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Explainable machine learning for hydrogen diffusion in metals and random binary alloys

Journal Article · · Physical Review Materials
 [1];  [2];  [2];  [2];  [1]
  1. Univ. of Illinois at Urbana-Champaign, IL (United States)
  2. Sandia National Laboratories (SNL-CA), Livermore, CA (United States)
Hydrogen diffusion in metals and alloys plays an important role in the discovery of new materials for fuel cell and energy storage technology. While analytic models use hand-selected features that have clear physical ties to hydrogen diffusion, they often lack accuracy when making quantitative predictions. Machine learning models are capable of making accurate predictions, but their inner workings are obscured, rendering it unclear which physical features are truly important. To develop interpretable machine learning models to predict the activation energies of hydrogen diffusion in metals and random binary alloys, we create a database for physical and chemical properties of the species and use it to fit six machine learning models. Our models achieve root-mean-squared errors between 98–119 meV on the testing data and accurately predict that elemental Ru has a large activation energy, while elemental Cr and Fe have small activation energies. By analyzing the feature importances of these fitted models, we identify relevant physical properties for predicting hydrogen diffusivity. While metrics for measuring the individual feature importances for machine learning models exist, correlations between the features lead to disagreement between models and limit the conclusions that can be drawn. Instead grouped feature importance, formed by combining the features via their correlations, agree across the six models and reveal that the two groups containing the packing factor and electronic specific heat are particularly significant for predicting hydrogen diffusion in metals and random binary alloys. In conclusion, this framework allows us to interpret machine learning models and enables rapid screening of new materials with the desired rates of hydrogen diffusion.
Research Organization:
Sandia National Laboratories (SNL-CA), Livermore, CA (United States)
Sponsoring Organization:
National Science Foundation (NSF); USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
NA0003525
OSTI ID:
2311334
Report Number(s):
SAND--2023-11844J
Journal Information:
Physical Review Materials, Journal Name: Physical Review Materials Journal Issue: 10 Vol. 7; ISSN 2475-9953
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

References (114)

Permeability, diffusivity, and solubility of hydrogen and deuterium in pure iron at 10 to 60 °C journal July 1978
The diffusion coefficients of hydrogen and deuterium in vanadium, niobium, and tantalum by gorsky‐effect measurements journal January 1970
Diffusion of H and D in Lutetium journal November 1987
Hydrogen permeability of some transition metals and metals of group I of the periodic system journal January 1968
Diffusion of hydrogen and deuterium in Nb and Ta at high concentrations journal March 1978
Hydrogen permeability through alpha-brass journal March 1977
Tritium permeability of nickel plated stainless steel 21-6-9 and of gold plated aluminum journal March 1983
Activation energy of hydrogen, oxygen, and nitrogen diffusion in metals journal April 2005
First-principles-based kinetic Monte Carlo studies of diffusion of hydrogen in Ni–Al and Ni–Fe binary alloys journal February 2015
Diffusion, Permeation and Solubility of Hydrogen in Copper journal January 2017
Thermodynamics of transition metal-hydrogen solid solutions journal October 1973
Hydrogen and deuterium in iron, 49–506°C journal June 1978
Electrochemical studies of hydrogen diffusion and permeability in Ni journal January 1980
Diffusion coefficient of hydrogen in alpha zirconium, Zircaloy-2 and Zircaloy-4 journal June 1972
Diffusivity and permeability of hydrogen in neutron irradiated molybdenum and platinum journal April 1983
Pressure modulated absorption-desorption: Permeation, diffusion and surface rate coefficients for hydrogen in nickel and palladium journal January 1987
Diffusivity and permeability of hydrogen in molybdenum journal January 1982
The low-temperature diffusion of Hydrogen through annealed, quenched and aged gold journal January 1985
Hydrogen absorption in LaNi5 and related compounds: Experimental observations and their explanation journal March 1974
Which intermetallic compounds of transition metals form stable hydrides ? journal September 1976
