The Manning factor for direct exchange and ring diffusion mechanisms

References

• L.S. Darken, Diffusion, mobility and their interrelation through free energy in binary metallic systems, Trans. AIME 180 (1949), pp. 430–438.
   Google Scholar
• I.V. Belova and G.E. Murch, Expressions for vacancy-wind factors occurring in interdiffusion in ternary and higher-order alloys, Acta Mater. 55 (2007), pp. 627–634.10.1016/j.actamat.2006.08.055
   Web of Science ®Google Scholar
• I.V. Belova and G.E. Murch, A new analysis of diffusion in ternary alloys: Application to Fe–Ni–Cr alloys, Acta Mater. 50 (2002), pp. 4617–4627.10.1016/S1359-6454(02)00312-9
   Web of Science ®Google Scholar
• I.V. Belova and G.E. Murch, Interdiffusion in ionic compounds, in Diffusion Phenomena in Engineering Materials, H. Mehrer, ed., Diffusion Foundations, TTP, Zurich, 2016, Vol. 6, pp. 44–58.
   Google Scholar
• J.R. Manning, Correlation factors for diffusion in nondilute alloys, Phys. Rev. B 4 (1971), pp. 1111–1121.10.1103/PhysRevB.4.1111
   Web of Science ®Google Scholar
• J.R. Manning, Diffusion in a chemical concentration gradient, Phys. Rev. 124 (1961), pp. 470–482.10.1103/PhysRev.124.470
   Web of Science ®Google Scholar
• I.V. Belova and G.E. Murch, Behaviour of the diffusion vacancy-wind factors in the concentrated random alloy, Philos. Mag. A 81 (2001), pp. 1749–1758.10.1080/01418610108216635
   Web of Science ®Google Scholar
• I.V. Belova and G.E. Murch, The six-jump cycle mechanism in intermetallics: The vacancy wind factor, Defect Diffus. Forum 213–215 (2003), pp. 95–106.10.4028/www.scientific.net/DDF.213-215
   Google Scholar
• I.V. Belova and G.E. Murch, Interdiffusion in intermetallics, Metall. Mater. Trans. A 44 (2013), pp. 4417–4421.10.1007/s11661-013-1853-1
   Google Scholar
• G.E. Murch and I.V. Belova, Tracer correlation, collective correlation and vacancy-wind factors in intermetallic compounds taking the B2 structure, Defect Diffus. Forum 179–180 (2000), pp. 1–16.10.4028/www.scientific.net/DDF.179-180
   Google Scholar
• B. Zhang, A. Griesche, and A. Meyer, Diffusion in Al–Cu melts studied by time-resolved X-ray radiography, Phys. Rev. Lett. 104 (2010), pp. 035902-1–035902-4.10.1103/PhysRevLett.104.035902
   Google Scholar
• A. Meyer, S. Stüber, D. Holland-Moritz, O. Heinen, and T. Unruh, Determination of self-diffusion coefficients by quasielastic neutron scattering measurements of levitated Ni droplets, Phys. Rev. B 77 (2008), pp. 092201-1–092201-4.10.1103/PhysRevB.77.092201
   Google Scholar
• S.K. Das, J. Horbach, M.M. Koza, S. Mavila Chatoth, and A. Meyer, Influence of chemical short-range order on atomic diffusion in Al–Ni melts, Appl. Phys. Lett. 86 (2005), pp. 011918-1–011918-3.10.1063/1.1845590
   Google Scholar
• S. Stüber, D. Holland-Moritz, T. Unruh, and A. Meyer, Ni self-diffusion in refractory Al–Ni melts, Phys. Rev. B 81 (2010), pp. 024204-1–024204-5.10.1103/PhysRevB.81.024204
   Google Scholar
• P. Kuhn, J. Horbach, F. Kargl, A. Meyer, and Th. Voigtmann, Diffusion and interdiffusion in binary metallic melts, Phys. Rev. B 90 (2014), pp. 024309-1–024309-14.10.1103/PhysRevB.90.024309
   Google Scholar
• A. Meyer and F. Kargl, Diffusion of mass in liquid metals and alloys – Recent experimental development and new perspectives, Int. J. Microgravity Sci. Appl. 30 (2013), pp. 30–35.
   Google Scholar
• F. Kargl, M. Engelhardt, F. Yang, H. Weis, P. Schmakat, B. Schillinger, A. Griesche, and A. Meyer, In situ studies of mass transport in liquid alloys by means of neutron radiography, J. Phys.: Condens. Matter, 23 (2011), pp. 254201-1–254201-8.
   Google Scholar
• F. Kargl, H. Weis, T. Unruh, and A. Meyer, Self diffusion in liquid aluminium, J. Phys.: Conf. Ser. 340 (2012), pp. 012077-1–012077-5.10.1088/1742-6596/340/1/012077
   Google Scholar
• E. Sondermann, F. Kargl, and A. Meyer, Influence of cross correlations on the interdiffusion in Al-rich Al–Ni melts, Phys. Rev. B 93 (2016), pp. 184201-1–184201-5.
   Web of Science ®Google Scholar
• J. Horbach, S.K. Das, A. Griesche, M.-P. Macht, G. Frohberg, and A. Meyer, Self-diffusion and interdiffusion in Al80Ni20 melts: Simulation and experiment, Phys. Rev. B 75 (2007), pp. 174304-1–174304-8.10.1103/PhysRevB.75.174304
   Web of Science ®Google Scholar
• T. Ahmed, A.V. Evteev, E.V. Levchenko, I.V. Belova, and G.E. Murch, To be submitted for publication.
