1 Basic popeties of X- ays and neutons Based on lectue notes of Sunil K. Sinha, UC San Diego, LANL J. Teixiea LLB Saclay G. Knelle, CBM Oléans/SOLEIL
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3 The photon also has wave and paticle popeties E=h! =hc/l= hck Chage = 0 Magnetic Moment = 0 Spin = 1 E (kev " (Å
4 Wave length and enegy of photons Wavelength! Object Size! Angstoms fo Condensed Matte Reseach![A] = [kev] E ph
5 Wilhelm Conad Röntgen : Discovey of X-Rays
6 Nobel Pizes fo Reseach with X-Rays 1901 W. C. Röntgen in Physics fo the discovey of x-ays M. von Laue in Physics fo x-ay diffaction fom cystals W. H. Bagg and W. L. Bagg in Physics fo cystal stuctue detemination C. G. Bakla in Physics fo chaacteistic adiation of elements. 194 K. M. G. Siegbahn in Physics fo x-ay spectoscopy. 197 A. H. Compton in Physics fo scatteing of x-ays by electons P. Debye in Chemisty fo diffaction of x-ays and electons in gases. 196 M. Peutz and J. Kendew in Chemisty fo the stuctue of hemoglobin. 196 J. Watson, M. Wilkins, and F. Cick in Medicine fo the stuctue of DNA A. McLeod Comack and G. Newbold Hounsfield in Medicine fo computed axial tomogaphy K. M. Siegbahn in Physics fo high esolution electon spectoscopy H. Hauptman and J. Kale in Chemisty fo diect methods to detemine x-ay stuctues J. Deisenhofe, R. Hube, and H. Michel in Chemisty fo the stuctues of poteins that ae cucial to photosynthesis.
7 Light, X-ays and Neutons Light, X-ays log E n X log! J. Teixiea LLB Saclay
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10 Fo neutons both, wavelength and enegy match typical distances and enegy of atoms in condensed matte systems!
11 Bightness & Fluxes fo Neuton & X-Ray Souces Bightness de/e Divegence Flux! 1!! 1 1! ( s m ste (% ( mad ( s! m Neutons ! Rotating Anode ! !10 Bending Magnet ! 5 5!10 Undulato (APS !
12 Why Synchotonadiation? Intensity!!!
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15 d! Scatteing Geomety Incident Radiation : k " Vecto : k i k i = # /$ Enegy : Polaization : E i p i Wavevecto q = k " k i f Enegy Tansfe : # E = E Polaization : p! p f f i " E i " Tansfe : = h$ Scatteed Radiation : k " Vecto : k f Enegy : Polaization : Fo X - Rays : # E << Ef, Ei " q = k i E f p f sin(! /
16 Fo neuton scatteing the momentum tansfe depends on the scatteing angle and the enegy tansfe 5 q / k θ = 0 o θ = ±90 o θ = ±180 o q = k 0 hω / E 0 ω 1 ω cos θ. E 0 E 0 G. Knelle, HERCULES 004
17 Diffeential scatteing coss section
18 Intinsic Coss Section k f k i 0 at Scatteing Cente = 0 i i i ( d d e ( e e f i i! = " # $ % & '!! + ( f f k k k * Plane Wave Plane & Spheical Wave! " "! " # # # $ $ d d sin, ( d d d Coss Section : Total %% %% = & ' ( * +, & = f
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20 & $ % ( #! d' " d 0 Intinsic Coss Section: Neutons = b = const.
