Neutron Scattering

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Schriften des Forschungszentrums Jülich . Reihe Materie und Material : 1 . Physik der Nanostrukturen Vorlesungsmanuskripte des 29 . IFF-Ferienkurses vom 9 . bis 20 .3.1998 (1998), ca . 1000 Seiten ISBN 3-89336-217-7 2 . Magnetische Schichtsysteme Vorlesungsmanuskripte des 30 . IFF-Ferienkurses vom 1 . bis 12 .3.1999 (1999), ca . 1300 Seiten, zahlreiche z.T. farb . Abb. ISBN 3-89336-235-5 3 . Femtosekunden und Nano-eV : Dynamik in kondensierter Materie Vorlesungsmanuskripte des 31 . IFF-Ferienkurses vom 13 . bis 24 .3.2000 (2000), ca . 1000 Seiten, zahlreiche z . T. farb . Abb . ISBN 3-89336-205-3 (Hardcover) 4 . Massenspektrometrische Verfahren der Elementspurenanalyse Kurzfassungen der Vorträge und Poster des 5 . Symposiums und des 12 . ICP-MS-Anwendertreffens vom 18 . bis 21 . September 2000 in Jülich zusammengestellt von HA . Dietze, J . S . Becker (2000), xvi, 109 Seiten ISBN 3-89336-267-3 5 . Neutron Scattering Lectures of the Laboratory Course held at the Forschungszentrum Jülich from 26 September to 6 October 2000 herausgegeben von Th . Brückel, G . Heger, D. Richter (2000), 382 pages ISBN 3-89336-269-X 6 . Baryon Excitations Lectures of the COSY Workshop held at the Forschungszentrum Jülich from 2 to3 May 2000 edited by T. Barnes and H .-P. Morsch (2000), 203 pages ISBN 3-89336-273-8 7 . Neue Materialien für die Informationstechnik Vorlesungsmanuskripte des 32 . IFF-Ferienkurses vom 05 . bis 16.03.2001 herausgegeben von R . Waser (2001), ca . 1200 Seiten, zahlreiche z . T. farb . Abb . ISBN 3-89336-279-7 B . Deutsche Neutronenstreutagung 2001 Kurzfassungen der Vorträge und Poster der Deutschen Neutronenstreutagung 2001 vom 19 . bis 21 . Februar 2001 in Jülich zusammengestellt von Th . Brückel (2001), xvi, 186 Seiten ISBN 3-89336-280-0
Schriften des Forschungszentrums Jülich . Reihe Materie und Material : 9 . Neutron Scattering Lectures of the 5th Laboratory Course held at the Forschungszentrum Jülich from 18 September to 28 September 2001 edited by Th . Brückel, G . Heger, D. Richter, R . Zorn (2001), 418 pages ISBN 3-89336-288-6 10 . Soft Matter. Complex Materials on Mesoscopic Scales Lecture manuscripts of the 33rd IFF winter school on March 04 - 14 2002 edited by J . K . G . Dhont, G . Gompper, D . Richter (2002), c . 1000 pages, many partly coloured illustrations ISBN 3-89336-297-5 (Hardcover) 11 . Proceedings of the symposium on threshold meson production in pp and pd interaction Extended COSY-1 1 Collaboration Meeting Cracow, 20 - 24 June 2001 edited by P Moskal, M . Wolke (2002), 274 pages ISBN 3-89336-307-6 12 . Polarized Neutron Scattering Lectures of the 1 st Summer School held at the Forschungszentrum Jülich from 10 to 14 September 2002 edited by Th . Brückel, W. Schweika (2002), 360 pages ISBN 3-89336-314-9 13 . Beam Cooling and Related Topics 255th International WE-Heraeus-Seminar, Bad Honnef, May 13 - 18, 2001 Proceedings edited by D. Prasuhn (2002), PDF-Datei auf CD ISBN 3-89336-316-5 14 . Fundamentals of Nanoelectronics 34th Spring School of the Department of Solid State Research, 10 - 21 March 2003, Jülich, Germany edited by S. Bluegel, M . Luysberg, K . Urban, R . Waser (2003), c . 1000 pages ISBN 3-89336-319-X (Hardcover) 15 . Neutron Scattering Lectures of the Laboratory Course held at the Forschungszentrum Jülich edited by Th . Brückel, G . Heger, D. Richter, R . Zorn (2003), 375 pages new revised edition from Materie und Material/Matter and Materials Vol . 9 ISBN 3-89336-324-6
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Forschungszentrum Jülich in der He
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Forschungszentrum Jülich GmbH Inst
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Contents . . 1 Neutron Sources H .
