Yilong Han, yilong@ust.hk
Co-authors: Yi Peng, Feng Wang
Nucleation in solid-solid transitions of colloidal crystals
Solid-solid phase transitions between different crystalline structures are ubiquitous in nature, but their kinetic
pathways and mechanisms present formidable challenges for theory, simulation and experiment. Here we
directly imaged the solid-solid transitions in colloidal thin films composed of diameter-tunable NIPAM microspheres with single-particle resolution by video microscopy. We discover a surprising two-step diffusive
nucleation behavior for transitions from square- to triangular-lattices with an intermediate liquid stage. The
observations and resulting theoretical analysis suggest that, provided solid-liquid interfacial energies are sufficiently small, s-s transitions in most traditional metals and alloys should follow this two-step nucleation with
intermediate liquid stage, and should generally arise in 2D, 3D and thin-film single crystals and polycrystals.
The nucleation precursors are particle-swapping loops rather than structural defects, which, in turn, provide a
new relaxation mode that makes s-s transitions easier and faster. This new kinetic factor controlling the s-s
transition rate has never been considered and should be incorporated in future s-s transition theories.
Applying a small anisotropic strain can reduces the liquid nucleus size. Above a threshold of the applied strain,
the intermediate liquid nuclei vanished. Instead, a few pairs of dislocations were first generated from the square
lattices as nucleation precursors, which triggered tens of particles to collectively transform to a triangular-lattice
nucleus and then grew diffusively. This martensitic transformation at the early stage and the diffusive nucleation
at the later stage is another novel type of kinetic pathway in solid-solid transition.
In addition, we observed that the coherent and incoherent facets of the evolving nuclei exhibit different energies
and growth rates which can dramatically alter nucleation kinetics. The coalescence of two crystalline nuclei
exhibits different behaviors for different lattice angles.
Nucleation in Solid-solid Transitions of
Colloidal Crystals
Yilong Han
韩一龙
Department of Physics
CMDS13, Salt Lake City, 2014
Introduction
Two-step nucleation
One-step nucleation
Other kinetics
Solid-solid Transitions
widely exist in nature…
Steel-production
Man-made Diamond
…
Earth science
Nano-materials
Classification
 Military transformation (Martensitic): all particles move
collectively, e.g.
 Civilian transformation (Diffusive): particles diffuse from
mother phase to daughter phase.
Nucleation: a free energy barrier
∆G = −V ∆µ + Aγ + Estrain − Edefect
only for crystalline
mother phase
Difficulties in Solid-solid Transitions
Theory: lack a group-subgroup relationship in
symmetry.
Simulation:
 small systems (ambiguous results)
 anisotropic pressure
 catastrophic transition at strong superheating
to speed up the sluggish dynamics, but they promote
martensitic transformation and suppress nucleation.
Atomic experiment: X-ray & STM cannot resolve
nucleation process, no single-particle dynamics.
Colloid— One Class of Soft Material
What are Colloids?
— small particles dispersed in a solution
Particle size: 10nm −10µm,
kBT dominated, Brownian motion…
milk, inks, paints, blood, smoke…
1.6 micron silica spheres
Colloids as Model Systems
Science 292, 258 (2001)
Science 314, 795 (2006)
Nucleation in crystallization Sublimation of colloidal crystals
Science 309, 1207 (2005)
Heterogeneous melting
of colloidal crystals
Colloidal Particle → Big Atom
— watch each atom!
Thermodynamic variable is volume
fraction φ instead of temperature.
Science 270, 1177 (1995) Science
287, 5453 (2000) Glass transition
Diameter-Tunable NIPA Microgel Spheres in Water
NIPA: N-isopropyl acrylamide
heat
water squeezed out
~96% water;
~ 4% NIPA polymers
Dynamic light scattering
pair potential
Look into the Bulk
focal
plane
Objective
The refractive indexes of spheres and water are very close.
Phase Diagram of Hard-Sphere Thin Films
1△
2□
2△
3□
3△ 4□ 4△…
M. Schmidt and H. Löwen,
Phys. Rev. Lett. 76, 4552 (1996).
H/σ
σ↓⇒ n□ → (n-1)△
Phase behavior is controlled
by volume fraction φ and film
thickness H/σ.
