Material World Network: Theoretical, Computational and Experimental Studies of 3D Microstructural Evolution in Ultra-high Volume Fraction Coarsening System
Final Report Abstract
It’s not only moviegoers whose imagination has been captured by the 3D revolution in imaging technology—even materials scientists have been swept up in the hype! Their excitement is understandable, given the power of modern techniques like x-ray tomography to map out microstructural evolution in 3D with high spatial and temporal resolution. Not only can such measurements offer deeper insight into the mechanisms that underlie transformations in microstructure, but the resulting data sets may also constitute a stringent test for the validation of computational models for these phenomena. Such considerations were the impetus behind an NSF/DFG Materials World Network collaboration focused on “Theoretical, computational and experimental studies of 3D microstructural evolution in ultra-high-volume-fraction coarsening systems.” A team of scientists in the USA and Germany—led by Ke-Gang Wang (Florida Institute of Technology), Long-Qing Chen (Penn State University), Stefan Odenbach (TU Dresden) and Carl Krill (Ulm University)—joined forces to investigate Ostwald ripening, a coarsening phenomenon that can occur in all manner of multiphase materials, including water/oil mixtures, steels, colloids, ceramic powders and even ice cream. In all of these cases, particles of one phase are surrounded by a matrix consisting of one (or more) other phases. During Ostwald ripening, larger particles are observed to grow at the expense of their smaller neighbors, driven by the concomitant reduction in interfacial energy. The mechanism is mediated by a net flux of atoms diffusing from smaller to larger particles through the matrix. Analytic models adequately describe Ostwald ripening when it takes place at low volume fractions VV of the coarsening phase, but when VV exceeds about 60%, the analytic approaches break down. In the latter regime, only computer simulations can attempt to predict the 3D evolution of microstructure. Validation of the underlying simulation algorithms remains an open question, however, as computational results have yet to be compared quantitatively to experiment for the coarsening of real multiphase materials at high VV. We aimed to remedy this situation using time-resolved x-ray microtomography. Samples of composition Al-5 wt% Cu were placed in a custom-built furnace designed to be compatible with the x-ray optics of synchrotron beamlines. At temperatures above the eutectic, the Al–Cu specimens consist of Al-rich solid particles embedded in a liquid matrix of higher Cu concentration. Precise control of temperature allowed VV to be held constant at values ranging from 0.74 to 0.93. Particle coarsening was followed in situ for up to 20 hours by recording tomograms every 10 to 30 minutes. After segmenting the tomographic reconstructions using a 3D watershed algorithm, we carried out a statistical analysis of quantities like the average particle size and the particle size distribution, and we wrote an automated tracking algorithm to determine the volumetric growth rate of hundreds of individual particles during Ostwald ripening. From the resulting particle size trajectories, we generated the first experimental plots of local growth rate as a function of normalized particle size, thereby confirming a longstanding prediction of theory and computer simulation regarding the nonlinearity of such plots. However, the most exciting result of our studies derives from treating the 3D tomography “movies” as a benchmark for computational simulations of Ostwald ripening. Adopting the reconstruction of an early time step with VV = 0.86 as the starting configuration for a phase field simulation, we compared the computational prediction for microstructural evolution to the true behavior observed experimentally. To our great surprise, simulation and experiment agreed closely not only in the overall statistics of coarsening but also in the detailed evolution of individual particle shapes and sizes! Occasionally, a calculated size trajectory deviated significantly from its experimental counterpart, but we could correlate such rare events with the liquid matrix incompletely wetting a nearby particle boundary. Otherwise, the “showdown” between simulation and experiment delivers emphatic validation for the computational algorithm’s underlying physical model for Ostwald ripening at high VV in Al–Cu.
Publications
- “Tomographic investigation of Ostwald ripening in an aluminum-based alloy.” In: 3D Microstructure Meeting 2011. Ed. by F Mücklich. MatInfo Werkstoffinformationsgesellschaft, Frankfurt, 2011, pp. 126–127. ISBN: 978-3-88355-388-7
T Werz, U Wolfram, and C E Krill III
- “Evaluating microstructural parameters of threedimensional grains generated by phase-field simulation or other voxel-based techniques.” In: Modelling and Simulation in Materials Science and Engineering 20 (2012), p. 75009
K Chang, C E Krill III, Q Du, and L-Q Chen
(See online at https://doi.org/10.1088/0965-0393/20/7/075009) - “Parametric Representation of 3D Grain Ensembles in Polycrystalline Microstructures.” In: Journal of Statistical Physics 154 (2014), pp. 913–928
A Spettl, T Werz, C E Krill III, and V Schmidt
(See online at https://doi.org/10.1007/s10955-013-0893-7) - “Particle tracking during Ostwald ripening using time-resolved laboratory x-ray microtomography.” In: Materials Characterization 90 (2014), pp. 185–195. ISSN: 1044-5803
T Werz, M Baumann, U Wolfram, and C E Krill III
(See online at https://doi.org/10.1016/j.matchar.2014.01.022) - “Stochastic 3D modeling of Ostwald ripening at ultra-high volume fractions of the coarsening phase.” In: Modelling and Simulation in Materials Science and Engineering 23 (2015), p. 65001
A Spettl, R Wimmer, T Werz, M Heinze, S Odenbach, C E Krill III, and V Schmidt
(See online at https://doi.org/10.1088/0965-0393/23/6/065001) - Direct observation of grain rotations during coarsening of a semisolid Al–Cu alloy. In: PNAS October 11, 2016 113 (41) E5998-E6006
J M Dake, J Oddershede, H O Sørensen, T Werz, J C Shatto, K Uesugi, S Schmidt, and C E Krill III
(See online at https://doi.org/10.1073/pnas.1602293113) - “Fitting Laguerre tessellation approximations to tomographic image data.” In: Philosophical Magazine Volume 96, 2016 - Issue 2, Pages 166-189
A Spettl, T Brereton, Q Duan, T Werz, C E Krill III, D P Kroese, and V Schmidt
