Atomic Migration Studies with X-Ray Photon Correlation Spectroscopy

Abstract:

The new technique of atomic-scale X-ray Photon Correlation Spectroscopy (aXPCS) makesuse of a coherent X-ray beam to study the dynamics of various processes in condensed matter systems.Particularly atomistic migration mechanisms are still far from being understood in most of intermetallicalloys and in amorphous systems. Special emphasis must be given to the opportunity to measureatomistic diffusion at relatively low temperatures where such measurements were far out of reach withpreviously established methods. The importance of short-range order is demonstrated on the basis ofMonte Carlo simulations.

• Periodical: Diffusion Foundations (Volume 2)
• Pages: 73-94
• DOI: https://doi.org/10.4028/www.scientific.net/DF.2.73
• Online since: September 2014
• Authors: Markus Stana*, Manuel Ross, Bogdan Sepiol
• Keywords: Chemical Diffusion, Diffuse Scattering, Diffusion, Dynamic Light Scattering, Ni-Pt Alloy, Short Range Order, Si-Ge, Synchrotron Radiation, XPCS

References

[1] L van Hove. Correlations in space and time and Born approximation scattering in systems of interacting particles. Physical Review, 95(1): 249, (1954).

DOI: 10.1103/physrev.95.249

[2] R Hempelmann. Quasielastic neutron scattering and solid state diffusion. Oxford University Press, Oxford, (2000).

[3] J V Michalowicz, J M Nichols, F Bucholtz, and C C Olson. An Isserlis theorem for mixed Gaussian variables: application to the auto-bispectral density. Journal of Statistical Physics, 136(1): 89-102, (2009).

DOI: 10.1007/s10955-009-9768-3

[4] P A Lemieux and D J Durian. Investigating non-Gaussian scattering processes by using nth-order intensity correlation functions. J. Opt. Soc. Am., 16(7): 1651-1664, (1999).

DOI: 10.1364/josaa.16.001651

[5] A S Gittings and D J Durian. Gaussian and non-Gaussian speckle fluctuations in the diffusingwave spectroscopy signal of a coarsening foam. Appl. Opt., 45(10): 2199-2204, Apr (2006).

DOI: 10.1364/ao.45.002199

[6] R Pecora. Dynamic Light Scattering: AQpplications of Photon Correlation Spectroscopy. Springer, (1985).

[7] L Cipelletti and E C Weeks. Glassy dynamics and dynamical heterogeneity in colloids. In L. Berthier, G. Biroli, J. -P. Bouchaud, L. Cipelletti, and W. van Saarlos, editors, Dynamical Heterogeneities in Glasses, Colloids and Granular Media, pages 110-151. Oxford University Press, (2011).

DOI: 10.1093/acprof:oso/9780199691470.003.0004

[8] J W Haus and K W Kehr. Diffusion in regular and disordered lattices. Physics Reports-Review Section of Physics Letters, 150(5-6): 263-406, JUN (1987).

DOI: 10.1016/0370-1573(87)90005-6

[9] M Sutton. X-ray intensity fluctuation spectroscopy. In F Hippert, E Geissler, J-L Hodeau, E Lelievre-Berna, and J-R Regnard, editors, Neutron and X-ray Spectroscopy, pages 297-318. Springer Netherlands, (2006).

DOI: 10.1007/1-4020-3337-0

[10] G Vogl and B Sepiol. The elementary diffusion step in metals studied by the interefrence of gamma-rays, X-rays and neutrons. In P. Heitjans and J. Kärger, editors, Diffusion in Condensed Matter, pages 65-91. Springer, (2005).

DOI: 10.1007/3-540-30970-5_2

[11] P G De Gennes. Liquid dynamics and inelastic scattering of neutrons. Physica, 25(7-12): 825- 839, (1959).

DOI: 10.1016/0031-8914(59)90006-0

[12] S K Sinha and D K Ross. Self-consistent density response function method for dynamics of light interstitials in crystals. Physica B+C, 149(1-3): 51 - 56, (1988).

DOI: 10.1016/0378-4363(88)90218-5

[13] M Leitner and G Vogl. Quasi-elastic scattering under short-range order: the linear regime and beyond. J. Phys. -Condens. Mat., 23: 254206, (2011).

DOI: 10.1088/0953-8984/23/25/254206

[14] M Leitner, B Sepiol, L-M Stadler, B Pfau, and G Vogl. Atomic diffusion studied with coherent X-rays. Nature Materials, 8(9): 717-720, (2009).

DOI: 10.1038/nmat2506

[15] M Stana, M Leitner, M Ross, and M Sepiol. Studies of atomic diffusion in Ni-Pt solid solution by X-ray photon correlation spectroscopy. Journal of Physics: Condensed Matter, 25(6): 065401, (2013).

