DOCSLIB.ORG

Electron Microscopy

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Electron Microscopy Electron microscopy 1 Plan 1. De Broglie electron wavelength. 2. Davisson – Germer experiment. 3. Wave-particle dualism. Tonomura experiment. 4. Wave: period, wavelength, mathematical description. 5. Plane, cylindrical, spherical waves. 6. Huygens-Fresnel principle. 7. Scattering: light, X-rays, electrons. 8. Electron scattering. Born approximation. 9. Electron-matter interaction, transmission function. 10. Weak phase object (WPO) approximation. 11. Electron scattering. Elastic and inelastic scattering 12. Electron scattering. Kinematic and dynamic diffraction. 13. Imaging phase objects, under focus, over focus. Transport of intensity equation. 2 Electrons are particles and waves 3 De Broglie wavelength PhD Thesis, 1924: “With every particle of matter with mass m and velocity v a real wave must be associated” h p 2 h mv p mv Ekin eU 2 2meU Louis de Broglie (1892 - 1987) – wavelength h – Planck constant hc eU – electron energy in eV eU eU2 m c2 eU m0 – electron rest mass 0 c – speed of light The Nobel Prize in Physics 1929 was awarded to Prince Louis-Victor Pierre Raymond de Broglie "for his discovery of the wave nature of electrons." 4 De Broigle “Recherches sur la Théorie des Quanta (Researches on the quantum theory)” (1924) Electron wavelength 142 pm 80 keV – 300 keV 5 Davisson – Germer experiment (1923 – 1929) The first direct evidence confirming de Broglie's hypothesis that particles can have wave properties as well 6 C. Davisson, L. H. Germer, "The Scattering of Electrons by a Single Crystal of Nickel" Nature 119(2998), 558 (1927) Davisson – Germer experiment (1923 – 1929) The first direct evidence confirming de Broglie's hypothesis that particles can have wave properties as well Clinton Joseph Davisson (left) and Lester Germer (right) George Paget Thomson Nobel Prize in Physics 1937: Davisson and Thomson 7 C. Davisson, L. H. Germer, "The Scattering of Electrons by a Single Crystal of Nickel" Nature 119(2998), 558 (1927) Wave-particle dualism. Tonomura experiment 8 A. Tonomura et al, Demonstration of single-electron buildup of an interference pattern. Am. J. Phys., 57, 117-120 (1989) Wave: period, wavelength, mathematical description A 2 y x Acos x 9 Plane, cylindrical, spherical waves 1 2U 2U ct22 Search solution in form U r, t u r eikct We obtain equation 22u k u 0 ikr 2 General solution u r A r e k 2 2 2 kr kx x k y y k z z const kr kr k x y z const x2 y 2 z 2 R 2 z k r r y k x 10 Plane, spherical waves Plane wave Spherical wave Surfaces where the phase is constant k 11 Wavefront propagation: Huygens-Fresnel principle expikr r Describes the wavefront propagation: every point on a wavefront is a source of secondary (spherical) wave. These secondary waves spread out in the forward direction, at the same speed as the source wave. 12 Christian Huygens (1629 - 1695), Augustin-Jean Fresnel (1788 - 1827) Scattering 13 Scattering. Light 14 http://www.atmo.arizona.edu/students/courselinks/spring08/atmo336s1/courses/fall13/atmo170a1s3/1S1P_stuff/scattering_of_light/scattering_of_light.html Scattering. X-rays X-rays are scattered by electron clouds 15 http://pd.chem.ucl.ac.uk/pdnn/diff1/scaten.htm Scattering. Electrons Electrons are scattered by potentials 16 https://www.microscopy.ethz.ch/elast.htm Electron-matter interaction 17 Electron scattering. Schrödinger equation Electron is scattered by atomic potential. The corresponding Schrödinger equation: H r E r where 2 H 2 V r . 2m We substitute 2 2 V r r E r 2m and re-write 22 2m k r 2 V r r where 2 2m kE 2 18 Electron scattering. Green functions The solution to this equation can be written in form: 2m r r G r r V r rd r 0 2 0 0 0 0 where 0 r is the solutions of the homogeneous equation 22 kr 0 0 and Gr is a solution of 22 k G r r . are the Green-functions: 1 eikr Gr 4 r For a stationary scattering wave we might choose G r G r 2m r r G r r V r rd r 0 2 0 0 0 0 meik r r0 r r V r rd r 0 2 0 0 0 2 rr 0 19 Electron scattering. Far-field approximation We suppose that scattering potential Vr is localized about , i.e. potential 0 r0 0 drops to zero outside of finite region. It is a typical case for a scattering problem. We would like to calculate the wave function far away from the