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Atomic mobilities and diffusivities in Al alloys

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Abstract

Knowledge of diffusivity is a prerequisite for understanding many scientific and technological disciplines. In this paper, firstly major experimental methods, which are employed to provide various diffusivity data, are briefly described. Secondly, the fundamentals of various computational methods, including first-principles method, embedded atomic method/molecular dynamic simulation, semi-empirical approaches, and phenomenological DICTRA technique, are demonstrated. Diffusion models recently developed for order/disorder transitions and stoichiometric compounds are also briefly depicted. Thirdly, a newly established diffusivity database for liquid, fcc_A1, L12, bcc_A2, bcc_B2, and intermetallic phases in the multicomponent Al alloys is presented via a few case studies in binary, ternary and quaternary systems. And the integration of various computational techniques and experimental methods is highlighted. The reliability of this diffusivity database is validated by comparing the calculated and measured concentration profiles, diffusion paths, and Kirkendall shifts in various binary, ternary and quaternary diffusion couples. Next, the established diffusivity databases along with thermodynamic and other thermo-physical properties are utilized to simulate the microstructural evolution for Al alloys during solidification, interdiffusion and precipitation. A special discussion is presented on the phase-field simulation of interdiffusion microstructures in a series of Ni-Al diffusion couples composed of γ, γ′, and β phases under the effects of both coherent strain and external compressive force. Future orientations in the establishment of next generation of diffusivity database are finally addressed.

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References

  1. Janz A, Groebner J, Schmid-Fetzer R. Thermodynamics and Constitution of Mg-Al-Ca-Sr-Mn Alloys: Part II. Procedure for Multicomponent Key Sample Selection and Application to the Mg-Al-Ca-Sr and Mg-Al-Ca-Sr-Mn Systems. J Phase Equilib Diffus, 2009, 30: 157–175

    Google Scholar 

  2. Pisch A, Schmid-Fetzer R, Cacciamani G, et al. Mg-rich phase equilibria and thermodynamic assessment of the Mg-Sc system. Z Metallkd, 1998, 89: 474–477

    Google Scholar 

  3. Du Y, Liu S H, Zhang L, et al. An overview on phase equilibria and thermodynamic modeling in multicomponent Al alloys: Focusing on the Al-Cu-Fe-Mg-Mn-Ni-Si-Zn system. CALPHAD, 2011, 35(3): 422–455

    Google Scholar 

  4. http://www.thermocalc.com/

  5. http://www.computherm.com/pandat.html

  6. Du Y, Chang Y A, Liu S, et al. Thermodynamic description of the Al-Fe-Mg-Mn-Si system and investigation of microstructure and microsegregation during directional solidification of an Al-Fe-Mg-Mn-Si alloy. Z Metallkd, 2005, 96: 1351–1362

    Google Scholar 

  7. http://www.thermocalc.se

  8. Purdy G R (Editor). Fundamentals and Applications of Ternary Diffusion. Proceedings of the International Symposium on Fundamentals and Applications of Ternary Diffusion, Canada, 1990

    Google Scholar 

  9. Zhao D, Kong Y, Wang A, et al. Self-diffusion coefficient of fcc Mg: First-principles calculations and semi-empirical predictions. J Phase Equilib Diffus, 2011, 32: 128–137

    Google Scholar 

  10. Du Y, Chang Y A, Huang B, et al. Diffusion coefficients of some solutes in fcc. and liquid Al: Critical evaluation and correlation. Mater Sci Eng, A, 2003, 363: 140–151

    Google Scholar 

  11. http://www.thermocalc.se

  12. Cui S, Du Y, Zhang L, et al. Assessment of atomic mobilities in fcc. Al-Zn and Ni-Zn alloys. CALPHAD, 2010, 34: 446–451

    Google Scholar 

  13. Liu D, Zhang L, Du Y, et al. Assessment of atomic mobilities of Al and Cu in fcc Al-Cu alloys. CALPHAD, 2009, 33: 761–768

    Google Scholar 

  14. Zhang L, Du Y, Steinbach I, et al. Diffusivities of an Al-Fe-Ni melt and their effects on the microstructure during solidification. Acta Mater, 2010, 58: 3664–3675

