skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: First-principles calculations of solute transport in zirconium: Vacancy-mediated diffusion with metastable states and interstitial diffusion

Journal Article · · Physical Review Materials
 [1];  [2];  [1]
  1. Univ. of Illinois, Urbana-Champaign, IL (United States). Dept. of Materials Science and Engineering
  2. Univ. of New South Wales, Sydney, NSW (Australia). School of Mechanical and Manufacturing Engineering; Imperial College London, London (United Kingdom). Materials Dept.

Zirconium alloys are the most widely used nuclear fuel cladding materials for light water power reactors where irradiation damage causes solute redistribution, leading to degradation of alloy properties such as corrosion resistance. Designing radiation-tolerant zirconium alloys requires a thorough understanding of the atomic-scale transport behavior of the alloying elements in Zr. In this work, we perform density function theory calculations to investigate the diffusion of Sn, Cr, Fe, Be, Al, and Ni in the hexagonal close-packed (HCP) Zr matrix. We develop a methodology to accurately model the metastable vacancy states along the basal migration path, known to occur in group IV metals. We compute the vacancy-mediated solute diffusion coefficients and drag ratios using the kinetic Monte Carlo method and an analytic Green's function method—the agreement between the two validates our methodology. The computed diffusion coefficients of Sn and Al show good agreement with the experimental data and we expect these solutes to diffuse via the vacancy-mediated mechanism. We use a Green's function approach, parameterized with data from density functional theory calculations, to compute the interstitial diffusion coefficients of Cr, Fe, Be, and Ni in the HCP Zr lattice. The computed diffusion coefficients of Cr, Ni, and Be agree with the experimental measurements within one order of magnitude, while those of Fe are within two orders of magnitude of the experimental measurements. The drag ratios for Cr, Fe, Be, and Ni are positive up to 1235 K, which suggests that nonequilibrium vacancy fluxes could drag these solutes toward sinks such as dislocation loops and grain boundaries. We also compute the transport coefficients without including the metastable states, and using the eight- and thirteen-frequency model. Our results show significant differences in drag ratio for the eight- and thirteen-frequency model predictions compared with the Green's function methodology, but smaller errors in the solute diffusivity. Combining interstitial and vacancy-mediated diffusivities, we predict the unusual result that increased vacancy concentration slows down solute diffusivity, while a sufficiently high vacancy concentration can change the dominant mechanism to an accelerated vacancy-mediated diffusion.

Research Organization:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
Sponsoring Organization:
USDOE Office of Nuclear Energy (NE), Nuclear Energy University Program (NEUP); USDOE
Grant/Contract Number:
IRP-12-4728
OSTI ID:
1530403
Alternate ID(s):
OSTI ID: 1546350
Journal Information:
Physical Review Materials, Vol. 3, Issue 3; ISSN 2475-9953
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 13 works
Citation information provided by
Web of Science

References (76)