scattering center. Therefore, we can assume rr0 then we can expand 2 2rr rr rr rr rrrr22 2 rrrr 2 2 1 00 r 0 0 0 0 0 rr2 r r r r r where 00 r a unit-vector, indicating direction of , sometimes called “emission vector” We re-write: meikr r r eikr0 V r r rd r 02 2 r 0 0 0 where we introduced kk 20 Electron scattering. Incident plane wave In the case of scattering of a plane wave ikz 0 r Ae we obtain meikr r Aeikz eikr0 V r rd r 2 2 r 0 0 0 which we can re-write as eikr r Aeikz f , A r Here Ae ikz is the incoming wave eikr A is the outgoing spherical wave (similar to Huygens-Fresnel principle) r f , is the scattering complex-valued amplitude m f,d eikr0 V r r r 2 2 A 0 0 0 21 Electron scattering. Born approximation The scattered wave is given by where m f,d eikr0 V r r r 2 2 A 0 0 0 Note that r 0 is in the integral. Born approximation considers only the first term of series expansion. Let's assume that the potential doesikr not significantly alter the ikz e wave function (weak potentialr approximation) Ae f : , A r ikz0 ik 0 r 0 r0 0 r 0 Ae Ae where k0 kez is the vector in the incident direction. This gives the scattering amplitude in Born approximation which is Fourier transform of potential: m i k k00 r f,d e V r r 2 2 A 00 In Born approximation, the scattering amplitude is Fourier transform of potential.22 Scattering amplitude and cross-section 23 Scattering amplitude and cross-section The scattered wave is given by where is the complex-valued scattering amplitude. eikr r Aeikz f , A The differential cross-section: r d 2 f d f , 24 Scattering amplitude distributions 25 Scattering amplitude as a composition of partial waves The scattered wave is given by where can be approximated as a composition of partial waves: f 2 l 1 f k P cosikr lle r l0 Aeikz f , A 1 r f k eikl ()sin ( k ) llk where are the phase shifts. l ()k f , 26 NIST electron elastic cross-section database 27 Scattering amplitude for carbon (C) 30 keV 50 eV 28 Electron-matter interaction 29 Electron interaction with single atom incident wave exit wave u x, y u', x y u',,, x y u x y t x y atom t x, y ei Vz x, y 2me , V x, y V x , y , z d z - projected potential h2 z 30 Phase of transmission function of single carbon (C) atom at 200 keV 1 Å 0 ... 0.157 rad 31 Phase of transmission function of single tungsten (W) atom at 200 keV 1 Å 0 ... 1.415 rad Not a weak phase object 32 Weak phase object (WPO) approximation incident wave exit wave u x, y u', x y u',,, x y u x y t x y atom i V x, y 2me t x, y e z , V x, y - projected potential h2 z t x, y 1 i Vz x , y - weak phase object approximation 33 Transmission function t x, y ea x,, y e i x y Absorption properties Phase-shifting properties 34 Object phase and phase problem 35 Object phase and phase problem u', x y 2 exit wave: u x, y u',,, x y U X Y U X Y u',,, x y u x y t x y t x, y ea x,, y e i x y Missing wave exit detector Missing phase of the wavefront when intensity is recorded36 Elastic and inelastic scattering 37 Elastic and inelastic scattering of electrons 38 http://web.tiscali.it/barlini/affidabilita/sem/e_tesina/e_primolink.htm Elastic and inelastic scattering of electrons eikr 20 r eikz f i r e Z d 2 f d 39 R. Egerton, “Electron elergy loss spectroscopy in the electron microscope” Inelastic mean free path (IMFP) t I t I0 exp E t – the travelling distance into the solid E) – inelastic mean free path (IMFP), is defined as the distance an electron beam can travel before its intensity decays to 1/e of its initial value 40 M. P. Seah and W. A. Dench, Surface and Interface Analysis 1, 2–11 (1979) R. Egerton, “Electron energy loss spectroscopy in the electron microscope” Kinematic and dynamic diffraction theories Kinematic: single scattering event, neglecting multiple scattering Dynamic: takes multiple scattering events into account 41 Multiple scattering The probability for n scattering events Pn is given by Poisson statistics as [1] n 1 tt Pn exp n!()() E E t – thickness E) – inelastic mean free path, 80 nm for 200 keV [2] 1. R. F. Egerton, Electron Energy-Loss Spectroscopy in the Electron Microscope (book). Section “3.4 Single, Plural, and Multiple Scattering” 2. R. Henderson, “The potential and limitations of neutrons, electrons and X-rays for atomic-resolution microscopy of unstained biological42 molecules," Q.