    Google Scholar 

  15. Zhang W, Du Y, Zhao D, et al. Assessment of the atomic mobility in fcc Al-Cu-Mg alloys. CALPHAD, 2010, 34: 286–293

    Google Scholar 

  16. Cui S, Zhang L, Du Y, et al. Assessment of atomic mobilities in fcc Cu-Ni-Zn alloys. CALPHAD, 2010, 35: 231–241

    Google Scholar 

  17. Steinbach I, Boettger B, Eiken J, et al. Calphad and phase-field modeling: A successful liaison. J Phase Equilib Diffus, 2007, 28: 101–106

    Google Scholar 

  18. Mehrer H. Diffusion in Solid Metals. Berlin, Heidelberg: Springer-Verlag, 1990

    Google Scholar 

  19. Mehrer H. Diffusion in Solids: Fundamentals, Methods, Materials, Diffusion-Controlled Processes. Berlin, Heidelberg: Springer-Verlag, 2007

    Google Scholar 

  20. Tyrrell H J V, Harris K R. Diffusion in Liquids: A Theoretical and Experimental Study. London, Boston: Butterworths, 1984

    Google Scholar 

  21. Griesche A, Macht M P, Frohberg G. Diffusion in metallic melts. Defect Diffus Forum, 2007, 266: 101–108

    Google Scholar 

  22. Griesche A, Zhang B, Horbach J, et al. Interdiffusion and thermodynamic forces in binary liquid alloys. Mater Sci Forum, 2010, 649: 481–486

    Google Scholar 

  23. Griesche A, Macht M P, Garandet J P, et al. Diffusion and viscosity in molten Pd40Ni40P20 and Pd40Cu30Ni10P20 alloys. J Non-Cryst Sol, 2004, 336: 173–178

    Google Scholar 

  24. Horbach J, Das S K, Griesche A, et al. Self-diffusion and interdiffusion in Al80Ni20 melts: Simulation and experiment. Phys Rev B, 2007, 75: 174304

    Google Scholar 

  25. Griesche A, Chathoth S M, Macht M P, et al. Self diffusion in Al-Ni-Ce and Al-Ni-La melts. High Temperatures-High Pressures, 2008, 37: 153–162

    Google Scholar 

  26. Griesche A, Macht M P, Frohberg G. First results from diffusion measurements in liquid multicomponent Al-based alloys. J Non-Cryst Sol, 2007, 353: 3305–3309

    Google Scholar 

  27. Praizey J P, Garandet J P, Frohberg G, et al. Diffusion experiments in liquid metals preliminary results (AGAT-Module on FOTON12). Proceedings of the first international symposium on microgravity research & applications in physical sciences and biotechnology, 2001. 481–490

  28. Griesche A, Macht M P, Suzuki S, et al. Self-diffusion of Pd, Cu and Ni in Pd-based equilibrium melts. Scr Mater, 2007, 57: 477–480

    Google Scholar 

  29. Frohberg G. Diffusion in Liquids. In: Sahm P R, Keller M H, Schiewe B, eds. Scientific Results of the German Spacelab Mission D-2, Cologne: DLR, 1987

    Google Scholar 

  30. Zhang B, Griesche A, Meyer A. Diffusion in Al-Cu melts studied by time-resolved X-ray radiography. Phys Rev Lett, 2010, 104: 035902

    Google Scholar 

  31. Griesche A, Zhang B, Horbach J, et al. Atomic diffusion and its relation to thermodynamic forces in Al-Ni melts. Defect Diffus Forum, 2009, 289–292: 705–710

    Google Scholar 

  32. Griesche A, Zhang B, Solorzano E, et al. Note: X-ray radiography for measuring chemical diffusion in metallic melts. Rev Sci Instrum, 2010, 81: 056104

    Google Scholar 

  33. Meyer A. Self-diffusion in liquid copper as seen by quasielastic neutron scattering. Phys Rev B, 2010, 81: 012102

    Google Scholar 

  34. Meyer A, Petry W, Koza M, et al. Fast diffusion in ZrTiCuNiBe melts. Appl Phys Lett, 2003, 83: 3894–3896

    Google Scholar 

  35. Holland-Moritz D, Stueber S, Hartmann H, et al. Structure and dynamics of liquid Ni36Zr64 studied by neutron scattering. Phys Rev B, 2009, 79: 064204

