yilong han, [email protected] co-authors: yi peng, feng wang...
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Yilong Han, [email protected]: 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