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1 . Neutron Sources Harald Conrad 1
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d) f, = v a, , q - ti = P a, - 0 .3
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Period Example Flux (D [1013 1950-6
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In stage 1 the primary proton knock
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get as heat, the rest is transporte
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down power and stronger absorption
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Appendix Neutron Sources - an overv
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led remotely. It is rauch more conv
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2 . Properties of the neutron, elem
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In the 60's the ferst high flux rea
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Hot neutrons in reactors are obtain
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elated values for the FRJ-2 reactor
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2 .5 Scattering amplitude and cross
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(A+k2 ) yr = u(Z:) yr V( u~r)= z "
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_du _ mn \2 A2-~2z r2~ I(k' IVI k)I
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E ô ô x z w 0 z _w U N Figure 2 .
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scattering is observed with the ave
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For a spherical electron distributi
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A more thorough introduction to neu
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3 . Elastie Seattering from Many-Bo
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Q = Q = k2 + k2 - 2kk' cos2B (3 .3)
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3 .2 Fundamental Scattering Theory
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The meaning of (3 .l4) is immediate
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1 . e. in the second approximation,
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The saure problem will bc dealt wit
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ALQ) = Y-bfe'Q'-rB(r-(n .a+m .b+p»
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du LQ) = ALQJ2 = e'Q .A' . * -i e-
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Tab . 3.1 : The scattering lengths
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We note immediately that we should
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These magnetic structures can be un
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M1LQ)=Q-MQ)xQ M(Q)= IM (r)e i Q " d
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Orbital magnetic spin angular ,,- m
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aQ . r 3 àQ . N . QR . aQ .t k _ML
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Schweika Analysis Polarization W .
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ducing a complex component and were
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ir v s ftft 3956 2 s 2 0.81[X] 80 c
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Some polarizers using Bragg reflect
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Different to the coherent nuclear s
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where QBG denotes the background .
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4 .4 Applications We now consider e
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Fig. 4 .3 .4 probably represents th
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. occur only in the non-spin flip c
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The results for the magnetization d
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a large solid angle with polarizers
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scattering to spin-flip scattering
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An experimental verification of thi
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Correlation Functions Measured by S
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In real liquids however usually an
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The term in big parentheses of equa
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4 0 -5 0 5 10 15 20 ho) [meV] Figur
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Figure 5 .5 : The pair correlation
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Figure 5 .6 : Partial differential
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Then equation (5 .21) can be conver
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The route from expression (5 .27) t
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In addition it is often useful to d
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2 . The pair correlation function h
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G(r, t) G(r, t) i(Q, t) r Q i(Q, t)
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Insertion of this result into (5 .6
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With this example we can also demon
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6. Continuum description : Grazing
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Starting point is the exact atomic
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For specular reflectivity measureme
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v v z l 2r V(z) = 2 -2erfC~ with er
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F{dV(z)/dz ) to calculate the refle
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Equation (6 .13) also shows that th
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ut is completely reflected . The cr
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0.4° . The full dynamical theory c
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1) If no magnetic induction B (whic
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Diffractometer Gernot Heger
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select a special wavelengths band (
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" The direction of the reciprocal l
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Bragg-intensities of single crystal
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monochromator, on the mosaic spread
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complex sample environments, such a
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the diffraction plane) two further
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Small-angle Scattering and Reflecto
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L= (1) ( k ) a e -(k/k T ) 2 Ak (8
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possible neutron wave lengths betwe
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figure and with neutrons of about 1
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1 .0 Danvinkurve 0 .8 0 .6 0 .4 0 .
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tails. This reflection curve leads
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For the Nickel film one gets a thic
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I The rotor of a velocity selector
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multiplier are arranged in a quadra
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9 . Crystal spectrometer : triple-a
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machine which will be followed by a
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10 .3 Beaur shaping Due to the fact
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G.k=zGz . (11) This case is fulfill
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tribution of bisecting planes (ntos
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directions which is exploited for t
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Fig . 14) Dispersion surfaces for B
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whereby E and v,, denote energy and
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[1] B . N. Brockhouse, in Inelastic
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10 . Time-of-flight spectrometers M
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Tnloderator /K V7 2/m/s A/nm Aiw/eV
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10.2 .1 Interpretation of spectra A
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----~ Probe ' (Chopper 2) Zeit I Ch
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the similar intensity distribution
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is performed without Jacobian due t
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10.2 .6 Crystal monochromators The
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larger energy transfers . However i
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10.3 Inverted TOF-spectrometer In t
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constant offset to the TOF . To be
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sample size of cm and a detection p
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Contents 10 .1 Introduction . . . .
