C 1'~> }-C'CC re ~ CH9700070 PSI Proceedings 96-01 PAUL SCHERRER INSTITUT Oktober 1996 ISSN 1019-6447 — — J s Introduction to Neutron Scattering Lecture Notes of the Introductory Course 1st European Conference on Neutron Scattering (ECNS '96) Interlaken, Switzerland October 6-11, 1996 VOL n 0 PSI-Proceedings 96-01 Oktober1996 ISSN 1019-6447 Introduction to Neutron Scattering Lecture Notes of the Introductory Course 1st European Conference on Neutron Scattering (ECNS '96) Interlaken, Switzerland October 6-11, 1996 edited by Albert Furrer Paul Scherrer Institut, 1996 Villigen, Switzerland HIXT !©f t BLANK Organization of the Conference Conference Chairman: A. Furrer (ETH Zurich / PSI Villigen) Organizing Committee: Chairman: A. Furrer (ETH Zurich / PSI Villigen) Scientific Secretary: J. Mesot (PSI Villigen) Treasurer: W. Buhrer(ETH Zurich / PSI Villigen) Proceedings Editors: G.Bauer (PSI Villigen) P. Boni (PSI Villigen) P. Fischer (ETH Zurich / PSI Villigen) Exhibition: W. Wagner (PSI Villigen) Public Relations: M. Salzmann (PSI Villigen) Transports: J. ScheferfPSI Villigen) Visit to SINQ: J. Duppich (PSI Villigen) Introductory Course & Controller P. Allenspach (PSI Villigen) Assessors: W. Fischer (PSI Villigen) H.U. Gudel (University of Berne) K. Yvon (University of Geneva) Administrative Secretaries: ft Bercher(PSI Villigen) D. Castellazzi (ETH Zurich / PSI Villigen) Chairman of the Introductory Course: P. Allenspach (PSI Villigen) International Programme Committee: Chairman: D. Richter (Julich) Members: V. Aksenov (Dubna), F. Barocchi (Florence), J.A.C. Bland (Cambridge), J. Colmenero (San Sebastian), R. Cywinski (St Andrews), A. Furrer (ZurichA/illigen), L de Graaf (Delft), B. Lebech (Riso), F. Mezei (Beriin), Ch. de Novion (Saclay), H. Rauch (Vienna), LP. Regnautt (Grenoble), L Rosta (Budapest), E. Sackmann (Munich), ft Scherm (Grenoble), A.D. Taylor (Didcot), L.M. Torell (Gothenburg), R. Vacher (Montpellier), R. Wagner (Geesthacht) ENSA Committee: Chairman: D. Richter (Germany) Vice-Chairman: A. Furrer (Switzeriand) Secretary: ft Cywinski (United Kingdom) Members: F. Barocchi (Italy), F.J. Bermejo (Spain), L Borjesson (Sweden), L de Graaf (Netherlands), B. Lebech (Denmark), L Rosta (Hungary), ft Vacher (France), G. Vogl (Austria) Observers: V. Aksenov (Russia), J.P. Gaspard (Belgium), O. Steinsvoll (Norway), C.J. Cariile (RAL), Ch. de Novion (LLB), J.L Finney (ESS), H.U. Karow(ESF), ft Scherm (ILL), M. Schuster (AUSTRON), M. Steiner(HMI) Foreword When the ENSA Committee thought about the organization of the 1st European Conference on Neutron Scattering, it was clear from the beginning that ECNS'96 should aim for attracting particularly the young generation of scientists, the decision makers of the future. The Organizing Committee of ECNS'96 has therefore devoted a particular effort to encourage and facilitate the participation of young scientists through several measures (low registration fee, convenient accommodation rates, 100 young scientists grants, attention to their scientific work by providing 11 young scientists awards). Being aware of the fact that young scientists usually have little or no knowledge of the field of neutron scattering - as most of them are casual users at neutron sources, it was decided to hold an Introductory Course before ECNS'96 in order to provide the basic concepts which in turn will help to digest the more specialized presentations of the Conference. More specifically, the aim of the Introductory Course was fourfold: • To learn the basic principles of neutron scattering; • To get introduced into the most important classes of neutron scattering instruments; • To learn concepts and their transformation into neutron scattering experiments in various fields of condensed matter research; • To recognize the limitations of the neutron scattering technique as well as to see the complementarity of other methods. The present Proceedings contain the key topics in neutron scattering. The relevant issues are thoroughly introduced, theoretically and methodically discussed, and highlighted with experimental results by acknowledged experts. I am extremely grateful to all the speakers who prepared their lecture notes for these Proceedings. They have done an excellent job in providing concise, though comprehensive reviews in their fields of expertise, for the benefit of the 120 young participants attending the Introductory Course of ECNS'96. Villigen, September 1996 Albert Furrer UEXT PAQEIS) left BLANK Contents Organization of the Conference 3 Foreword 5 A. Furrer Table of Contents 7 1. Fundamentals of Neutron Scattering by Condensed Matter 9 ft Scherm 2. Instruments 33 WilliBuhrer 3. Neutron Diffraction 52 G. Heger 4. Excitations 69 Bruno Dorner 5. Critical Scattering 86 W.G. Stirling and S.C. Perry 6. Quasieiastic Neutron Scattering Study of Large Amplitude Motions in Molecular