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:

Zhang & Liu, JACS (2007)  =  0 =   256  256 grid r eq =  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

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

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

Advanced PFC for Fe: T = T f 300  300  300 grid n 0 = 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

- 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

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 /  = Tóth et al. PRL (2012). Please read comment to the slide

Single mode PFC of particle induced freezing in 3D (solving the Euler-Lagrange equation):  =  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

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 /  = Fig. 18 Please read comment to the slide