Abstract
Crystallization of supersaturated liquids usually starts by epitaxial growth or by heterogeneous nucleation on foreign surfaces. Herein, we review recent advances made in modeling heteroepitaxy and heterogeneous nucleation on flat/modulated surfaces and nanoparticles within the framework of a simple dynamical density functional theory, known as the phase-field crystal model. It will be shown that the contact angle and the nucleation barrier are nonmonotonous functions of the lattice mismatch between the substrate and the crystalline phase. In continuous cooling studies for substrates with lattice mismatch, we recover qualitatively the Matthews–Blakeslee mechanism of stress release via the misfit dislocations. The simulations performed for particle-induced freezing will be confronted with recent analytical results, exploring thus the validity range of the latter. It will be demonstrated that time-dependent studies are essential, as investigations based on equilibrium properties often cannot identify the preferred nucleation pathways. Modeling of these phenomena is essential for designing materials on the basis of controlled nucleation and/or nano-patterning.
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References
K.F. Kelton and L. A. Greer: Nucleation in Condensed Matter. Pergamon Materials Series, vol. 15 (Elsevier, Amsterdam, 2010).
B.A. Grzybowski, K.J.M. Bishop, C.J. Campbell, M. Fialkowski and S.K. Smoukov: Soft Matter, 2005, vol. 1, pp. 114–28, and references therein.
J. Aizenberg, A. J. Black and G.M. Whitesides, Nature, 1999, vol. 398, pp. 495–98.
C.X. Cui, Y.H. Chen, P. Jin, B. Xu, Y.Y. Ren, C. Zhao, and Z.G. Wang: Physica E, 2006, vol. 31, pp. 43–47.
K.-H. Chen, C.-Y. Chien, W.-T. Lai, T. George, A. Scherer and P.-W. Li: Cryst. Growth Des., 2011, vol. 11, pp. 3222–6.
A.J.M. Mackus, M.A. Verheijen, N. Leick, A.A. Bol and W.M.M. Kessel: Chem. Mater., 2013, vol. 25, pp. 1905–11.
G.I. Tóth, J. R. Morris and L. Gránásy, Phys. Rev. Lett., 2011, vol. 106, art. no. 045701.
W. Cheng, N. Park, M. T. Walter, M. Hartman, and D. Luo, Nat Nanotechnol., 2008, vol. 3, pp. 682–690.
S. Auer and D. Frenkel: Phys. Rev. Lett., 2003, vol. 91, art. no. 015703.
D. Winter, P. Virnau, and K. Binder: Phys. Rev. Lett., 2009, vol. 103, art. no. 225703.
M. Heni and H. Löwen: J. Phys.: Condens. Matter, 2001, vol. 13, pp. 4675–96.
A. Esztermann and H. Löwen: J. Phys.: Condens. Matter, 2005, vol. 17, pp. S429–S441.
S. Toxvaerd: J. Chem. Phys., 2002, vol. 117, pp. 10303–10.
E.B. Webb III, G.S. Grest and D.R. Heine: Phys. Rev. Lett., 2003, vol. 91, art. no. 236102.
L. Gránásy, T. Pusztai, D. Saylor, and J.A. Warren: Phys. Rev. Lett., 2007, vol. 98, art. no. 035703.
J.A. Warren, T. Pusztai, L. Környei, and L. Gránásy: Phys. Rev. B, 2009, vol. 79, art. no. 014204.
S. van Teeffelen, C.N. Likos, and H. Löwen: Phys. Rev. Let., 2008, vol. 100, art. no. 108302.
T. Neuhaus, M. Marechal, M. Schmiedeberg, and H. Löwen: Phys. Rev. Lett., 2013, vol. 110, art. no. 118301.
A.L. Greer, A.M. Brunn, A. Tronche, P.V. Evans and D.J. Bristow: Acta Mater., 2000, vol. 48, pp. 2823–35.
T.E. Quested and A. L. Greer: Acta Mater., 2005, vol. 53, pp. 2683–92.
S.A. Reavley and A.L. Greer, Philos. Mag., 2008, vol. 88, pp. 561–79.
K.R. Elder, M. Katakowski, M. Haataja and M. Grant: Phys. Rev. Lett., 2002, vol. 88, art. no. 245701.
H. Emmerich, H. Löwen, R. Wittkowski, T. Gruhn, G.I. Tóth, G. Tegze, and L. Gránásy: Adv. Phys., 2012, vol. 61, pp. 665–743, and references therein.
G.I. Tóth, G. Tegze, T. Pusztai, and L. Gránásy: Phys. Rev. Lett., 2012, vol. 108, art. no. 025502.