On the heats of formation of the binary hydrides of transition metals journal May 1980
Structural-stability domains for single-coordination intermetallic phases journal May 1987
Hydrogen diffusion in cobalt journal May 1974
Diffusivity of hydrogen in silver journal January 1979
Diffusion of hydrogen in high purity aluminium journal February 1981
Diffusion of hydrogen in pure large grain aluminum journal March 1982
Diffusivity permeability and solubility of hydrogen in platinum journal February 1979
1153. Mass spectrometer investigations of the degassing of Molybdenum, Tungsten and Niobium on heating them in vacuo journal November 1964
Hydrogen and deuterium permeation through metallic and surface-oxidized chromium journal July 1986
Hydrogen permeation and diffusion in molybdenum journal September 1992
Stochastic gradient boosting journal February 2002
On extending Miedema’s model to predict hydrogen content in binary and ternary hydrides journal May 2002
Hydrogen permeation through magnesium journal December 1999
The role of palladium in a hydrogen economy journal June 2011
An application of Pettifor structure maps for the identification of pseudo-binary quasicrystalline intermetallics journal August 2006
Hydrogen diffusion and vacancies formation in tungsten: Density Functional Theory calculations and statistical models journal August 2015
A comprehensive first-principles study of pure elements: Vacancy formation and migration energies and self-diffusion coefficients journal May 2016
Machine learning assisted design of FeCoNiCrMn high-entropy alloys with ultra-low hydrogen diffusion coefficients journal February 2022
Ab initio lattice stability in comparison with CALPHAD lattice stability journal March 2004
First-principles investigation on diffusion and permeation behaviors of hydrogen isotopes in molybdenum journal March 2012
Robust FCC solute diffusion predictions from ab-initio machine learning methods journal June 2017
Prediction of interstitial diffusion activation energies of nitrogen, oxygen, boron and carbon in bcc, fcc, and hcp metals using machine learning journal March 2018
Matminer: An open source toolkit for materials data mining journal September 2018
Ab initio study of diffusion of hydrogen, silver and lithium in PbS and Ag2S journal August 2019
Error assessment and optimal cross-validation approaches in machine learning applied to impurity diffusion journal November 2019
Robust activation energy predictions of solute diffusion from machine learning method journal November 2020
Theoretical evaluation of diffusivity of hydrogen in palladium and rhodium journal December 2004
Metal hydride materials for solid hydrogen storage: A review☆ journal June 2007
Magnesium based materials for hydrogen based energy storage: Past, present and future journal March 2019
Theoretical study of the insertion and diffusivity of hydrogen in the Ti3Al-D019 system: Comparison with Ti-hcp and TiAl-L10 systems journal December 2019
First-principles study on dissolution and diffusion properties of hydrogen in molybdenum journal September 2010
First-principles study of the stability and diffusion properties of hydrogen in zirconium carbide journal October 2016
A review of catalyst-enhanced magnesium hydride as a hydrogen storage material journal September 2015
Prediction of diffusion coefficients in fcc, bcc and hcp phases remained stable or metastable by the machine-learning methods journal January 2021
A comparison of hydrogen diffusivities in Pd and CuPd alloys using density functional theory journal November 2003
Solubility, diffusivity, and permeability of hydrogen at PdCu phases journal November 2017
Fundamental effects of Ag alloying on hydrogen behaviors in PdCu journal March 2018
Data-Driven Discovery and Synthesis of High Entropy Alloy Hydrides with Targeted Thermodynamic Stability journal April 2021
Gaussian Process Regression for Materials and Molecules journal August 2021
Nanostructured Metal Hydrides for Hydrogen Storage journal October 2018
Extracting an Empirical Intermetallic Hydride Design Principle from Limited Data via Interpretable Machine Learning journal December 2019
Correlation of Bulk Modulus and the Constituent Element Properties of Binary Intermetallic Compounds journal November 2001
Diffusivity of hydrogen isotopes in liquid lithium and in solid yttrium journal May 1985
Diffusion and solubility of hydrogen in palladium and palladium--silver alloys journal February 1970
Random Forests journal January 2001
Hydrogen-storage materials for mobile applications journal November 2001
Atomic mechanism and prediction of hydrogen embrittlement in iron journal November 2012
