Anisotropic hydrogen diffusion in α-Zr and Zircaloy predicted by accelerated kinetic Monte Carlo simulations

Zhang, Yongfeng; Jiang, Chao; Bai, Xianming

doi:10.1038/srep41033

Title: Anisotropic hydrogen diffusion in α-Zr and Zircaloy predicted by accelerated kinetic Monte Carlo simulations

Abstract

Here, this report presents an accelerated kinetic Monte Carlo (KMC) method to compute the diffusivity of hydrogen in hcp metals and alloys, considering both thermally activated hopping and quantum tunneling. The acceleration is achieved by replacing regular KMC jumps in trapping energy basins formed by neighboring tetrahedral interstitial sites, with analytical solutions for basin exiting time and probability. Parameterized by density functional theory (DFT) calculations, the accelerated KMC method is shown to be capable of efficiently calculating hydrogen diffusivity in α-Zr and Zircaloy, without altering the kinetics of long-range diffusion. Above room temperature, hydrogen diffusion in α-Zr and Zircaloy is dominated by thermal hopping, with negligible contribution from quantum tunneling. The diffusivity predicted by this DFT + KMC approach agrees well with that from previous independent experiments and theories, without using any data fitting. The diffusivity along < c > is found to be slightly higher than that along < a >, with the anisotropy saturated at about 1.20 at high temperatures, resolving contradictory results in previous experiments. Demonstrated using hydrogen diffusion in α-Zr, the same method can be extended for on-lattice diffusion in hcp metals, or systems with similar trapping basins.

Authors:

Zhang, Yongfeng ^[1]; Jiang, Chao ^[1]; Bai, Xianming ^[2]

Idaho National Lab. (INL), Idaho Falls, ID (United States)
Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)

Publication Date:: Fri Jan 20 00:00:00 EST 2017

Research Org.:: Idaho National Lab. (INL), Idaho Falls, ID (United States)

Sponsoring Org.:: USDOE Office of Nuclear Energy (NE)

OSTI Identifier:: 1357778

Report Number(s):: INL/JOU-16-40134
Journal ID: ISSN 2045-2322; srep41033

Grant/Contract Number:: AC07-05ID14517

Resource Type:: Accepted Manuscript

Journal Name:: Scientific Reports

Additional Journal Information:: Journal Volume: 7; Journal ID: ISSN 2045-2322

Publisher:: Nature Publishing Group

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE; accelerated kinetic Monte Carlo; hydrogen diffusion; atomistic models; condensed-matter physics; metals and alloys

Citation Formats


                    Zhang, Yongfeng, Jiang, Chao, and Bai, Xianming. Anisotropic hydrogen diffusion in α-Zr and Zircaloy predicted by accelerated kinetic Monte Carlo simulations.  United States: N. p., 2017. 
Web.  doi:10.1038/srep41033.

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                    Zhang, Yongfeng, Jiang, Chao, & Bai, Xianming. Anisotropic hydrogen diffusion in α-Zr and Zircaloy predicted by accelerated kinetic Monte Carlo simulations.  United States.  https://doi.org/10.1038/srep41033

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                    Zhang, Yongfeng, Jiang, Chao, and Bai, Xianming. Fri .  
"Anisotropic hydrogen diffusion in α-Zr and Zircaloy predicted by accelerated kinetic Monte Carlo simulations".  United States.  https://doi.org/10.1038/srep41033.  https://www.osti.gov/servlets/purl/1357778.

