Neutron Scattering

More documents

Recommendations

Info

Contents 11 .1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-1 11 .2 Setup and Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-2 11 .2 .1 Flippers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-5 11 .3 The detector signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-8 11 .3 .1 Symmetric Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-9 11 .3 .2 Elastic <strong>Scattering</strong> of a Finite Width Wavelength Distribution . . . . 11-10 11 .4 Experimental Procedures and Evaluation . . . . . . . . . . . . . . . . . . 11-11 11 .5 Field Integral Homogeneity and Resolution . . . . . . . . . . . . . . . . . . 11-14 11 .6 Practical Aspects, Peculiarities . . . . . . . . . . . . . . . . . . . . . . . . 11-16
Page 1 and 2:
Forschungszentrum Jülich in der He
Page 4 and 5:
Forschungszentrum Jülich GmbH Inst
Page 6:
Contents . . 1 Neutron Sources H .
Page 10 and 11:
1 . Neutron Sources Harald Conrad 1
Page 12 and 13:
d) f, = v a, , q - ti = P a, - 0 .3
Page 14 and 15:
Period Example Flux (D [1013 1950-6
Page 16 and 17:
In stage 1 the primary proton knock
Page 18 and 19:
get as heat, the rest is transporte
Page 20 and 21:
down power and stronger absorption
Page 22 and 23:
Appendix Neutron Sources - an overv
Page 24:
led remotely. It is rauch more conv
Page 28 and 29:
2 . Properties of the neutron, elem
Page 30 and 31:
In the 60's the ferst high flux rea
Page 32 and 33:
Hot neutrons in reactors are obtain
Page 34 and 35:
elated values for the FRJ-2 reactor
Page 36 and 37:
2 .5 Scattering amplitude and cross
Page 38 and 39:
(A+k2 ) yr = u(Z:) yr V( u~r)= z "
Page 40 and 41:
_du _ mn \2 A2-~2z r2~ I(k' IVI k)I
Page 42 and 43:
E ô ô x z w 0 z _w U N Figure 2 .
Page 44 and 45:
scattering is observed with the ave
Page 46 and 47:
For a spherical electron distributi
Page 48:
A more thorough introduction to neu
Page 52 and 53:
3 . Elastie Seattering from Many-Bo
Page 54 and 55:
Q = Q = k2 + k2 - 2kk' cos2B (3 .3)
Page 56 and 57:
3 .2 Fundamental Scattering Theory
Page 58 and 59:
The meaning of (3 .l4) is immediate
Page 60 and 61:
1 . e. in the second approximation,
Page 62 and 63:
The saure problem will bc dealt wit
Page 64 and 65:
ALQ) = Y-bfe'Q'-rB(r-(n .a+m .b+p»
Page 66 and 67:
du LQ) = ALQJ2 = e'Q .A' . * -i e-
Page 68 and 69:
Tab . 3.1 : The scattering lengths
Page 70 and 71:
We note immediately that we should
Page 72 and 73:
These magnetic structures can be un
Page 74 and 75:
M1LQ)=Q-MQ)xQ M(Q)= IM (r)e i Q " d
Page 76 and 77:
Orbital magnetic spin angular ,,- m
Page 78 and 79:
aQ . r 3 àQ . N . QR . aQ .t k _ML
Page 80:
Schweika Analysis Polarization W .
Page 83 and 84:
ducing a complex component and were
Page 85 and 86:
ir v s ftft 3956 2 s 2 0.81[X] 80 c
Page 87 and 88:
Some polarizers using Bragg reflect
Page 89 and 90:
Different to the coherent nuclear s
Page 91 and 92:
where QBG denotes the background .
Page 93 and 94:
4 .4 Applications We now consider e
Page 95 and 96:
Fig. 4 .3 .4 probably represents th
Page 97 and 98:
. occur only in the non-spin flip c
Page 99 and 100:
The results for the magnetization d
Page 101 and 102:
a large solid angle with polarizers
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 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 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
Page 200 and 201:
directions which is exploited for t
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
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
Page 244 and 245: esults, where il is an irrelevant c
Page 246 and 247: 10000 - 8000 - co 6000 - C ô 4000-
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 256: 12 Structure Determination Gernot H
Page 259 and 260: Besides of the related seven primit
Page 261 and 262: fM(H) = Jv Mj(r)-exp[2ni(H-r)]- &r
Page 263 and 264: 12 .3 .1 Example ofcontrast variati
Page 265 and 266: Fig . 2 . Magnetic phase diagram of
Page 267 and 268: Fig . 3 . Na2S-9D20 : A partial vie