    Google Scholar 

  36. Stueber S, Holland-Moritz D, Unruh T, et al. Ni self-diffusion in refractory Al-Ni melts. Phys Rev B, 2010, 81: 024204

    Google Scholar 

  37. Chathoth S M, Meyer A, Koza M M, et al. Atomic diffusion in liquid Ni, NiP, PdNiP, and PdNiCuP alloys. Appl Phys Lett, 2004, 85: 4881–4883

    Google Scholar 

  38. Das S K, Horbach J, Koza M M, et al. Influence of chemical short-range order on atomic diffusion in Al-Ni melts. Appl Phys Lett, 2005, 86: 011918

    Google Scholar 

  39. Meyer A, Stueber S, Holland-Moritz D, et al. Determination of self-diffusion coefficients by quasielastic neutron scattering meas urements of levitated Ni droplets. Phys Rev B, 2008, 77: 092201

    Google Scholar 

  40. Pommrich A, Meyer A, Holland-Moritz D, et al. Nickel self-diffusion in silicon-rich Si-Ni melts. Appl Phys Lett, 2008, 92: 241922

    Google Scholar 

  41. Holland-Moritz D, Stueber S, Hartmann H, et al. Ni self-diffusion in Zr-Ni(-Al) melts. J Phys, 2009, 144: 012119

    Google Scholar 

  42. Kordel T, Holland-Moritz D, Yang F, et al. Neutron scattering experiments on liquid droplets using electrostatic levitation. Phys Rev B, 2011, 83: 104205

    Google Scholar 

  43. Rhim W K, Chung S K, Barber D, et al. An electrostatic levitator for high-temperature containerless materials processing in 1-g. Rev Sci Instrum, 1993, 64: 2961–2970

    Google Scholar 

  44. Tang K, Ovrelid E J, Tranell G, et al. Critical assessment of the impurity diffusivities in solid and liquid silicon. JOM, 2009; 61: 49–55

    Google Scholar 

  45. Zoellmer V, Raetzke K, Faupel F. Diffusion in a metallic melt at the critical temperature of mode coupling theory. Phys Rev Lett, 2003, 90: 195502

    Google Scholar 

  46. Bartsch A, Raetzke K, Meyer A, et al. Dynamic arrest in multicomponent glass-forming alloys. Phys Rev Lett, 2010, 104: 195901

    Google Scholar 

  47. Nowick A S, Berry B S. Anelastic Relaxation in Crystalline Solids. New York: Academic Press, 1972

    Google Scholar 

  48. Kanert O. Dynamical properties of defects in solids. Phys Reports, 1982, 91: 183–232

    Google Scholar 

  49. Bergner D. Diffusion of impurity elements in aluminum. Neue Huette, 1984, 29: 207–210

    Google Scholar 

  50. Murch C E, Nowick A S. The measurement of tracer diffusion coefficients in solids. Diffusion in Crystalline Solids. In: Rothman S J, ed. New York: Academic Press, 1984.1

    Google Scholar 

  51. Madelung O, Mehrer H. Numerical Data and Functional Relationshiops in Science and Technology. In: Bakker H, Bruff C M, et al. editor Group III: Crystal and Solid State Physics, Diffusion in Solid Metals and Alloys. Berlin, Heidelberg: Springer-Verlag, 1990. 13–24

    Google Scholar 

  52. Ushino S, Fujikawa S, Hirano K. Impurity diffusion of three radioactive isotopes of copper in aluminum. Keikinzoku, 1991, 41: 433–439

    Google Scholar 

  53. Shi Y, Frohberg G, Wever H. Diffusion of 63Ni and 114mIn in the γ′-phase Ni3Al. Phys Status Solidi A, 1995, 152: 361–375

    Google Scholar 

  54. Cserhati C, Szabo I A, Marton Z, et al. Tracer diffusion of 63Ni in Ni3(Al, Ge) ternary intermetallic compound. Intermetallics, 2002, 10: 887–892