Load more

Recommended publications
  • Von Richthofen, Einstein and the AGA Estimating Achievement from Fame
    Von Richthofen, Einstein and the AGA Estimating achievement from fame Every schoolboy has heard of Einstein; fewer have heard of Antoine Becquerel; almost nobody has heard of Nils Dalén. Yet they all won Nobel Prizes for Physics. Can we gauge a scientist’s achievements by his or her fame? If so, how? And how do fighter pilots help? Mikhail Simkin and Vwani Roychowdhury look for the linkages. “It was a famous victory.” We instinctively rank the had published. However, in 2001–2002 popular French achievements of great men and women by how famous TV presenters Igor and Grichka Bogdanoff published they are. But is instinct enough? And how exactly does a great man’s fame relate to the greatness of his achieve- ment? Some achievements are easy to quantify. Such is the case with fighter pilots of the First World War. Their achievements can be easily measured and ranked, in terms of their victories – the number of enemy planes they shot down. These aces achieved varying degrees of fame, which have lasted down to the internet age. A few years ago we compared1 the fame of First World War fighter pilot aces (measured in Google hits) with their achievement (measured in victories); and we found that We can estimate fame grows exponentially with achievement. fame from Google; Is the same true in other areas of excellence? Bagrow et al. have studied the relationship between can this tell us 2 achievement and fame for physicists . The relationship Manfred von Richthofen (in cockpit) with members of his so- about actual they found was linear.
    [Show full text]
  • Sculpturing the Electron Wave Function
    Sculpturing the Electron Wave Function Roy Shiloh, Yossi Lereah, Yigal Lilach and Ady Arie Department of Physical Electronics, Fleischman Faculty of Engineering, Tel Aviv University, Tel Aviv 6997801, Israel Coherent electrons such as those in electron microscopes, exhibit wave phenomena and may be described by the paraxial wave equation1. In analogy to light-waves2,3, governed by the same equation, these electrons share many of the fundamental traits and dynamics of photons. Today, spatial manipulation of electron beams is achieved mainly using electrostatic and magnetic fields. Other demonstrations include simple phase-plates4 and holographic masks based on binary diffraction gratings5–8. Altering the spatial profile of the beam may be proven useful in many fields incorporating phase microscopy9,10, electron holography11–14, and electron-matter interactions15. These methods, however, are fundamentally limited due to energy distribution to undesired diffraction orders as well as by their binary construction. Here we present a new method in electron-optics for arbitrarily shaping of electron beams, by precisely controlling an engineered pattern of thicknesses on a thin-membrane, thereby molding the spatial phase of the electron wavefront. Aided by the past decade’s monumental leap in nano-fabrication technology and armed with light- optic’s vast experience and knowledge, one may now spatially manipulate an electron beam’s phase in much the same way light waves are shaped simply by passing them through glass elements such as refractive and diffractive lenses. We show examples of binary and continuous phase-plates and demonstrate the ability to generate arbitrary shapes of the electron wave function using a holographic phase-mask.