DOI: 10.1088/0953-8984/25/6/065401

[16] M Ross, M Stana, M Leitner, and B Sepiol. Direct observation of atomic network migration in glass. New J. Phys. in press.

DOI: 10.1088/1367-2630/16/9/093042

[17] C T Chudley and R J Elliott. Neutron scattering from a liquid on a jump diffusion model. Proc. Phys. Soc., 77: 353, (1961).

DOI: 10.1088/0370-1328/77/2/319

[18] G Sauthoff. Intermetallics. Wiley-VCH Verlag GmbH, (2007).

[19] R Kutner and I Sosnowska. Thermal neutron scattering from a hydrogen-metal system in terms of a general multi-sublattice jump diffusion model I: Theory. Journal of Physics and Chemistry of Solids, 38(7): 741 - 746, (1977).

DOI: 10.1016/0022-3697(77)90067-1

[20] J M Rowe, K Skoeld, H E Flotow, and J J Rush. Quasielastic neutron scattering by hydrogen in the alpha and beta phases of vanadium hydride. Journal of Physics and Chemistry of Solids, 32(1): 41 - 54, (1971).

DOI: 10.1016/s0022-3697(71)80006-9

[21] I S Anderson, A Heidemann, J E Bonnet, D K Ross, S K P Wilson, and M W McKergow. Proton residence times in the solid solution phase of the Y-H system studied by quasi-elastic neutron scattering. Journal of the Less Common Metals, 101: 405-418, (1984).

DOI: 10.1016/0022-5088(84)90116-4

[22] O G Randl, B Sepiol, G Vogl, R Feldwisch, and K Schroeder. Quasielastic Mössbauer spectroscopy and quasielastic neutron scattering from non-Bravais lattices with differently occupied sublattices. Phys. Rev. B, 49: 8768-8773, (1994).

DOI: 10.1103/physrevb.49.8768

[23] B Sepiol and K F Ludwig. High-resolution experimental methods. In W Pfeiler, editor, Alloy Physics: A Comprehensive Reference, pages 707-773. Wiley-VCH, (2007).

[24] B Sepiol and G Vogl. Atomistic determination of diffusion mechanism on an ordered lattice. Phys. Rev. Lett., 71(5): 731-734, Aug (1993).

DOI: 10.1103/physrevlett.71.731

[25] R Feldwisch, B Sepiol, and G Vogl. Elementary diffusion jump of iron atoms in intermetallic phases studied by Mössbauer spectroscopy - II. from order to disorder. Acta metall. mater., 43(5): 2033-2039, (1995).

DOI: 10.1016/0956-7151(94)00382-r

[26] B Sepiol, A Meyer, G Vogl, R Ruffer, A I Chumakov, and A Q R Baron. Time domain study of Fe-57 diffusion using nuclear forward scattering of synchrotron radiation. Phys. Rev. Lett., 76(17): 3220-3223, APR 22 (1996).

DOI: 10.1103/physrevlett.76.3220

[27] M Kaisermayr, J Combet, H Ipser, H Schicketanz, B Sepiol, and G Vogl. Nickel diffusion in B2-NiGa studied with quasielastic neutron scattering. Phys. Rev. B, 61(18): 12038-12044, (2000).

DOI: 10.1103/physrevb.61.12038

[28] M Kaisermayr, J Combet, H Ipser, H Schicketanz, B Sepiol, and G Vogl. Determination of the elementary jump of Co in CoGa by quasielastic neutron scattering. Phys. Rev. B, 63: 054303, Jan (2001).

DOI: 10.1103/physrevb.63.054303

[29] M Kaisermayr, C Pappas, B Sepiol, and G Vogl. Probing jump diffusion in crystalline solids with neutron spin-echo spectroscopy. Phys. Rev. Lett., 87(17), (2001).

DOI: 10.1103/physrevlett.87.175901

[30] M Kaisermayr, M Rennhofer, G Vogl, C Pappas, and S Longeville. Neutron spin-echo spectroscopy for diffusion in crystalline solids. Phys. Rev. B, 66: 024302, Jun (2002).

DOI: 10.1103/physrevb.66.024302

[31] T Salditt, S Kalbfleisch, M Osterhoff, S P Krüger, M Bartels, K Giewekemeyer, H Neubauer, and M Sprung. Partially coherent nano-focused x-ray radiation characterized by Talbot interferometry. Optics Express, 19(10): 9656-9675, (2011).

DOI: 10.1364/oe.19.009656

[32] M Leitner. Studying Atomic Dynamics with Coherent X-rays. Springer, (2012).

[33] F Livet, F Bley, J Mainville, R Caudron, S G J Mochrie, E Geissler, G Dolino, D Abernathy, G Grübel, and M Sutton. Using direct illumination CCDs as high-resolution area detectors for X-ray scattering. Nucl. Instrum. Meth. A, 451(3): 596-609, (2000).

