Abstract

X-ray photon correlation spectroscopy (XPCS) is a novel technique for the study of slow dynamics in disordered materials. It overcomes limitations of visible light scattering techniques such as multiple scattering or limitations in Q-range by using coherent X-rays from third generation synchrotron radiation sources. Applications to the static and dynamic behavior of complex fluids and to slow dynamics in hard condensed matter systems are reviewed.

Author Keywords: X-ray photon correlation spectroscopy (XPCS); Photon correlation spectroscopy; Speckle; Coherent X-rays; Colloidal suspensions; Capillary waves; Non-equilibrium dynamics; Magnetic disorder

Article Outline

1. Introduction

2. Scattering with coherent X-rays

3. Disorder under coherent illumination

4. X-ray photon correlation spectroscopy (XPCS)

5. XPCS in soft condensed matter systems

5.1. Static and dynamic properties of colloidal suspensions

5.2. XPCS and SAXS measurements in colloidal suspensions

5.3. Slow dynamics in polymer systems, membranes and liquids

6. Slow dynamics in hard condensed matter systems

7. Conclusions and outlook

Acknowledgements

References

(26K)
Fig. 1. Frequency–scattering vector space covered by X-ray photon correlation spectroscopy (XPCS) and complementary techniques: photon correlation spectroscopy with visible coherent light (PCS), Raman and Brillouin scattering, inelastic neutron (INS) and X-ray scattering (IXS), neutron spin-echo and nuclear forward scattering (NFS).

(5K)
Fig. 2. Schematic set-up of the ID10A beamline at ESRF for coherent X-ray scattering. Typical distances are: source–deflecting mirror/monochromator, 44.2 m; deflecting mirror–focusing mirror, 0.8 m; focusing mirror–pinhole, 0.5 m; pinhole–sample, 0.1 m; sample–detector, 2 m.

(25K)
Fig. 3. Speckle pattern from an aerogel recorded with a 22 m pixel size CCD detector using 8.2 keV coherent X-rays (top). Circular averaged scattering from the sample, normalized to give detected photons per second. The line is the intensity in one pixel row in the horizontal direction, showing the speckle structure (bottom) [17].

(6K)
Fig. 4. Measured intermediate scattering function f^M(Q, t) for a concentrated suspension of colloidal PMMA particles in cis-decalin. The solid black line shows a cumulant fit to the data using terms up to the fourth order. The red line shows the contribution of the first cumulant Γ(Q).

(9K)
Fig. 5. X-ray small angle scattering intensity as a function of the momentum transfer Q for a 1 vol.% suspension of colloidal silica (R=2427 Å) in a glycerol/water mixture at 293 K (top). Q dependence of the correlation rate Γ as determined from intensity correlation functions taken at various Q values (middle). The solid line is the result of a fit to the data with D_o as a fit parameter. Normalized, inverse diffusion coefficient D_o/D(Q) as a function of Q (bottom) [39].

(12K)
Fig. 6. X-ray small angle scattering intensity as a function of the momentum transfer Q for a 37.3 vol.% suspension of colloidal PMMA particles (R=1112 Å) in cis-decalin at 293 K. The solid line describes the particle form factor (Eq. (5.4)) and deviations are due to interparticle correlations S(Q). (b) Q dependence of the correlation rate Γ. The solid line is the result of a fit to the dilute data (not shown) with D_o as a fit parameter. (c) Normalized, inverse diffusion coefficient D_o/D(Q) as a function of Q [40], compared to the static (time-averaged) structure factor S(Q). The solid line is a calculated Percus–Yevick hard-sphere structure factor for =37.3%. (d) Hydrodynamic function H(Q)=S(Q)/(D_o/D(Q)). The solid line is the result of a model calculation (see text).

(5K)
Fig. 7. Correlation times ₀ of overdamped capillary waves in glycerol for different temperatures as a function of the lateral lengthscale x₀=2/Q [52].

