Automated calculation and convergence of defect transport tensors

Abstract

Defect diffusion is a key process in materials science and catalysis, but as migration mechanisms are often too complex to enumerate a priori, calculation of transport tensors typically have no measure of convergence and require significant end-user intervention. These two bottlenecks prevent high-throughput implementations essential to propagate model-form uncertainty from interatomic interactions to predictive simulations. In order to address these issues, we extend a massively parallel accelerated sampling scheme, autonomously controlled by Bayesian estimators of statewide sampling completeness, to build atomistic kinetic Monte Carlo models on a state-space irreducible under exchange and space group symmetries. Focusing on isolated defects, we derive analytic expressions for drift and diffusion coefficients, providing a convergence metric by calculating the Kullback–Leibler divergence across the ensemble of diffusion processes consistent with the sampling uncertainty. The autonomy and efficacy of the method is demonstrated on surface trimers in tungsten and Hexa-interstitials in magnesium oxide, both of which exhibit complex, correlated migration mechanisms.

Estimating linear mass transport coefficients in solid solutions via correlation splitting and a law of total diffusion

“…2(a)], and many among them may differ from d(χ 0 , χ 1 ). This consequent sampling burden is avoided by analytically integrating the underlying conditional expected displacements e a (χ h ) E a [r u h→h+1 |χ h ], in a similar way to [15,47]. Letting E o [•] denote expectation with respect to P o , both cumulants of overlying displacement r 0→1 are determined by the underlying sequences r u 0→1 + r u 1→∞ ≡ r 0→1 associated with the successive states of the AMC, {χ u h } h 1 , and where χ u 0 = χ 0 and χ u ∞ = χ 1 .…”

“…This makes it possible to construct realistic discrete-space models satisfying the Markov property. Such a description does not preclude complex transport mechanisms to involve concerted atomic displacements [15]. Generic models based on master equations are also very useful as they allow investigating the interplay between transition rates and transport properties by varying their physical parameters in a systematic manner [3].…”

“…However, the method is hindered by the low occurrence of important events. A considerable amount of computations are often needed to collect sufficient statistics in many systems of interest [18,19], including basic models of defect migration through homogeneous media [15]. Besides, low-complexity models are amenable to nonstochastic master-equation approaches [20][21][22][23] that may yield accurate predictions at much lower cost.…”

Reaction-drift-diffusion models from master equations: application to material defects

“…In this limit, the atomic dynamics can be mapped to a continuous time, discrete state Markov chain 19 , which provides the theoretical basis of off-lattice, or atomistic kinetic Monte Carlo (akMC) methods 20 , up to an error exponentially small in the timescale separation 21 . We have employed this rigorous connection in our massively parallel sampling scheme TAMMBER 15,16,22 (available at github.com/tomswinburne/tammber), which optimally manages many thousands of molecular dynamics 'workers' to rapidly discover migration pathways of complex defects, with a novel Bayesian metric of sampling completeness which can be used to assign well defined uncertainty bounds on the resulting akMC model. Further discussion of TAMMBER can be found in a recent review 23 .…”

“…This approach can produce local kinetic models for use in more complex microstrutures, retaining sufficient complexity to exhibit a rich range of behaviors, including internal transitions (that can significantly affect mobility 6,16 ), spontaneous disassociation 15 , or interaction with existing microstructural features such as dislocations or grain boundaries.…”