φ
A. Fortini and M. Dijkstra, J. Phys.:
Condens. Matter 18, 371 (2006)
Sample Preparation
1△
2□
2△
3□
3△ 4□ 4△…
e.g. 4 layers at the center, 6 layers at the edges in a (2cm)2 sample
⇒ uniform thickness in 0.1mm region
Mechanical and
thermal anneal
>106-particle
large crystal domain
How to heat ?
Transitions always start from interface.
… 4□ 4△
A focused beam of light heats the
interior of a crystal domain.
Heated region ∆T = 1.6°C
Steady temperature reached in 2 s
5□ 5△ …
~80µm
Introduction
Two-step nucleation
Y. Peng, F. Wang, Z. Wang, A. Alsayed, Z. Zhang, A. G. Yodh and Y. Han*,
Nature Materials, in press
One-step nucleation
Other kinetics
‘Homogeneous’ Nucleation
Two steps: 5□ ⇒ liquid ⇒ 4△
Nucleus precursor: Particle-swapping loops instead of defects
This novel relaxation mode makes transition in solid easier.
Diffusive Nucleation
50× real time
Lindemann
Parameter
0.02
0.2
Transition Path:
metastable 5□ crystal ⇒ post-critical liquid nucleus (metastable)
⇒ 4△ nucleus ⇒ 4△ crystal (stable phase)
Heterogeneous Nucleation
Nucleation from dislocations
Nucleation from a grain boundary
Diffusive Nucleation on a Grain Boundary
100× real time
Lindemann
parameter
0.02
5□ crystal ⇒ liquid nucleus ⇒ 4△ nucleus ⇒ 4△ crystal
θ1
θ2
lattice orientation
g.b.
θ1 ≠ θ2 ⇒ asymmetric nucleus
0.2
Why □ ⇒ liquid ⇒ △ ?
∆G = −V ∆µ + Aγ + Estrain
= −V ( ∆µ − ∆ε ) + Aγ
Dominates in large nuclei
Dominates in small nuclei
liquid is more favorable for small nuclei ⇔ γliquid-□ < γ△-□
γ□-liquid < γ△-□
γ□-liquid > γ△-□
θ
Why □ ⇒ liquid ⇒ △ ?
∆G = −V ∆µ + Aγ + Estrain
= −V ( ∆µ − ∆ε ) + Aγ
Dominates in large nuclei
Dominates in small nuclei
liquid is more favorable for small nuclei ⇔ γliquid-□ < γ△-□
γ□-liquid < γ△-□
θ
0
liquid
γ□-liquid > γ△-□
△
Why □ ⇒ liquid ⇒ △ ?
∆G = −V ∆µ + Aγ + Estrain
= −V ( ∆µ − ∆ε ) + Aγ
Dominates in large nuclei
Dominates in small nuclei
liquid is more favorable for small nuclei ⇔ γliquid-□ < γ△-□
Hold in 2D, 3D and thin films
(wall-nucleus interface can be
absorbed into the bulk term)
Hold with or without defects
(Edefect = constant)
Ostwald’s step rule
Wilhelm Ostwald
(1853-1932)
Intermediate States in Crystallization
liquid with middleranged order
PNAS 107, 14036 (2010)
liquid
dense liquid droplet
Small BCC nucleus,
Science 277, 1975 (1997)
PRL 105, 025701 (2010)
PRL 41, 702 (1978), PRL
75, 2714 (1995)
classical nucleation theory
FCC nucleus
Intermediated States in S-S Transitions
intermediate state crystalline lattices
(with group-subgroup
relations)
martensitic
nucleation
liquid
(highest symmetry)
observed in
molecular crystals
observed in
colloidal crystals
 Why not observed in simulations?
Small system, strong superheating or anisotropic stress promotes
martensitic transformation and suppresses two-step nucleation.
 Intermediate liquid was only suggested in a graphite-diamond
experiment: Bull. Mater. Sci. 24, 1-21 (2001).
Liquid in S-S Transitions of Metal and Alloy?