    Google Scholar 

  55. Hirano K, Fujikawa S. Impurity diffusion in aluminum. J Nucl Mater, 1978, 69–70: 564–566

    Google Scholar 

  56. Anand M S, Murarka S P, Agarwala R P. Diffusion of copper in nickel and aluminum. J Appl Phys, 1965, 36: 3860–3862

    Google Scholar 

  57. Fujikawa S, Hirano K. Diffusion of 28magnesium in aluminum. Mater Sci Eng, 1977, 27: 25–33

    Google Scholar 

  58. Hirano K, Agarwala R P, Averbaeh B L, et al. Diffusion in cobaltnickel alloys. J Appl Phys, 1962, 33: 3049–3054

    Google Scholar 

  59. Mehrer H, Divinski S. Diffusion in metallic elements and intermetallics. Diffus Defect Data, 2009, 289–292: 15–38

    Google Scholar 

  60. Mantina M. A first-principles methodology for diffusion coefficients in metals and dilute alloys. In: The Graduate School College of Earth and Mineral Sciences. Pennsylvania: The Pennsylvania State University, 2008

    Google Scholar 

  61. Yao J, Cui Y W, Liu H, et al. Diffusional mobility for fcc phase of Al-Mg-Zn system and its applications. CALPHAD, 2008, 32: 602–607

    Google Scholar 

  62. Engström A, Ågren J. Assessment of diffusional mobilities in face-centered cubic Ni-Cr-Al alloys. Z Metallkd, 1996, 87: 92–97

    Google Scholar 

  63. Cui Y W, Oikawa K, Kainuma R, et al. Study of diffusion mobility of Al-Zn solid solution. J Phase Equilib Diffus, 2006, 27: 333–342

    Google Scholar 

  64. Zhang L, Du Y, Chen Q, et al. Atomic mobilities and diffusivities in the fcc, L12 and B2 phases of the Ni-Al system. Int J Mater Res, 2010, 101: 1461–1475

    Google Scholar 

  65. Le Claire A D, Lidiard A B. Correlation effects in diffusion in crystals. Philos Mag (1798–1977), 1956, 1: 518–527

    Google Scholar 

  66. Hehenkamp T. Absolute vacancy concentrations in noble metals and some of their alloys. J Phys Chem Solids, 1994, 55: 907–915

    Google Scholar 

  67. Fultz B. Vibrational thermodynamics of materials. Prog Mater Sci, 2009, 55: 247–352

    Google Scholar 

  68. Eyring H. The Activated complex in chemical reactions. J Chem Phys, 1935, 3: 107–115

    Google Scholar 

  69. Henkelman G, Jónsson H. Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. J Chem Phys, 2000, 113: 9978–9985

    Google Scholar 

  70. Vineyard G H. Frequency factors and isotope effects in solid-state rate processes. Phys Chem Soli, 1957, 3: 121–127

    Google Scholar 

  71. Huang S, Worthington D L, Asta M, et al. Calculation of impurity diffusivities in a-Fe using first-principles methods. Acta Mater, 2009, 58: 1982–1293

    Google Scholar 

  72. Mantina M, Wang Y, Chen L Q, et al. First principles impurity diffusion coefficients. Acta Mater, 2009, 57: 4102–4108

    Google Scholar 

  73. Van der Ven A, Ceder G. First principles calculation of the interdiffusion coefficient in binary alloys. Phys Rev Lett, 2005, 94: 045901

    Google Scholar 

  74. Allnatt A R. Einstein and linear response formulas for the phenomenological coefficients for isothermal matter transport in solids. J Phys C, 1982, 15: 5605–5613

    Google Scholar 

  75. Cahn J W, Larche F C. An invariant formulation of multicomponent diffusion in crystals. Scr Metall, 1983, 17: 927–932

    Google Scholar 

  76. Szpunar B, Smith R. A molecular dynamics simulation of the diffusion of the solute (Au) and the self-diffusion of the solvent (Cu) in a very dilute liquid Cu-Au solution. J Phys-Condens Matter, 2010, 22: 035105

    Google Scholar 

  77. Jang J, Kwon J, Lee B. Effect of stress on self-diffusion in bcc Fe: An atomistic simulation study. Scr Mater, 2010, 63: 39–42

