Neutron Scattering

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Crystal Spectrometer : Triple-axis and Back-scattering Spectrometer F . Güthoff and H . Grimm
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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
Page 138 and 139: Starting point is the exact atomic
Page 140 and 141: For specular reflectivity measureme
Page 142 and 143: v v z l 2r V(z) = 2 -2erfC~ with er
Page 144 and 145: F{dV(z)/dz ) to calculate the refle
Page 146 and 147: Equation (6 .13) also shows that th
Page 148 and 149: ut is completely reflected . The cr
Page 150 and 151: 0.4° . The full dynamical theory c
Page 152 and 153: 1) If no magnetic induction B (whic
Page 154: Diffractometer Gernot Heger
Page 157 and 158: select a special wavelengths band (
Page 159 and 160: " The direction of the reciprocal l
Page 161 and 162: Bragg-intensities of single crystal
Page 163 and 164: monochromator, on the mosaic spread
Page 165 and 166: complex sample environments, such a
Page 167 and 168: the diffraction plane) two further
Page 170: 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: multiplier are arranged in a quadra
Page 191 and 192: 10 .1 Common features of crystal sp
Page 193 and 194: undergo appreciable fluctuations .
Page 195 and 196: Fig. 4) vertical focusing : The gai
Page 197 and 198: Back to the "bottled" neutrons : in
Page 199 and 200: Choosing PG or Cu one gets contribu
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Page 203 and 204: 10.5 Back-Scattering Spectrometer I
Page 205 and 206: After all ttrose constraints on the
Page 208: 10 Time-of-Flight Spectrometers Mic
Page 211 and 212: ackscattering-z-spectrometer ; for
Page 213 and 214: From the thermal spectrum of the ne
Page 215 and 216: times is performed at the detector
Page 217 and 218: energy transfers (gains) structures
Page 219 and 220: is obtained, all constant factors a
Page 221 and 222: Figure 10 .7 : Disc chopper . 10% t
Page 223 and 224: etween the two choppers . See also
Page 225 and 226: 10 .2 .8 TOF-TOF : TOF-monochromato
Page 227 and 228: the associated paths are indicated
Page 229 and 230: 10 .3 .1 Analysis by filters The an
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Page 234: Neutron Spich-echo Spectrometer, NS
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through one arm of the spectrometer
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direction that gives rise to a new
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11 .3 The detector signal As mentio
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proportional to the current through
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I (Q, t) and the exact symmetry poi
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then additional deactivation of the
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ô 0 .8 0 0 Im 0 .6 X ,a, `RMRXI km
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Many isotopes-especially normal hyd
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12 Structure Determination Gernot H
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Besides of the related seven primit
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fM(H) = Jv Mj(r)-exp[2ni(H-r)]- &r
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12 .3 .1 Example ofcontrast variati
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Fig . 2 . Magnetic phase diagram of
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Fig . 3 . Na2S-9D20 : A partial vie
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Remember: The scattering lengths of
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(3m symmetiy) on crystallographic s
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Textbooks G . E. Bacon, Neutron Dif
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13 . Inelastic neutron scattering :
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(000) Figure 2 Schematic drawing of
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o o o o bo ao Lambda lattice parame
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Tau Figure 5 Scattering triangle co
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e performed in an efficient manner
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1 r x z -- w --Z x E r A -+ L 6 5 _
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1s. - 1 tUMl [cc01 ~ 1 ~ 10 517 if
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Similar branches may induce larger
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Figure 10 Schematic picture of a di
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T>Tc TTc O O O O " O " O 8 8 " " 2
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14 a15spin-wave Magnon- energy the
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Ferromagnetic materials are still o
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; ' . r,°'r, Figure 17 Crystal fie
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14 Soft Matter : Structure Dietmar
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with the macroscopic scattering cro
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The probability that a freely joint
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2.5 2.0 0.0 0.5 1 .0 1 .5 2.0 2.5 3
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Equations (14 .12) and (14 .13) are
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`l ~(Q)- ,"o (D(1-d)VP(Q) dn NA - ~
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with c the volume fraction of polym
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3 .0 ô 2 .5 U 2 .0 O 1 .5 a 1 .0 0
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6 Û ô 4 3 .0 2 .5 ; 0 1 .5 0 .0 0
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[11] D . Schwahn, K . Mortensen, T.
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15 . Polymer Dynamics D. Richter 15
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is the Kohlrausch-William-Watts rel
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Figure 15 .2 : Elastic and inelasti
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S (Q, t) = Sa (Q, t) S ß (Q, t) /
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Fig .15 .6 displays the elastic int
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C 0.8 d 0.6 ô, 0.4 0.2 o I-Ll1 I I
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15.3 .1 Entropie forces - the Rouse
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By means of neutron scattering two
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The pair correlation function arisi
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The dashed line gives the Rouse pre
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Having obtained very good agreement
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2 diameter d . At that time (ze) th
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Figure 15.17 : Dynamic structure fa
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Finally, one may test whether only
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C Theoretieal Work [14] G . Ronca,
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16 Magnetisin Thomas Bi ückel, IFF
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ole, compared to the stronger excha
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16.2 Magnetic Structure Determinati
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The scattering power density can bc
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the magnetisation density of one at
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y r f R(Q)- (du /dS2) ++ - u a b z1
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fluctuate in space and time . A pha
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same and do not depend on the detai
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Figures 16 .10 and 16.11 show the m
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temperature superconductors, or exc
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Chapter 17 Translation and Rotation
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(T2 is related to the mean square d
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Figure 17 .1 : Mean square displace
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site with possible neighbour sites
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decreased barrier increases the pro
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17 .3 Rotation Molecules represent
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,~ 1 = 0 represents the totally sym
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The Id rotor : solution based on 'f
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The Id rotor : pocket state formali
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Each new model of coupled motion re
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18 Texture in Materials and Earth S
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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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