Trans-interface diffusion-controlled coarsening

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ABSTRACT Accurate theoretical predictions of the volume-fraction dependence during diffusion-controlled coarsening of a polydisperse assembly of particles have proved difficult. Here, a new


model of coarsening is presented, involving diffusive transport through the coherent interface between ordered and disordered phases, which atomistic calculations show has a ragged


structure. The interface is a diffusion bottleneck when the ordered phase is dispersed. It is predicted that the square of the average radius grows linearly with time, that the depletion of


solute decreases as the inverse square-root of time, and that there is no effect of volume fraction on kinetics and the scaled particle-size distributions. These differ dramatically from


predictions of modern theories of diffusion-controlled coarsening. Data on coarsening in Ni-Al alloys is examined. We show that no other theory is consistent with the experimentally observed


absence of an effect of volume fraction on coarsening of ordered γ′ (Ni3Al) precipitates in a disordered Ni-Al (γ) matrix, and the strong volume-fraction dependence of coarsening of γ


precipitates in an ordered γ′ matrix. Access through your institution Buy or subscribe This is a preview of subscription content, access via your institution ACCESS OPTIONS Access through


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Read our FAQs * Contact customer support SIMILAR CONTENT BEING VIEWED BY OTHERS SUPERDIFFUSION-LIKE BEHAVIOR IN ZERO-TEMPERATURE COARSENING OF THE \(D=3\) ISING MODEL Article Open access 15


August 2023 A CLASSICAL EQUATION THAT ACCOUNTS FOR OBSERVATIONS OF NON-ARRHENIUS AND CRYOGENIC GRAIN BOUNDARY MIGRATION Article Open access 21 July 2022 MOLECULAR DYNAMICS STUDY OF THE


EFFECT OF EXTENDED INGRAIN DEFECTS ON GRAIN GROWTH KINETICS IN NANOCRYSTALLINE COPPER Article Open access 13 January 2021 REFERENCES * Lifshitz, I. M. & Slyozov, V. V. The kinetics of


precipitation from supersaturated solid solutions. _J. Phys. Chem. Solids_ 19, 35–50 (1961). Article  Google Scholar  * Wagner, C. Theorie der alterung von niederschlägen durch umlösen


(Ostwald-reifung). _Z. Elektrochem._ 65, 581–591 (1961). CAS  Google Scholar  * Ardell, A. J. in _Phase Transformations '87_ (ed. Lorimer, G. W.) 485–494 (Institute of Metals, London,


1988). Google Scholar  * Voorhees, P. W. The theory of Ostwald ripening. _J. Stat. Phys._ 38, 231–252 (1985). Article  Google Scholar  * Voorhees, P. W. Ostwald ripening of two-phase


mixtures _Annu. Rev. Mater. Sci._ 22, 197–215 (1992). Article  CAS  Google Scholar  * Thornton, K., Akaiwa, N. & Voorhees, P. W. Dynamics of late-stage phase separation in crystalline


solids. _Phys. Rev. Lett._ 86, 1259–1262 (2001). Article  CAS  Google Scholar  * Ardell, A. J. & Nicholson, R. B. The coarsening of γ´ in Ni-Al alloys. _J. Phys. Chem. Solids_ 27,


1793–1804 (1966). Article  CAS  Google Scholar  * Ardell, A. J. The growth of gamma prime precipitates in aged Ni-Ti alloys. _Metall. Trans._ 1, 525–534 (1970). Article  CAS  Google Scholar


  * Maheshwari, A. & Ardell, A. J. Anomalous coarsening behavior of small volume fractions of Ni3Al precipitates in binary Ni-Al alloys. _Acta Metall. Mater._ 40, 2661–2667 (1992).


Article  CAS  Google Scholar  * Kim, D. M. & Ardell, A. J. Coarsening behavior of Ni3Ga precipitates in Ni-Ga alloys: dependence of microstructure and kinetics on volume fraction.


_Metall. Mater. Trans. A_ 35, 3063–3069 (2004). Article  Google Scholar  * Kim, D. M. & Ardell, A. J. Coarsening of Ni3Ge in binary Ni-Ge alloys: microstructures and volume fraction


dependence of kinetics. _Acta Mater._ 51, 4073–4082 (2003). Article  CAS  Google Scholar  * Cho, J.-H. & Ardell, A. J. Coarsening of Ni3Si precipitates at volume fractions from 0.03 to


0.30. _Acta Mater._ 46, 5907–5916 (1998). Article  CAS  Google Scholar  * Kim, D. M. & Ardell, A. J. The volume-fraction dependence of Ni3Ti coarsening kinetics—new evidence of anomalous


behavior. _Scripta Mater._ 43, 381–384 (2000). Article  CAS  Google Scholar  * Ardell, A. J. Observations on the effect of volume fraction on the coarsening of γ′ precipitates in binary


Ni-Al alloys. _Scripta Metall. Mater._ 24, 343–346 (1990). Article  CAS  Google Scholar  * Chellman, D. J. & Ardell, A. J. The coarsening of γ′ precipitates at large volume fractions.