A general-purpose machine learning framework for predicting properties of inorganic materials journal August 2016
A simple constrained machine learning model for predicting high-pressure-hydrogen-compressor materials journal January 2018
Hydrogen diffusion out of ruthenium—an ab initio study of the role of adsorbates journal January 2020
Hydrogen in magnesium: new perspectives toward functional stores journal January 2010
Diffusivity and solubility of hydrogen and deuterium in yttrium journal January 1993
Solubility and Diffusion of Hydrogen and Deuterium in Platinum journal October 1968
Calculation of Activation Energies for Interstitial Diffusion by a Simple Elastic Model journal July 1965
Theory of Diffusion Constants in Interstitial Solid Solutions of b.c.c. Metals journal August 1957
First-principles study of temperature-dependent diffusion coefficients: Hydrogen, deuterium, and tritium in α-Ti journal May 2013
First-principles study of hydrogen diffusion and self-clustering below tungsten surfaces journal April 2019
An Introduction to Kernel and Nearest-Neighbor Nonparametric Regression journal August 1992
Hierarchical Grouping to Optimize an Objective Function journal March 1963
Tritium diffusion in V, Nb and Ta journal October 1983
Solubility and diffusivity of hydrogen and deuterium in alpha -hafnium at high temperatures journal February 1990
First-principles study of diffusion and interactions of vacancies and hydrogen in hcp-titanium journal September 2011
A comparative investigation of the behaviors of H in Au and Ag from first principles journal March 2016
Artificial neural network-based path integral simulations of hydrogen isotope diffusion in palladium journal July 2022
Hydrogen: the future energy carrier
  • Züttel, Andreas; Remhof, Arndt; Borgschulte, Andreas
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 368, Issue 1923 https://doi.org/10.1098/rsta.2010.0113
journal July 2010
Quantum Theory of Diffusion with Application to Light Interstitials in Metals journal May 1970
Proton andSc45nuclear-magnetic-resonance study of hydrogen diffusive hopping in hcp scandium journal July 1987
Diffusion of H 2 , D 2 , and T 2 in Single-Crystal Ni and Cu journal July 1971
Diffusion of interstitial hydrogen into and through bcc Fe from first principles journal August 2004
Quantitative assessment of hydrogen diffusion by activated hopping and quantum tunneling in ordered intermetallics journal December 2005
Temperature-dependent diffusion coefficients from ab initio computations: Hydrogen, deuterium, and tritium in nickel journal April 2008
Crystal Graph Convolutional Neural Networks for an Accurate and Interpretable Prediction of Material Properties journal April 2018
Diffusion of Hydrogen in Tantalum Studied by Motional Narrowing of Mössbauer Lines journal January 1976
Solute Diffusion in Metals: Larger Atoms Can Move Faster journal February 2004
Nearest neighbor pattern classification journal January 1967
Regularization and variable selection via the elastic net journal April 2005
Solution and Diffusion of Hydrogen in Tungsten journal May 1969
Hydrogen Permeation through Nickel journal September 1984
Diffusion of Deuterium and Isotope Effect in Nickel journal July 1979
High‐Temperature Diffusion of Hydrogen and Deuterium in Titanium and Ti3Al journal July 1998
The Diffusion Coefficients for Hydrogen in β-Zirconium journal January 1963
Diffusion of Hydrogen and Deuterium in High Purity Zirconium journal January 1954
machine. journal October 2001
Solubility and Diffusion of Hydrogen in Pure Metals and Alloys journal January 2001
Hydrogen Permeation and Diffusion in Beryllium journal October 1995
Bestimmung der Diffusionskoeffizienten für Tritium in den α-Phasen von Titan und Hafnium journal May 1983
Notizen: Reversed Isotope Dependence for Hydrogen Diffusion in Palladium journal May 1971
Über die Diffusion von Wasserstoff und von Deuterium in Palladium. II journal January 1940
Measurements of the Hydrogen Diffusivity in Tantalum by the Pulsed-Field Gradient NMR Technique* journal January 1989
Long Range Diffusion of Hydrogen in Yttrium* journal January 1989
Hydrogen Storage: High-Pressure Gas Containment journal September 2002
Error assessment and optimal cross-validation approaches in machine learning applied to impurity diffusion dataset January 2022
Hydrogen Permeation and Diffusion through Pure Fe, Pure Ni and Fe–Ni Alloys journal January 1983
Diffusion Coefficients of Hydrogen in Ni–Cu and Ni–Co Alloys journal January 1986

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