γliquid-solid < γsolid-solid ⇒ liquid is more favorable for small nuclei
For most metals and alloys:
solid-liquid γ ~30 -250 mJ/m2 < solid-solid γ ~ 500-1000 mJ/m2
⇒ Intermediate metastable liquid should exist
Introduction
Two-step nucleation
Facet growth, critical size …
One-step nucleation
Other kinetics
Three Types of S-S Interfaces
small nuclei: more irregular shape
medium nuclei: more circular
large nuclei: faceted
Coherent
low interfacial energy γ
Semi-coherent
Incoherent
high γ
Facet Growth Speed
730s
Incoherent
b0
a0
Semi-coherent
c0
d0
e0
c
796s
r
c0
d
Coherent
f0
− coherent
coherent
⇔ v||incoherent < v|semi
<
v
|
||
b
a
e
f
v⊥incoherent > v⊥semi −coherent > v⊥coherent
⇒ elongates along the coherent facet
(lower surface energy)
Coherent Facet Pinned During Shrinking
Switch off the local heating
Not a barrier-crossing process ⇒ No intermediate liquid
Broad Angle Distribution ⇒ Not Martensitic
50 experiments
A typical method to identify martensitic in molecular crystals.
Critical Nucleus Size
Method 1
Method 3
Method 2
Apply a Stress (small flow < 1 particle/100 sec)
Liquid vanishes at flow > 0.007 µm/s !
Introduction
Two-step nucleation
One-step nucleation
Under small flow (anisotropic stress)
Other kinetics
Martensitic
+ Diffusive
Nucleation
One-Step
Nucleation
Flow
Transition Path:
5□ crystal ⇒ 4△ nucleus ⇒ 4△ crystal
‘One-step’ Nucleation in a Defect-Free Region
394s
398s
409s
400s
5μm
415s
460s
420s
45o
Martensitic
Diffusive
One-step: n□ → (n-1)△.
The nucleus precursor is dislocation pairs which glide as a “zipper”
to trigger more pairs.
The later growth is diffusive although with a fixed angle 45°.
Near a Dislocation
Similar to defect-free regions:
martensitic first, then diffusive nucleation
Parameter Regimes for 1-step & 2-step
one-step
two-step
Flow
in colloids
(Mg, Fe)2SiO4 in Earth’s mantleα-lattice ⇒ γ- lattice
Low stress: Diffusive. High stress: Martensitic
P.C. Burnley & H.W. Green II, Nature 338,753 (1989)
Stress in
molecular crystals
1-step vs 2-step Nucleation
Flow rate
Diffusive
≈ 0 (<0.01 µm/s)
Martensitic
small (0.01-0.1 µm/s)
Nucleation path
two-step: civilian
‘one’-step:
military + civilian
No
dislocation pairs
45o
Intermediate state liquid nucleus
Precursor
swapping loops
Angle between two random
lattices
Nucleus shape
evolution
circular → faceted
ellipse →
parallelogram
Most above behaviors in defect-free regions also hold near
dislocations or grain boundaries.
Introduction
Two-step nucleation
One-step nucleation
Under small flow (anisotropic stress)
At some tri-junctions (can have no flow)
Other kinetics
5 □ ⇒ 4△ at a Trijunction
all three facets are
coherent,
γcoherent < γ□ -liquid
⇒ no liquid
Introduction
Two-step nucleation
One-step nucleation
Other kinetics
Nuclei coalescence
Nuclei Coalescence 1: liquid + liquid
Can merge then transform to △, or transform to △ then merge.
Liquids formed around vacancies are more mobile than those from
dislocations.
No attraction/repulsion between liquids and dislocations/g.b.
Nuclei Coalescence 2 & 3: solid + solid (large / small angle)
B-D: large angle between two △ lattices
grain boundary ⇒ propagate through small nucleus
E-H: small angle between two △ lattices
dislocations ⇒ diffuse into large nucleus
Nuclei Coalescence 4: solid + solid (// lattices)
When distance is
~5 particles, □
lattice in between
rotates and
collectively
transforms to △
Nuclei Coalescence 5: solid + solid (⊥ lattices)
small △ nucleus ⇒ liquid ⇒ absorbed by big △ nucleus
Why liquid?
Summary
1st experiment on solid-solid transition with
single-particle dynamics.
Discovered a novel intermediate liquid state
and understood its mechanism which should
hold in 2D, 3D, thin films, most metals & alloys,
with or without defects.
A novel relaxation mode before s-s transition
(loop-motion as nucleus precursor).
A novel (martensitic + diffusive nucleation)
kinetic path under flow.
Acknowledgement
HKUST
Ph.D. Students:
Yi Peng
彭毅
Feng Wang
王峰
Ahmed Alsayed, Arjun Yodh
synthesized NIPA spheres