    [Show full text]
  • A Brief History of Nuclear Astrophysics
    A BRIEF HISTORY OF NUCLEAR ASTROPHYSICS PART I THE ENERGY OF THE SUN AND STARS Nikos Prantzos Institut d’Astrophysique de Paris Stellar Origin of Energy the Elements Nuclear Astrophysics Astronomy Nuclear Physics Thermodynamics: the energy of the Sun and the age of the Earth 1847 : Robert Julius von Mayer Sun heated by fall of meteors 1854 : Hermann von Helmholtz Gravitational energy of Kant’s contracting protosolar nebula of gas and dust turns into kinetic energy Timescale ~ EGrav/LSun ~ 30 My 1850s : William Thompson (Lord Kelvin) Sun heated at formation from meteorite fall, now « an incadescent liquid mass » cooling Age 10 – 100 My 1859: Charles Darwin Origin of species : Rate of erosion of the Weald valley is 1 inch/century or 22 miles wild (X 1100 feet high) in 300 My Such large Earth ages also required by geologists, like Charles Lyell A gaseous, contracting and heating Sun 푀⊙ Mean solar density : ~1.35 g/cc Sun liquid Incompressible = 4 3 푅 3 ⊙ 1870s: J. Homer Lane ; 1880s :August Ritter : Sun gaseous Compressible As it shrinks, it releases gravitational energy AND it gets hotter Earth Mayer – Kelvin - Helmholtz Helmholtz - Ritter A gaseous, contracting and heating Sun 푀⊙ Mean solar density : ~1.35 g/cc Sun liquid Incompressible = 4 3 푅 3 ⊙ 1870s: J. Homer Lane ; 1880s :August Ritter : Sun gaseous Compressible As it shrinks, it releases gravitational energy AND it gets hotter Earth Mayer – Kelvin - Helmholtz Helmholtz - Ritter A gaseous, contracting and heating Sun 푀⊙ Mean solar density : ~1.35 g/cc Sun liquid Incompressible = 4 3 푅 3 ⊙ 1870s: J.
    [Show full text]
  • Nobel Prizes Social Network
    Nobel prizes social network Marie Skłodowska Curie (Phys.1903, Chem.1911) Nobel prizes social network Henri Becquerel (Phys.1903) Pierre Curie (Phys.1903) = Marie Skłodowska Curie (Phys.1903, Chem.1911) Nobel prizes social network Henri Becquerel (Phys.1903) Pierre Curie (Phys.1903) = Marie Skłodowska Curie (Phys.1903, Chem.1911) Irène Joliot-Curie (Chem.1935) Nobel prizes social network Henri Becquerel (Phys.1903) Pierre Curie (Phys.1903) = Marie Skłodowska Curie (Phys.1903, Chem.1911) Irène Joliot-Curie (Chem.1935) = Frédéric Joliot-Curie (Chem.1935) Nobel prizes social network Henri Becquerel (Phys.1903) Pierre Curie (Phys.1903) = Marie Skłodowska Curie (Phys.1903, Chem.1911) Paul Langevin Irène Joliot-Curie (Chem.1935) = Frédéric Joliot-Curie (Chem.1935) Nobel prizes social network Henri Becquerel (Phys.1903) Pierre Curie (Phys.1903) = Marie Skłodowska Curie (Phys.1903, Chem.1911) Paul Langevin Maurice de Broglie Louis de Broglie (Phys.1929) Irène Joliot-Curie (Chem.1935) = Frédéric Joliot-Curie (Chem.1935) Nobel prizes social network Sir J. J. Thomson (Phys.1906) Henri Becquerel (Phys.1903) Pierre Curie (Phys.1903) = Marie Skłodowska Curie (Phys.1903, Chem.1911) Paul Langevin Maurice de Broglie Louis de Broglie (Phys.1929) Irène Joliot-Curie (Chem.1935) = Frédéric Joliot-Curie (Chem.1935) Nobel prizes social network (more) Sir J. J. Thomson (Phys.1906) Nobel prizes social network (more) Sir J. J. Thomson (Phys.1906) Owen Richardson (Phys.1928) Nobel prizes social network (more) Sir J. J. Thomson (Phys.1906) Owen Richardson (Phys.1928) Clinton Davisson (Phys.1937) Nobel prizes social network (more) Sir J. J. Thomson (Phys.1906) Owen Richardson (Phys.1928) Charlotte Richardson = Clinton Davisson (Phys.1937) Nobel prizes social network (more) Sir J.