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@article{osti_1357778,

  title        = {Anisotropic hydrogen diffusion in α-Zr and Zircaloy predicted by accelerated kinetic Monte Carlo simulations},

  author       = {Zhang, Yongfeng and Jiang, Chao and Bai, Xianming},

  abstractNote = {Here, this report presents an accelerated kinetic Monte Carlo (KMC) method to compute the diffusivity of hydrogen in hcp metals and alloys, considering both thermally activated hopping and quantum tunneling. The acceleration is achieved by replacing regular KMC jumps in trapping energy basins formed by neighboring tetrahedral interstitial sites, with analytical solutions for basin exiting time and probability. Parameterized by density functional theory (DFT) calculations, the accelerated KMC method is shown to be capable of efficiently calculating hydrogen diffusivity in α-Zr and Zircaloy, without altering the kinetics of long-range diffusion. Above room temperature, hydrogen diffusion in α-Zr and Zircaloy is dominated by thermal hopping, with negligible contribution from quantum tunneling. The diffusivity predicted by this DFT + KMC approach agrees well with that from previous independent experiments and theories, without using any data fitting. The diffusivity along < c > is found to be slightly higher than that along < a >, with the anisotropy saturated at about 1.20 at high temperatures, resolving contradictory results in previous experiments. Demonstrated using hydrogen diffusion in α-Zr, the same method can be extended for on-lattice diffusion in hcp metals, or systems with similar trapping basins.},

  doi          = {10.1038/srep41033},

  journal      = {Scientific Reports},

  number       = ,

  volume       = 7,

  place        = {United States},

  year         = {Fri Jan 20 00:00:00 EST 2017},

  month        = {Fri Jan 20 00:00:00 EST 2017}

}

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The Journal of Chemical Physics, Vol. 150, Issue 21
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Effects of anisotropy and regime of diffusion on the measurement of lattice diffusion coefficient of hydrogen in metals
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Title: Anisotropic hydrogen diffusion in α-Zr and Zircaloy predicted by accelerated kinetic Monte Carlo simulations

Abstract

Citation Formats

Metal hydride materials for solid hydrogen storage: A review☆ journal, June 2007

Generalized Gradient Approximation Made Simple journal, October 1996

Low-Pressure Solubility and Diffusion of Hydrogen in Zirconium journal, January 1957

First-principles study of temperature-dependent diffusion coefficients: Hydrogen, deuterium, and tritium in α-Ti journal, May 2013

Lattice Parameters, Thermal Expansions, and Grüneisen Coefficients of Zirconium, 4.2 to 1130°K journal, April 1966

Determination of fracture strength of δ-zirconium hydrides embedded in zirconium matrix at high temperatures journal, April 2013

Diffusion coefficient of hydrogen in alpha zirconium, Zircaloy-2 and Zircaloy-4 journal, June 1972

The study of hydrogen segregation on Zr(0001) and Zr(1010) surfaces by static secondary ion mass spectroscopy, work function, Auger electron spectroscopy and nuclear reaction analysis journal, December 1995

Diffusion coefficient in crystals with multiple jump frequencies journal, August 1985

A review on hydride precipitation in zirconium alloys journal, November 2015

DFT calculations of hydrogen diffusion and phase transformations in magnesium journal, September 2015

Monte Carlo simulation of hydrogen diffusion in metal and alloys journal, December 1988

Corrosion of Zirconium Alloys book, January 2012

The H-Zr (hydrogen-zirconium) system journal, August 1990

Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set journal, October 1996

Using density functional theory to study hydrogen diffusion in metals: A brief overview journal, October 2007

Terminal solubility and partitioning of hydrogen in the alpha phase of zirconium, Zircaloy-2 and Zircaloy-4 journal, June 1967

Influence of hydrogen loading conditions on the blocking effect of nanocrystalline Mg films journal, May 2011

Diffusion of H 2 , D 2 , and T 2 in Single-Crystal Ni and Cu journal, July 1971

Adaptive kinetic Monte Carlo for first-principles accelerated dynamics journal, September 2008

Hydrogen accommodation in Zr second phase particles: Implications for H pick-up and hydriding of Zircaloy-2 and Zircaloy-4 journal, April 2013

A climbing image nudged elastic band method for finding saddle points and minimum energy paths journal, December 2000

H in α -Zr and in zirconium hydrides: solubility, effect on dimensional changes, and the role of defects journal, December 2014

Homogeneous hydride formation path in α-Zr: Molecular dynamics simulations with the charge-optimized many-body potential journal, June 2016

