Yilong Han, Co-authors: Yi Peng, Feng Wang Nucleation in solid-solid transitions of colloidal crystals

Transcription

1 Yilong Han, 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.

2 Nucleation in Solid-solid Transitions of Colloidal Crystals Yilong Han 韩一龙 Department of Physics CMDS13, Salt Lake City, 2014

3 Introduction Two-step nucleation One-step nucleation Other kinetics

4 Solid-solid Transitions widely exist in nature Steel-production Man-made Diamond Earth science Nano-materials

5 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 + E strain E defect only for crystalline mother phase

6 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.

7 Colloid One Class of Soft Material What are Colloids? small particles dispersed in a solution Particle size: 10nm 10µm, k B T dominated, Brownian motion milk, inks, paints, blood, smoke 1.6 micron silica spheres

8 Colloids as Model Systems Science 292, 258 (2001) Nucleation in crystallization Colloidal Particle Big Atom watch each atom! Science 314, 795 (2006) Sublimation of colloidal crystals Science 309, 1207 (2005) Heterogeneous melting of colloidal crystals Thermodynamic variable is volume fraction φ instead of temperature. Science 270, 1177 (1995) Science 287, 5453 (2000) Glass transition

9 Diameter-Tunable NIPA Microgel Spheres in Water heat NIPA: N-isopropyl acrylamide water squeezed out ~96% water; ~ 4% NIPA polymers Dynamic light scattering pair potential

10 Look into the Bulk focal plane Objective The refractive indexes of spheres and water are very close.

11 Phase Diagram of Hard-Sphere Thin Films M. Schmidt and H. Löwen, Phys. Rev. Lett. 76, 4552 (1996). σ n (n-1) H/σ 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)

12 Sample Preparation 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 >10 6 -particle large crystal domain

13 How to heat? Transitions always start from interface A focused beam of light heats the interior of a crystal domain. Heated region T = 1.6 C Steady temperature reached in 2 s ~80µm

14 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

15 Homogeneous Nucleation Two steps: 5 liquid 4 Nucleus precursor: Particle-swapping loops instead of defects This novel relaxation mode makes transition in solid easier.

16 Diffusive Nucleation 50 real time Lindemann Parameter Transition Path: metastable 5 crystal post-critical liquid nucleus (metastable) 4 nucleus 4 crystal (stable phase)

17 Nucleation from dislocations Heterogeneous Nucleation Nucleation from a grain boundary

18 Diffusive Nucleation on a Grain Boundary 5 crystal liquid nucleus 4 nucleus 4 crystal 100 real time Lindemann parameter θ 1 θ 2 lattice orientation g.b. θ 1 θ 2 asymmetric nucleus

19 Why liquid? G = V µ + Aγ + E strain = V µ ε + A ( ) γ Dominates in large nuclei Dominates in small nuclei liquid is more favorable for small nuclei γ liquid- < γ - γ -liquid < γ - θ γ -liquid > γ -

20 Why liquid? G = V µ + Aγ + E strain = V µ ε + A ( ) γ Dominates in large nuclei Dominates in small nuclei liquid is more favorable for small nuclei γ liquid- < γ - γ -liquid < γ - 0 liquid θ γ -liquid > γ -

21 Why liquid? G = V µ + Aγ + E strain = V µ ε + A ( ) γ Dominates in large nuclei Dominates in small nuclei liquid is more favorable for small nuclei γ liquid- < γ - Hold in 2D, 3D and thin films (wall-nucleus interface can be absorbed into the bulk term) Hold with or without defects (E defect = constant)

22 Ostwald s step rule Wilhelm Ostwald ( )

23 Intermediate States in Crystallization liquid with middleranged order PNAS 107, (2010) dense liquid droplet Science 277, 1975 (1997) PRL 105, (2010) Small BCC nucleus, PRL 41, 702 (1978), PRL 75, 2714 (1995) liquid classical nucleation theory FCC nucleus

24 Intermediated States in S-S Transitions intermediate state crystalline lattices martensitic nucleation (with group-subgroup relations) observed in molecular crystals liquid (highest symmetry) 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).

25 Liquid in S-S Transitions of Metal and Alloy? γ liquid-solid < γ solid-solid liquid is more favorable for small nuclei For most metals and alloys: solid-liquid γ ~ mj/m 2 < solid-solid γ ~ mj/m 2 Intermediate metastable liquid should exist

26 Introduction Two-step nucleation Facet growth, critical size One-step nucleation Other kinetics

27 Three Types of S-S Interfaces small nuclei: more irregular shape medium nuclei: more circular large nuclei: faceted Coherent Semi-coherent Incoherent low interfacial energy γ high γ

28 Facet Growth Speed 730s Incoherent c 0 d 0 b 0 a 0 Semi-coherent e 0 f 0 Coherent d c r c 0 796s b v incoherent semi coherent > v > v < v < v coherent incoherent semi coherent coherent v e f a elongates along the coherent facet (lower surface energy)

29 Coherent Facet Pinned During Shrinking Switch off the local heating Not a barrier-crossing process No intermediate liquid

30 Broad Angle Distribution Not Martensitic 50 experiments A typical method to identify martensitic in molecular crystals.

31 Critical Nucleus Size Method 1 Method 2 Method 3

32 Apply a Stress (small flow < 1 particle/100 sec) Liquid vanishes at flow > µm/s!

33 Introduction Two-step nucleation One-step nucleation Under small flow (anisotropic stress) Other kinetics

34 One-Step Nucleation Martensitic + Diffusive Nucleation Flow Transition Path: 5 crystal 4 nucleus 4 crystal

35 One-step Nucleation in a Defect-Free Region 394s 398s 400s 409s 5μm 415s 420s 460s Martensitic 45 o 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.

36 Near a Dislocation Similar to defect-free regions: martensitic first, then diffusive nucleation

37 Parameter Regimes for 1-step & 2-step one-step two-step Flow in colloids (Mg, Fe) 2 SiO 4 in Earth s mantleα-lattice γ- lattice Low stress: Diffusive. High stress: Martensitic Stress in P.C. Burnley & H.W. Green II, Nature 338,753 (1989) molecular crystals

38 1-step vs 2-step Nucleation Diffusive Martensitic Flow rate 0 (<0.01 µm/s) small ( µm/s) Nucleation path two-step: civilian one -step: military + civilian Intermediate state liquid nucleus No Precursor swapping loops dislocation pairs Angle between two random 45 o lattices Nucleus shape evolution circular faceted ellipse parallelogram Most above behaviors in defect-free regions also hold near dislocations or grain boundaries.

39 Introduction Two-step nucleation One-step nucleation Under small flow (anisotropic stress) At some tri-junctions (can have no flow) Other kinetics

40 5 4 at a Trijunction all three facets are coherent, γ coherent < γ -liquid no liquid

41 Introduction Two-step nucleation One-step nucleation Other kinetics Nuclei coalescence

42 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.

43 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

44 Nuclei Coalescence 4: solid + solid (// lattices) When distance is ~5 particles, lattice in between rotates and collectively transforms to

45 Nuclei Coalescence 5: solid + solid ( lattices) small nucleus liquid absorbed by big nucleus Why liquid?

46 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.

47 Acknowledgement HKUST Ph.D. Students: Yi Peng Feng Wang 彭毅 王峰 Ahmed Alsayed, Arjun Yodh synthesized NIPA spheres