Contents

Lattice-Conditioned Arrhenius Residual Learning for Phase-Resolved Hydrogen Transport in Titanium Hydrides

T. Layne1, W. Kim2, J. E. Greene2
1Department of Materials Science and Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Republic of Korea
2Materials Research Laboratory and Materials Science Department, University of Illinois, 104 South Goodwin, Urbana, Illinois 61801
T. Layne
Department of Materials Science and Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Republic of Korea
W. Kim
Materials Research Laboratory and Materials Science Department, University of Illinois, 104 South Goodwin, Urbana, Illinois 61801
J. E. Greene
Materials Research Laboratory and Materials Science Department, University of Illinois, 104 South Goodwin, Urbana, Illinois 61801

Abstract

Modeling hydrogen mobility in titanium hydrides on the basis of a single diffusivity is impossible due to the different connectivity, activation energy, and heat capacity of the face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal close-packed (HCP) titanium–hydrogen compounds. This paper presents a new lattice-conditioned Arrhenius residual learning algorithm (LC-ARL) to convert predictions of the diffusion process based on lattice moment tensor potentials into the temperature dependence of the physically meaningful diffusivity value. The main problem to be solved here concerns whether a residual mapping could provide the physically meaningful ordering between Ti-H phases and which Ti-H transport phase needs further physical validation by characterizing its effective diffusivity. The developed LC-ARL algorithm includes two-dimensional evaluation of residual spaces for MTP-AL and MTP-DIRECT moment tensor potentials, determination of the phase-resolved reliability weighting factor, calculation of Arrhenius prefactor parameters using reference state diffusivities, and construction of Arrhenius diffusivity curves based on phase-resolved geometric average. The selected phase-resolved validation examples are FCC Ti648H1296, BCC Ti648H648, and dilute HCP Ti648H36. LC-ARL leads to the much lower mean absolute activation energy error (0.0084 eV) relative to MTP-AL (0.0567 eV) and MTP-DIRECT (0.0167 eV) algorithms without increasing the mean absolute logarithmic diffusivity error (identical 0.074 decade). Moreover, the temperature sweep preserves the Ti-H transport phase sequence BCC \(>\) HCP \(>>\) FCC within the 300-1000 K range. Thus, the proposed research question was positively answered concerning this particular data set – a combination of magnitude and slope errors resulted in physically meaningful Arrhenius diffusivity function. Dilute HCP titanium hydride was identified as the most appealing validation example because of non-coordinated optimization of magnitude and activation energy.

Keywords: titanium hydride, hydrogen diffusion, machine learning interatomic potential, Arrhenius modelling, moment tensor potential, residual learning, phase-aware transport
Copyright © 2024 T. Layne, W. Kim, J. E. Greene. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.