An energy basin finding algorithm for kinetic Monte Carlo acceleration journal, April 2010

Hydride Formation in Zirconium Alloys journal, October 2012

Monte-carlo simulations of interstitial diffusion and trapping—I. One type of traps and dislocations journal, February 1987

Quantitative assessment of hydrogen diffusion by activated hopping and quantum tunneling in ordered intermetallics journal, December 2005

The diffusion and trapping of hydrogen in steel journal, January 1970

Atomic-scale Ab-initio study of the Zr-H system: I. Bulk properties journal, August 2002

The diffusion and solubility of hydrogen in the alpha phase of zircaloy-2 journal, March 1960

The thermodynamics of hydride precipitation: The importance of entropy, enthalpy and disorder journal, October 2014

Modeling proton mobility in acidic zeolite clusters: II. Room temperature tunneling effects from semiclassical rate theory journal, April 2000

A first-principles study of surface and subsurface H on and in Ni(111): diffusional properties and coverage-dependent behavior journal, August 2003

Ab initio study on plane defects in zirconium–hydrogen solid solution and zirconium hydride journal, June 2010

Corrosion of zirconium alloys journal, August 1965

Corrosion of Zirconium Alloys book, January 1964

Hydrogen accommodation in Zr second phase particles: Implications for H pick-up and hydriding of Zircaloy-2 and Zircaloy-4 text, January 2013

The thermodynamics of hydride precipitation: the importance of entropy, enthalpy and disorder text, January 2014

Monte-carlo simulations of interstitial diffusion and trapping—I. One type of traps and dislocations journal, February 1987

The diffusion and solubility of hydrogen in the alpha phase of zircaloy-2 journal, March 1960

Determination of fracture strength of δ-zirconium hydrides embedded in zirconium matrix at high temperatures journal, April 2013

Influence of hydrogen loading conditions on the blocking effect of nanocrystalline Mg films journal, May 2011

An energy basin finding algorithm for kinetic Monte Carlo acceleration journal, April 2010

Modeling proton mobility in acidic zeolite clusters: II. Room temperature tunneling effects from semiclassical rate theory journal, April 2000

Monte Carlo simulation of hydrogen diffusion in metal and alloys journal, December 1988

Low-Pressure Solubility and Diffusion of Hydrogen in Zirconium journal, January 1957

Solubility and Diffusion of Hydrogen in Zirconium journal, January 1960

The thermodynamics of hydride precipitation: the importance of entropy, enthalpy and disorder text, January 2014

Influence of morphology of colloidal nanoparticle gels on ion transport and rheology journal, June 2019

Effects of anisotropy and regime of diffusion on the measurement of lattice diffusion coefficient of hydrogen in metals journal, July 2018

Metal hydride materials for solid hydrogen storage: A review☆
journal, June 2007

Generalized Gradient Approximation Made Simple
journal, October 1996

Low-Pressure Solubility and Diffusion of Hydrogen in Zirconium
journal, January 1957

First-principles study of temperature-dependent diffusion coefficients: Hydrogen, deuterium, and tritium in α-Ti
journal, May 2013

Lattice Parameters, Thermal Expansions, and Grüneisen Coefficients of Zirconium, 4.2 to 1130°K
journal, April 1966

Determination of fracture strength of δ-zirconium hydrides embedded in zirconium matrix at high temperatures
journal, April 2013

Diffusion coefficient of hydrogen in alpha zirconium, Zircaloy-2 and Zircaloy-4
journal, June 1972

The study of hydrogen segregation on Zr(0001) and Zr(1010) surfaces by static secondary ion mass spectroscopy, work function, Auger electron spectroscopy and nuclear reaction analysis
journal, December 1995

Diffusion coefficient in crystals with multiple jump frequencies
journal, August 1985

A review on hydride precipitation in zirconium alloys
journal, November 2015

DFT calculations of hydrogen diffusion and phase transformations in magnesium
journal, September 2015

Monte Carlo simulation of hydrogen diffusion in metal and alloys
journal, December 1988

