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591:'s time-dependent pair correlation function. It can be shown (see below), that the intermediate scattering function is the correlation function of the Fourier components of the density
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31:) is a mathematical function that contains information about inter-particle correlations and their time evolution. It is a generalization of the
1518:
1368:{\displaystyle G({\vec {r}},t)=\left\langle {\frac {1}{N}}\int \rho ({\vec {r}}'+{\vec {r}},t)\rho ({\vec {r}}',0)d{\vec {r}}'\right\rangle }
1593:
1193:{\displaystyle G({\vec {r}},t)=\left\langle {\frac {1}{N}}\int \sum _{i=1}^{N}\sum _{j=1}^{N}\delta \delta d{\vec {r}}'\right\rangle }
1669:
1536:
1679:
1417:
van Hove, L. (1954). "Correlations in Space and Time and Born
Approximation Scattering in Systems of Interacting Particles".
874:{\displaystyle {\frac {d^{2}\sigma }{d\Omega d\omega }}=a^{2}\left({\frac {E_{f}}{E_{i}}}\right)^{1/2}S({\vec {k}},\omega )}
1643:
326:{\displaystyle S({\vec {k}},\omega )\equiv {\frac {1}{2\pi }}\int _{-\infty }^{\infty }F({\vec {k}},t)\exp(i\omega t)\,dt}
40:
1674:
1510:
738:
1684:
1636:
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1527:
Lovesey, Stephen W. (1986). Theory of
Neutron Scattering from Condensed Matter - Volume I: Nuclear Scattering.
20:
1528:
53:
1586:
44:
573:{\displaystyle F({\vec {k}},t)\equiv \int G({\vec {r}},t)\exp(-i{\vec {k}}\cdot {\vec {r}})\,d{\vec {r}}}
727:{\displaystyle F({\vec {k}},t)={\frac {1}{N}}\langle \rho _{\vec {k}}(t)\rho _{-{\vec {k}}}(0)\rangle }
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The dynamic structure is exactly what is probed in coherent inelastic neutron scattering. The
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155:
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32:
1551:
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1663:
1503:
588:
1616:
1483:
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1440:
1608:
1454:
Vineyard, George H. (1958). "Scattering of Slow
Neutrons by a Liquid".
388:
spectroscopy. The intermediate scattering function is the spatial
152:) is a wave vector (or wave number for isotropic materials), and
916:
The van Hove function for a spatially uniform system containing
583:
Thus we see that the dynamical structure factor is the spatial
39:
time. Experimentally, it can be accessed most directly by
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50:The dynamic structure factor is most often denoted
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8:
1501:Ashcroft, Neil W.; Mermin, N. David (1976).
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35:that considers correlations in both space
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172:a frequency (sometimes stated as energy,
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55:
1398:Hansen, J. P.; McDonald, I. R. (1986).
1387:
179:
87:{\displaystyle S({\vec {k}},\omega )}
7:
1605:
1603:
1548:
1546:
16:Function in condensed matter physics
1623:. You can help Knowledge (XXG) by
1566:. You can help Knowledge (XXG) by
772:
263:
258:
14:
1607:
1550:
1505:Solid State Physics (Appendix N)
382:intermediate scattering function
936:point particles is defined as:
587:temporal Fourier transform of
432:{\displaystyle G({\vec {r}},t)}
373:{\displaystyle F({\vec {k}},t)}
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188:{\displaystyle \hbar \omega }
41:inelastic neutron scattering
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1545:
1511:Holt, Rinehart and Winston
739:differential cross section
145:{\displaystyle {\vec {q}}}
116:{\displaystyle {\vec {k}}}
29:dynamical structure factor
1203:It can be rewritten as:
1670:Condensed matter physics
1560:condensed matter physics
1400:Theory of Simple Liquids
25:dynamic structure factor
21:condensed matter physics
1529:Oxford University Press
1476:10.1103/PhysRev.110.999
384:and can be measured by
165:{\displaystyle \omega }
1680:Condensed matter stubs
1619:–related article is a
1562:-related article is a
1441:10.1103/PhysRev.95.249
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45:X-ray Raman scattering
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912:The van Hove function
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604:{\displaystyle \rho }
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195:). It is defined as:
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1468:1958PhRv..110..999V
1433:1954PhRv...95..249V
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1675:Neutron scattering
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929:{\displaystyle N}
906:scattering length
897:{\displaystyle a}
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394:van Hove function
390:Fourier transform
386:neutron spin echo
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1685:Scattering stubs
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33:structure factor
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1495:Further reading
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1462:(5): 999–1010.
