Neutron Scattering

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0.4° . The full dynamical theory can only be deduced for the specular reflectivity. For the diffuse scattering no exact solution exist right now . 6.6 Important Applications of <strong>Neutron</strong> Reflectrometry For many standard scattering experiments on layer systems x-rays are much more suitable than neutrons because of the higher flux, the better collimation and the less divergence . In numbers : A standard synchrotron radiation source bas a primary beam intensity of about 10' ° counts/sec at a typical spot size of (0.2x1)mm2 . The beam divergence which determines the Q- space resolution is less than 1/100 of a degree . For a modern neutron source one gets less than 10 7 counts/sec in an area of (0.5x20)mm2 with a divergence of larger than 0 .02° . However, for some topics of research neutron scattering is superior . One example is the investigation of materials which mainly contain hydrogen, carbon, nitrogen or oxygen such as organic molecules . In this case the electron density [which for x-rays replaces the potentiel V(r)] is very low and the x-ray contrast becomes very small. In contrast, for neutron V(r) strongly depends on the isotope of the elements . Therefore, by using deuterated or hydrogenated organic materials the scattering contrast can easily be tuned without changing the chemical properties of the semples . Figure 6.11 shows an example of apolymer bilayer. h-PS 12 10 ö s 6 rn 4 0 50 100 150 200 250 300 Figure 6 .11 : Comperison of an x-ray (left column) and a neutron (right column) reflectivity of a polymer bilayer (210Â polystyrene [PSI on 70Â deuterated polyvinylpyrridine [d-P2VP] on a sifcon z ra1 substrate) . The x-ray contrast between the two polymes given by the electron density lis only about 5% . 0.10 0,15 020 0 .25 A 30 2 0 .00 0.05 010 015 0.20 0 .25 0.30 0. rß - ' 1 0= rx- ' 1 It can clearly be seen that the x-ray reflectivity only exhibits one signiflcant oscillation period which is due to the whole fihm thickness . The x-ray contrast at the polymer interface is 6 . 15
too small to modulate the intensity. Advanced analyzing methods have to be used to extract the information of the polymer-polymer interface [11] . This is different for neutrons : By deuterating the bottom polymer the contrast is enhanced dramatically. The reflectivity shows separate oscillations : a long period due to the thin d-P2VP film and a short period which is caused by the h-PS film. The analysis is straightforward and usually very reliable . Another very important application is the magnetic neutron scattering . <strong>Neutron</strong>s have a spin of 1/2 which means that they are sensitive to the magnetization ofthe sample . A sketch of a magnetic neutron reflectivity experiment is depicted in Fig. 6.12 . The sample is illuminated with polarized neutrons . The polarization is determined by the direction of the neutron spins with respect to an external fieldH: They are usually either parallel or antiparallel toH. Figure 6.12: Sketch of a neutron reflectivity experiment on a magnetic layer. The spins of the incident neutrons s are oriented parallel (either up or down) to an external field H. After the scattering the direction of the spins s' may have flipped depending on B which is given by the magnetization of thefilm and H . After the scattering process the spin direction of the neutrons may have flipped. Thus, four différent reflectivities can be measured : " R++ : The spins ofthé incident neutrons are parallel to H. The spins of thé scattered neutrons are also parallel toH (non-spin-flip process) . " R__ : The spins of thé incident neutrons are antiparallel to H. The spins of thé scattered neutrons are also antiparallel toH (non-spin-flip process) . " R+ _ : The spins of thé incident neutrons are parallel to H. The spins of thé scattered neutrons are antiparallel to H (spin-flip process). " R_+ : The spins of thé incident neutrons are antiparallel to H. The spins of thé scattered neutrons are parallel toH (spin-flip process) . The four reflectivities can be deduced from thé Schrödinger equation considering thé external field, thé magnetization of thé sample and thé spin direction of thé neutrons [12] . In thé following only some qualitative descriptions are given . 6 . 16
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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
Page 99 and 100: The results for the magnetization d
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Page 103 and 104: scattering to spin-flip scattering
Page 105 and 106: An experimental verification of thi
Page 108: Correlation Functions Measured by S
Page 111 and 112: In real liquids however usually an
Page 113 and 114: The term in big parentheses of equa
Page 115 and 116: 4 0 -5 0 5 10 15 20 ho) [meV] Figur
Page 117 and 118: Figure 5 .5 : The pair correlation
Page 119 and 120: Figure 5 .6 : Partial differential
Page 121 and 122: Then equation (5 .21) can be conver
Page 123 and 124: The route from expression (5 .27) t
Page 125 and 126: In addition it is often useful to d
Page 127 and 128: 2 . The pair correlation function h
Page 129 and 130: G(r, t) G(r, t) i(Q, t) r Q i(Q, t)
Page 131 and 132: Insertion of this result into (5 .6
Page 133 and 134: With this example we can also demon
Page 136 and 137: 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 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 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
Page 196 and 197: G.k=zGz . (11) This case is fulfill
Page 198 and 199: 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
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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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