Corrosion of Zirconium Alloys
book, January 2012

The H-Zr (hydrogen-zirconium) system
journal, August 1990

Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
journal, October 1996

Using density functional theory to study hydrogen diffusion in metals: A brief overview
journal, October 2007

Terminal solubility and partitioning of hydrogen in the alpha phase of zirconium, Zircaloy-2 and Zircaloy-4
journal, June 1967

Influence of hydrogen loading conditions on the blocking effect of nanocrystalline Mg films
journal, May 2011

Diffusion of $H_{2}$ , $D_{2}$ , and $T_{2}$ in Single-Crystal Ni and Cu
journal, July 1971

Adaptive kinetic Monte Carlo for first-principles accelerated dynamics
journal, September 2008

Hydrogen accommodation in Zr second phase particles: Implications for H pick-up and hydriding of Zircaloy-2 and Zircaloy-4
journal, April 2013

A climbing image nudged elastic band method for finding saddle points and minimum energy paths
journal, December 2000

H in α -Zr and in zirconium hydrides: solubility, effect on dimensional changes, and the role of defects
journal, December 2014

Homogeneous hydride formation path in α-Zr: Molecular dynamics simulations with the charge-optimized many-body potential
journal, June 2016

An energy basin finding algorithm for kinetic Monte Carlo acceleration
journal, April 2010

Hydride Formation in Zirconium Alloys
journal, October 2012

Monte-carlo simulations of interstitial diffusion and trapping—I. One type of traps and dislocations
journal, February 1987

Quantitative assessment of hydrogen diffusion by activated hopping and quantum tunneling in ordered intermetallics
journal, December 2005

The diffusion and trapping of hydrogen in steel
journal, January 1970

Atomic-scale Ab-initio study of the Zr-H system: I. Bulk properties
journal, August 2002

The diffusion and solubility of hydrogen in the alpha phase of zircaloy-2
journal, March 1960

The thermodynamics of hydride precipitation: The importance of entropy, enthalpy and disorder
journal, October 2014

Modeling proton mobility in acidic zeolite clusters: II. Room temperature tunneling effects from semiclassical rate theory
journal, April 2000

A first-principles study of surface and subsurface H on and in Ni(111): diffusional properties and coverage-dependent behavior
journal, August 2003

Ab initio study on plane defects in zirconium–hydrogen solid solution and zirconium hydride
journal, June 2010

Corrosion of zirconium alloys
journal, August 1965

Corrosion of Zirconium Alloys
book, January 1964

Hydrogen accommodation in Zr second phase particles: Implications for H pick-up and hydriding of Zircaloy-2 and Zircaloy-4
text, January 2013

The thermodynamics of hydride precipitation: the importance of entropy, enthalpy and disorder
text, January 2014

Monte-carlo simulations of interstitial diffusion and trapping—I. One type of traps and dislocations
journal, February 1987

The diffusion and solubility of hydrogen in the alpha phase of zircaloy-2
journal, March 1960

Determination of fracture strength of δ-zirconium hydrides embedded in zirconium matrix at high temperatures
journal, April 2013

Influence of hydrogen loading conditions on the blocking effect of nanocrystalline Mg films
journal, May 2011

An energy basin finding algorithm for kinetic Monte Carlo acceleration
journal, April 2010

Modeling proton mobility in acidic zeolite clusters: II. Room temperature tunneling effects from semiclassical rate theory
journal, April 2000

Monte Carlo simulation of hydrogen diffusion in metal and alloys
journal, December 1988

Low-Pressure Solubility and Diffusion of Hydrogen in Zirconium
journal, January 1957

Solubility and Diffusion of Hydrogen in Zirconium
journal, January 1960

The thermodynamics of hydride precipitation: the importance of entropy, enthalpy and disorder
text, January 2014

Influence of morphology of colloidal nanoparticle gels on ion transport and rheology
journal, June 2019

Effects of anisotropy and regime of diffusion on the measurement of lattice diffusion coefficient of hydrogen in metals
journal, July 2018