Electronic Supplementary Information for Chem. Soc. Rev. paper.

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L L . . Gr Gr áná áná sy sy 1,2 1,2 , F. Podmaniczky, , F. Podmaniczky, G. I. Tóth I. Tóth 1 , G. , G. Tegze, & T. Pusztai Tegze, & T. Pusztai 1 1 Wigner Research Centre for Physics, POB 49, H-1525 Budapest Wigner Research Centre for Physics, POB 49, H-1525 Budapest , , HU HU 2 BCAST, Brunel University, Uxbridge, Middlesex, UB8 3PH, UK 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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1. 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). L . Gr áná sy 1,2 , F. Podmaniczky, G . I. Tóth 1 , G. Tegze, & T. Pusztai 1 - PowerPoint PPT Presentation

Transcript of Electronic Supplementary Information for Chem. Soc. Rev. paper.

Page 1: Electronic Supplementary Information for Chem. Soc. Rev. paper.

LL. . GrGránáánásysy1,21,2, F. Podmaniczky, , F. Podmaniczky, GG.. I. Tóth I. Tóth11, G. Tegze, & T. Pusztai, G. Tegze, & T. Pusztai11

11Wigner Research Centre for Physics, POB 49, H-1525 BudapestWigner Research Centre for Physics, POB 49, H-1525 Budapest , HU, HU22BCAST, Brunel University, Uxbridge, Middlesex, UB8 3PH, UKBCAST, 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

Page 2: Electronic Supplementary Information for Chem. Soc. Rev. paper.

Zhang & Liu, JACS (2007)Zhang & Liu, JACS (2007)

= 0.16840 = 0.25

256256256 grid

req = 0.1330

A. Nucleation ( = 1, single mode-PFC)

A. Nucleation ( = 1, single mode-PFC)

2

TTóthóth et al. et al. PRL (2011).PRL (2011).

Red (bcc-like) if q4 [0.02, 0.07]q6 [0.48, 0.52]

Steinhardt, Nelson, Ronchetti, PRB (1983)Steinhardt, Nelson, Ronchetti, PRB (1983)

Starts to solidify as amorphous, Starts to solidify as amorphous, then crystallizesthen crystallizes ! ! A’la 2D & 3D colloids.A’la 2D & 3D colloids.

Fig. 9

Please read comment to the slide

Page 3: Electronic Supplementary Information for Chem. Soc. Rev. paper.

Black: bcc Yellow: Icosah. Green: hcpRed: fcc

qi of Steinhardt et al.B. Structural evolution:

Greenq6 > 0.4Redq6 [0.28, 0.4]

Whiteq6 < 0.28

Red (bcc-like) if q4 [0.02, 0.07]q6 [0.48, 0.52]

Solid bond no.: Pink: lowBlue: 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)

qi of Lechner & Dellago

3

Figs. 9, 10, 11

Please read comment to the slide

Page 4: Electronic Supplementary Information for Chem. Soc. Rev. paper.

4Further structural analysis:

Solid bond no.: Pink: lowBlue: high

Solid bond number, :

Fig. 9

Page 5: Electronic Supplementary Information for Chem. Soc. Rev. paper.

Advanced PFC for Fe:Advanced PFC for Fe: Advanced PFC for Fe:Advanced PFC for Fe: T = Tf

300300300 grid

n0 = 0.5125

n0 = 0.52

n0 = 0.55

MD am. Fe: Hong, Nanotech. (2009)

The appearance of an The appearance of an amorphous precursor amorphous precursor

prior to crystal prior to crystal nucleation might be nucleation might be

fairly general. fairly general.

5

Please read comment to the slide

Page 6: Electronic Supplementary Information for Chem. Soc. Rev. paper.

- Cylindrical particles ~ wet by the crystal on top/bottom, not on sides; (e.g., Al + Al-Ti-B inoculant Ti2B particles with AlTi3 coating on

{0001} faces different contact angles on different faces)

- Free growth for

- PFT simulations Tc 1/d; Tc < classical Ld

TTT mSLc

4

40 nm 40 nm 40 nm

T = 17 K d = 30 nm T = 18 K

Horizontal: Horizontal: 11 = 75 = 75 Vertical: Vertical: 22 = 175 = 175

((GrGreereer et al., Acta Mater., 2002)et al., Acta Mater., 2002)

B. Particle induced freezing in 2D and 3D (solving the Euler-Lagrange equation):B. Particle induced freezing in 2D and 3D (solving the Euler-Lagrange equation): B. Particle induced freezing in 2D and 3D (solving the Euler-Lagrange equation):B. Particle induced freezing in 2D and 3D (solving the Euler-Lagrange equation): 6

Please read comment to the slide

Page 7: Electronic Supplementary Information for Chem. Soc. Rev. paper.

Fig. 14

= 0.5 as/ = 1.0

Single mode PFC modeling of nanoparticle induced crystallization in 2D: Single mode PFC modeling of nanoparticle induced crystallization in 2D:

(results obtained by solving the Euler-Lagrange equation)(results obtained by solving the Euler-Lagrange equation) Single mode PFC modeling of nanoparticle induced crystallization in 2D: Single mode PFC modeling of nanoparticle induced crystallization in 2D:

(results obtained by solving the Euler-Lagrange equation)(results obtained by solving the Euler-Lagrange equation)

= 0.25

EL solutions for increasing driving force:

Homogeneous nuclei at Homogeneous nuclei at the critical driving forcethe critical driving force

Results:Results:- Small anisotropy: - Small anisotropy: Greer’s model OKGreer’s model OK - Faceted: free-growth at a much larger - Faceted: free-growth at a much larger driving forcedriving force

as/ = 1.0

7

Tóth et al. PRL (2012).

)(),()(:Potential 10 rrr haSVVV s

Please read comment to the slide

Page 8: Electronic Supplementary Information for Chem. Soc. Rev. paper.

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

= 0.25

256 256 256 grid

SC substrateCubic shape

512 512 512 grid

8

Tóth et al. PRL (2012).

Fig. 16Please read comment to the slide

Page 9: Electronic Supplementary Information for Chem. Soc. Rev. paper.

Heterogeneous crystal nucleation in 2D Heterogeneous crystal nucleation in 2D

(solving Equation of Motion):(solving Equation of Motion): Heterogeneous crystal nucleation in 2D Heterogeneous crystal nucleation in 2D

(solving Equation of Motion):(solving Equation of Motion):

RealizationRealization::- - Square latticeSquare lattice ( (periodic potentialperiodic potential) ) - - Noise represents thermal fluctuations.Noise represents thermal fluctuations.

ObservationObservation::- - Heterogeneous crystal nucleationHeterogeneous crystal nucleation - - Capillary waves on the crystal-liquid frontCapillary waves on the crystal-liquid front

= 0.250 = 0.32 = 0.1as/ = 1.39

9

)(),()(:Potential 10 rrr haSVVV s

Fig. 18

Please read comment to the slide


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