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L. Gr áná sy 1,2, F. Podmaniczky, G. I. Tóth 1, G. Tegze, & T. Pusztai 1 1 Wigner Research Centre for Physics, POB 49, H-1525 Budapest, HU 2 BCAST, Brunel University, Uxbridge, Middlesex, UB8 3PH, UK Heterogeneous nucleation of/on nanoparticles: a density functional study using the phase-field crystal model (Animations for Figs. 9, 10, 11, 14, 16 & 18 and for pure Fe) 1 Ppt file downloadable from: http://www.szfki.hu/~grana/rsc_review/Elect_Suppl_Info.ppt

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Zhang & Liu, JACS (2007) = 0.1684 0 = 0.25 256 256 256 grid r eq = 0.1330 A. Nucleation ( = 1, single mode-PFC) A. Nucleation ( = 1, single mode-PFC) 2 Tóth et al. PRL (2011). Red (bcc-like) if q 4 [0.02, 0.07] q 6 [0.48, 0.52] Steinhardt, Nelson, Ronchetti, PRB (1983) Starts to solidify as amorphous, then crystallizes ! A’la 2D & 3D colloids. Fig. 9 Please read comment to the slide

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14 Black: bcc Yellow: Icosah. Green: hcp Red: fcc q i of Steinhardt et al. B. Structural evolution: Green q 6 > 0.4 Red q 6 [0.28, 0.4] White q 6 < 0.28 Red (bcc-like) if q 4 [0.02, 0.07] q 6 [0.48, 0.52] Solid bond no.: Pink: low Blue: high Observations: - PFC does not see MRCO of Kawasaki & Tanaka - Some grain boundaries are “amorphous” - Am. precursor is structurally like LJ liquid - Heterogeneous bcc nucleation on am. surfaces Kawasaki & Tanaka, PNAS (2010) Medium Range Crystalline Order (MRCO) q i of Lechner & Dellago 3 Figs. 9, 10, 11 Please read comment to the slide

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4 Further structural analysis: Solid bond no.: Pink: low Blue: high Solid bond number, : Fig. 9

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Advanced PFC for Fe: T = T f 300 300 300 grid n 0 = 0.5125 n 0 = 0.52 n 0 = 0.55 MD am. Fe: Hong, Nanotech. (2009) The appearance of an amorphous precursor prior to crystal nucleation might be fairly general. 5 Please read comment to the slide

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- Cylindrical particles ~ wet by the crystal on top/bottom, not on sides; (e.g., Al + Al-Ti-B inoculant Ti 2 B particles with AlTi 3 coating on {0001} faces different contact angles on different faces) - Free growth for - PFT simulations T c 1/ d ; T c < classical 40 nm 40 nm 40 nm T = 17 K d = 30 nm T = 18 K Horizontal: 1 = 75 Vertical: 2 = 175 (Greer et al., Acta Mater., 2002) (Greer et al., Acta Mater., 2002) B. Particle induced freezing in 2D and 3D (solving the Euler-Lagrange equation): 6 Please read comment to the slide

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Fig. 14 = 0.5 a s / = 1.0 Single mode PFC modeling of nanoparticle induced crystallization in 2D: (results obtained by solving the Euler-Lagrange equation) Single mode PFC modeling of nanoparticle induced crystallization in 2D: (results obtained by solving the Euler-Lagrange equation) = 0.25 EL solutions for increasing driving force: Homogeneous nuclei at the critical driving force Results: - Small anisotropy: Greer’s model OK - Faceted: free-growth at a much larger driving force driving force a s / = 1.0 7 Tóth et al. PRL (2012). Please read comment to the slide

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Single mode PFC of particle induced freezing in 3D (solving the Euler-Lagrange equation): = 0.25 256 256 256 grid SC substrate Cubic shape 512 512 512 grid 8 Tóth et al. PRL (2012). Fig. 16 Please read comment to the slide

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Heterogeneous crystal nucleation in 2D (solving Equation of Motion): Heterogeneous crystal nucleation in 2D (solving Equation of Motion): Realization: - Square lattice (periodic potential) - Noise represents thermal fluctuations. Observation: - Heterogeneous crystal nucleation - Capillary waves on the crystal-liquid front = 0.25 0 = 0.32 = 0.1 a s / = 1.39 9 Fig. 18 Please read comment to the slide

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