Nucleation Don H. Rasmussen Box 5705 Clarkson University

Slides:



Advertisements
Similar presentations
Diffusion (continued)
Advertisements

Mineral Surfaces Minerals which are precipitated can also interact with other molecules and ions at the surface Attraction between a particular mineral.
Summary to Date Solutions are thermodynamically stable within a range of temperatures and compositions. Solutions more concentrated than their limit will.
Hot Under the Collar (part II) Crystallisation Fluorite Igneous petrology is all about crystals and how they get there.
1 Kinetics – time dependence of transformation rate.
Chapter 10 Phase Transformations in Metals (1)
2. Formation of Cloud droplets
Thermodynamics of surfaces and interfaces Atkins (ed. 10): §16C.2 Atkins (ed. 9): § Atkins (ed. 8): § Atkins (ed. 7): §
Fat Crystallization April 14, 2015.
Solidification and Strengthening Chapter 9
Interfacial transport So far, we have considered size and motion of particles In above, did not consider formation of particles or transport of matter.
Solidification and Grain Size Strengthening
Nucleation: Formation of Stable Condensed Phase Homogeneous – Homomolecular H 2 O (g)  H 2 O (l) Homogeneous – Heteromolecular nH 2 O (g) + mH 2 SO 4(g)
NC State University Department of Materials Science and Engineering1 MSE 440/540: Processing of Metallic Materials Instructors: Yuntian Zhu Office: 308.
Crystallisation from melts  Why do crystals form?  What controls their shape and size?  Three aspects to the growth of a crystal are Nucleation: formation.
SOLID-LIQUID INTERACTIONS. Zero-order reactions have a constant rate. This rate is independent of the concentration of the reactants. A first order reaction.
Water in the Atmosphere Water vapor in the air Saturation and nucleation of droplets Moist Adiabatic Lapse Rate Conditional Instability Cloud formation.
Surfaces Lecture 18. Diffusion Rates Probability of atom making a jump to vacancy is where ℵ is number of attempts and E B is the activation or barrier.
Integration of the rate laws gives the integrated rate laws
Different heterogeneous routes of the formation of atmospheric ice Anatoli Bogdan Institute of Physical Chemistry, University of Innsbruck Austria and.
PC4259 Chapter 5 Surface Processes in Materials Growth & Processing Homogeneous nucleation: solid (or liquid) clusters nucleated in a supersaturated vapor.
Chapter 10: Phase Transformations
 Temperature When temperature increases, the particles move faster causing more collisions & the reaction rate increases  Simulation Simulation.
Chapter 10 Phase Transformations. Kinetics and Phase Transformations Phase diagrams show which phases are in equilibrium under certain conditions, such.
Lecture 26: Crystallization PHYS 430/603 material Laszlo Takacs UMBC Department of Physics.
Growing Numerical Crystals Vaughan Voller, SAFL Feb
Materials science I - Metallic materials Metallic materials Solid state atomic structure atomic arrangement microstructure macrostructure Pure materials.
GEF2200 Stordal - based on Durkee 10/11/2015 Relative sizes of cloud droplets and raindrops; r is the radius in micrometers, n the number per liter of.
Cold Working is Actually Strain Hardening Basic equation relating flow stress (strain hardening) to structure is:  o =  i +  Gb  1/2 Yield stress increases.
Today’s lecture objectives: –Nucleation of Water Vapor Condensation (W&H 4.2) What besides water vapor do we need to make a cloud? Aren’t all clouds alike?
Schmid's Law F r = F cos λ A 0 = Acos ψ τ r = σ cos ψ cos λ.
Diffusional Limitation in Immobilized Enzyme System Immobilized enzyme system normally includes - insoluble immobilized enzyme - soluble substrate, or.
Solidification, Lecture 2
SUPERSATURATION NUCLEATION CRYSTAL GROWTH CRYSTAL Non equilibrium Equilibrium.
Pursuing the initial stages of crystal growth using dynamic light scattering (DLS) and fluorescence correlation spectroscopy (FCS) Takashi Sugiyama Miyasaka.
Byeong-Joo Lee Byeong-Joo Lee Motivation.
Nucleation and Growth of Crystals
Surfaces Lecture 17. Reactions at Surfaces Homogeneous reactions are those occurring within a single phase (e.g., an aqueous solution). Heterogeneous.
0-D, 1-D, 2-D Structures (not a chapter in our book!)
Diffusion (continued)
Byeong-Joo Lee Byeong-Joo Lee POSTECH - MSE Nucleation Kinetics.
Crystal Growth General Formalism    Phase growing into  with velocity v : f ( “site factor” ) : fraction of sites where a new atom can be incorporated.
Affect of Variables on Recrystallization
Microstructure From Processing: Evaluation and Modelling Diffusional growth: Lecture 5 Martin Strangwood, Phase Transformations and Microstructural Modelling,
Kinetics. Rate of Reaction Reaction kinetics is the study of rates of reaction. The rate of a reaction is defined as the change in concentration per unit.
Reaction Rates and Equilibrium Chapter 19 C.Smith.
Phase Transformation by Dr.Srimala.
Chapter 10: Phase Transformations
Physics and Chemistry of Hybrid Organic-Inorganic Materials Lecture 4: The physics of phase separation and solutions Professor Douglas A. Loy Visiting.
Second-Phase Shape: Misfit Strain Effects
Microstructure From Processing: Evaluation and Modelling Nucleation: Lecture 4 Martin Strangwood, Phase Transformations and Microstructural Modelling,
MIT Microstructural Evolution in Materials 12: Nucleation
Chapter 10: Phase Transformations
MSE 440/540: Processing of Metallic Materials
Kinetics of Nucleation
DR S. & S. S. GHANDHY GOVERNMENT ENGINEERING COLLEGE , SURAT.
Review for Exam 2 Fall 2011 Topics on exam: Class Lectures:
Condensational Growth
Surfaces Lecture 17.
Nucleation & Growth Driving Force
MIT Microstructural Evolution in Materials 12: Nucleation
Film Formation   1. Introduction Thin film growth modes.
Collision Theory – Explains Reaction Rates
MIT Microstructural Evolution in Materials 13: Precipitate Growth
Non equilibrium systems
Hypoeutectoid Steel T(°C) d L +L g (austenite) Fe3C (cementite) a
Particle formation and growth
Description of Phase Transformation
Nucleation Kinetics Byeong-Joo Lee Phase Transformations POSTECH - MSE
Presentation transcript:

