Neutron Scattering

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C Theoretieal Work [14] G . Ronca, Frequency spectrum and dynamic correlations of concentrated polymer liquids, J . Chem . Phys . 79, 1031 (1983) [15] A . Chatterjee, R. Loring, Calculation of the dynamic structure factor in polymer melts, J. Chem . Phys . 101, 1595 (1994) [16] J. des Cloizeaux, Dynamic form function of a long polymer constrained by entanglement in a polymer melt, J. Phys . 1 . (France) 3, 1523 (1993) [17] K .S . Schweizer, G. Szamel, Crossover to entangled dynamics in polymer solutions and melts, J. Chem. Phys . 103, 1934 (1995)
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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
Page 301 and 302: . . 2 H . Bilz and W . Kress, Phono
Page 304 and 305: 14 . Soft Matter : Structure Dietma
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Page 308 and 309: 2 P(Q) = 1 ~exp(-Ii - j'6 Q2 ) (14
Page 310 and 311: fraction. In the region of large Q
Page 312 and 313: with the partial structure factor S
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Page 316 and 317: For the intramolecular and intermol
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Page 320 and 321: scaling behavior of the susceptibil
Page 322: 15 Polymer Dynamics Dieter Richter
Page 325 and 326: constraints due to the mutual inter
Page 327 and 328: (15 .3) T ß ( E)=T ô exp E k,T -
Page 329 and 330: This incoherent approximation does
Page 331 and 332: 10 an 0 2 0 Figure 15.4 : Relaxatio
Page 333 and 334: In order to test Eq .[15 .9] the re
Page 335 and 336: Arrhenius temperature dependence wi
Page 337 and 338: 1 3kBT ~ z 2 72 2 p2 a = f2 N2 P =W
Page 339 and 340: S (Q,t) = 12 fdu exp ~ -u_ (S2Rt) v
Page 341 and 342: We now use these data, in order to
Page 343 and 344: c 0 .8 0 .6 00 .055 x 0 .1 110 .14
Page 345 and 346: small but systematic deviations fro
Page 347 and 348: S(Q,t) is predicted . Such a platea
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Page 351: confinement of the relaxation of la
Page 356 and 357: 16 Magnetisin Thomas Bi ückel, IFF
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Page 360 and 361: 16.2 Magnetic Structure Determinati
Page 362 and 363: The scattering power density can bc
Page 364 and 365: the magnetisation density of one at
Page 366 and 367: y r f R(Q)- (du /dS2) ++ - u a b z1
Page 368 and 369: fluctuate in space and time . A pha
Page 370 and 371: same and do not depend on the detai
Page 372 and 373: Figures 16 .10 and 16.11 show the m
Page 374: temperature superconductors, or exc
Page 378 and 379: Chapter 17 Translation and Rotation
Page 380 and 381: (T2 is related to the mean square d
Page 382 and 383: Figure 17 .1 : Mean square displace
Page 384 and 385: site with possible neighbour sites
Page 386 and 387: decreased barrier increases the pro
Page 388 and 389: 17 .3 Rotation Molecules represent
Page 390 and 391: ,~ 1 = 0 represents the totally sym
Page 392 and 393: The Id rotor : solution based on 'f
Page 394 and 395: The Id rotor : pocket state formali
Page 396 and 397: Each new model of coupled motion re
Page 398: 18 Texture in Materials and Earth S
Page 401 and 402: In this contribution, however, we w
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material . Texture is an important
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. . It is convenient to plot these
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Fig . 18 .12 : Examples of crystall
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pole figures require numbers of 104
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5 .1 Pole Figure Inversion The dét
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lization (generation of dislocation
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1990 1994 1996 Fig. 18.23 : Experim
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Quartz HK407 ô m 6 Fig . 20 . . .
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(3) Preferred orientations of the f
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Schriften des Forschungszentrums J
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