L. Gránásy, F. Podmaniczky, G.I. Tóth, G. Tegze, and T. Pusztai: Chem. Soc. Rev, 2014, vol. 43, pp. 2159–73.
Z. Fan: Proc. J. Hunt Int. Symposium, Z. Fan and I.C. Stone, eds., Brunel University Press, Uxbridge, 2001, pp 29–44.
Z. Fan: Metall. Mater. Trans. A, 2013, vol. 44A, pp. 1409–18.
O. Galkin and P. Vekilov, Proc. Natl. Acad. Sci. USA, 2000, vol. 97, pp. 6277–81.
P.G. Vekilov: Cryst. Growth Des., 2004, vol. 4, pp. 671–85.
P.R. TenWolde and D. Frenkel: Science, 1997, vol. 277, pp. 1975–78.
V. Talanquer and D.W. Oxtoby: J. Chem. Phys., 1998, vol. 109, pp. 223–7.
G.I. Tóth and L. Gránásy, J. Chem. Phys., 2007, vol. 127, art. no. 074710.
T. Kawasaki and H. Tanaka, Proc. Natl. Acad. Sci. USA, 2010, vol. 107, pp. 14036–41.
T.H. Zhang and X.Y. Liu, J. Am. Chem. Soc., 2007, vol. 129, pp. 13520–26.
H.J. Schöpe, G. Bryant, and W. van Megen: Phys. Rev. Lett., 2006, vol. 96, art. no. 175701.
J.F. Lutsko and G. Nicolis, Phys. Rev. Lett., 2006, vol. 96, art. no. 046102.
T. Schilling, H.J. Schöpe, M. Oettel, G. Opletal, and I. Snook: Phys. Rev. Lett., 2010, vol. 105, art. no. 025701.
G.I. Tóth, T. Pusztai, G. Tegze, G. Tóth, and L. Gránásy: Phys. Rev. Lett., 2011, vol. 107, art. no. 175702.
K.R. Elder, N. Provatas, J. Berry, P. Stefanovic, and M. Grant: Phys. Rev. B, 2007, vol. 75, art. no. 064107.
S. van Teeffelen, R. Backofen, A. Voigt, and H. Löwen: Phys. Rev. E, 2009, vol. 79, art. no. 051404.
U.M.B. Marconi and P. Tarazona; J. Chem. Phys., 1999, vol. 110, pp. 8032–44.
H. Löwen; J. Phys.: Condens. Matter, 2003, vol. 15, pp. V1–V3.
A.J. Archer and M. Rauscher, J. Phys. A: Math. Gen., 2004, vol. 37, pp. 9325–33.
G.I. Tóth, G. Tegze, T. Pusztai, G. Tóth, and L. Gránásy: J. Phys.: Condens. Matter, 2010, vol. 22, art. no. 364101.
G. Tegze, G. Bansel, G.I. Tóth, T. Pusztai, Z. Fan, and L. Gránásy: J. Comput. Phys., 2009, vol. 228, pp. 1612–23.
R. Backofen and A. Voigt: J. Phys.: Condens. Matter, 2009, vol. 21, art. no. 464109.
L. Gránásy, G. Tegze, G.I. Tóth, and T. Pusztai: Philos. Mag., 2011, vol. 91, pp. 123–49.
J.W. Matthews and A.E. Blakeslee: J. Cryst. Growth, 1974, vol. 27, pp. 118–25.
R.J. Asaro and W.A. Tiller: Metall. Trans., 1972, vol. 3, pp. 1789–96.
K.R. Elder and M. Grant: Phys. Rev. E, 2004, vol. 70, art. no. 051605.
M. Castro: Phys. Rev. B, 2003, vol. 67, art. no. 035412.
R. Backofen and A. Voigt: J. Phys.: Condens. Matter., 2010, vol. 22, art. no. 364104.
G. Tegze, L. Gránásy, G.I. Tóth, F. Podmaniczky, A. Jaatinen, T. Ala-Nissila, and T. Pusztai: Phys. Rev. Lett., 2009, vol. 103, art. no. 035702.
Acknowledgments
This work includes techniques developed in the framework of the EU FP7 Collaborative Project “EXOMET” (Contract No. NMP-LA-2012-280421, co-funded by ESA), and by the ESA MAP/PECS projects MAGNEPHAS III, PARSEC, and GRADECET.
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Podmaniczky, F., Tóth, G.I., Tegze, G. et al. Recent Developments in Modeling Heteroepitaxy/Heterogeneous Nucleation by Dynamical Density Functional Theory. Metall Mater Trans A 46, 4908–4920 (2015). https://doi.org/10.1007/s11661-015-2986-1
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DOI: https://doi.org/10.1007/s11661-015-2986-1