DOI: 10.1016/s0168-9002(00)00333-8

[34] D Lumma, L B Lurio, S G J Mochrie, and M Sutton. Area detector based photon correlation in the regime of short data batches: Data reduction for dynamic X-ray scattering. Review of Scientific Instruments, 71(9): 3274-3289, (2000).

DOI: 10.1063/1.1287637

[35] R Dinapoli, A Bergamaschi, D Greiffenberg, B Henrich, R Horisberger, I Johnson, A Mozzanica, V Radicci, B Schmitt, X Shi, et al. EIGER characterization results. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, (2013).

DOI: 10.1016/j.nima.2013.04.047

[36] J Philibert. Atom Movements Diffusion and Mass Transport in Solids, translated from the French by Steven J Rothman. Les Editions de Physique, Paris, France, (1991).

[37] H Mehrer. Diffusion in solids: fundamentals, methods, materials, diffusion-controlled processes. Springer Verlag, (2007).

[38] D Wolf. Theory of Mössbauer line broadening due to correlated diffusion in crystals. Appl. Phys. Lett., 30(12): 617-619, (1977).

DOI: 10.1063/1.89281

[39] F Haider, R Kozubski, and T A Abinandanan. Simulation Techniques. In W Pfeiler, editor, Alloy Physics: A Comprehensive Reference, pages 653-706. Wiley-VCH, (2007).

DOI: 10.1002/9783527614196.ch12

[40] J M Cowley. Short- and long-range order parameters in disordered solid solutions. Phys. Rev., 120: 1648-1657, (1960).

DOI: 10.1103/physrev.120.1648

[41] G E Murch and I V Belova. Chemical diffusion by vacancy pairs in intermetallic compounds with the B2 structure. Philosophical Magazine Letters, 80(8): 569-575, (2000).

DOI: 10.1080/09500830050110503

[42] L So Darken. Diffusion, mobility and their interrelation through free energy in binary metallic systems. Trans. Aime, 175(184): 41, (1948).

DOI: 10.1007/s11663-010-9344-x

[43] J R Manning. Diffusion kinetics in crystals. Van Norstrand, Princeton, New Jersey, page 117, (1968).

[44] I V Belova and G E Murch. Test of the validity of the Darken/Manning relation for diffusion in ordered alloys taking the L12 structure. Philosophical Magazine A, 78(5): 1085-1092, (1998).

DOI: 10.1080/01418619808239976

[45] M C Cadeville, C E Dahmani, and F Kern. Magnetism and spatial order in Ni-Pt and Co-Pt alloys. J. Magn. Magn. Mater., 54: 1055-1056, (1986).

DOI: 10.1016/0304-8853(86)90378-1

[46] R E Parra and J W Cable. Neutron study of magnetic-moment distribution in Ni-Pt alloys. Phys. Rev. B, 21: 5494-5504, (1980).

DOI: 10.1103/physrevb.21.5494

[47] R E Parra, R Medina, and J W Cable. Determination of lattice distortions in concentrated alloys by neutron diffuse scattering. Solid State Communications, 40(6): 679-682, (1981).

DOI: 10.1016/0038-1098(81)90618-9

[48] B E Warren, B L Averbach, and B W Roberts. Atomic Size Effect in the X-Ray Scattering by Alloys. Journal of Applied Physics, 22(12): 1493-1496, (1951).

DOI: 10.1063/1.1699898

[49] M Leitner and R Podloucky. Preliminary ab initio calculations of the interaction constants in Ni-Pt alloys. private communication, (2013).

[50] R Weinkamer, P Fratzl, B Sepiol, and G Vogl. Monte Carlo simulations of Mössbauer spectra in diffusion investigations. Phys. Rev. B, 59: 8622-8625, (1999).

DOI: 10.1103/physrevb.59.8622

[51] R Feldwisch, B Sepiol, and G Vogl. Elementary diffusion jump of iron atoms in intermetallic phases studied by Mössbauer spectroscopy - I. Fe-Al close to equiatomic stoichiometry. Acta metall. mater., 42(9): 3175 - 3181, (1994).

DOI: 10.1016/0956-7151(94)90416-2

[52] D Le Bolloc'h, J L Robertson, H Reichert, S C Moss, and M L Crow. X-ray and neutron scattering study of Si-rich Si-Ge single crystals. Phys. Rev. B, 63: 035204, Jan (2001).

DOI: 10.1103/physrevb.63.035204

[53] Y Shimizu, M Uematsu, and K M Itoh. Experimental evidence of the vacancy-mediated silicon self-diffusion in single-crystalline silicon. Phys. Rev. Lett., 98: 095901, Mar (2007).

DOI: 10.1103/physrevlett.98.095901