    [Show full text]
  • Marischal College
    The Scientific Tourist: Aberdeen Marischal College George P Thomson – Nobel Prize winning physicist Sir George Paget Thomson FRS (1892-1975) was the only son of Sir J. J. Thomson, the Cavendish Professor of Physics who is probably most famous for discovering the existence of the electron and measuring its mass. G. P. Thomson was one of a select group of academics in the University of Aberdeen to be awarded the Nobel Prize. He earned it for his work in the Department of Natural Philosophy at Marischal College during his tenure from 1922-1930. There is now a commemorative plaque in the Marischal College quadrangle. Thomson was a high achieving Trinity College, Cambridge, scholar who graduated in 1913 and was elected Fellow and Lecturer at Corpus Christi College in the following year. He was, though, of the generation whose adult lives were to be shaped by two World Wars and their aftermaths. Thomson spent most of the First World War in France and in the research wing of the Royal Flying Corps. His first book1 came out of this experience and is simply entitled “Applied Aerodynamics”. It is a well-illustrated summary of the lessons of wartime work on the science of aircraft design and operation, underlining the basic physics involved. Upon Thomson’s return to Cambridge he took up research into his father’s long-standing interest of electrical discharges in gases. He brought this interest with him when he came to Aberdeen in 1922 and did much of the work enlarging J. J. Thomson’s “Conduction of Electricity through Gases” into a long awaited 3rd edition that was published in their joint names in 1928.
    [Show full text]
  • Physics 1928 OWEN WILLANS RICHARDSON
    Physics 1928 OWEN WILLANS RICHARDSON <<for his work on the thermionic phenomenon and especially-for the discovery of the law named after him>> Physics 1928 Presentation Speech by Professor C. W. Oseen, Chairman of the Nobel Committee for Physics of the Royal Swedish Academy of Sciences Your Majesty, Your Royal Highnesses, Ladies and Gentlemen. Among the great problems that scientists conducting research in electro- technique are today trying to solve, is that of enabling two men to converse in whatever part of the world each may be. In 1928 things had reached the stage when we could begin to establish telephonic communication between Sweden and North America. On that occasion there was a telephone line of more than 22,000 kilometres in length between Stockholm and New York. From Stockholm, speech was transmitted via Berlin to England by means of a cable and overhead lines; from England by means of wireless to New York; then, via a cable and lines by land, over to Los Angeles and back to New York, and from there by means of a new line to Chicago, returning finally to New York. In spite of the great distance, the words could be heard distinctly and this is explained by the fact that there were no fewer than 166 amplifiers along the line. The principle of construction of an amplifier is very simple. A glowing filament sends out a stream of electrons. When the speech waves reach the amplifier, they oscillate in tune with the sound waves but are weakened. The speech waves are now made to put the stream of electrons in the same state of oscillation as they have themselves.
    [Show full text]
  • (Owen Willans) Richardson
    O. W. (Owen Willans) Richardson: An Inventory of His Papers at the Harry Ransom Center Descriptive Summary Creator: Richardson, O. W. (Owen Willans), 1879-1959 Title: O. W. (Owen Willans) Richardson Papers Dates: 1898-1958 (bulk 1920-1940) Extent: 112 document boxes, 2 oversize boxes (49.04 linear feet), 1 oversize folder (osf), 5 galley folders (gf) Abstract: The papers of Sir O. W. (Owen Willans) Richardson, the Nobel Prize-winning British physicist who pioneered the field of thermionics, contain research materials and drafts of his writings, correspondence, as well as letters and writings from numerous distinguished fellow scientists. Call Number: MS-3522 Language: Primarily English; some works and correspondence written in French, German, or Italian . Note: The Ransom Center gratefully acknowledges the assistance of the Center for History of Physics, American Institute of Physics, which provided funds to support the processing and cataloging of this collection. Access: Open for research Administrative Information Additional The Richardson Papers were microfilmed and are available on 76 Physical Format reels. Each item has a unique identifying number (W-xxxx, L-xxxx, Available: R-xxxx, or M-xxxx) that corresponds to the microfilm. This number was recorded on the file folders housing the papers and can also be found on catalog slips present with each item. Acquisition: Purchase, 1961 (R43, R44) and Gift, 2005 Processed by: Tessa Klink and Joan Sibley, 2014 Repository: The University of Texas at Austin, Harry Ransom Center Richardson, O. W. (Owen Willans), 1879-1959 MS-3522 2 Richardson, O. W. (Owen Willans), 1879-1959 MS-3522 Biographical Sketch The English physicist Owen Willans Richardson, who pioneered the field of thermionics, was also known for his work on photoelectricity, spectroscopy, ultraviolet and X-ray radiation, the electron theory, and quantum theory.