(30K)
Fig. 8. Magnetic speckle pattern on the first order magnetic diffraction ring from meandering magnetic stripe domains in a 350-Å-thick film of GdFe₂ illuminated by a 15-m diameter beam of circularly polarized X-rays tuned to the Gd M₅ resonance at 1183.6 eV [56].

Table 1. Bandpass Δ/, longitudinal coherence length _l at 1 Å wavelength and coherent flux F_c (B=10²⁰ phonons/s/0.1% bandwidth/mm²/mrad²) for Si(220), Si(111) and a configuration using the intrinsic bandwidth Δ/=1/nN of the third (n=3) harmonic of an N=35 period undulator

References

1. G. Grübel, J. Als-Nielsen, D. Abernathy, G. Vignaud, S. Brauer, G.B. Stephenson, S.G.J. Mochrie, M. Sutton, I.K. Robinson, R. Fleming, R. Pindak, S. Dierker and J.F. Legrand. ESRF Newslett. 20 (1994), p. 14.
G. Grübel, D. Abernathy, G.B. Stephenson, S. Brauer, I. McNulty, S.G.J. Mochrie, B. McClain, A. Sandy, M. Sutton, E. Dufresne, I.K. Robinson, R. Fleming, R. Pindak and S. Dierker. ESRF Newslett. 23 (1995), p. 14.

2. S. Brauer, G.B. Stephenson, M. Sutton, R. Brüning, E. Dufresne, S.G.J. Mochrie, G. Grübel, J. Als-Nielsen and D. Abernathy. Phys. Rev. Lett. 74 (1995), p. 2010. Abstract-INSPEC   | $Order Document | Full Text via CrossRef

3. S.B. Dierker, R. Pindak, R.M. Fleming, I.K. Robinson and L. Berman. Phys. Rev. Lett. 75 (1995), p. 449. Abstract-INSPEC   | $Order Document | Full Text via CrossRef

4. T. Thurn-Albrecht, W. Steffen, A. Patkowski, G. Meier, E.W. Fischer, G. Grübel and D. Abernathy. Phys. Rev. Lett. 77 (1996), p. 5437. Abstract-Compendex | Abstract-INSPEC | Abstract-INSPEC   | $Order Document | APS full text | Full Text via CrossRef

5. S.G.J. Mochrie, A.M. Mayes, A.R. Sandy, M. Sutton, S. Brauer, G.B. Stephenson, D.L. Abernathy and G. Grübel. Phys. Rev. Lett. 78 (1997), p. 1275. Abstract-Compendex | Abstract-INSPEC   | $Order Document | APS full text | Full Text via CrossRef

6. See Refs. [17, 20, 22, 23, 25, 26, 27, 28 and 29].

7. P. Cloetens, R. Barrett, J. Baruchel, J.P. Guigay and M. Schlenker. J. Phys. D: Appl. Phys. 29 (1996), p. 133. Abstract-Compendex | Abstract-INSPEC   | $Order Document | Full Text via CrossRef

8. A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov and I. Schelokov. Rev. Sci. Instrum. 66 (1995), p. 5486. Abstract-Compendex | Abstract-INSPEC   | $Order Document | Full Text via CrossRef
C. Raven, A. Snigirev, I. Snigireva, P. Spanne, A. Souvorov and V. Kohn. Appl. Phys. Lett. 69 (1996), p. 1826. Abstract-Compendex | Abstract-INSPEC   | $Order Document | OJPS full text | Full Text via CrossRef

9. T. Gog, P.M. Len, G. Materlik, D. Bahr, C.S. Fadley and C. Sanchez-Hanke. Phys. Rev. Lett. 76 (1996), p. 3132. Abstract-INSPEC   | $Order Document | APS full text | Full Text via CrossRef

10. B.J. Berne and R. Pecora. Dynamic Light Scattering with Applications, John Wiley, New York (1976).
B. Chu. In: (2nd Edition ed.),Laser Light Scattering: Basic Principles and Practices, Academic Press, San Diego (1991).

