Atomistic origin of the thermodynamic activation energy for self-diffusion and order-order relaxation in intermetallic compounds I: analytical approach

References

• W. Pueschl, H. Numakura, and W. Pfeiler, Point defects atom jumps and diffusion, in Alloy Physics: A Comprehensive Reference, W. Pfeiler, ed., Wiley-VCH, Weinheim, 2007, pp. 173–280.10.1002/9783527614196
   Google Scholar
• E. Wimmer, W. Wolf, J. Sticht, P. Saxe, C.B. Geller, R. Najafabadi, and G.A. Young, Temperature-dependent diffusion coefficients from ab initio computations: Hydrogen, deuterium, and tritium in nickel, Phys. Rev. B 77 (2008), p. 134305.10.1103/PhysRevB.77.134305
   Web of Science ®Google Scholar
• R. Kozubski, Long-range order kinetics in Ni3Al-based intermetallic compounds with L12-type superstructure, Prog. Mater. Sci. 41 (1997), pp. 1–59.10.1016/S0079-6425(97)00002-9
   Web of Science ®Google Scholar
• P. Oramus, R. Kozubski, V. Pierron-Bohnes, M.C. Cadeville, and W. Pfeiler, Monte Carlo computer simulation of order-order kinetics in L12 – ordered Ni3Al binary system, Phys. Rev. B 63 (2001), p. 174109.10.1103/PhysRevB.63.174109
   Web of Science ®Google Scholar
• P. Oramus, C. Massobrio, M. Kozłowski, R. Kozubski, V. Pierron-Bohnes, M.C. Cadeville, and W. Pfeiler, Ordering kinetics in Ni3Al by molecular dynamics, Comput. Mater. Sci. 27 (2003), pp. 186–190.10.1016/S0927-0256(02)00444-5
   Web of Science ®Google Scholar
• R. Kozubski, D. Kmieć, E. Partyka, and M. Danielewski, Order-order kinetics in Ni50.5Al49.5 single crystal, Intermetallics 11 (2003), pp. 897–905.10.1016/S0966-9795(03)00099-2
   Web of Science ®Google Scholar
• M. Kozłowski, R. Kozubski, C. Goyhenex, V. Pierron-Bohnes, M. Rennhofer, and S. Malinov, Atomic ordering in nano-layered FePt, Intermetallics 17 (2009), pp. 907–913.10.1016/j.intermet.2009.03.019
   Web of Science ®Google Scholar
• M. Nikiel and R. Kozubski, Order-order kinetics in Ni50.5Al49.5 single crystal by quasi-residual resistometry, Intermetallics 25 (2012), pp. 5–8.10.1016/j.intermet.2012.02.002
   Web of Science ®Google Scholar
• P. Sowa, R. Kozubski, A. Biborski, E.V. Levchenko, A.V. Evteev, I.V. Belova, G.E. Murch, and V. Pierron-Bohnes, Self-diffusion and order-order kinetics in B2-ordering AB binary systems with a tendency for triple-defect formation: Monte Carlo simulation, Philos. Mag. 93 (2013), pp. 1987–1998.10.1080/14786435.2012.742591
   Web of Science ®Google Scholar
• A. Biborski, R. Kozubski, and V. Pierron-Bohnes, Order-order kinetics in triple-defect B2-ordered binary intermetallics: kinetic Monte Carlo simulation, Diffusion Foundations 2 (2014), pp. 191–220.10.4028/www.scientific.net/DF.2
   Google Scholar
• A. Biborski, L. Zosiak, R. Kozubski, R. Sot, and V. Pierron-Bohnes, Semi-grand canonical Monte Carlo simulation of ternary bcc lattice-gas decomposition: vacancy formation correlated with B2 atomic ordering in A-B intermetallics, Intermetallics 18 (2010), pp. 2343–2352.10.1016/j.intermet.2010.08.007
   Web of Science ®Google Scholar
• W.L. Bragg and E.J. Williams, The effect of thermal agitation on atomic arrangement in alloys, Proc. Royal Soc. London 145A. 145 (1934), pp. 699–730.10.1098/rspa.1934.0132