    [Show full text]
  • 1 Electron Diffraction Chez Thomson. Early Responses to Quantum
    Electron diffraction chez Thomson. Early responses to quantum physics in Britain. Jaume Navarro Abstract In 1927, George Paget Thomson, professor at the University of Aberdeen, obtained photographs that he interpreted as evidence for electron diffraction. These photographs were in total agreement with de Broglie’s principle of wave-particle duality, a basic tenet of the new quatum wave mechanics. His experiments were an initially unforeseen spin-off from a project he had started in Cambridge with his father, Joseph John Thomson, on the study of positive rays. This paper addresses the scientific relationship between the Thomsons, father and son, as well as the influence that the institutional milieu of Cambridge had on the early work of the latter. Both Thomsons were trained in the pedagogical tradition of classical physics in the Cambridge Mathematical Tripos, and this certainly influenced their understanding of quantum physics and early quantum mechanics. In this paper, I analyse the responses of both father and son to the photographs of electron diffraction: a confirmation of the existence of the ether in the former, and a partial embrace of some ideas of the new quantum mechanics in the latter. Introduction 1 In the summer of 1922, a young Cambridge physicist applied for the recently vacated chair of Natural Philosophy at the University of Aberdeen. The testimonials he enclosed with the application letter, nine in total, all came from well-established scholars directly related to Cambridge.1 This comes to no surprise if we take into account that the applicant, George Paget Thomson (G.P.), had not only received all his academic training in that university, but had also been born in that town, son of one of the best- known British physicists of his time, and then Master of Trinity College, Joseph John Thomson (J.J.).
    [Show full text]
  • Lsu-Physics Iq Test 3 Strikes You're
    LSU-PHYSICS IQ TEST 3 STRIKES YOU'RE OUT For Physics Block Party on 9 September 2016: This was run where all ~70 people start answering each question, given out one-by-one. Every time a person missed an answer, they made a 'strike'. All was done with the Honor System for answers, plus a fairly liberal statement of what constitutes a correct answer. When the person accumulates three strikes, then they are out of the game. The game continue until only one person was left standing. Actually, there had to be one extra question to decide a tie-break between 2nd and 3rd place. The prizes were: FIRST PLACE: Ravi Rau, selecting an Isaac Newton 'action figure' SECOND PLACE: Juhan Frank, selecting an Albert Einstein action figure THIRD PLACE: Siddhartha Das, winning a Mr. Spock action figure. 1. What is Einstein's equation relating mass and energy? E=mc2 OK, I knew in advance that someone would blurt out the answer loudly, and this did happen. So this was a good question to make sure that the game flowed correctly. 2. What is the short name for the physics paradox depicted on the back of my Physics Department T-shirt? Schroedinger's Cat 3. Give the name of one person new to our Department. This could be staff, student, or professor. There are many answers, for example with the new profs being Tabatha Boyajian, Kristina Launey, Manos Chatzopoulos, and Robert Parks. Many of the people asked 'Can I just use myself?', with the answer being "Sure". 4. What Noble Gas is named after the home planet of Kal-El? Krypton.
    [Show full text]
  • Diffraction of Light Prelab by Dr
    Diffraction of Light Prelab by Dr. Christine P. Cheney, Department of Physics and Astronomy, 401 Nielsen Physics Building, The University of Tennessee, Knoxville, Tennessee 37996-1200 © 2018 by Christine P. Cheney* *All rights are reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage or retrieval system, without the permission in writing from the author. Read the introduction to Diffraction in your lab manual.1 Light is very interesting because it can behave as a wave or as a particle. You will observe both types of properties in the Diffraction of Light lab but will focus on the wave-like properties. (The particle-like properties come from the two light sources, a helium-neon laser and a mercury discharge lamp. The colors of light that these sources emit are discrete colors that have energy E=hn where E is the energy of the light, h is Planck’s constant, and n is the frequency of the light. Each photon of light has energy hn. This aspect of light is particle-like, and you will learn more about the particle-like behavior of light next week in the Photoelectric Effect lab.) Diffraction is used to study materials. The lattice spacing in crystalline materials is very small. For example the lattice spacing of a NaCl crystal is 5.64 Å.2 This small spacing can be used as a diffraction grating for x-rays. X-rays have a wavelength range of 0.01- 10 nm.
