Neutron Scattering

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Contents . . 1 Neutron Sources H . Conrad 2 Properties of the Neutron, Elementary Scattering Processes D . Richter 3 Elastic Scattering from Many-Body Systems Th . Brückel 4 Polarization Analysis w Schweika 5 Correlation Functions Measured by Scattering Experiments R . Zorn D . Richter 6 Continuum Description : Grazing Incidence Neutron Scattering O .H . Seeck 7 Diffractometer G . Heger 8 Small-angle Scattering and Reflectometry D . Schwahn 9 Crystal Spectrometer : Triple-axis and Back-scattering Spectrometer F . Güthoff H . Grimm 10 Time-of Flight Spectrometers M . Monkenbusch 11 Neutron Spin-echo Spectrometer, NSE M . Monkenbusch R . Zorn 12 Structure Determination G . Heger 13 Inelastic Neutron Scattering : Phonons and Magnons M . Braden 14 Soft Matter : Structure D . Schwahn 15 Polymer Dynamics D . Richter 16 Magnetism Th . Brückel 17 Translation and Rotation M . Prager 18 Texture in Materials and Earth Sciences w Schäfer
Page 1 and 2: Forschungszentrum Jülich in der He
Page 4 and 5: Forschungszentrum Jülich GmbH Inst
Page 8: Neutron Sources Harald Conrad
Page 11 and 12: number of neutron sources is descri
Page 13 and 14: ofthe reactor being a point source
Page 15 and 16: If we set aside the costs and ask a
Page 17 and 18: For uranium, which releases neutron
Page 19 and 20: neutron beann channels Fi 1 .5 Sche
Page 21 and 22: For these reasons a pulsed spallati
Page 23 and 24: (p,n)- and (d n)-Reactions Bombardi
Page 26: Properties of the Neutron Elementar
Page 29 and 30: In December 1942 Ferme build his fe
Page 31 and 32: For any practical application the i
Page 33 and 34: Table 2 .1 : Comparison of X-rays a
Page 35 and 36: this way even at a comparatively lo
Page 37 and 38: describes the solid angle dependent
Page 39 and 40: 9 We note one important exception,
Page 41 and 42: Therefore, for any scattering event
Page 43 and 44: Thereby we now also consider the sp
Page 45 and 46: 2 .7 Comparison between X-ray and n
Page 47 and 48: is also named magnetic form factor
Page 50: Elastic Scattering from Many-Body S
Page 53 and 54: Fit. 3 .1 : A sketch of the scatter
Page 55 and 56: A = 1Ps (r) - e'Q 'Yd3r (3 .6) Le.
Page 57 and 58:
k[Ä-1 ]z 0.695 E meV ,,[Ä] 9.0451
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1 ik, r 2rnn fexp(iklr -i"'I) h 2 4
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Under the assumption IRI » ~r 'I ,
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translated pattern coincide for thi
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more periods contribute to coherent
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terni corresponds to thé scatterin
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The most prominent example for nucl
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Fil Schematic illustration of the i
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Here, the magnetic moment ofthe neu
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Fig. 3.10 : For magnetic neutron sc
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Since the scattering amplitude is p
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Here the magnetic form factor write
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4 . Polarization analysis W . Schwe
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40- E¢. 0. or P travel -03 E4- é0
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1'10 tarns 1 MM ~2( Al WIRE (enamel
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It follows that the nuclear scatter
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Therefore the non-spin flip matrix
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corrections for the ideal case can
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ABA (deg ) Figure 4 .7 : Isotopic i
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i Figure 4 .9 : Paramagnetic scatte
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So far we have discussed the nuclea
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With triple axis instruments one ca
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The instrument DNS [15] (see Fig .
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Current methods for complete polari
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References [1] O . Halpern and M.R
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5 . Correlation Functions Measured
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S(Q) rnn =21r/r nn Figure 5 .1 : Sc
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White" neutrons from reactor Sample
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2 0 0 2 4 6 8 10 12 0 (A -1 ) Figur
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where rit denotes the monomer dista
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, TIIIIV~i~.~1111 a" Aj A(t) i ~M ~
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(A(0)A(T» Figure 5 .9 : Simulated
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where we can arbitrarily set ri = r
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With this definition the pair corre
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espectively. The former equation ex
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to a volume V is simply a plane wav
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is the Hamiltonian of a free atom a
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Continuation Description : Grazing
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A straightforward method to investi
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To study the morphology of surfaces
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6.3 Specular Neutron Reflectivity i
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0 z>d d V(z) = 2nh2b,P, / mz =V, :
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Figure 6 .7 : Sonie examples of mon
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6.5 The Regime of the Total Externa
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n, = 1- 8, + i(3, (6.19) The effect
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too small to modulate the intensity
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[9] V . Holt', U. Pietsch, T . Baum
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7 . Diffractometer G . Heger 7 .1 I
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scattered beam behind the sample, t
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In the case of single crystal diffr
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Powder diffraction also may be disc
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For a ADP-powder diffractometer the
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Ili1'i 11111111 i 0Y5 0.76 d spacï
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The influence ofthe primary collima
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8 . Small-angle Scattering and Refl
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8 .3 .1 . Pin-Hole SANS The princip
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determined by the maximum divergenc
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the focusing SANS is known for long
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three times, then one measures a Da
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Figure 8 .12 : Schematic design ofa
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Neutron guides also enable to trans
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into two ionic particles with kinet
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Crystal Spectrometer : Triple-axis
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10 .1 Common features of crystal sp
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undergo appreciable fluctuations .
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Fig. 4) vertical focusing : The gai
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Back to the "bottled" neutrons : in
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Choosing PG or Cu one gets contribu
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scan direction v scan direction dis
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10.5 Back-Scattering Spectrometer I
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After all ttrose constraints on the
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10 Time-of-Flight Spectrometers Mic
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ackscattering-z-spectrometer ; for
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From the thermal spectrum of the ne
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times is performed at the detector
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energy transfers (gains) structures
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is obtained, all constant factors a
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Figure 10 .7 : Disc chopper . 10% t
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etween the two choppers . See also
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10 .2 .8 TOF-TOF : TOF-monochromato
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the associated paths are indicated
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10 .3 .1 Analysis by filters The an
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if an increase in resolution may be
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Neutron Spich-echo Spectrometer, NS
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affecting application are caused by
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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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