Diffusional behavior of nanoscale lead inclusions in crystalline aluminum
-
Erik Johnson
,
Sergei Prokofjev
Abstract
In-situ transmission electron microscopy (TEM) observations reveal a permanent chaotic motion of nanosized liquid Pb inclusions embedded in thin aluminum foils. Individual trajectories of the inclusions were analysed to determine the character of their motion. The inclusions moving freely inside a crystal display motion with three-dimensional random walk characteristics while inclusions attached to dislocations display spatially confined random motion localized to the close vicinity of the dislocation lines. The diffusion coefficients of inclusions moving freely in the matrix were determined using Einstein’s classical equation for diffusion of Brownian particles. The diffusion coefficients of inclusions trapped on dislocations were found using an equation based on Smoluchowski’s analysis of Brownian motion of a particle under the action of a linear elastic restoring force. The dependence of the diffusivity on the size of the inclusions suggests that their mobility is controlled by kinetic processes on the inclusion/matrix interfaces. The Arrhenius analysis exhibits two regions with different temperature dependencies. We suppose that this is related to the existence of {111} facets on the inclusion/matrix interfaces.
References
[1] Y.E. Geguzin, M.A. Krivoglaz: Migration of macroscopic inclusions in solids, Consultants Bureau, New York (1973).10.1007/978-1-4757-5842-9Search in Google Scholar
[2] G.A. Cottrell: Fusion Eng. Design 66– 68 (2003) 253.10.1016/S0920-3796(03)00299-0Search in Google Scholar
[3] G. Gottstein, L.S. Shvindlerman: Grain boundary migration in metals, CRC Press, Boca Raton a.o. (1999).Search in Google Scholar
[4] K.N. Tu, J.W. Mayer, L.C. Feldman: Electronic thin film science. For electrical engineers and materials scientists, Macmillan Publishing Company, New York (1992).Search in Google Scholar
[5] A. Christou (Ed.): Electromigration and electronic device degradation, John Wiley & Sons, New York (1993).Search in Google Scholar
[6] E. Johnson, A. Johansen, U. Dahmen, S. Chen, T. Fujii: Mater. Sci. Eng. A 304 (2001) 187.10.1016/S0921-5093(00)01462-3Search in Google Scholar
[7] H. Gabrisch, L. Kjeldgaard, E. Johnson, U. Dahmen: Acta Mater.49 (2001) 4259.10.1016/S1359-6454(01)00307-XSearch in Google Scholar
[8] E. Johnson, H.H. Andersen, U. Dahmen: Microsc. Res. Techn. 64 (2004) 356. 10.1002/jemt.20097Search in Google Scholar
[9] S. Prokofjev, V. Zhilin, E. Johnson, M.T. Levinsen, J.S. Andersen, U. Dahmen, T. Radetic, J.H. Turner, in: J. Čermák., J. Vřešt’ál (Eds.) Proc. VIII Seminar on Diffusion and Thermodynamics of Materials, Brno, Czech Republic (2002) 241.Search in Google Scholar
[10] S.I. Prokofjev, V.M. Zhilin, E. Johnson, M. Levinsen, U. Dahmen, in: V.P. Ginkin (Ed.), Proc. 5th Int. Conf. Single Crystal Growth and Heat & Mass Transfer, Vol. 2, Obninsk, Russia (2003) 487.Search in Google Scholar
[11] E. Johnson, J.S. Andersen, M.T. Levinsen, S. Steenstrup, S. Prokofjev, V. Zhilin, U. Dahmen, T. Radetic, J.H. Turner: Mater. Sci. Eng. A 375 (2004) 951.10.1016/j.msea.2003.10.076Search in Google Scholar
[12] E. Johnson, M. Levinsen, S. Steenstrup, S. Prokofjev, V. Zhilin, U. Dahmen, T. Radetic: Phil. Mag. 84 (2004) 2663.10.1080/14786430410001671412Search in Google Scholar
[13] S. Prokofjev, V. Zhilin, E. Johnson, M.T. Levinsen, U. Dahmen: Def. Diff. Forum 337 (2005) 1072.10.4028/www.scientific.net/DDF.237-240.1072Search in Google Scholar
[14] A.J. McAlister: Bull. Alloy Phase Diagrams 5 (1984) 69.10.1007/BF02868728Search in Google Scholar
[15] M. Smoluchowski: Bull. Int. de l’cad. de Cracovie, Serie A (1913) 418.Search in Google Scholar
[16] S.I. Prokofjev, V.M. Zhilin, E. Johnson: To be submitted.Search in Google Scholar
[17] E. Johnson, S.I. Prokofjev, V.M. Zhilin: Unpublished data (2003).Search in Google Scholar
[18] J.P. Hirth, J. Lothe: Theory of dislocations, McGraw-Hill, New York (1968).Search in Google Scholar
[19] D. Gerlich, E.S. Fisher: J. Phys. Chem. Solids 30 (1969) 1197.10.1016/0022-3697(69)90377-1Search in Google Scholar
[20] C.J. Smithells, E.A. Brandes (Eds.): Metal Reference Book, Butterworths, Boston (1976).Search in Google Scholar
[21] M. Smoluchowski: Sitzungsber. Kais. Akad. Wissensch. Wien (IIa), 123 (1914) 2381.Search in Google Scholar
[22] A. Einstein: Ann. d. Phys. 17 (1905) 549.10.1002/andp.19053220806Search in Google Scholar
[23] A.A. Chernov, in: B.K. Vainshtein (Ed.), Modern Crystallography, Vol. 3., Springer, Berlin (1984) Chapter 1.10.1007/978-3-642-81835-6Search in Google Scholar
