- Rizzi, F. and Salloum, M. and Marzouk, Y. M. and Xu, R. G. and Falk, M. L. and Weihs, T. P. and Fritz, G. and Knio, O. M., BAYESIAN INFERENCE OF ATOMIC DIFFUSIVITY IN A BINARY NI/AL SYSTEM BASED ON MOLECULAR DYNAMICS,
MULTISCALE MODELING & SIMULATION, vol. 9 no. 1
pp. 486--512 [doi] .
(last updated on 2011/07/05)
This work focuses on characterizing the integral features of atomic diffusion in Ni/Al nanolaminates based on molecular dynamics (MD) computations. Attention is focused on the simplified problem of extracting the diffusivity, D, in an isothermal system at high temperature. To this end, a mixing measure theory is developed that relies on analyzing the moments of the cumulative distribution functions (CDFs) of the constituents. The mixing measures obtained from replica simulations are exploited in a Bayesian inference framework, based on contrasting these measures with corresponding moments of a dimensionless concentration evolving according to a Fickian process. The noise inherent in the MD simulations is described as a Gaussian process, and this hypothesis is verified both a priori and using a posterior predictive check. Computed values of D for an initially unmixed system rapidly heated to 1500 K are found to be consistent with experimental correlation for diffusion of Ni into molten Al. On the contrary, large discrepancies with experimental predictions are observed when D is estimated based on large-time mean-square displacement (MSD) analysis, and when it is evaluated using the Arrhenius correlation calibrated against experimental measurements of self-propagating front velocities. Implications are finally drawn regarding extension of the present work and potential refinement of continuum modeling approaches.