Upload
dwain-gibbs
View
216
Download
2
Tags:
Embed Size (px)
Citation preview
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
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
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
4Further structural analysis:
Solid bond no.: Pink: lowBlue: high
Solid bond number, :
Fig. 9
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
- 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
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
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
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