Bayesian inference of atomic diffusivity in a binary NI/AL system based on molecular dynamics

F. Rizzi*, M. Salloum, Y. M. Marzouk, R. G. Xu, M. L. Falk, T. P. Weihs, G. Fritz, O. M. Knio

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)486-512
Number of pages27
JournalMultiscale Modeling and Simulation
Issue number1
StatePublished - 2011
Externally publishedYes


  • Atomic diffusion
  • Bayesian interference
  • Molecular dynamics
  • Reactive multilayers

ASJC Scopus subject areas

  • General Chemistry
  • Modeling and Simulation
  • Ecological Modeling
  • General Physics and Astronomy
  • Computer Science Applications


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