Robust FCC solute diffusion predictions from ab-initio machine learning methods

Abstract

We evaluate the performance of four machine learning methods for modeling and predicting FCC solute diffusion barriers. More than 200 FCC solute diffusion barriers from previous density functional theory (DFT) calculations served as our dataset to train four machine learning methods: linear regression (LR), decision tree (DT), Gaussian kernel ridge regression (GKRR), and artificial neural network (ANN). We separately optimize key physical descriptors favored by each method to model diffusion barriers. We also assess the ability of each method to extrapolate when faced with new hosts with limited known data. GKRR and ANN were found to perform the best, showing 0.15 eV cross-validation errors and predicting impurity diffusion in new hosts to within 0.2 eV when given only 5 data points from the host. We demonstrate the success of a combined DFT + data mining approach towards solving materials science challenges and predict the diffusion barrier of all available impurities across all FCC hosts.Keywords: Diffusion; Data-mining; Machine learning; DFT; Neural network 1: Introduction Atomic migration in solids governs the kinetics of many materials processes, including precipitation, high-temperature creep, phase transformation, and solution homogenization. A particular class of atomic diffusion is dilute impurity diffusion, which refers to the diffusion of a dilute solute in a host. Such diffusion is relevant in many materials applications as dilute solutes are common due to either undesired impurities or intentional dopants in materials. Due to its importance to materials science, large experimental catalogues of impurity diffusion measurements have been collected [1,2], and more recently, first-principles predictions of dilute impurity diffusion coefficients have been conducted [3][4][5][6][7][8]. However, both experimental and theoretical approaches are limited by several drawbacks. Experimental diffusivities often vary significantly due to uncertainties introduced by different measurement techniques and other impurity effects in sample materials. In addition, experiments require significant diffusion kinetics to achieve good data, which generally limits them to be relatively high temperature (e.g., above about 50% of the melting temperature of the host) [9]. Finally, experiments are time consuming and expensive relative to first-principles calculations, as they require significant equipment and human interaction. First-principles calculations are an increasingly powerful tool for predicting dilute impurity diffusion, and compared to experiments can be done at a tiny fraction of the cost of equipment and human time. Furthermore, first-principles predicted energies are expected to be most accurate at lower temperatures, where vibrational and electronic excitations play a minor role, which suggests that these methods may have their best accuracy in temperature domains complimentary to experiments. First-principles methods bring with them significant approximations in both the fundamental energetics and in trea...

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