   Google Scholar
• U. Sarder, A.V. Evteev, E.V. Levchenko, I.V. Belova, and G.E. Murch, Molecular Dynamics Study of Mass Transport Properties of Liquid Cu-Ag Alloys, in Mass Transport in Advanced Engineering Materials, A. Öchsner, G.E. Murch, and I.V. Belova, eds., Diffusion Foundations-TTP, Zürich, 2016, Vol. 9, pp. 58–73.
   Google Scholar
• X.-P. Tang, U. Geyer, R. Busch, W.L. Johnson, and Y. Wu, Diffusion mechanisms in metallic supercooled liquids and glasses, Nature 402 (1999), pp. 160–162.
   Web of Science ®Google Scholar
• F. Faupel, Diffusion in non-crystalline metallic and organic media, Phys. Status Solidi A 134 (1992), pp. 9–59.10.1002/(ISSN)1521-396X
   Web of Science ®Google Scholar
• F.H. Stillinger, Relaxation and flow mechanisms in “fragile” glass-forming liquids, J. Chem. Phys. 89 (1988), pp. 6461–6469.10.1063/1.455365
   Web of Science ®Google Scholar
• S.A. Kivelson, X. Zhao, D. Kivelson, T.M. Fischer, and C.M. Knobler, Frustration-limited clusters in liquids, J. Chem. Phys. 101 (1994), pp. 2391–2397.10.1063/1.468414
   Web of Science ®Google Scholar
• S.J. Rothman, The measurement of tracer diffusion coefficients in solids, in Diffusion in Crystalline Solids, G.E. Murch and A.S. Nowick, eds., Academic Press, Orlando, FL, 1984, pp. 1–61.
   Google Scholar
• H. Bakker, Self-Diffusion in homogeneous binary alloys and intermetallic phases, in Diffusion in Solids Metals and Alloys, H. Mehrer, ed., New Series III/26, Landolt-Börnstein, Berlin, 1990, pp. 213–278.
   Google Scholar
• J. Tuggle, A. Giordani, N. Kulkarni, R. Warmack, and J. Hunter, Secondary ion mass spectrometry for Mg tracer diffusion: Issues and solutions, Surf. Interface Anal. 46 (2014), pp.291–293. 10.1002/sia.5618.
   Web of Science ®Google Scholar
• R.A. De Souza and M. Martin, Secondary ion mass spectrometry (SIMS) – A powerful tool for studying mass transport over various length scales, Phys. Status Solidi C 4 (2007), pp. 1785–1801.10.1002/(ISSN)1610-1642
   Google Scholar
• J. Bardeen, C. Herring, and W. Shockley, Imperfections in Nearly Perfect Crystals, Wiley, New York, 1952, p. 261.
   Google Scholar
• R. Howard and A. Lidiard, Matter transport in solids, Rep. Prog. Phys. 27 (1964), pp. 161–240.10.1088/0034-4885/27/1/305
   Web of Science ®Google Scholar
• J.R. Manning, Diffusion kinetics for atoms in crystals, Am. J. Phys. 36 (1968), pp. 922–923.10.1119/1.1974325
   Google Scholar
• H. Sato and R. Kikuchi, Theory of many-body diffusion by the path-probability method: Conversion from ensemble averaging to time averaging, Phys. Rev. B 28 (1983), pp. 648–656.10.1103/PhysRevB.28.648
   Web of Science ®Google Scholar
• N. El-Meshad and R.A. Tahir-Kheli, Diffusion in mixed A-B alloys in two and three dimensions, Phys. Rev. B 32 (1985), pp. 6176–6180.10.1103/PhysRevB.32.6176
   Web of Science ®Google Scholar
• P.C. Holdsworth and R.J. Elliott, Correlated random walk in a multicomponent alloy self-consistent decoupling approximation, Philos. Mag. A 54 (1986), pp. 601–609.10.1080/01418618608244021
   Web of Science ®Google Scholar
• L. Moleko and A. Allnatt, Exact linear relations between the phenomenological coefficients for matter transport in a random alloy, Philos. Mag. A 58 (1988), pp. 677–682.10.1080/01418618808209945
   Web of Science ®Google Scholar
• L. Moleko, A. Allnatt, and E. Allnatt, A self-consistent theory of matter transport in a random lattice gas and some simulation results, Philos. Mag. A 59 (1989), pp. 141–160.10.1080/01418618908220335
   Web of Science ®Google Scholar
• I. Belova and G. Murch, Tracer correlation factors in the random alloy, Philos. Mag. A 80 (2000), pp. 1469–1479.10.1080/01418610008212131
   Web of Science ®Google Scholar
• I.V. Belova and G.E. Murch, Analysis of interdiffusion and intrinsic diffusion in multicomponent alloys to obtain information about diffusion mechanisms, Def. Diff. Forum (2007), pp. 237–246.
   Google Scholar
• I.V. Belova, A.R. Allnatt, and G.E. Murch, Interdiffusion in strongly ionic insulating compounds: The Nernst–Planck equation, Philos. Mag. 87 (2007), pp. 4169–4180.10.1080/14786430701531014
   Web of Science ®Google Scholar
• A.R. Allnatt and A.B. Lidiard, Atomic transport in solids, Cambridge University Press, Cambridge, 1993.10.1017/CBO9780511563904
   Google Scholar