Page 269 and 270: Remember: The scattering lengths of
Page 271 and 272: (3m symmetiy) on crystallographic s
Page 273 and 274: Textbooks G . E. Bacon, Neutron Dif
Page 276 and 277: 13 . Inelastic neutron scattering :
Page 278 and 279: (000) Figure 2 Schematic drawing of
Page 280 and 281: o o o o bo ao Lambda lattice parame
Page 282 and 283: Tau Figure 5 Scattering triangle co
Page 284 and 285: e performed in an efficient manner
Page 286 and 287: 1 r x z -- w --Z x E r A -+ L 6 5 _
Page 288 and 289: 1s. - 1 tUMl [cc01 ~ 1 ~ 10 517 if
Page 290 and 291: Similar branches may induce larger
Page 292 and 293: Figure 10 Schematic picture of a di
Page 294 and 295: T>Tc TTc O O O O " O " O 8 8 " " 2
Page 296 and 297: 14 a15spin-wave Magnon- energy the
Page 298 and 299: Ferromagnetic materials are still o
Page 300 and 301: ; ' . r,°'r, Figure 17 Crystal fie
Page 302: 14 Soft Matter : Structure Dietmar
Page 305 and 306:
with the macroscopic scattering cro
Page 307 and 308:
The probability that a freely joint
Page 309 and 310:
2.5 2.0 0.0 0.5 1 .0 1 .5 2.0 2.5 3
Page 311 and 312:
Equations (14 .12) and (14 .13) are
Page 313 and 314:
`l ~(Q)- ,"o (D(1-d)VP(Q) dn NA - ~
Page 315 and 316:
with c the volume fraction of polym
Page 317 and 318:
3 .0 ô 2 .5 U 2 .0 O 1 .5 a 1 .0 0
Page 319 and 320:
6 Û ô 4 3 .0 2 .5 ; 0 1 .5 0 .0 0
Page 321 and 322:
[11] D . Schwahn, K . Mortensen, T.
Page 324 and 325:
15 . Polymer Dynamics D. Richter 15
Page 326 and 327:
is the Kohlrausch-William-Watts rel
Page 328 and 329:
Figure 15 .2 : Elastic and inelasti
Page 330 and 331:
S (Q, t) = Sa (Q, t) S ß (Q, t) /
Page 332 and 333:
Fig .15 .6 displays the elastic int
Page 334 and 335:
C 0.8 d 0.6 ô, 0.4 0.2 o I-Ll1 I I
Page 336 and 337:
15.3 .1 Entropie forces - the Rouse
Page 338 and 339:
By means of neutron scattering two
Page 340 and 341:
The pair correlation function arisi
Page 342 and 343:
The dashed line gives the Rouse pre
Page 344 and 345:
Having obtained very good agreement
Page 346 and 347:
2 diameter d . At that time (ze) th
Page 348 and 349:
Figure 15.17 : Dynamic structure fa
Page 350 and 351:
Finally, one may test whether only
Page 352:
C Theoretieal Work [14] G . Ronca,
Page 356 and 357:
16 Magnetisin Thomas Bi ückel, IFF
Page 358 and 359:
ole, compared to the stronger excha
Page 360 and 361:
16.2 Magnetic Structure Determinati
Page 362 and 363:
The scattering power density can bc
Page 364 and 365:
the magnetisation density of one at
Page 366 and 367:
y r f R(Q)- (du /dS2) ++ - u a b z1
Page 368 and 369:
fluctuate in space and time . A pha
Page 370 and 371:
same and do not depend on the detai
Page 372 and 373:
Figures 16 .10 and 16.11 show the m
Page 374:
temperature superconductors, or exc
Page 378 and 379:
Chapter 17 Translation and Rotation
Page 380 and 381:
(T2 is related to the mean square d
Page 382 and 383:
Figure 17 .1 : Mean square displace
Page 384 and 385:
site with possible neighbour sites
Page 386 and 387:
decreased barrier increases the pro
Page 388 and 389:
17 .3 Rotation Molecules represent
Page 390 and 391:
,~ 1 = 0 represents the totally sym
Page 392 and 393:
The Id rotor : solution based on 'f
Page 394 and 395:
The Id rotor : pocket state formali
Page 396 and 397:
Each new model of coupled motion re
Page 398:
18 Texture in Materials and Earth S
Page 401 and 402:
In this contribution, however, we w
Page 403 and 404:
material . Texture is an important
Page 405 and 406:
. . It is convenient to plot these
Page 407 and 408:
Fig . 18 .12 : Examples of crystall
Page 409 and 410:
pole figures require numbers of 104
Page 411 and 412:
5 .1 Pole Figure Inversion The dét
Page 413 and 414:
lization (generation of dislocation
Page 415 and 416:
1990 1994 1996 Fig. 18.23 : Experim
Page 417 and 418:
Quartz HK407 ô m 6 Fig . 20 . . .
Page 419 and 420:
(3) Preferred orientations of the f
Page 421:
Schriften des Forschungszentrums J
show all

Neutron Scattering

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?