Yilong Han, yilong@ust.hkCo-authors: Yi Peng, Feng WangNucleation in solid-solid transitions of colloidal crystals

Solid-solid phase transitions between different crystalline structures are ubiquitous in nature, but their kineticpathways and mechanisms present formidable challenges for theory, simulation and experiment. Here wedirectly imaged the solid-solid transitions in colloidal thin films composed of diameter-tunable NIPAM mi-crospheres with single-particle resolution by video microscopy. We discover a surprising two-step diffusivenucleation behavior for transitions from square- to triangular-lattices with an intermediate liquid stage. Theobservations and resulting theoretical analysis suggest that, provided solid-liquid interfacial energies are suffi-ciently small, s-s transitions in most traditional metals and alloys should follow this two-step nucleation withintermediate 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 anew relaxation mode that makes s-s transitions easier and faster. This new kinetic factor controlling the s-stransition 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 squarelattices as nucleation precursors, which triggered tens of particles to collectively transform to a triangular-latticenucleus and then grew diffusively. This martensitic transformation at the early stage and the diffusive nucleationat 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 energiesand growth rates which can dramatically alter nucleation kinetics. The coalescence of two crystalline nucleiexhibits different behaviors for different lattice angles.

Nucleation in Solid-solid Transitions of Colloidal Crystals

Department of Physics

Yilong Han

韩 一 龙

CMDS13, Salt Lake City, 2014

Introduction Two-step nucleation One-step nucleation Other kinetics

Solid-solid Transitions

Steel-production

Earth science

Man-made Diamond

Nano-materials

widely exist in nature…

…

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

strain defectEG EV Aµ γ= −−∆ +∆ +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…

1.6 micron silica spheres milk, inks, paints, blood, smoke…

Colloids as Model Systems

Science 309, 1207 (2005) Heterogeneous melting

of colloidal crystals

Science 292, 258 (2001) Nucleation in crystallization

Science 314, 795 (2006) Sublimation 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

~96% water; ~ 4% NIPA polymers water squeezed out

Dynamic light scattering pair potential

Look into the Bulk

Objective

focal plane

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).

A. Fortini and M. Dijkstra, J. Phys.: Condens. Matter 18, 371 (2006)

Phase behavior is controlled by volume fraction φ and film thickness H/σ.

H/σ

φ

σ↓⇒ n□ → (n-1)△

Sample Preparation

1△ 2□ 2△ 3□ 3△ 4□ 4△…

>106-particle large crystal domain

Mechanical and thermal anneal

e.g. 4 layers at the center, 6 layers at the edges in a (2cm)2 sample ⇒ uniform thickness in 0.1mm region

~80µm

How to heat ?

A focused beam of light heats the interior of a crystal domain. Heated region ∆T = 1.6°C Steady temperature reached in 2 s

Transitions always start from interface.

… 4□ 4△ 5□ 5△ …

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

0.02 0.2

Lindemann Parameter

50× real time

metastable 5□ crystal ⇒ post-critical liquid nucleus (metastable)

⇒ 4△ nucleus ⇒ 4△ crystal (stable phase)

Transition Path:

Heterogeneous Nucleation Nucleation from dislocations

Nucleation from a grain boundary

Diffusive Nucleation on a Grain Boundary

Lindemann parameter

100× real time

5□ crystal ⇒ liquid nucleus ⇒ 4△ nucleus ⇒ 4△ crystal

0.02 0.2

g.b.

θ1

θ2 lattice orientation

θ1 ≠ θ2 ⇒ asymmetric nucleus

Why □ ⇒ liquid ⇒ △ ?

liquid is more favorable for small nuclei ⇔ γliquid-□ < γ△-□ Dominates in small nuclei Dominates in large nuclei

strainV EAG γµ∆ + +∆= −( )V Aε γµ− ∆ − +∆=

γ□-liquid > γ△-□

θ γ□-liquid < γ△-□

Why □ ⇒ liquid ⇒ △ ?

γ□-liquid > γ△-□

θ γ□-liquid < γ△-□

0

liquid

△

liquid is more favorable for small nuclei ⇔ γliquid-□ < γ△-□ Dominates in small nuclei Dominates in large nuclei

strainV EAG γµ∆ + +∆= −( )V Aε γµ− ∆ − +∆=

Why □ ⇒ liquid ⇒ △ ?

liquid is more favorable for small nuclei ⇔ γliquid-□ < γ△-□ Dominates in small nuclei Dominates in large nuclei

strainV EAG γµ∆ + +∆= −( )V Aε γµ− ∆ − +∆=

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)

dense liquid droplet Science 277, 1975 (1997) PRL 105, 025701 (2010)

liquid with middle-ranged order PNAS 107, 14036 (2010)

liquid FCC nucleus

Small BCC nucleus, PRL 41, 702 (1978), PRL 75, 2714 (1995)

Intermediate States in Crystallization

classical nucleation theory

Intermediated States in S-S Transitions

intermediate state crystalline lattices (with group-subgroup relations)

liquid (highest symmetry)

martensitic observed in molecular crystals

nucleation 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).

For most metals and alloys: solid-liquid γ ~30 -250 mJ/m2 < solid-solid γ ~ 500-1000 mJ/m2

⇒ Intermediate metastable liquid should exist

Liquid in S-S Transitions of Metal and Alloy?

γliquid-solid < γsolid-solid ⇒ liquid is more favorable for small nuclei

Introduction Two-step nucleation Facet growth, critical size …

One-step nucleation Other kinetics

Three Types of S-S Interfaces

Coherent Semi-coherent Incoherent

small nuclei: more irregular shape medium nuclei: more circular large nuclei: faceted

low interfacial energy γ high γ

a0

b0

c0

d0

f0 e0

730s

a

b

c

d

f e

r c0

796s

Facet Growth Speed

Coherent

Semi-coherent

Incoherent

semi coherentincoherent coherentv vv −⊥ ⊥⊥ > >

|| ||| | semi coherentincoh coherenterent vv v −⇔ < <

⇒ 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 2

Method 3

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

One-Step Nucleation

Transition Path: 5□ crystal ⇒ 4△ nucleus ⇒ 4△ crystal

Martensitic + Diffusive Nucleation

Flow

‘One-step’ Nucleation in a Defect-Free Region

398s 400s

420s

45o

409s

5μm

394s

415s

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°.

Martensitic

460s

Diffusive

Near a Dislocation

Similar to defect-free regions: martensitic first, then diffusive nucleation

Parameter Regimes for 1-step & 2-step

Flow in colloids

Stress in molecular crystals

(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)

two-step

one-step

1-step vs 2-step Nucleation

Diffusive Martensitic Flow rate ≈ 0 (<0.01 µm/s) small (0.01-0.1 µm/s) Nucleation path two-step: civilian ‘one’-step:

military + civilian Intermediate state liquid nucleus No Precursor swapping loops dislocation pairs Angle between two lattices

random 45o

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

When distance is ~5 particles, □ lattice in between rotates and collectively transforms to △

(// lattices)

Nuclei Coalescence 5: solid + solid

small △ nucleus ⇒ liquid ⇒ absorbed by big △ nucleus

(⊥ lattices)

Why liquid?

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.

Summary

Ahmed Alsayed, Arjun Yodh synthesized NIPA spheres

Acknowledgement

HKUST

Ph.D. Students: Yi Peng Feng Wang 彭毅 王峰