    Google Scholar 

  78. Arrhenius S. Chemical reaction velocities. Zeit Physikal Chem, 1899, 28: 317–35

    Google Scholar 

  79. Askill J. Tracer Diffusion Data for Metals Alloys, and Simple Oxides. New York: IFI/Plenum, 1970. 19–26

    Google Scholar 

  80. Sherby O D, Simnad M T. Prediction of atomic mobility in metallic systems. ASM Trans Q, 1961, 54: 227–240

    Google Scholar 

  81. LeClaire A D. Diffusion in Body Centre Cubic Metals. Ohio: American Society for Metals, Metals Park, 1962. 10

  82. Cahoon J R. A modified hole theory for solute impurity diffusion in liquid metals. Metall Mater Trans A, 1997, 28: 583–593

    Google Scholar 

  83. Gòrecki T. Changes in the activation energy for self- and impurity-diffusion in metals on passing through the melting point. J Mater Sci Lett, 1990, 9: 167–169

    Google Scholar 

  84. Dushman S, Langmuir I. The diffusion coefficient in solids and its temperature coefficient. Proc Am Phys Soc, 1922: 113

  85. Zener C. Relation between residual strain energy and elastic moduli. Acta Crystallogr, 1949, 2: 163–166

    Google Scholar 

  86. Swalin R A. Correlation between frequency factor and activation energy for solute diffusion. J Appl Phys, 1956, 27: 554–555

    Google Scholar 

  87. Liu Y, Long Z, Wang H, et al. A predictive equation for solute diffusivity in liquid metals. Scr Mater, 2006, 55: 367–370

    Google Scholar 

  88. Su X, Yang S, Wang J, et al. A new equation for temperature dependent solute impurity diffusivity in liquid metals. J Phase Equilib Diffus, 2010, 31: 333–340

    Google Scholar 

  89. Brown A M, Ashby M F. Correlations for diffusion constants. Acta Metall, 1980, 28: 1085–1101

    Google Scholar 

  90. Vignes A, Birchenall C E. Concentration dependence of the interdiffusion coefficient in binary metallic solid solution. Acta Metall, 1968, 16: 1117–1125

    Google Scholar 

  91. Jönsson B. Assessment of the mobility of carbon in fcc C-Cr-Fe-Ni alloys. Z Metallkd, 1994, 85: 502–509

    Google Scholar 

  92. Andersson JO, Höglund L, Jönsson B, et al. Fundamentals and Applications of Ternary Diffusion. In: Prudy G R, ed. New York: Pergamon Press, 1990. 153

    Google Scholar 

  93. Girifalco L A. Vacancy concentration and diffusion in order-disorder alloys. Phys Chem Solids, 1964, 25: 323–333

    Google Scholar 

  94. Helander T, Ågren J. A phenomenological treatment of diffusion in Al-Fe and Al-Ni alloys having B2-bcc. ordered structure. Acta Mater, 1999, 47: 1141–1152

    Google Scholar 

  95. Campbell C E. Assessment of the diffusion mobilities in the γ′ and B2 phases in the Ni-Al-Cr system. Acta Mater, 2008, 56: 4277–4290

    Google Scholar 

  96. Du Y, Schuster J C. An effective approach to describe growth of binary intermediate phases with narrow ranges homogeneity. Metall Mater Trans A, 2001, 32: 2396–2400

    Google Scholar 

  97. Zhang L, Du Y, Ouyang Y, et al. Atomic mobilities, diffusivities and simulation of diffusion growth in the Co-Si system. Acta Mater, 2008, 56: 3940–3950

    Google Scholar 

  98. Zhang L, Du Y, Xu H, et al. Experimental investigation and thermodynamic description of the Co-Si system. CALPHAD, 2006, 30: 470–481

    Google Scholar 

  99. Liu Y, Yu D, Zhang L, et al. Atomic mobilities and diffusional growth in solid phases of the V-Nb and V-Zr systems. CALPHAD, 2009, 33: 425–432

    Google Scholar 

  100. Brick R M, Phillips A. Diffusion of copper and magnesium into aluminum. Am Inst Mining Met Eng, Inst Metals Div, Tech Pub, 1937, 781: 17–36

