1 MIT 3.022 Microstructural Evolution in Materials 12: NucleationJuejun (JJ) Hu
2 Thermodynamics of phase transitionG H Liquid Supercooled liquid Liquid Crystal Crystal melting usually does not require superheating due to surface nucleation. For example, the surface energies of ice/water follows the Antonov’s rule, and therefore there is no surface energy barrier for liquid water formation on solid ice surface. Crystal Tm Tm
3 Homogeneous nucleation from a fluid phaseLiquid Crystal nucleus r Volumetric Surface
4 Thermodynamics of homogeneous nucleationLiquid Volumetric Gibbs free energy change Surface energy change Crystal T Tm
5 Gibbs free energy change in solidificationGibbs free energy change of nucleation Critical nucleus size Energy barrier towards nucleation Gibbs free energy change Nucleus size r
6 Vapor-liquid nucleation of water
7 Density of critical nucleiNumber of clusters with size greater than r Example: number of ice clusters in 1 g of water at 0 °C r > 0.4 nm (~ 9 molecules): 1.3 × 1015 r > 0.7 nm (~ 48 molecules): 0.7 where g = J/m2, DHm = J/g, Tm = K The pre-exponential factor n0 is usually linked to atomic numbers in the classical nucleation theory. This is, however, heuristic. See for example, Ford, I. J. "Statistical mechanics of nucleation: a review“ for more detailed discussions. A supercooling threshold exists for onset of nucleation events
8 Homogeneous nucleation rateNucleation rate I Number of nuclei with size just under r* × Rate of atoms hopping to the nuclei I DT Nucleation onset Driving force limited Diffusion limited
9 Experimental measurement of nucleation rateLiquid Nucleation Growth Nucleation rate in lithium silicate glass T Tm For vapor-liquid transition latest technology leverages Mie scattering measurement to quantify nucleation rate Nucleation zone Nucleation zone t Phys. Chem. Glasses 15, 95 (1974)
10 Heterogeneous nucleationGibbs free energy change of cluster formation Volumetric term Surface term Cluster Liquid Substrate Y-L equation:
11 Heterogeneous nucleationGibbs free energy change of cluster formation Volumetric term Surface term
12 Heterogeneous nucleationCritical nucleus size Energy barrier towards nucleation Gibbs free energy change Wetting on a substrate reduces energy barrier towards nucleation Nucleus size r
13 Nucleation kinetics and grain sizeFast cooling and addition of secondary phase contribute to grain refinement Magnesium alloy w/o SiC particles Magnesium alloy with SiC particles Acta Mater. 54, 5591 (2006)
14 Vapor-Liquid-Solid (VLS) nanowire growthSiCl4 vapor + H2 Interface where growth continues Growth direction Melted gold nano-particles saturated with SiH4 Substrate Substrate Heterogeneous nuleation of Si at the interface Diameter of nanowire is determined by the gold droplet size Temperature for Si deposition on a planar substrate (homogeneous nucleation): ~ 800 ˚C
15 Nanowires formed by VLS growthGold nano-particle Growth direction S. Kodambaka, J. Tersoff, M. C. Reuter, and F. M. Ross, Science 316, 729 (2007).
16 Why gold? Reason #1: Low eutectic temperatureQuestion: what would happen if we were to grow nanowires at high temperature? “The influence of the surface migration of gold on the growth of silicon nanowires,” Nature 440, (2006).
17 Albert P. Levitt, Whisker Technology (1975)Why gold? Reason #2: Small gold solubility in Si (Eutectoid transformation) Question: why is such small solubility important? 99.8% Solubility: 0.2% Albert P. Levitt, Whisker Technology (1975)
18 Tapering during nanowire growth“A Systematic Study on the Growth of GaAs Nanowires by Metal-Organic Chemical Vapor Deposition,” Nano Lett. 8, (2008).
19 Summary Driving force for nucleation Supercooling (undercooling)Volumetric Gibbs free energy reduction Energy barrier against nucleation Surface energy Kinetics of nucleation Number of sub-critical nuclei Diffusion Heterogeneous nucleation Lowering the surface energy barrier of nucleation