    [Show full text]
  • Studying Charged Particle Optics: an Undergraduate Course
    IOP PUBLISHING EUROPEAN JOURNAL OF PHYSICS Eur. J. Phys. 29 (2008) 251–256 doi:10.1088/0143-0807/29/2/007 Studying charged particle optics: an undergraduate course V Ovalle1,DROtomar1,JMPereira2,NFerreira1, RRPinho3 and A C F Santos2,4 1 Instituto de Fisica, Universidade Federal Fluminense, Av. Gal. Milton Tavares de Souza s/n◦. Gragoata,´ Niteroi,´ 24210-346 Rio de Janeiro, Brazil 2 Instituto de Fisica, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, Brazil 3 Departamento de F´ısica–ICE, Universidade Federal de Juiz de Fora, Campus Universitario,´ 36036-900, Juiz de Fora, MG, Brazil E-mail: [email protected] (A C F Santos) Received 23 August 2007, in final form 12 December 2007 Published 17 January 2008 Online at stacks.iop.org/EJP/29/251 Abstract This paper describes some computer-based activities to bring the study of charged particle optics to undergraduate students, to be performed as a part of a one-semester accelerator-based experimental course. The computational simulations were carried out using the commercially available SIMION program. The performance parameters, such as the focal length and P–Q curves are obtained. The three-electrode einzel lens is exemplified here as a study case. Introduction For many decades, physicists have been employing charged particle beams in order to investigate elementary processes in nuclear, atomic and particle physics using accelerators. In addition, many areas such as biology, chemistry, engineering, medicine, etc, have benefited from using beams of ions or electrons so that their phenomenological aspects can be understood. Among all its applications, electron microscopy may be one of the most important practical applications of lenses for charged particles.
    [Show full text]
  • 1 Transport of Charged Particle Beams
    COURSE OUTLINE Final September 30, 2013 CPOTS 2013 CHARGED PARTICLE OPTICS – THEORY AND SIMULATION (CPOTS) Erasmus Intensive Programme Physics Department University of Crete August 15 – 31, 2013 Heraklion, Crete, Greece Participating Institutions and Instructors 1. University of Crete (UoC) Prof. Theo Zouros* (Project coordinator) 2. Afyon Kocatepe University (AKU) Prof. Mevlut Dogan (contact) Dr. Zehra Nur Ӧzer* 3. Selçuk University (SU) Prof. Hamdi Sukur Kilic (contact) 4. Universidad Computense Madrid (UCM) Prof. Genoveva Martinez - Lopez (contact) Pilar Garcés* 5. University of Ioannina (UoI) Prof. Manolis Benis* (contact) 6. Technische Universität Wien (TUW) Prof. Christoph Lemell* 7. Queen’s University Belfast (QUB) Prof. Jason Greenwood* (contact) Louise Belshaw* 8. University of Debrecen (UoD) Prof. Béla Sulik (contact) 9. University of Athens (UoA) Prof. Theo Mertzimekis (contact – was not able to be present) *SIMION user CPOTS 2013 – Erasmus IP August 15 –31, Heraklion, Crete Page 1 COURSE OUTLINE Final September 30, 2013 CPOTS 2013 Medical University of South Carolina Prof. Dan Knapp (guest) General IP rules and participant information Attendance sheet An attendance sheet will be maintained for all lectures and labs for all participants (teachers and students). Teachers 1. Minimum suggested stay at an Erasmus IP including travel both ways: 5 days (as certified by the attendance sheet). 2. Minimum number of suggested lecturing + lab hours at an Erasmus IP: 5 hours(as certified by the attendance sheet). 3. A minimum of two laboratory instructors will be available at every afternoon laboratory session. 4. The instructor in charge of each unit will be responsible for: i) The proper execution of the lectures as described in the work program.
    [Show full text]