Nucleation Don H. Rasmussen Box 5705 Clarkson University

Homogeneous Nucleation l Fluctuations in composition and structure which are small in extent but large in degree result in small new phase nuclei which are in local equilibrium but unstable to growth in an undercooled or supersaturated parent phase.

How does Homogeneous Nucleation Occur? l Stable clusters form when their formation decreases total free energy. l Growth of small clusters is limited because new particle surface costs more free energy than the bulk free energy reduction. Only large clusters are stable. l Clusters grow and decay by monomer addition/evaporation and there is in a metastable cluster size distribution. l The larger the supersaturation or undercooling, the greater the number and maximum size of the existing clusters and the smaller the necessary critical cluster size for continued growth. l For clusters just larger than critical, the growth rate increases along with the size in an autocatalytic fashion.

l Nucleation Rate, J, is the product of n q, the net probability of an atom jumping across interface and into the critical cluster (per unit surface area)  jump frequency of monomer is fluid n A c, the surface area of the critical cluster n n c, the concentration of critical clusters per unit volume Numerical Model of Homogeneous Nucleation

q is the net rate of diffusion across the surface of a cluster where D o is the diffusion coefficient in the liquid. and c i and c o are the concentration of crystallizing atoms on the two sides of the interface of thickness, l.

The surface area of a spherical cluster is The concentration of critical clusters is

The pre-exponential factors are almost constant and approximately nuclei/cm 3 sec. Nucleation Rate per Unit Volume, J

Effect of Temperature on Bulk Free Energy Change Free energy Temperature  G v L S TT TETE T G L G S

Free Energy of a Cluster as a Function of Size

Influence of increasing Undercooling or Supersaturation From 1 to 5 the supersaturation or undercooling increases which results in a decrease in both the critical cluster size and the barrier to nucleation.

Conditions for critical cluster or nucleus

Critical Cluster Size and Free Energy Barrier versus Undercooling

Temperature Dependence of Nucleation Rate J(T) TT

Time Temperature Transformation Curves  Time (Seconds) The delay time is related to the reciprocal of the nucleation rate and here the delay time is plotted as a function of the undercooling.

Heterogeneous Nucleation l Nucleation at the surface of an impurity particle or on the walls of the container. l “Catalysts for Nucleation” are surfaces which significantly lower the barrier to new phase formation. l Heterogeneous nucleation occurs at low undercooling and at high rates.

Nucleation on a substrate takes less material  sl  nl  sn liquid substrate nucleus 

Fraction of the critical cluster which must form at any specific undercooling

Free Energy of Formation of the Nucleus versus Contact Angle at Fixed Undercooling