    Google Scholar 

  101. Beerwald A. Diffusion of various metals in aluminum. Z Elektrochem Angew Phys Chem, 1939, 45: 789–795

    Google Scholar 

  102. Buckle H. The diffusion of Cu, Mg, Mn and Si into Al, Z. Elektrochem Angew Phys Chem, 1943, 49: 238–242

    Google Scholar 

  103. Bungardt W. Corrosion protection of aluminum-copper-magnesium alloys by layers of calcium-bearing aluminum. Z Metallkd, 1940, 32: 363–368

    Google Scholar 

  104. Bungardt W, Bollenrath F. The diffusion of magnesium in aluminum. Z Metallkd, 1938, 30: 377–383

    Google Scholar 

  105. Moreau G, Cornet J A, Calais D. Acceleration de la diffusion chimique sous irradiation dans le systeme aluminium-magnesium. J Nucl Mater, 1971, 38: 197–202

    Google Scholar 

  106. Hirano K, Fujikawa S. Impurity diffusion in aluminum. Kakuriken Kenkyu Hokoku (Tohoku Daigaku), 1976, 9: 291–296

    Google Scholar 

  107. Verlinden J, Gijbels R. Impurity diffusion in aluminum as determined from ion-probe mass analysis. Adv Mass Spectrom, 1980, 8A: 485–495

    Google Scholar 

  108. Rothman S J, Peterson N L, Nowicki L J, et al. Tracer diffusion of magnesium in aluminum single crystals. Phys Status Solidi B, 1974, 63: K29–K33

    Google Scholar 

  109. Doig P, Edington J W, Hibbert G. Measurement of magnesium supersaturations within precipitate-free zones in aluminum-zinc-magnesium alloys. Philos Mag, 1973, 28: 971–981

    Google Scholar 

  110. van Horn K R. Properties, Physical Metallurgy and Phase Diagrams. In: Fricke W G, ed. Ohio: American Society for Metals, Metals Park, 1967

    Google Scholar 

  111. Minamino Y, Yamane T, Shimomura A, et al. Effect of high pressure on interdiffusion in an aluminum-magnesium alloy. J Mater Sci, 1983, 18: 2679–2687

    Google Scholar 

  112. Fujikawa S, Takada Y. Interdiffusion between aluminum and Al-Mg alloys. Defect Diffusion Forum, 1997, 143–147: 409–414

    Google Scholar 

  113. Swalin R A, Martin A. Solute diffusion in nickel-base substitutional solid solutions. J Met, 1956, 8: 567–572

    Google Scholar 

  114. Whittenberger J D. Diffusion in the nickel-rich, nickel-aluminum solid solution at 1260°C. Metall Mater Trans B, 1972, 3: 2010–2012

    Google Scholar 

  115. Janssen M M P. Diffusion in the nickel-rich part of the nickelaluminum system at 1000 to 1300°C. Nickel-Aluminum (Ni3A1) layer growth, diffusion coefficients, and interface concentrations. Metall Trans, 1973, 4: 1623–1633

    Google Scholar 

  116. Yamamoto T, Takashima T, Nishida K. Interdiffusion in z-solid solution of the nickel-aluminum system. Nippon Kinzoku Gakkaishi, 1980, 44: 294–299

    Google Scholar 

  117. Green A, Swindells N. Measurement of interdiffusion coefficients in cobalt-aluminum and nickel-aluminum systems between 1000 and 1200°C. Mater Sci Tech, 1985, 1: 101–103

    Google Scholar 

  118. Watanabe M, Horita Z, Fujinami T, et al. Application of analytical electron microscopy to diffusivity measurement in nickel-aluminum system. Defect Diffusion Forum, 1993, 95–98: 579–585

    Google Scholar 

  119. Watanabe M, Horita Z, Smith D J, et al. Observation and microanalysis across nickel/nickel-aluminum (Ni3Al) diffusion-couple interface. Defect Diffusion Forum, 1993, 95–98: 587–592

    Google Scholar 

  120. Watanabe M, Horita Z, Sano T, et al. Electron microscopy study of Ni/Ni3Al diffusion-couple interface-II. Diffusivity measurement. Acta Metall, 1994, 42: 3389–3396

    Google Scholar 

  121. Watanabe M, Horita Z, Smith D J, et al. Electron microscopy study of Ni/Ni3Al diffusion-couple interface-I. Microstructural observation and microchemical analysis. Acta Metall, 1994, 42: 3381–3387