Chromium diffusion in α-zirconium, Zircaloy-2 and Zr-2.5Nb journal March 1993
Ni Diffusion in Zr and Zr Alloys journal January 1987
Anomalous self-diffusion in a single crystal of α-zirconium journal November 1984
Generalized Gradient Approximation Made Simple journal October 1996
First principles calculations of beryllium stability in zirconium surfaces journal January 2017
Projector augmented-wave method journal December 1994
Corrosion of Zirconium Alloys Used for Nuclear Fuel Cladding journal July 2015
51Cr diffusion in α-Zr single crystals journal November 1983
Relaxation of Crystals with the Quasi-Newton Method journal February 1997
Investigating the thermal stability of irradiation-induced damage in a zirconium alloy with novel in situ techniques journal February 2018
Redistribution of alloying elements in Zircaloy-2 after in-reactor exposure journal November 2014
First-principles investigation on diffusion mechanism of alloying elements in dilute Zr alloys journal August 2018
Ab initio approach to the effect of Fe on the diffusion in hcp Zr II: The energy barriers journal July 2009
A ‘missing’ family of classical orthogonal polynomials journal January 2011
A generalized synchronous transit method for transition state location journal October 2003
The vacancy properties of α-Zr journal February 1981
Ultra-fast solute diffusion in α-Ti and α-Zr journal August 1972
Vacancy clustering in zirconium: An atomic-scale study journal October 2014
A first-principles study of the diffusion coefficients of alloying elements in dilute α-Ti alloys journal January 2016
A climbing image nudged elastic band method for finding saddle points and minimum energy paths journal December 2000
Light-element diffusion in Mg using first-principles calculations: Anisotropy and elastodiffusion journal August 2016
Anomalous energy pathway of vacancy migration and self-diffusion in hcp Ti journal June 2011
From solid solution to cluster formation of Fe and Cr in α -Zr journal December 2015
First-principles appraisal of solute ultra-fast diffusion in hcp Zr and Ti journal March 2013
High-precision sampling for Brillouin-zone integration in metals journal August 1989
Diffusion calculations with two atomic models in h.c.p Zr-Nb diluted alloys journal August 2017
Diffusion kinetics in dilute binary alloys with the h.c.p. crystal structure journal June 2014
Point defect modeling in materials: Coupling ab initio and elasticity approaches journal October 2013
Self-diffusion in α-Zr single crystals journal May 1991
Frequency factors and isotope effects in solid state rate processes journal January 1957
First-principles study of atomic hydrogen adsorption and initial hydrogenation of Zr(0001) surface journal January 2013
Automatic numerical evaluation of vacancy-mediated transport for arbitrary crystals: Onsager coefficients in the dilute limit using a Green function approach journal June 2017
Enrichment of Fe and Ni at metal and oxide grain boundaries in corroded Zircaloy-2 journal December 2012
Self-diffusion in the hexagonal structure of Zirconium and Hafnium: computer simulation studies journal December 2005
Thermal equations of state of the α , β , and ω phases of zirconium journal May 2005
Representations of quasi-Newton matrices and their use in limited memory methods journal January 1994
EELS and atom probe tomography study of the evolution of the metal/oxide interface during zirconium alloy oxidation journal July 2015
The effect of Sn concentration on oxide texture and microstructure formation in zirconium alloys journal October 2015
Barrier oxide chemistry and hydrogen pick-up mechanisms in zirconium alloys journal January 2016
Issues in the ab-initio assessment of hcp transition metals self-diffusion journal August 2012
Effect of alloying elements on the properties of Zr and the Zr–H system journal February 2014
Special points for Brillouin-zone integrations journal June 1976
Diffusivity and derivatives for interstitial solutes: activation energy, volume, and elastodiffusion tensors journal July 2016
Ab initio atomic-scale determination of point-defect structure in hcp zirconium journal February 2005
α-Zr self-diffusion anisotropy journal May 1995
Mechanism of Diffusion of Copper in Germanium journal November 1956
Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set journal October 1996
Atomistic calculation of point-defect diffusion anisotropy and irradiation growth in α -zirconium journal June 2007
Performance of iron–chromium–aluminum alloy surface coatings on Zircaloy 2 under high-temperature steam and normal BWR operating conditions journal March 2016
Elemental vacancy diffusion database from high-throughput first-principles calculations for fcc and hcp structures journal January 2014
Tracer diffusion in α-Zr journal April 1974
Ab initio magnesium-solute transport database using exact diffusion theory journal May 2018
Hydrogen and vacancy clustering in zirconium journal January 2016
The effect of matrix chemistry on dislocation evolution in an irradiated Zr alloy journal May 2017
Atom probe tomography study of alloying element distributions in Zr alloys and their oxides journal November 2013
Diffusion and vacancy properties of α-Zr journal July 1986
Unrelaxed vacancy formation energies in group-IV elements calculated by the full-potential linear muffin-tin orbital method: Invariance with crystal structure journal April 1999
A review of microstructure evolution in zirconium alloys during irradiation journal October 1988
Beryllium diffusion in zirconium journal March 1976
Anisotropy of the Vacancy Migration in Ti, Zr and Hf Hexagonal Close-Packed Metals from First Principles journal November 2007
Pressure effect on stabilities of self-Interstitials in HCP-Zirconium journal July 2014
Nano-scale chemical evolution in a proton-and neutron-irradiated Zr alloy journal April 2017
The Kinetic Monte Carlo method: Foundation, implementation, and application journal July 2008
Soft self-consistent pseudopotentials in a generalized eigenvalue formalism journal April 1990
Initial observation of grain boundary solute segregation in a zirconium alloy (ZIRLO) by three-dimensional atom probe journal August 2009
Radiation-Induced Dislocation and Growth Behavior of Zirconium and Zirconium Alloys – a Review journal June 2013
First principles methods using CASTEP journal January 2005
New Technique for Calculating Correlations for Vacancy Diffusion journal June 1962
Tin clustering and precipitation in the oxide during autoclave corrosion of Zircaloy-2 journal January 2015
Exact Model of Vacancy-Mediated Solute Transport in Magnesium journal March 2017
Microstructure Evolution in Zr Alloys during Irradiation: Dose, Dose Rate, and Impurity Dependence journal January 2008
Redistribution of the alloying elements during Zircaloy-2 oxidation journal September 1997
Self-interstitial configurations in hcp Zr: a first principles analysis journal February 2013
Diffusion of 59 Fe in single-crystal α-Zr journal September 1988
Evolution of dislocation structure in neutron irradiated Zircaloy-2 studied by synchrotron x-ray diffraction peak profile analysis journal March 2017
Vacancy Mediated and Interstitial Solute Transport in Zr from Density Functional Theory Calculations dataset January 2018

Cited By (2)