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11 . Neutron spin-echo spectrometer
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2 0 L Tr -0 L 2 ArDet Figure 11 .1
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initial velocity-reassemble at the
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distribution (current sheets) that
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esults, where il is an irrelevant c
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10000 - 8000 - co 6000 - C ô 4000-
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e0 oX n .5 1 .0 1 .5 so 0 .0 0 .0 1
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nel" coils) the required homogeneit
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Figure 11 .9 : S(Q, t)IS(Q) of a 2
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Contents 11 .1 Introduction . . . .
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12 . Structure determination G . He
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Important: Thc measured Bragg inten
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determination of accurate atomic pa
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The knowledge of the overall occupa
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(even anharmonic) effects. This com
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Fig . 4 . Coordination ofthe D20 mo
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fenoelectric phase of orthorhombic
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(c) and (d) calculated densities at
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13 Inelastic Neutron Scattering Pho
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Figurel Schematical drawing of a ge
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equilibrium position the atom is in
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s - ' f N .mwn .I )oo K L .~um..un
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esults from the quantum mechanics o
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y absorption . 13 .1 .3 Magnetic in
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Figure 7 The plane in reciprocal sp
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5 100s1 [OSl ] IOSSI [SSS y i 4 0 r
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dynamics of ionic compounds with th
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16 14 12 F.. . 10 ô 8 q 6 cr 4 G.
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21 [ooç 1 " - 19 18 17 16 "" 298 K
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n = v - cap[i(pga . - wt)] (13 .22)
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Y c 3 c Cc E Figure 16 Magnon dispe
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. . 2 H . Bilz and W . Kress, Phono
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14 . Soft Matter : Structure Dietma
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length density of a sample against
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2 P(Q) = 1 ~exp(-Ii - j'6 Q2 ) (14
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fraction. In the region of large Q
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with the partial structure factor S
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and which lead to the scattering cr
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For the intramolecular and intermol
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500 450 -400 U 0 ;, 350 42, 300 s~.
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scaling behavior of the susceptibil
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15 Polymer Dynamics Dieter Richter
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constraints due to the mutual inter
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(15 .3) T ß ( E)=T ô exp E k,T -
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This incoherent approximation does
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10 an 0 2 0 Figure 15.4 : Relaxatio
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In order to test Eq .[15 .9] the re
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Arrhenius temperature dependence wi
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1 3kBT ~ z 2 72 2 p2 a = f2 N2 P =W
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S (Q,t) = 12 fdu exp ~ -u_ (S2Rt) v
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We now use these data, in order to
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c 0 .8 0 .6 00 .055 x 0 .1 110 .14
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small but systematic deviations fro
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S(Q,t) is predicted . Such a platea
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only one single parameter, the tube
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confinement of the relaxation of la
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16 Magnetism Thomas Brückel
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the ground state of metallic magnet
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c~ ~ o 0 `,~i) g',, b o 0 Q! b o 0
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only "sec" this component and not t
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200 ¬ 400 500 600 700 E 3 QI J (h0
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Fie. 16.4: Scattering geometry for
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0 .8 ' D3 ° Stassis 3d spin - - 3d
Page 369 and 370: Here, J;j denotes the exchange cons
Page 371 and 372: Fig. 16.8 : Contour plot of the mag
Page 373 and 374: 0.0001 0.001 0 .01 0.1 2 Fig. 16 .1
Page 376: 17 Translation and Rotation M . Pra
Page 379 and 380: 17.1 Introduction Atomic and molecu
Page 381 and 382: 17 .2.2 Diffusion, microscopic appr
Page 383 and 384: 0.6 H20 2 x2tÄ z ) Figure 17 .2 :
Page 385 and 386: The scattering function of a polycr
Page 387 and 388: e (2) 1 (j 1, 0 > - 0,1 >), respect
Page 389 and 390: leads to the eigenvalue problem ~q
Page 391 and 392: allow a good determination of the E
Page 393 and 394: m Eu W Figure 17 .7 : Eigenenergies
Page 395 and 396: -so o so Energy transfer (NeV) Ener
Page 397 and 398: Bibliography [1] T. Springer, Quasi
Page 400 and 401: 18 . Texture in Materials and Earth
Page 402 and 403: Further important structure related
Page 404 and 405: The axes of the cartesian Kp coordi
Page 406 and 407: 4.0 Experimental Texture Analysis T
Page 408 and 409: Fig. 18.14: Variation of reflection
Page 410 and 411: measurements can be performed in tr
Page 412 and 413: Apart from the global description o
Page 414 and 415: In the following, two experimental
Page 416 and 417: The neutron diffraction pole figure
Page 418 and 419: dependent pole densities, and (4) g
Page 423: Forschungszentrum Jülich in der He
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Neutron Scattering

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