1456:Physical Review
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1420:Physical Review
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1625:expanding it
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1568:expanding it
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28:
24:
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741:is :
123:(sometimes
1664:Categories
1617:scattering
1427:(1): 249.
1382:References
1484:0031-899X
1351:→
1322:→
1309:ρ
1294:→
1275:→
1262:ρ
1259:∫
1226:→
1176:→
1142:→
1132:−
1122:→
1109:δ
1085:→
1075:−
1069:→
1050:→
1037:δ
1017:∑
996:∑
992:∫
959:→
866:ω
857:→
779:ω
773:Ω
765:σ
722:⟩
705:→
696:−
692:ρ
675:→
666:ρ
662:⟨
634:→
599:ρ
565:→
546:→
537:⋅
531:→
519:−
513:
495:→
480:∫
477:≡
462:→
415:→
356:→
308:ω
299:
281:→
264:∞
259:∞
256:−
252:∫
245:π
233:≡
227:ω
218:→
183:ω
180:ℏ
160:ω
137:→
108:→
79:ω
70:→
1362:⟩
1357:′
1328:′
1281:′
1245:⟨
1187:⟩
1182:′
1128:′
1056:′
978:⟨
589:van Hove
94:, where
1464:Bibcode
1429:Bibcode
904:is the
392:of the
1535:
1517:
1482:
884:where
23:, the
1615:This
1558:This
336:Here
1621:stub
1564:stub
1533:ISBN
1515:ISBN
1480:ISSN
27:(or
1472:doi
1460:110
1437:doi
908:.
611::
585:and
510:exp
296:exp
43:or
37:and
19:In
1666::
1531:.
1513:.
1509:.
1478:.
1470:.
1458:.
1435:.
1425:95
1423:.
1402:.
1390:^
439::
47:.
1652:e
1645:t
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1627:.
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1588:t
1581:v
1570:.
1539:.
1523:.
1486:.
1474::
1466::
1443:.
1439::
1431::
1406:.
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1335:0
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1312:(
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1285:+
1272:r
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1238:)
1235:t
1232:,
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1217:(
1214:G
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1157:0
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1100:t
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1027:1
1024:=
1021:j
1011:N
1006:1
1003:=
1000:i
987:N
984:1
974:=
971:)
968:t
965:,
956:r
950:(
947:G
924:N
892:a
869:)
863:,
854:k
848:(
845:S
840:2
836:/
832:1
827:)
820:i
816:E
810:f
806:E
800:(
793:2
789:a
785:=
776:d
770:d
760:2
756:d
719:)
716:0
713:(
702:k
688:)
685:t
682:(
672:k
657:N
654:1
649:=
646:)
643:t
640:,
631:k
625:(
622:F
562:r
556:d
552:)
543:r
528:k
522:i
516:(
507:)
504:t
501:,
492:r
486:(
483:G
474:)
471:t
468:,
459:k
453:(
450:F
427:)
424:t
421:,
412:r
406:(
403:G
368:)
365:t
362:,
353:k
347:(
344:F
321:t
318:d
314:)
311:t
305:i
302:(
293:)
290:t
287:,
278:k
272:(
269:F
242:2
238:1
230:)
224:,
215:k
209:(
206:S
134:q
105:k
82:)
76:,
67:k
61:(
58:S
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