[24] R. Kelly: Phys. Stat. Sol. 21 (1967) 451.10.1002/pssb.19670210202Search in Google Scholar
[25] F.A. Nichols: J. Nucl. Mater. 30 (1969) 143.10.1016/0022-3115(69)90176-7Search in Google Scholar
[26] N.A. Gjostein, in: J.J. Burke, N.L. Reed, V. Weiss (Eds.), Surfaces and Interfaces, Vol. 1, Syracuse University Press, Syracuse (1967) 271.10.1007/978-1-4684-7514-2_11Search in Google Scholar
[27] F. Sawanayagi, R.R. Hasiguti: Jpn. J. Inst. Met. 42 (1978) 1155.10.2320/jinstmet1952.42.12_1155Search in Google Scholar
[28] B.S. Bokstein, Ch.V. Kopetskii, L.S. Shvindlerman: Thermodynamics and kinetics of grain boundaries in metals, Metallurgiya, Moscow (1986) (In Russian).Search in Google Scholar
© 2005 Carl Hanser Verlag, München
Articles in the same Issue
- Frontmatter
- Editorial
- Editorial
- Articles Basic
- Thermodynamics of grain boundary adsorption in binary systems with limited solubility
- Microstructural characteristics of 3-d networks
- On the three-dimensional twin-limited microstructure
- Grain growth kinetics in 2D polycrystals: impact of triple junctions
- Thermal stability of polycrystalline nanowires
- Conservative motion of parent-martensite interfaces
- Enthalpy – entropy compensation effect in grain boundary phenomena
- Thermodynamic stabilization of nanocrystallinity
- On the relation between the anisotropies of grain boundary segregation and grain boundary energy
- Influence of faceting-roughening on triple-junction migration in zinc
- The influence of triple junction kinetics on the evolution of polycrystalline materials during normal grain growth: New evidence from in-situ experiments using columnar Al foil
- Grain boundary dynamics and selective grain growth in non-ferromagnetic metals in high magnetic fields
- Grain boundary mobility under a stored-energy driving force: a comparison to curvature-driven boundary migration
- Diffusional behavior of nanoscale lead inclusions in crystalline aluminum
- Quantitative experiments on the transition between linear to non-linear segregation of Ag in Cu bicrystals studied by radiotracer grain boundary diffusion
- Room-temperature grain boundary diffusion data measured from historical artifacts
- Solid state infiltration of porous steel with aluminium by the forcefill process
- A mechanism of plane matching boundary-assisted α/γ phase transformation in Fe–Cr alloy based on in-situ observations
- Fast penetration of Ga in Al: liquid metal embrittlement near the threshold of grain boundary wetting
- High-pressure effect on grain boundary wetting in aluminium bicrystals
- Grain boundary segregation and fracture
- Notifications/Mitteilungen
- Personal/Personelles
- Press/Presse
- Conferences/Konferenzen
Articles in the same Issue
- Frontmatter
- Editorial
- Editorial
- Articles Basic
- Thermodynamics of grain boundary adsorption in binary systems with limited solubility
- Microstructural characteristics of 3-d networks
- On the three-dimensional twin-limited microstructure
- Grain growth kinetics in 2D polycrystals: impact of triple junctions
- Thermal stability of polycrystalline nanowires
- Conservative motion of parent-martensite interfaces
- Enthalpy – entropy compensation effect in grain boundary phenomena
- Thermodynamic stabilization of nanocrystallinity
- On the relation between the anisotropies of grain boundary segregation and grain boundary energy
- Influence of faceting-roughening on triple-junction migration in zinc
- The influence of triple junction kinetics on the evolution of polycrystalline materials during normal grain growth: New evidence from in-situ experiments using columnar Al foil
- Grain boundary dynamics and selective grain growth in non-ferromagnetic metals in high magnetic fields
- Grain boundary mobility under a stored-energy driving force: a comparison to curvature-driven boundary migration
- Diffusional behavior of nanoscale lead inclusions in crystalline aluminum
- Quantitative experiments on the transition between linear to non-linear segregation of Ag in Cu bicrystals studied by radiotracer grain boundary diffusion
- Room-temperature grain boundary diffusion data measured from historical artifacts
- Solid state infiltration of porous steel with aluminium by the forcefill process
- A mechanism of plane matching boundary-assisted α/γ phase transformation in Fe–Cr alloy based on in-situ observations
- Fast penetration of Ga in Al: liquid metal embrittlement near the threshold of grain boundary wetting
- High-pressure effect on grain boundary wetting in aluminium bicrystals
- Grain boundary segregation and fracture
- Notifications/Mitteilungen
- Personal/Personelles
- Press/Presse
- Conferences/Konferenzen