11. M. Sutton, S.G.J. Mochrie, T. Greytak, S.E. Nagler, L.E. Berman, G.A. Held and G.B. Stephenson. Nature 353 (1991), p. 608. Abstract-INSPEC   | $Order Document | Full Text via CrossRef

12. D. Attwood, K. Halbach and K.J. Kim. Science 228 (1985), p. 1265. Abstract-INSPEC   | $Order Document

13. M.V. Klein and T.E. Furtak. In: (2nd Edition ed.),Optics, John Wiley, New York (1986).

14. M. Born and E. Wolf. In: (6th Edition ed.),Principles of Optics, Pergamon Press, Oxford (1985).

15. G. Grübel and D.L. Abernathy. SPIEE 3154 (1997), p. 103. Abstract-Compendex | Abstract-INSPEC   | $Order Document

16. A.Q.R. Baron, A.I. Chumakov, H.F. Grunsteudel, H. Grunsteudel, L. Niesen and R. Rüffer. Phys. Rev. Lett. 77 (1996), p. 4808. Abstract-Compendex | Abstract-INSPEC   | $Order Document | APS full text | Full Text via CrossRef

17. D.L. Abernathy, G. Grübel, S. Brauer, I. McNulty, G.B. Stephenson, S.G.J. Mochrie, A.R. Sandy, N. Mulders and M. Sutton. J. Synchr. Rad. 5 (1998), p. 37. Abstract-INSPEC   | $Order Document | Full Text via CrossRef

18. G. Grübel, J. Als-Nielsen and A.K. Freund. J. Phys. IV C9 4 (1994), p. 27.

19. A.R. Sandy, L.B. Lurio, S.G.J. Mochrie, A. Malik and G.B. Stephenson. SPIEE 3154 (1997), p. 27. Abstract-Compendex | Abstract-INSPEC   | $Order Document
A.R. Sandy, L.B. Lurio, S.G.J. Mochrie, A. Malik, G.B. Stephenson, J.F. Pelletier and M. Sutton. J. Synchr. Rad. 6 (1999), p. 1174. Abstract-INSPEC   | $Order Document | Full Text via CrossRef

20. O.K.C. Tsui, S.G.J. Mochrie and L.E. Berman. J. Synchr. Rad. 5 (1998), p. 30. Abstract-INSPEC   | $Order Document | Full Text via CrossRef

21. I.K. Robinson, R. Pindak, R.M. Fleming, S.B. Dierker, K. Ploog, G. Grübel, D.L. Abernathy and J. Als-Nielsen. Phys. Rev. B 52 (1995), p. 9917. Abstract-INSPEC   | $Order Document | Full Text via CrossRef
D.L. Abernathy, J. Als-Nielsen, S.B. Dierker, R.M. Fleming, G. Grübel, R. Pindak, K. Ploog and I.K. Robinson. Solid-State Electron. 40 (1996), p. 531. SummaryPlus | Full Text + Links | PDF (590 K)

22. Z.H. Cai, B. Lai, W.B. Yun, I. McNulty, K.G. Huang and T.P. Russel. Phys. Rev. Lett. 73 (1994), p. 82. Abstract-Compendex | Abstract-INSPEC   | $Order Document | Full Text via CrossRef

23. J.L. Libbert, R. Pindak, S.B. Dierker and I.K. Robinson. Phys. Rev. B 56 (1997), p. 6454. Abstract-INSPEC   | $Order Document | APS full text | Full Text via CrossRef

24. F. Bley, F. Livet, J.C. Leroux, J.P. Simon, D. Abernathy, J. Als-Nielsen, G. Grübel, G. Vignaud, G. Dolino, J.F. Legrand, D. Camel, N. Menguy and M. Papoular. Acta Crystallogr. A 51 (1995), p. 746. Abstract-INSPEC   | $Order Document | Full Text via CrossRef

25. I.A. Vartanyants, J. Pitney, J. Libbert and I.K. Robinson. Phys. Rev. B 55 (1997), p. 13193. Abstract-INSPEC   | $Order Document | APS full text | Full Text via CrossRef
I.K. Robinson, J.L. Libbert, I.A. Vartanyants, J.A. Pitney, D.M. Smilgies, D.L. Abernathy and G. Grübel. Phys. Rev. B 60 (1999), p. 9965. Abstract-INSPEC   | $Order Document | APS full text | Full Text via CrossRef