    Google Scholar 

  122. Watanabe M, Horita Z, Nemoto M. Measurements of interdiffusion coefficients in Ni-Al system. Defect Diffusion Forum, 1997, 143–147: 345–350

    Google Scholar 

  123. Watanabe M, Horita Z, Nemoto M. Analytical electron microscopy study of diffusion-bonded multiphase system. Interface Sci 1997, 4: 229–241

    Google Scholar 

  124. Susan D F, Marder A R. Ni-Al composite coatings: Diffusion analysis and coating lifetime estimation. Acta Mater, 2001, 49: 1153–1163

    Google Scholar 

  125. Adams J B, Foiles S M, Wolfer W G. Self-diffusion and impurity diffusion of fcc. metals using the five-frequency model and the embedded atom method. J Mater Res, 1989, 4: 102–112

    Google Scholar 

  126. Mantina M, Wang Y, Arroyave R, et al. First-principles calculation of self-diffusion coefficients. Phys Rev Lett, 2008, 100: 215901

    Google Scholar 

  127. Hancock G F. Diffusion of nickel in alloys based on the intermetallic compound Ni3Al(γ′). Phys Status Solidi A, 1971, 7: 535–540

    Google Scholar 

  128. Bronfin M B, Bulatov G S, Drugova I A. Self-diffusion of nickel in the nickel-aluminum (Ni3Al) intermetallide and in pure nickel. Fiz Met Metalloved, 1975, 40: 363–366

    Google Scholar 

  129. Larikov L N, Geichenko V V, Fal schenko V M. Diffusion Process in Ordered Alloys. Kiev: Naukova Dumka, 1975

    Google Scholar 

  130. Hoshino K, Rothman S J, Averback R S. Tracer diffusion in pure and boron-doped nickel-aluminide (Ni3Al). Acta Metall, 1988, 36: 1271–1279

    Google Scholar 

  131. Frank S, Soedervall U, Herzig C. Self-diffusion of Ni in single and polycrystals of Ni3Al. A study of sims and radiotracer analysis. Phys Status Solidi B, 1995, 191: 45–55

    Google Scholar 

  132. Horbach J, Das S K, Griesche A, et al. Self-diffusion and interdiffusion in Al80Ni20 melts: Simulation and experiment. Phys Rev B, 2007, 75: 174–304

    Google Scholar 

  133. Zhang W, Du Y, Zhang L, et al. Atomic mobility, diffusivity and diffusion growth simulation for fcc Cu-Mn-Ni alloys. CALPHAD, 2011, 35: 367–375

    Google Scholar 

  134. Iijima Y, Hirano K, Sato K. Interdiffusion in copper-manganese alloys. Trans JIM, 1977, 18: 835–842

    Google Scholar 

  135. Gulpen J H. Eindhoven. The Netherlands: Eindhoven University of Technology, 1995

    Google Scholar 

  136. Yin M, Du Y, Cui S, et al. Assessment of atomic mobilities in fcc Al-Cu-Mn alloys. Int J Mater Res, 2011, accepted

  137. Takahashi T, Kato M, Minamino Y, et al. Interdiffusion in the α solid solution of Al-Cu-Mg system. Keikinzoku, 1989, 39(4): 287–292.

    Google Scholar 

  138. Takahashi T, Minamino Y, Yamane T. Interdiffusion in the α solid solution of Cu-Ni-Mn system. Nippon Kinzoku Gakkaishi, 1987. 51

  139. Kansky K E, Dayananda M A. Quaternary diffusion in Cu-Mn-Ni-Zn system at 775°C. Metall Trans A, 1985, 16: 1123–1132

    Google Scholar 

  140. Chen L Q. Phase-field models for microstructure evolution. Annu Rev Mater Res, 2002, 32: 113–140

    Google Scholar 

  141. Boettinger W J, Warren J A, Beckermann C, et al. Phase-field simulation of solidification. Annu Rev Mater Res, 2002, 32: 163–194

    Google Scholar 

  142. Steinbach I. Phase-field models in materials science. Modell Simul Mater Sci Eng, 2009, 17: 073001

    MathSciNet  Google Scholar 

  143. Steinbach I, Nestler B, Seeßelberg M, et al. A phase field concept for multiphase systems. Physica D, 1996, 94: 135–147

