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602:'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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42:) is a mathematical function that contains information about inter-particle correlations and their time evolution. It is a generalization of the
1529:
1379:{\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 }
1604:
1204:{\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 }
1680:
1547:
1690:
1428:
van Hove, L. (1954). "Correlations in Space and Time and Born
Approximation Scattering in Systems of Interacting Particles".
885:{\displaystyle {\frac {d^{2}\sigma }{d\Omega d\omega }}=a^{2}\left({\frac {E_{f}}{E_{i}}}\right)^{1/2}S({\vec {k}},\omega )}
1654:
337:{\displaystyle S({\vec {k}},\omega )\equiv {\frac {1}{2\pi }}\int _{-\infty }^{\infty }F({\vec {k}},t)\exp(i\omega t)\,dt}
51:
1685:
1521:
749:
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Lovesey, Stephen W. (1986). Theory of
Neutron Scattering from Condensed Matter - Volume I: Nuclear Scattering.
31:
1539:
64:
1597:
55:
584:{\displaystyle F({\vec {k}},t)\equiv \int G({\vec {r}},t)\exp(-i{\vec {k}}\cdot {\vec {r}})\,d{\vec {r}}}
738:{\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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1619:
1465:
Vineyard, George H. (1958). "Scattering of Slow
Neutrons by a Liquid".
399:
spectroscopy. The intermediate scattering function is the spatial
163:) is a wave vector (or wave number for isotropic materials), and
927:
The van Hove function for a spatially uniform system containing
594:
Thus we see that the dynamical structure factor is the spatial
50:
time. Experimentally, it can be accessed most directly by
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61:The dynamic structure factor is most often denoted
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1512:Ashcroft, Neil W.; Mermin, N. David (1976).
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46:that considers correlations in both space
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1409:Hansen, J. P.; McDonald, I. R. (1986).
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98:{\displaystyle S({\vec {k}},\omega )}
7:
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27:Function in condensed matter physics
1634:. You can help Knowledge (XXG) by
1577:. You can help Knowledge (XXG) by
783:
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25:
1618:
1561:
1516:Solid State Physics (Appendix N)
393:intermediate scattering function
18:Intermediate scattering function
947:point particles is defined as:
598:temporal Fourier transform of
443:{\displaystyle G({\vec {r}},t)}
384:{\displaystyle F({\vec {k}},t)}
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199:{\displaystyle \hbar \omega }
52:inelastic neutron scattering
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1556:
1522:Holt, Rinehart and Winston
750:differential cross section
156:{\displaystyle {\vec {q}}}
127:{\displaystyle {\vec {k}}}
40:dynamical structure factor
1214:It can be rewritten as:
1681:Condensed matter physics
1571:condensed matter physics
1411:Theory of Simple Liquids
36:dynamic structure factor
32:condensed matter physics
1540:Oxford University Press
1487:10.1103/PhysRev.110.999
395:and can be measured by
176:{\displaystyle \omega }
1691:Condensed matter stubs
1630:–related article is a
1573:-related article is a
1452:10.1103/PhysRev.95.249
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56:X-ray Raman scattering
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923:The van Hove function
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615:{\displaystyle \rho }
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1479:1958PhRv..110..999V
1444:1954PhRv...95..249V
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1686:Neutron scattering
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940:{\displaystyle N}
917:scattering length
908:{\displaystyle a}
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405:van Hove function
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397:neutron spin echo
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16:(Redirected from
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44:structure factor
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1506:Further reading
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1473:(5): 999–1010.
1467:Physical Review
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1431:Physical Review
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1636:expanding it
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1579:expanding it
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29:
752:is :
134:(sometimes
1675:Categories
1628:scattering
1438:(1): 249.
1393:References
1495:0031-899X
1362:→
1333:→
1320:ρ
1305:→
1286:→
1273:ρ
1270:∫
1237:→
1187:→
1153:→
1143:−
1133:→
1120:δ
1096:→
1086:−
1080:→
1061:→
1048:δ
1028:∑
1007:∑
1003:∫
970:→
877:ω
868:→
790:ω
784:Ω
776:σ
733:⟩
716:→
707:−
703:ρ
686:→
677:ρ
673:⟨
645:→
610:ρ
576:→
557:→
548:⋅
542:→
530:−
524:
506:→
491:∫
488:≡
473:→
426:→
367:→
319:ω
310:
292:→
275:∞
270:∞
267:−
263:∫
256:π
244:≡
238:ω
229:→
194:ω
191:ℏ
171:ω
148:→
119:→
90:ω
81:→
1373:⟩
1368:′
1339:′
1292:′
1256:⟨
1198:⟩
1193:′
1139:′
1067:′
989:⟨
600:van Hove
105:, where
1475:Bibcode
1440:Bibcode
915:is the
403:of the
1546:
1528:
1493:
895:where
34:, the
1626:This
1569:This
347:Here
1632:stub
1575:stub
1544:ISBN
1526:ISBN
1491:ISSN
38:(or
1483:doi
1471:110
1448:doi
919:.
622::
596:and
521:exp
307:exp
54:or
48:and
30:In
1677::
1542:.
1524:.
1520:.
1489:.
1481:.
1469:.
1446:.
1436:95
1434:.
1413:.
1401:^
450::
58:.
1663:e
1656:t
1649:v
1638:.
1606:e
1599:t
1592:v
1581:.
1550:.
1534:.
1497:.
1485::
1477::
1454:.
1450::
1442::
1417:.
1359:r
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1349:)
1346:0
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1330:r
1323:(
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1314:t
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1296:+
1283:r
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1114:)
1111:t
1108:(
1103:j
1093:r
1077:r
1071:+
1058:r
1051:[
1043:N
1038:1
1035:=
1032:j
1022:N
1017:1
1014:=
1011:i
998:N
995:1
985:=
982:)
979:t
976:,
967:r
961:(
958:G
935:N
903:a
880:)
874:,
865:k
859:(
856:S
851:2
847:/
843:1
838:)
831:i
827:E
821:f
817:E
811:(
804:2
800:a
796:=
787:d
781:d
771:2
767:d
730:)
727:0
724:(
713:k
699:)
696:t
693:(
683:k
668:N
665:1
660:=
657:)
654:t
651:,
642:k
636:(
633:F
573:r
567:d
563:)
554:r
539:k
533:i
527:(
518:)
515:t
512:,
503:r
497:(
494:G
485:)
482:t
479:,
470:k
464:(
461:F
438:)
435:t
432:,
423:r
417:(
414:G
379:)
376:t
373:,
364:k
358:(
355:F
332:t
329:d
325:)
322:t
316:i
313:(
304:)
301:t
298:,
289:k
283:(
280:F
253:2
249:1
241:)
235:,
226:k
220:(
217:S
145:q
116:k
93:)
87:,
78:k
72:(
69:S
20:)
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