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An Inverse Gibbs-Thomson Effect in Nanoporous Nanoparticles Ian McCue Jonah Erlebacher Department of Materials Science and Engineering Materials Research Society, November 29th, 2012 This work is supported by NSF DMR 1003901 Department of Materials Science and Engineering Nanoporous Gold (NPG) Characteristics of NPG • bicontinuous, open porosity • tunable pore size ~5 nm 10 microns via electrochemical processing and/or thermal annealing • porosity is sub-grain size NPG is not nanoparticulate • porosity retains a long-range single crystal network grain boundary Department of Materials Science and Engineering single-crystalline to a scale > 3 orders of magnitude larger than any pore/ligament diameter Electrochemistry of Porosity Evolution The “critical potential” separates two potential windows: • below Ec planar, passivated morphologies • sufficiently far above Ec porosity evolution What changes with potential? • rate of silver dissolution (fast), surface diffusivity (slow) Department of Materials Science and Engineering Formation Mechanism in Bulk Systems A. Nucleation and growth of vacancy islands B. Development of gold-passivated mounds C. Evolution of gold-poor mound bases D. Mound undercutting, nucleation of new gold mounds, and pore bifurcation E. Evolution of gold-passivated porosity F. Post-dealloying coarsening, and/or further dissolution Erlebacher, J., J. Electrochem. Soc. 151 (2004), C614 Department of Materials Science and Engineering Kinetic Monte Carlo (KMC): A simulation tool to study coarsening KMC Algorithm simulated nanoporous metal 1. Tabulate all possible transitions ki real nanoporous gold 2. The time for an event to occurNwith 100% probability is: t ln ki i 1 where is a random number in 0,1 3. Pick an event i to occur during theN time interval with probability Pi ki k j 1 j 1 4. Move atoms corresponding to event i 5. Update neighbors, transition list, go to step 2 and repeat Rate Parameter for Surface Diffusion: Rate Parameter for Dissolution: nE kdiff v1 exp B v1 1013 sec1 EB 0.15eV n coordination kbT nEB v 104 sec 1 applied potential kdiss v2 exp kbT 2 Department of Materials Science and Engineering Nanoporous Nanoparticles J. Snyder, J. Erlebacher Initial Conditions Looked at four different particle sizes: radii of 10, 15, 25 and 40 atoms Looked at three different compositions: 65%, 75%, and 85% Ag Simulations ran for 104-105 simulated seconds, or ~ 5 x108 iterations Department of Materials Science and Engineering Gibbs-Thomson Effects on Electrochemical Stability • • • • L. Tang, B. Han, K. Persson, C. Friesen, T. He, K. Sieradzki, G. Ceder, J. Electrochem. Soc. 132, 596 (2010). Department of Materials Science and Engineering Particle of radius r will have additional surface energy increase per atom by: 2 r where is the atomic vol. Smaller means more unstable G-T effect manifests in electrochemical stability of nanoparticles Decrease in dissolution potential of atom by: E n where n is the number of electrons given up to form metal cation What about Binary Particles? NO! The potential we are measuring is not a certain critical current, but an intrinsic potential based on the propensity that a particle will dealloy • • Does not mean Ag atoms require more energy to dissolve As size decreases more potential is required to form porosity Department of Materials Science and Engineering Porosity Evolution in Nanoparticles • Low-coordination surface silver sites are dissolved • Surface gold atoms quickly passivate the surface • Regions of bulk are exposed due to fluctuations in the outermost layer and porosity can occur Department of Materials Science and Engineering Porosity Evolution in Nanoparticles (cont) Below Ep Smaller volume corresponds to fully dealloyed particles Diffuse threshold between passivation and porosity evolution 1:1 Ratio Above Ep Larger volume corresponds to passivated particles Define Ep as potential where the distribution area of each Gaussian was equal Department of Materials Science and Engineering Observation on Porosity Evolution in NP Surface Diffusion events are controlled by kink fluctuations Ag terrace atoms are the rate limiting step in dissolution Department of Materials Science and Engineering Kinetic Derivation Can setup a first order rate equation for the change in the number of surface silver atoms dNAg kdiss Pkink Pperc NAg dt kdiss exp 9 EB EP k BT Probability of Au fluctuation at a kink site Probability Ag atom is connected to bulk Ag atoms Equilibrium Number of Ag atoms on the surface Department of Materials Science and Engineering Solution to Kinetic Equation • • Single dissolution event at the passivated state leads to porosity evolution Simplest criterion for Ep is that over a time interval ∆t- the lifetime of the step edge fluctuation- is that N Ag t N Ag 0 1 N 0 1 1 EP 9EB kbT ln ln Ag vP P t N 0 perc Ag kink Department of Materials Science and Engineering Percolation Probability for Surface Ag Atoms What does percolation probability mean: • Can we trace a path of silver atoms from one side of the particle to the other Department of Materials Science and Engineering Number of Ag Terrace Atoms As particle size increases: • Facet size does not appreciably increase • Ag atoms are found on the edges of facets • As a result the number of Ag terrace sites scales with the radius Ag terrace atoms distributed evenly across facets Department of Materials Science and Engineering Surface Diffusion Radius 10 Radius 40 Key points: • Peak at ~10-6 corresponds to adatom fluctuations • Peak at ~101 corresponds to fluctuations at step edges • Area under kink interval curve corresponds to Pkink Department of Materials Science and Engineering Evaluation of Kinetic Expression Department of Materials Science and Engineering Summary • Porosity evolution in nanoparticles is dependent on a chorus of size dependent variables and exhibits rich complexity • Gibbs-Thomson effects dictate the size dependence, but not as we initially expected • First order rate equation gives an awesome fit to our observed results • Major conclusion is that surface diffusion changes the critical potential • Could potentially tailor porosity in nanoparticles adding an alloying component that will kill the formation of a passivating monolayer Department of Materials Science and Engineering Acknowledgements • Jonah Erlebacher • Erlebacher Research Group • Josh Snyder • Ellen Benn • Felicitee Kertis Department of Materials Science and Engineering