Neutron Scattering

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10.3 Inverted TOF-spectrometer In the spectrometer types described above the sample was "illuminated" by pulses of neutrons with a single defined wavelength (velocity which have been prepared by a choppermonochromator combination . The analysis of the velocities of the scattered neutrons was effected by TOF-measurement . It is also possible to invert this sequence, the incoming velocity (i .e . wavelength, energy, k) is determined by the TOF between chopper (pulsed source) and sample . Then -to obtain a defined energy and momentum transfer- only scattered neutrons of a given final wavelength that may pass an analyzer are detected . 1111III M/F 1 1 1 1 1 1' LLU 1 4 -~ Probe Zeit Figure 10 .11 : Path-time diagram of a TOF spectrometer with inverted geometry . The corresponding path-time diagram is displayed in figure 10 .11 . Neutrons emerging the pulsed source fly according to their individual velocity in direction of the Sample, 10- 17
the associated paths are indicated by the grey triangle . The intensity within the range of this triangle is of course not uniform but depends on the spectral properties of the source . s Neutrons that have been elastically scattered by the Sample (path 2) pass the analyzer/filter M/F and lead to the elastic line in the TOF-histogram . Neutrons that loose energy (path 1) are faster before the Sample scattering and arrive earlier at the detector than the elastically scattered ones . Analogously path 3 represents neutrons that gained energy during scattering . Compared to a "normal" TOF instrument the energy gain and energy loss sides of the histogram are reversed . Therefore also high energy excitations that are thermally not occupied may be measured . (Spallationstarget) Chopper Figure 10 .12 : Setup of a TOF spectrometer with inverted geometry. Figure 10 .12 shows a corresponding setup . The pulse at the chopper contains neutrons from a broad velocity distribution (Maxwellian spectrum at moderator temperature) . During the path from chopper (pulsed source) to Sample this pulse separates into different wavelengths A, resp . different incident energies, that arrive ai different times ai the sample . Since a wavelength selection (to Ao) is performed between Sample and detectors, all detected neutrons have the saine velocity and the distance Sample-detector adds a a In particular overlap of the triangles ( "frame overlap") may lzappen, wlziclz may be suppressed by filters tayloring tlze incoming spectrum . 10- 18
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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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Page 177 and 178: figure and with neutrons of about 1
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Page 181 and 182: tails. This reflection curve leads
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Page 185 and 186: I The rotor of a velocity selector
Page 187 and 188: multiplier are arranged in a quadra
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Page 192 and 193: machine which will be followed by a
Page 194 and 195: 10 .3 Beaur shaping Due to the fact
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Page 202 and 203: Fig . 14) Dispersion surfaces for B
Page 204 and 205: whereby E and v,, denote energy and
Page 206: [1] B . N. Brockhouse, in Inelastic
Page 210 and 211: 10 . Time-of-flight spectrometers M
Page 212 and 213: Tnloderator /K V7 2/m/s A/nm Aiw/eV
Page 214 and 215: 10.2 .1 Interpretation of spectra A
Page 216 and 217: ----~ Probe ' (Chopper 2) Zeit I Ch
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Page 222 and 223: 10.2 .6 Crystal monochromators The
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Page 232: Contents 10 .1 Introduction . . . .
Page 236 and 237: 11 . Neutron spin-echo spectrometer
Page 238 and 239: 2 0 L Tr -0 L 2 ArDet Figure 11 .1
Page 240 and 241: initial velocity-reassemble at the
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Page 250 and 251: nel" coils) the required homogeneit
Page 252 and 253: Figure 11 .9 : S(Q, t)IS(Q) of a 2
Page 254: Contents 11 .1 Introduction . . . .
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Page 260 and 261: Important: Thc measured Bragg inten
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Page 264 and 265: The knowledge of the overall occupa
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Page 268 and 269: Fig . 4 . Coordination ofthe D20 mo
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Page 274: 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
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Here, J;j denotes the exchange cons
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Fig. 16.8 : Contour plot of the mag
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0.0001 0.001 0 .01 0.1 2 Fig. 16 .1
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17 Translation and Rotation M . Pra
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17.1 Introduction Atomic and molecu
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17 .2.2 Diffusion, microscopic appr
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0.6 H20 2 x2tÄ z ) Figure 17 .2 :
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The scattering function of a polycr
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e (2) 1 (j 1, 0 > - 0,1 >), respect
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leads to the eigenvalue problem ~q
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allow a good determination of the E
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m Eu W Figure 17 .7 : Eigenenergies
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-so o so Energy transfer (NeV) Ener
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Bibliography [1] T. Springer, Quasi
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18 . Texture in Materials and Earth
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Further important structure related
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The axes of the cartesian Kp coordi
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4.0 Experimental Texture Analysis T
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Fig. 18.14: Variation of reflection
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measurements can be performed in tr
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Apart from the global description o
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In the following, two experimental
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The neutron diffraction pole figure
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dependent pole densities, and (4) g
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Schriften des Forschungszentrums J
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Forschungszentrum Jülich in der He
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Neutron Scattering

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