   Google Scholar
• G.J. Dienes, Kinetics of order-disorder transformations, Acta Metall. 3 (1955), pp. 549–557.10.1016/0001-6160(55)90114-0
   Google Scholar
• G.H. Vineyard, Theory of order-disorder kinetics, Phys. Rev. 102 (1956), pp. 981–992.10.1103/PhysRev.102.981
   Web of Science ®Google Scholar
• R. Kikuchi The path probability method, Prog. Theor. Phys. Supp. 35 (1966), pp. 1–64. 10.1143/PTPS.35.1
   Google Scholar
• R. Kikuchi, A theory of cooperative phenomena, Phys. Rev. 81 (1951), pp. 988–1003.10.1103/PhysRev.81.988
   Google Scholar
• M. Kogachi, T. Tanahashi, Y. Shirai, and M. Yamaguchi, Determination of vacancy concentration and defect structure in the B2 type NiAl β-phase alloys, Scr. Mater. 34 (1996), pp. 243–248.10.1016/1359-6462(95)00514-5
   Web of Science ®Google Scholar
• H.-E. Schaefer, K. Frenner, and R. Würschum, High-temperature atomic defect properties and diffusion processes in intermetallic compounds, Intermetallics 7 (1999), pp. 277–287.10.1016/S0966-9795(98)00121-6
   Web of Science ®Google Scholar
• R. Würschum, C. Grupp, and H.-E. Schaefer, Simultaneous study of vacancy formation and migration at high temperatures in B2-Type Fe Aluminides, Phys. Rev. Lett. 75 (1995), pp. 97–100.10.1103/PhysRevLett.75.97
   PubMed Web of Science ®Google Scholar
• H.-E. Schaefer, K. Frenner, and R. Würschum, Time-differential length change measurements for thermal defect investigations: intermetallic B2-FeAl and B2-NiAl compounds, a case study, Phys. Rev. Lett. 82 (1999), pp. 948–951.10.1103/PhysRevLett.82.948
   Web of Science ®Google Scholar
• H. Lang, K. Rohrhofer, P. Rosenkranz, R. Kozubski, W. Püschl, and W. Pfeiler, Long-range ordering in B2 FeAl: a resistometric study, Intermetallics 10 (2002), pp. 283–292.10.1016/S0966-9795(01)00135-2
   Web of Science ®Google Scholar
• S. Frank, S.V. Divinski, U. Södervall, and C. Herzig, Ni tracer diffusion in the B2-compound NiAl: influence of temperature and composition, Acta Mater. 49 (2001), pp. 1399–1411.10.1016/S1359-6454(01)00037-4
   Web of Science ®Google Scholar
• M. Leitner, B. Sepiol, L.-M. Stadler, B. Pfau, and G. Vogl, Atomic diffusion studied with coherent X-rays, Nat. Mater. 8 (2009), pp. 717–720.10.1038/nmat2506
   PubMed Web of Science ®Google Scholar
• M. Stana, M. Leitner, M. Ross, and B. Sepiol, Studies of atomic diffusion in Ni–Pt solid solution by X-ray photon correlation spectroscopy, J. Phys. Condens. Matter 25 (2013), p. 065401.
   Web of Science ®Google Scholar
• H. Bakker, in Diffusion in crystalline solids, G. E. Murch and A. S. Nowick eds., Academic Press, Orlando, 1984, pp. 189–256.
   Google Scholar
• I.V. Belova and G.E. Murch, The contribution of the tracer correlation factor to the diffusion activation energy in intermetallic compounds, J. Phys. Chem. Solids 61 (2000), pp. 1755–1760.10.1016/S0022-3697(00)00052-4
   Web of Science ®Google Scholar
• G.E. Murch Diffusion in crystalline solids, G. E. Murch, and A. S. Nowick, eds., Academic Press, Orlando, 1984, pp. 379–427.
   Google Scholar