21 0 0 0 in ad ( cos (1 1 d d ( ( (, (! " # $ #! " R f P R E t R E + = % & ' ( * + + = = Intinsic Coss Section: X-Rays 0 d d!" # $ % & ' (!! !" " " " " # i ( $ $ = Resonance Scatteing!! " Thomson Scatteing P 0 0 d d =! " # $ % & ' ( >> * * 4 "! Rayleigh Scatteing
22 Adding up phases at the detecto of the wavelets scatteed fom all the scatteing centes in the sample:
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24 Coheent Pat
25 X-ays d! = 0 [1 + Cos ("] S(q d# S(q = $% ij exp[-iq.( i - j ]& { i } == electon positions.
26 Now,! i exp[-iq.r i ] = " N (q Fouie Tansfom of nuclea density [ sometimes also efeed to as F(q ] Poof: " N ( =! i #( - R i " N (q =! " N ( exp[-iq.] d =!! i #( - R i exp[-iq.] d Similaly, =! i exp[-iq.r i ]! i exp[-iq. i ] = " el (q Fouie Tansfom of electon density So, fo neutons, S(q = $ " N (q " N* (q % And, fo x-ays, S(q = $ " el (q " el* (q %
27 If electons ae bound to atoms centeed on nuclei at R i! el ( = " i f el ( - R i! el (q =! d exp[-iq.] " i f el ( - R i = " i {! d exp[-iq.(- R i ] f el ( - R i } exp[-iq. R i ] = f(q " i exp[-iq. R i ] = f(q! N (q f(q is called the Atomic Fom Facto
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29 The imaginay pat of the fom facto descibes absoption
30 V e q f q d ( ( i 0! " = # Atomic Fom Facto: ( 0 q f (A -1 q Z q f = = 0 ( 0 0 ( 0 = q "! f ( i ( (, ( '' ' 0!!! h h h f f q f q f + + = Atomic Fom Facto with Dispesion Coections:
31 Scatteing Length of a Molecule q = k! k f i k i k f Molecule with N Atoms 3 F mol. ( q = N # j=1 f ( q e -i q " j j 1 1
32 Example: CF4 - Molecule 1 FMo (q FCF4 (q 4 3 FCF4 (q FCF4 (q = f C (q + -i q " 1 + f F (q (e + +e -i q " +e -i q " 3 +e -i q " 4 q
33 Liquids and glasses
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35 Moe than one kind of atom
36 Cystals
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38 1 c * c * 3 c * c ( a a V a a a V a a a V a a a a V! =! =! =! " = # # # Recipocal Lattice: Real Recipocal
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42 Ewald-Constuction q kf ki q kf ki ki kint kf Laue Patten of BeylliumAluminumSilicate ( "Beyl"
43 Elastic Scatteing fom a Cystal Diffeential Scatteing Coss Section d( d' = & $ % d( d' #! " Intinsic Coss Section Coupling Beam! Sample 0 S( q Popeties of the Sample without Beam S ( q = F ( q cystal
44 F cystal ( q = $ N f ( q e -i q " # & j j % j=1 Unit Cell Stuctue Facto M e -i q " R ' # n $ M >>1 fo ( n=1 a Recipocal Lattice: i G Rn = *! aj = Ghkl! R hkl n n 1 1 "# = ha = a + ij * 1 n " (hn a 1 0 othewise i, j + ka n = 1,,3 * + la * + + kn 3 a ln 3 ' $ M " &# e-i ( % n=1 q " R n Lattice Sum ' ( q " R = % & intege n Laue Condition q = G hkl
45 Scatteing fom a Cystal a Bagg's Law: m" = d sin! a1 N M # & # i q'j & i q ' Rn $! Fcystal (q = $ ( f j (q e! ' $ ( e! " % j=1 " % n =1 Unit Cell Stuctue Facto Fuc( q Lattice Sum
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47 The Measued Intensity fom a Cystallite ' % & d( $ " = d! # ' % & d* d( Numbe of $ " # = Thomson Scatteing of an Electon Photons Scatteed pe Second into d! (Incident Flux (d! P F ( q MV * ( q! G 0 hkl c Stuctue Facto of the Unit Cell Numbe of Unit Cells hkl Recipocal Space Unit Cell Volume
48 Pulsed Laue Diffaction Patten fom the PhotoActive Yellow Potein: 10 Exposues of 100 ps 3700 Reflections with Fhkl(q STRUCTURE M. Wulff ( ESRF B. Peman ( Univ. of Chicago
49 Synchotonand Neuton Scatteing Places
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