Systems 103 M.Bee 7. Neutron Scattering in Liquids 113 Fabrizio Barocchi 8. Diffuse Scattering 129 Gernot Kostorz 9. Small Angle Scattering and Polymers 144 J.P. Cotton 10. Small-Angle Neutron Scattering in Materials Science - An Introduction 162 Peter Fratzl tef tBLANK CH9700071 FUNDAMENTALS OF NEUTRON SCATTERING BY CONDENSED MATTER R. SCHERM Institut Max von Laue-Paul Langevin, Grenoble The following text is copied from an article in Annales de Physique 1972, tome 7, n° 5, pp. 349-370. It is part of a series of lectures given 1972 at a schummer school at Autrans. Why rewrite? While the technique and applications of neutron scattering have made gigantic progress in these 24 years, the fundamental theoretical basis is still valid. Today in 1996, the SI system is en vogue, numbers are more precise and some statements have to be commented. # 1 Table 1: SI units and more precise: lmeV= 1.602189 xlO-22J 1 meV corresponds to T = 11.60450 K v = 0.241797 x 1012 Hz v/c= 8.06548 cm-1 k = .6947 A-l = 6.947 nm v = 437 m/s X = 9.04 A = 0.904 nm # 2 Today in 1996, synchrotron radiation has revolutionized X-ray techniques. They can see magnetic structures. Inelastic X-ray specrroscopy does exist and has reached resolutions of 3 meV. # 3 flux = [n/area s] current = [n/s] # 4 For cross sections and scattering lengths see Sears and Scherm in Kohlrausch "Praktische Physik", Vol. 3, p. 544, http://www.ne.uiuc.edu/n-scatter/n-lengths # 5 Literature: still the most concise: Squires G.L. "Introduction to the Theory of Thermal Neutron Scattering", Cambridge Univ. Press, London, 1978 10 Ann. Pbys., 1972, t. 7, pp. 549-570 INSTITUT PAUL-LANGEVIX Ctdex tfi i;6 — F }t - Grenoble FUNDAMENTALS OF NEUTRON SCATTERING BY CONDENSED MATTER By R. SCHERM ABSTRACT RESUME The purpose of this introductory lecture is to give the Les principes de la diffusion dcs neutrons basic facts about the scattering of neutrons by condensed par la matiere condensee matter. This lecture is restricted to nuclear scattering. whereas magnetic scattering will be dealt with in the follow- Le but de cette introduction est de donner les principes ing course. Most of the formalism however, can also be de base de la diffusion des neutrons par la matiere conden- easily extended to magnetic scattering. see. Ce cours se limite i la diffusion nucleaire. tandis que la diffusion magnetique sera traitee dans le cours suivant. La plus grande partie du formalisme peut aussi s'adapter facilement a la diffusion magnetique. 1. — INTRODUCTION Neutrons are particles with the following properties: Instead of k we will often find: :a rrkrk2 mass: m = 1.660.10~ g Energy 1 2m spin :-, momentum p = hk magnetic moment: /i = — 1.913 nuclear magnetons. (1.1) velocity The state of a neutron is described by its wave- m In vector k and its spin component S. = + -. wavelength k 11 550 R. SCHERM Ami. Pbjs., 1972, t. 7, n° 5 Table I gives a list of conversion factors for these You might check that the dashed pair k'ok't gives the quantities. same y. and ii<a. TABLE I Conversion factors. Energy E temperature T : A-.T - E [*K1 : frequency CO fttd - E Irad/scc] V V [Hz] " 2Jt optical I" [cm-'J 1 wave-number c ' j neutron : 1 . 1 : wave-number k = E fA- ] Fie. !. — The « k rector triangle ». ! velocity V >" . « E fm/sccj k , k\ are the momenta of the incoming at scattered neutron ; 2n 0 wave-lcngih }. A * k y. = momentum transferred to the sample. 1 meV corresponds to I.6OI9 JO"11 erg / 0.02305 kcal'molc \ E 11.605 K T 1 We call positive y energy loss processes corres- j 1.52 .10" rad/scc co '•• ~ E ponding to the creation of an excitation like a phonon 0.242 .10" Hz 1 '• I | S.066 cm- vie \ or a magnon of energy hu and quasimomentum fix. ; 0.4S3 A"= k'- 1 The inverse process is cu < 0, /. e. energy gain = anni- 0.695 A"1 hilation of an excitation. 43S "r\~ VI m/scc Figure 2 is particularly useful for time of flight 9.04 A • ^ 1 measurements, lc shows for fixed k0 and fixed scattering Vi 1 angle <j> the energy transfer fico and the modulus | hy. \ corresponding to various | A-, |. 1.1. Kinematics of scattering creation annihilation neutron looses gains Quite generally one could try to describe neutron IK! scattering by giving the exact fate of a neutron O)=1^ " impinging on an oriented sample with wave-vector k0 and emerging with wave-vector k,. Note that the modulus as well as ihe direction of /t, may be different 90^. from A:o. That means we have 6 variables. It will turn out to be completly sufficient to know the cross-section for a certain momentum-transfer hy. and energy- transfer hw. These are per. def. momentum transfer ; y. = k0 — k, (1.2) energy transfer ho — — (kl — k\) (1.3) FIG. 2. — Kinematics t>(| y. j) for fixed k0. The « k vector triangle » is illustrated in figure I. <p = scattering angle. 12 Ann. Pijs., 1972, t. 7, n° 5 FUNDAMENTALS OF NEUTRON" SCATTERING BY CONDENSED MATTER 1.2.