_Acta Metall._ 22, 577–588 (1974). Article  CAS  Google Scholar  * Irissari, A. M., Urcola, J. J. & Fuentes, M. Kinetics of growth of γ´-precipitates in Ni-6.75Al alloy. _Mater. Sci.


Tech._ 1, 516–519. * Cornwell, L. R. & Purdy, G. R. Precipitation of γ in γ′ particles in a nickel-aluminum alloy. _Metall. Trans._ 5, 780–781 (1974). Article  CAS  Google Scholar  * Ma,


Y & Ardell, A. J. The (γ + γ′)/ γ′ phase boundary in the Ni-Al phase diagram from 600 to 1200 °C. _Z. Metallkd._ 94, 972–975 (2003). Article  CAS  Google Scholar  * Ma, Y. & Ardell,


A. J. Coarsening of γ (Ni-Al solid solution) precipitates in a γ′ (Ni3Al) matrix: a striking contrast in behavior from normal γ/γ′ alloys. _Scripta Mater._ (in the press). * Ikeda, T. et


al. Single-phase interdiffusion in Ni3Al. _Acta Mater._ 46, 5369–5376 (1998). Article  CAS  Google Scholar  * Fujiwara, K. & Horita, Z. Measurement of intrinsic diffusion coefficients of


Al and Ni in Ni3Al using Ni/NiAl diffusion couples. _Acta Mater._ 50, 1571–1579 (2002). Article  CAS  Google Scholar  * Watanabe, M., Horita, Z., Sano T. & Nemoto, M. Electron


microscopy study of Ni/Ni3Al diffusion-couple interface - II. Diffusivity measurement. _Acta Metall. Mater._ 42, 3389–3396 (1994). Article  CAS  Google Scholar  * Janssen, M. M. P. Diffusion


in the nickel-rich part of the nickel-aluminum system at 1000 to 1300 deg. nickel-aluminum (Ni3A1) layer growth, diffusion coefficients, and interface concentrations. _Metall. Trans._ 4,


1623–1633 (1973). CAS  Google Scholar  * Ansara, I., Dupin, N., Lukas, H. L. & Sundman, B. Thermodynamic assessment of the Al-Ni system. _J. Alloys Compd_ 247, 20–30 (1997). Article  CAS


  Google Scholar  * Huang, W. & Chang, Y. A. A thermodynamic analysis of the Ni-Al system. _Intermetallics_ 6, 487–498 (1998). Article  CAS  Google Scholar  * Zhang, F. et al.


Application of the cluster-site approximation (CSA) model to the f.c.c. phase in the Ni-Al system. _Acta Mater._ 51, 207–216 (2003). Article  CAS  Google Scholar  * Wang, Y. &


Khachaturyan, A. G. Effect of antiphase domains on shape and spatial arrangement of coherent ordered intermetallics. _Scripta Metall. Mater._ 31, 1425–1430 (1994). Article  CAS  Google


Scholar  * Mishin, Y. Atomistic modeling of the γ and γ′-phases of the Ni-Al system. _Acta Mater._ 52, 1451–1467 (2004). Article  CAS  Google Scholar  * Hillert, M. On the theory of normal


and abnormal grain growth. _Acta Metall._ 13, 227–238 (1965). Article  CAS  Google Scholar  * Todes, O. M. & Khrushchev, V. V. Theory of coagulation and particle growth in sols. III.


kinetics of particle growth in a polydisperse system in a vacuum. _J. Phys. Chem. (USSR)_ 21, 301–312 (1947). CAS  Google Scholar  * Greenwood, G. W. The growth of dispersed precipitates in


solutions. _Acta Metall._ 4, 243–248 (1956). Article  CAS  Google Scholar  * Ardell, A. J. An application of the theory of particle coarsening: the γ´ precipitate in Ni-Al alloys. _Acta


Metall._ 16, 511–516 (1968). Article  CAS  Google Scholar  * Livingston, J. D. Critical particle size for precipitation hardening. _Trans. AIME_ 215, 566–571 (1959). CAS  Google Scholar  *