    MATH  Google Scholar 

  144. Tiaden J, Nestler B, Diepers H J, et al. The multiphase-field model with an integrated concept for modeling solute diffusion. Physica D, 1998, 115: 73–86

    MATH  Google Scholar 

  145. Steinbach I. A generalized field method for multiphase transformations using interface fields. Physica D, 1999, 134: 385–393

    MathSciNet  MATH  Google Scholar 

  146. Steinbach I. Multi phase field model for solid state transformation with elastic strain. Physica D, 2006, 217: 153–160

    MATH  Google Scholar 

  147. Eiken J, Boettger B, Steinbach I. Multiphase-field approach for multicomponent alloys with extrapolation scheme for numerical application. Phys Rev E, 2006, 73: 066122

    Google Scholar 

  148. Boettger B, Eiken J, Steinbach I. Phase field simulation of equiaxed solidification in technical alloys. Acta Mater, 2006, 54: 2697–2704

    Google Scholar 

  149. Boettger B, Apel M, Eiken J, et al. Phase-field simulation of solidification and solid-state transformations in multicomponent steels. Steel Res Int, 2008, 79: 608–616

    Google Scholar 

  150. Zhang L, Steinbach I, Du Y. Phase-field simulation of diffusion couples in the Ni-Al system. Int J Mater Res, 2011, 102: 371–380

    Google Scholar 

  151. Cserhati C, Paul A, Kodentsov A A, et al. Intrinsic diffusion in Ni3Al system. Intermetallics, 2003, 11: 291–297

    Google Scholar 

  152. Liu W, Rosner H, Nembach E. Search for γ-precipitate hardenable quaternary L12-ordered γ′-intermetallics with compositions around Ni3(Al,Si,Ti), (Ni,Co)3(Al,Ti), and (Ni,Co)3(Si,Ti). Z Metallkd, 1997, 88: 648–651

    Google Scholar 

  153. Ma Y, Ardell A J. Coarsening of γ-(Ni-Al solid solution) precipitates in a γ′-(Ni3Al) matrix. Acta Mater, 2007, 55: 4419–4427

    Google Scholar 

  154. Sun W, Cui S, Zhang L, et al. Phase-field simulation of microstructure evolution of γ precipitate in γ′ matrix in Ni-Al alloys. 12th International Conference in Asia, Taiwan, Sept. 19–22, 2011

  155. Divinski S. Systematics of grain boundary diffusion and solute segregation in copper poly- and bicrystals. Defect Diffusion Forum, 2008, 273–276: 168–175

    Google Scholar 

  156. Divinski S, Herzig C. Solute segregation studied by grain boundary diffusion. Defect Diffusion Forum, 2005, 237–240: 499–501

    Google Scholar 

  157. Divinski S, Herzig C. Radiotracer investigation of diffusion, segregation and wetting phenomena in grain boundaries. J Mater Sci, 2008, 43: 3900–3907

    Google Scholar 

  158. Divinski S, Lohmann M, Herzig C. Grain boundary diffusion and linear and non-linear segregation of Ag in Cu. Interface Sci, 2003, 11: 21–31

    Google Scholar 

  159. Divinski S, Lohmann M, Herzig C. Grain boundary diffusion and segregation of Bi in Cu: Radiotracer measurements in B and C diffusion regimes. Acta Mater, 2004, 52: 3973–3982

    Google Scholar 

  160. Divinski S, Lohmann M, Herzig C, et al. Grain-boundary melting phase transition in the Cu-Bi system. Phys Rev B, 2005, 71: 104104/ 1–/8

    Google Scholar 

  161. Divinski S, Ribbe J, Schmitz G, et al. Grain boundary diffusion and segregation of Ni in Cu. Acta Mater, 2007, 55: 3337–3346

    Google Scholar 

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Correspondence to Yong Du.

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Du, Y., Zhang, L., Cui, S. et al. Atomic mobilities and diffusivities in Al alloys. Sci. China Technol. Sci. 55, 306–328 (2012). https://doi.org/10.1007/s11431-011-4692-6

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