26. I.K. Robinson, I.A. Vartanyants, G.J. Williams, M.A. Pfeifer and J.A. Pitney. Phys. Rev. Lett. 87 (2001), p. 195505. Full Text via CrossRef

27. J. Miao, P. Charalambous, J. Kirz and D. Sayre. Nature 400 (1999), p. 342. Abstract-EMBASE | Abstract-Elsevier BIOBASE   | $Order Document | Full Text via CrossRef

28. J. Miao, K.O. Hodgson and D. Sayre. Proc. Natl. Acad. Sci. 98 (2001), p. 6641. Abstract-EMBASE | Abstract-Elsevier BIOBASE | Abstract-MEDLINE   | $Order Document | Full Text via CrossRef

29. R. Eisenhower, R. Gehrke, G. Materlik, M. Drakopolous, A. Simionovici and A. Snigirev. J. Synchr. Rad. 6 (1999), p. 1168. Abstract-INSPEC   | $Order Document | Full Text via CrossRef

30. J.W. Goodman. In: J.C. Dainty, Editor, Laser Speckle and Related Phenomena, Springer, Berlin (1975).
J.W. Goodman. Statistical Optics, John Wiley, New York (1985).

31. S.K. Sinha, M. Tolan and A. Gibaud. Phys. Rev. B 57 (1998), p. 2740. Abstract-INSPEC   | $Order Document | APS full text | Full Text via CrossRef

32. P.N. Pusey. In: J.P. Hansen, D. Levesque and J. Zinn-Justin, Editors, Liquids, Freezing and Glass TransitionLes Houches, Session L1, Elsevier, Amsterdam (1989), p. 763.

33. P.N. Segre and P.N. Pusey. Physica A 235 (1997), p. 9. Abstract | Abstract + References | PDF (460 K)

34. F. Livet, F. Blay, J. Mainville, R. Caudron, S.G.J. Mochrie, E. Geissler, G. Dolino, D. Abernathy, G. Grübel and M. Sutton. Nucl. Instrum. Methods A 451 (2000), p. 596. SummaryPlus | Full Text + Links | PDF (435 K)

35. D. Lumma, L.B. Lurio, S.G.J. Mochrie and M. Sutton. Rev. Sci. Instrum. 71 (2000), p. 3274. Abstract-INSPEC   | $Order Document | OJPS full text | Full Text via CrossRef

36. N.W. Ashcroft and J. Lekner. Phys. Rev. 145 (1966), p. 145.

37. C.W.J. Beenakker and P. Mazur. Physica 120A (1983), p. 388. Abstract | Abstract + References | PDF (847 K)
C.W.J. Beenakker and P. Mazur. Physica 126A (1984), p. 349. Abstract | Abstract + References | PDF (938 K)

38. R. Klein and B. d’Aguanno. In: W. Brown, Editor, Light Scattering, Principles and Development, Clarendon Press, Oxford (1996), p. 30.

39. G. Grübel, A. Robert and D.L. Abernathy, Slow dynamics in complex systems. In: M. Tokuyama and I. Oppenheim, Editors, Eighth Tohwa University International Symposium (1999), p. 158.

40. F. Zontone, A. Moussaid, A. Robert, G. Grübel, to be published.

41. O.K.C. Tsui and S.G.J. Mochrie. Phys. Rev. E 57 (1998), p. 2030. Abstract-Compendex | Abstract-INSPEC   | $Order Document | APS full text | Full Text via CrossRef

42. G. Grübel, D.A. Abernathy, D.O. Riese, W.L. Vos and G.H. Wegdam. J. Appl. Crystallogr. 33 (2000), p. 424. Abstract-INSPEC   | $Order Document | Full Text via CrossRef