Mahalingam, K., Gu, B. P., Liedl, G. L. & Sanders, T. H. Jr. Coarsening of δ´ (Al3Li) precipitates in binary aluminum-lithium alloys. _Acta Metall._ 35, 483–98 (1987). Article  CAS 


Google Scholar  * Sluiter, M. & Kawazoe, Y. Prediction of matrix-precipitate interfacial free energies: Application to Al-Al3Li. _Phys. Rev. B_ 54, 10381–10384 (1986). Article  Google


Scholar  * Asta, M. Theoretical study of the thermodynamic properties of α-δ′ interphase boundaries in Al-Li. _Acta Mater._ 44, 4131–4136 (1996). Article  CAS  Google Scholar  * Seyhan, I.


et al. Ostwald ripening of solid-liquid Pb-Sn dispersions. _Metall. Mater. Trans. A_ 27, 2470–2478 (1996). Article  Google Scholar  * Hoyt, J. J., Asta, M. & Karma, A. Atomistic and


continuum modeling of dendritic solidification. _Mater. Sci. Eng. R_ 41, 121–163 (2003). Article  Google Scholar  * Coriell, S. R. & Turnbull, D. H. Relative roles of heat transport and


interface rearrangement rates in the rapid growth of crystals in undercooled melts. _Acta Metall._ 30, 2135–2139 (1982). Article  CAS  Google Scholar  * Broughton, J. Q., Gilmer, G. H. &


Jackson, K. A. Crystallization rates of a Lennard-Jones liquid. _Phys. Rev. Lett._ 49, 1496–1500 (1982). Article  CAS  Google Scholar  * Vaithyanathan, V. & Chen, L. Q. Coarsening of


ordered intermetallic precipitates with coherency stress. _Acta Mater._ 50, 4061–4073 (2002). Article  CAS  Google Scholar  * Jayanth, C. S. & Nash, P. Experimental evaluation of


particle coarsening theories. _Mater. Sci. Tech._ 6, 405–413 (1990). Article  CAS  Google Scholar  * Lund, A. C. & Voorhees, P. W. The effects of elastic stress on coarsening in the


Ni-Al system. _Acta Mater._ 50, 2085–2098 (2002). Article  CAS  Google Scholar  * Kresse, G. & Hafner, J. _Ab initio_ molecular dynamics for liquid metals. _Phys. Rev. B_ 47, 558–561


(1993). Article  CAS  Google Scholar  * Kresse, G & Furthmüller, J. Efficient iterative schemes for _ab initio_ total-energy calculations using a plane-wave basis set. _Phys. Rev. B_ 54,


11169–11186 (1996). Article  CAS  Google Scholar  * Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented wave method. _Phys. Rev. B_ 59, 1758–1775 (1999).


Article  CAS  Google Scholar  * Calderon, H. A. et al. Ostwald ripening in concentrated alloys. _Acta Metall. Mater._ 42, 991–1000 (1994). Article  CAS  Google Scholar  * Ardell, A. J. The


Ni-Ni3Al Phase diagram: Thermodynamic modelling and the requirements of coherent equilibrium. _Model. Simul. Mater. Sci._ 8, 277–286 (2000). Article  CAS  Google Scholar  * Ardell, A. J.


Interfacial free energies and solute diffusivities from data on Ostwald ripening. _Interface Sci._ 3, 119–125 (1995). Article  CAS  Google Scholar  Download references ACKNOWLEDGEMENTS We


benefited from helpful discussions with Mark Asta. A.J.A. is grateful to the National Science Foundation for financial support of this research under Grant DMR-0209260. V.O. was supported by


the MARCO Focus Center for Functional Engineered Nano Architectonics (FENA) and by the National Science Foundation under Grant DMR-0427638. AUTHOR INFORMATION AUTHORS AND AFFILIATIONS *


Department of Materials Science and Engineering, University of California, Los Angeles, Los Angeles, 90095-1595, California, USA Alan J. Ardell & Vidvuds Ozolins Authors * Alan J. Ardell


View author publications You can also search for this author inPubMed Google Scholar * Vidvuds Ozolins View author publications You can also search for this author inPubMed Google Scholar


CORRESPONDING AUTHORS Correspondence to Alan J. Ardell or Vidvuds Ozolins. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing financial interests. RIGHTS AND


PERMISSIONS Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Ardell, A., Ozolins, V. Trans-interface diffusion-controlled coarsening. _Nature Mater_ 4, 309–316 (2005).


https://doi.org/10.1038/nmat1340 Download citation * Received: 27 July 2004 * Accepted: 19 January 2005 * Published: 20 March 2005 * Issue Date: 01 April 2005 * DOI:


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