Neutron Scattering

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10.2 .6 Crystal monochromators The monochromator indicated in fig . 10 .2 has the function to select neutrons from a narrow band of velocities (approx . 1%) out of the Maxwellian spectrum of the incoming primary beam . It may be realized by different means . First the crystal monochromator is described . It uses the matter wave properties of the neutrons to select neutrons of a defined wavelength (i .e . velocity) by interference in a crystal lattice (Bragg reflection) . <strong>Neutron</strong>s with a wavelength of A - 2d sin(OA11/2) (10 .13) n are reflected in direction of the sample; here d is the distance of lattice planes of the monochromator crystal (often pyrolytic graphite 002, d = 0.6708nm), n the diffraction order and OAvt the angle of reflection . Le . a simple crystal monochromator rotates the beam direction by Ont ; if the wavelength should be changed the bulky rest of the spectrometer must be rotated around the location of the monochromator crystal. Sec figure 10 .9 in the following section . 7 In addition Eqn . 10 .13 implies that generally several diffraction orders are reflected . To suppress the unwanted orders mainly three methods are used : 1 . Filter : if the desired wavelength A is long enough it is possible to use a block of polycrystalline material (mostly beryllium) which has negligible neutron absorption . The shorter wavelength neutrons are Bragg reflected by some crystallites in the block and removed from the beam direction while the long wavelength neutrons with A > 2d,ax are transmitted with low losses . 2 . Curved slit choppers : by curving the slits of a Fermi chopper it is possible to achieve that the chopper is only transparent for a certain band of neutron velocities . This band may be selected such that only the selected diffraction order is included . 3 . Second (coarse) chopper : by a second (coarse) chopper at seine distance from the main chopper it is possible to select the desired diffraction order via the TOF TThis may be avoided by the use of t%vo crystals in a parallel arrangement . The second crystal performs a reflection that restores the original beam direction and rotation and translation of the crystals in such a "double monochromator" are performed such that the direction and position of the monochromatized beam stays the came for all wavelengths . However this advantage is connected with an intensity loss . More about crystal monochromators may be found in the chapter "Crystal spectrometers" . 10-13
etween the two choppers . See also section TOF-TOF . 10 .2.7 Time focussing It seems unsatisfactory that by a TOF spectrometer ai a continuous source (reactor) only a sinall fraction (1%) of the continuous primary beam is utilized . On the other hand the TOF-analysis correlates the energy resolution with the length of the neutron pulses OT . However there is trick to partly compensate for this correlation and to achieve a multiplication of the intensity without resolution loss (at the elastic line), see fig . 10 .8 . The chopper opening may last longer if there is a correlation between time and wavelength (velocity) of the neutrons during the opening interval such that all neutrons arrive at the saine time at the detector -as indicated in fig . 10 .8 . By this means the elastic line remains Zeit Figure 10 .8 : Path-time diagram, time focussing . narrow but the focussing effect depends on energy transfer and becomes ineffective for 10-14
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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
Page 173 and 174: L= (1) ( k ) a e -(k/k T ) 2 Ak (8
Page 175 and 176: possible neutron wave lengths betwe
Page 177 and 178: figure and with neutrons of about 1
Page 179 and 180: 1 .0 Danvinkurve 0 .8 0 .6 0 .4 0 .
Page 181 and 182: tails. This reflection curve leads
Page 183 and 184: For the Nickel film one gets a thic
Page 185 and 186: I The rotor of a velocity selector
Page 187 and 188: multiplier are arranged in a quadra
Page 190 and 191: 9 . Crystal spectrometer : triple-a
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 198 and 199: tribution of bisecting planes (ntos
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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
Page 218 and 219: the similar intensity distribution
Page 220 and 221: is performed without Jacobian due t
Page 224 and 225: larger energy transfers . However i
Page 226 and 227: 10.3 Inverted TOF-spectrometer In t
Page 228 and 229: constant offset to the TOF . To be
Page 230 and 231: sample size of cm and a detection p
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
Page 242 and 243: distribution (current sheets) that
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Page 248 and 249: e0 oX n .5 1 .0 1 .5 so 0 .0 0 .0 1
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 . . . .
Page 258 and 259: 12 . Structure determination G . He
Page 260 and 261: Important: Thc measured Bragg inten
Page 262 and 263: determination of accurate atomic pa
Page 264 and 265: The knowledge of the overall occupa
Page 266 and 267: (even anharmonic) effects. This com
Page 268 and 269: Fig . 4 . Coordination ofthe D20 mo
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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
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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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