43. D.O. Riese, W.L. Vos, G.H. Wegdam, F.J. Poelwijk, D.L. Abernathy and G. Grübel. Phys. Rev. E 61 (2000), p. 1676. Abstract-INSPEC   | $Order Document | APS full text | Full Text via CrossRef

44. D.O. Riese, G.H. Wegdam, W.L. Vos, R. Sprik, D. Feinstein, J.H.H. Bongaerts and G. Grübel. Phys. Rev. Lett. 85 (2000), p. 5460. Abstract-Compendex | Abstract-INSPEC   | $Order Document | Full Text via CrossRef

45. D. Lumma, L.B. Lurio, M.A. Borthwick, P. Falus and S.G.J. Mochrie. Phys. Rev. E 62 (2000), p. 8258. Abstract-Compendex | Abstract-INSPEC   | $Order Document | Full Text via CrossRef

46. L.B. Lurio, D. Lumma, A.R. Sandy, M.A. Borthwick, P. Falus, S.G.J. Mochrie, J.F. Pelletier, M. Sutton, L. Regan, A. Malik and G.B. Stephenson. Phys. Rev. Lett. 84 (2000), p. 785. Abstract-INSPEC | Abstract-MEDLINE   | $Order Document | APS full text | Full Text via CrossRef

47. J. Lal, D. Abernathy, L. Auvray, O. Diat and G. Grübel. Eur. Phys. J. E 4 (2001), p. 263. Abstract-INSPEC   | $Order Document | Full Text via CrossRef

48. D. Lumma, M.A. Borthwick, P. Falus, L.B. Lurio and S.G.J. Mochrie. Phys. Rev. Lett. 86 (2001), p. 2042. Abstract-Compendex | Abstract-INSPEC   | $Order Document | Full Text via CrossRef

49. A.C. Price, L.B. Sorensen, S.D. Kevan, J. Toner, A. Poniewierski and R. Kolyst. Phys. Rev. Lett. 82 (1999), p. 755. Abstract-INSPEC   | $Order Document | APS full text | Full Text via CrossRef

50. A. Fera, I.P. Dolbyna, G. Grübel, H.G. Muller, B.I. Ostrovskii, A.N. Shalaginov and W.H. deJeu. Phys. Rev. Lett. 85 (2000), p. 2316. Abstract-Compendex | Abstract-INSPEC   | $Order Document | Full Text via CrossRef

51. I. Sikharulidze, I.P. Dolbyna, A. Fera, A. Madsen, B.I. Ostrovskii and W. de Jeu. Phys. Rev. Lett. 88 (2002), p. 115503. Full Text via CrossRef

52. T. Seydel, A. Madsen, M. Tolan, G. Grübel and W. Press. Phys. Rev. B 63 (2001), p. 73409.

53. A. Malik, A.R. Sandy, L.B. Lurio, G.B. Stephenson, S.G.J. Mochrie, I. McNulty and M. Sutton. Phys. Rev. Lett. 81 (1998), p. 5832. Abstract-INSPEC   | $Order Document | APS full text | Full Text via CrossRef

54. J. Mainville, F. Bley, F. Livet, E. Geissler, J.F. Legrand, D. Abernathy, G. Grübel, S.G.J. Mochrie and M. Sutton. J. Appl. Crystallogr. 30 (1997), p. 828. Abstract-INSPEC   | $Order Document | Full Text via CrossRef
F. Livet, F. Bley, E. Geissler, R. Goudron, M. Sutton and G. Grübel. Phys. Rev. E 63 (2001), p. 36108. Abstract-Compendex   | $Order Document

55. F. Yakhou, A. Letoublon, F. Livet, M. de Boissieu, F. Bley and C. Vettier. ESRF Newslett. 32 (1999), p. 12. Abstract-INSPEC   | $Order Document

56. J.F. Peters, M.A. de Fries, J. Miguel, O. Toulemonde and J. Goedkoop. ESRF Newslett. 34 (2000), p. 15. Abstract-INSPEC   | $Order Document

Corresponding author. Tel.: +33-4-7688-2555; fax: +33-4-7688-2160.