Neutron Scattering

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Figure 8 .12 : Schematic design ofa diffractometerfor neutron refectometry . Nickelschicht auf Glas 0.00 0.02 0.04 0.06 0.08 Q = 41r/Ä*sin0 (A') " Messung (HADAS-Reflektometer) Fit : d = 837,5 A ; 6 = 14,5 A ; SQ = 2,08e s A' -------- Simulation : d = 837,5 A ; a = 14,5 A ; SQ = 0 --- Simulation : d = 837,5 A ; a = 0 ; SQ = 0 -- Simulation : nur das Substrat o Messung an der Substratoberflaeche Figure 8 .13 : Curve ofrefectionfrom a Nickel surface measure at the "HADAS" instrument. 8- 1 1
For the Nickel film one gets a thickness of 838 A and a roughness of 15 A . The open dots in Fig . 8 .13 show the reflection from glass alone . One clearly observes a smaller angle of total reflection and a decrease equivalent to the Darwin cuive in Eq. (8 .9) . At relatively small intensities of 10-3 scattering from background becomes visible . One can also study heterogeneities within the surface which are f i . formed by phase separation. In those cases one also observes nonspecular reflection in direction parallel to the surface. 8 .5. Important Elements of Small Angle Scattering and Reflection The most important elements of small angle scattering and reflection are (1) the neutron guides for an effective transport of neutrons, (2) the velocity selector and the perfect single ciystals for monochromatization ofthe neutrons, and (3) the local sensitive detector for a fast detennination of the scattering angle . 8 .5.1. Neutron Guide The phenomenon of total reflection is demonstrated in Fig .8 .13 on a Nickel film . This effect is used to transport neutrons through neutron guides over long distances without much loses . The angle of total reflection is given as o c = ;~ (P / 7L) o .s (8 .11) with the coherent scattering length density p . Natural Nickel is a good choice for coating material in order to have a large angle of total reflection (see Figure 8 .13) ; an even better choice is the isotope Nickel 58 because of its large coherent scattering length. So, for natural Nickel one gets a total angular of reflection of Oc = 6' . A, [A] and for the isotope 58 a O c =7.1' .k[A] . About 30 years ago neutron guides were invented at the research reactor in München ; Neutron guides lead to a much broader use ofneutron scattering wich instruments posed far from the source and with much better conditions . Neutron guides coated with a so-called super minor transport neutrons with even larger angles of divergence. In addition to Nickel those minors consist of altemating layers of two different metals (their coherent scattering length density must be sufficiently different) wich an ingenious sequence of different thickness, in order to excite Bragg scattering in a continuous range of Q perpendicular to the surface . In this way the angle of reflection of Nickel can bc increased by more than a factor of two ; however, the best achieved reflectivity of super minors is still slightly less than one so that one gets appreciably losses of neutrons if transported over long distances . . 8-12
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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)
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 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: tails. This reflection curve leads
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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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 222 and 223: 10.2 .6 Crystal monochromators The
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
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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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