Abstract
A complete set of migration energies for a He atom moving inside the bulk of the bcc-W and fcc-Cu crystals has been calculated in different configurations using the nudged elastic band method as a tool within the density functional theory formalism. Although the most stable site in the perfect crystal is the tetrahedral position in both cases, the He atoms jump preferentially between two first nearest tetrahedral positions in tungsten, while they migrate through an octahedral position in the case of Cu. As reported before, the He atoms are trapped when they find an n-vacancy. Our results show that the migration energies are lower when the n-vacancies do not contain He atoms, suggesting that vacancies are stabilized and their mobility is reduced by helium trapping, that may end up in bubble coalescence, in agreement with previous findings. The migration energy of the clean n-vacancy decreases as the number n increases, at least up to n = 3, while the situation when He atoms are inside the vacancies is a little bit more complicated. In all the analyzed cases, the energy barriers in W are higher than in Cu. Additionally, a complete analysis of the evolution of the electronic density of states has been performed, that leads to the confirmation of a non-negligible He–metal interaction that significantly contributes to the trapping of helium atoms inside the n-vacancies.
Similar content being viewed by others
References
Demkowicz MJ, Hoagland RG, Hirth JP (2008) Interface structure and radiation damage resistance in Cu-Nb multilayer nanocomposites. Phys Rev Lett 100:136102
Hattar K, Demkowicz MJ, Misra A, Robertson IM, Hoagland RG (2008) Arrest of He bubble growth in CuNb multilayer nanocomposites. Scr Mater 58:541–544
Demkowicz MJ, Misra A, Caro A (2012) The role of interface structure in controlling high helium concentrations. Curr Opin Solid State Mater Sci 16:101–108
Gao Y, Yang T, Xue J, Yan S, Zhou S, Wanga Y, Kwok DTK, Chu PK, Zhang Y (2011) Radiation tolerance of Cu/W multilayered nanocomposites. J Nucl Mater 413:11–15
Becquart CS, Domain C (2006) Migration energy of He in W revisited by Ab initio calculations. Phys Rev Lett 97:196402
Becquart CS, Domain C (2009) An object kinetic Monte Carlo simulation of the dynamics of helium and point defects in tungsten. J Nucl Mater 385:223–227
Becquart CS, Domain C (2007) Ab initio calculations about intrinsic point defects and He in W. Nucl Instrum Methods Phys Res B 225:23–26
Becquart CS, Domain C, Sarkar U, DeBacker A, Hou M (2010) Microstructural evolution of irradiated tungsten: Ab initio parameterisation of an OKMC model. J Nucl Mater 403:75–88
Li X-C, Shu X, Liu Y-N, Yu Y, Gao F, Lu G-H (2012) Analytical WHe and HHe interatomic potentials for a WHHe system. J Nucl Mater 426:31–37
Henriksson KOE, Nordlund K, Keinonen J, Sundholm D, Patzschle M (2004) Simulations of the initial stages of blistering in helium implanted tungsten. Phys Scr T108:95–98
Henriksson KOE, Nordlund K, Keinonen J (2006) Molecular dynamics simulations of helium cluster formation in tungsten. Nucl Instrum Methods Phys Res Sect B 244:377–391
Amano J, Seidman D (1984) Diffusivity of 3He atoms in perfect tungsten crystals. J Appl Phys 56:983–992
Wagner A, Seidman DN (1979) Range profiles of 300- and 475-eV He+4 ions and the diffusivity of He4 in tungsten. Phys Rev Lett 42:515
Juslin N, Wirth BD (2013) Interatomic potentials for simulation of He bubble formation in W. J Nucl Mater 432:61–66
Juslin N, Nordlund K (2008) Pair potential for FeHe. J Nucl Mater 382:143–146
Terentyev D, Juslin N, Nordlund K, Sandberg N (2009) Fast three dimensional migration of He clusters in bcc Fe and FeCr alloys. J Appl Phys 105:103509
Ventelon L, Willaime F, Fu C-C, Heran M, Ginoux I (2012) Ab initio investigation of radiation defects in tungsten: structure of self-interstitials and specificity of di-vacancies compared to other bcc transition metals. J Nucl Mater 425:16–21
Lam NQ, Doan NV, Dagens L (1985) Multiple defects in copper and silver. J Phys F 15:799–808
Sabochick MJ, Yip S (1988) Migration energy calculations for small vacancy clusters in copper. J Phys F 18:1689–1701
Zhao P, Shimomura Y (1999) Molecular dynamics calculations of properties of the selfinterstitials in copper and nickel. Comp Mat Sci 14:84–90
Wilson WD, Baskes MI, Bisson CL (1976) Atomistics of helium bubble formation in a face-centeretl-cubic metal. Phys Rev B 13:2470–2478
Wang L, Ning X-J (2003) Molecular dynamics simulations of helium behaviour in copper crystals. Chin Phys Lett 20:1416–1419
Evans JH, Escobar Galindo R (2004) A description of bubble growth and gas release during thermal annealing of helium implanted copper. Nucl Instrum Methods Phys Res B 217:276–280
Kashinath A, Demkowicz MJ (2011) A predictive interatomic potential for He in Cu and Nb. Model Simul Mater Sci Eng 19:035007
Dunn AY, McPhie MG, Capolungo L, Martínez E, Cherkaoui M (2013) A rate theory study of helium bubble formation and retention in CuNb nanocomposites. J Nucl Mater 435:141–152
González C, Fernández-Pello D, Cerdeira MA, Palacios SL, Iglesias R (2014) Helium bubble clustering in copper from first principles. Model Simul Mater Sci Eng 22:035019
Kresse G, Hafner J (1993) Ab initio molecular dynamics for liquid metals. Phys Rev B 47:R558
Kresse G, Furthmuller JJ (1996) Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B 54:11169
Kresse G, Joubert D (1999) From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B 59:1758
Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77:3865
Blöchl PE (1994) Projector augmented-wave method. Phys Rev B 50:17953
James AM, Lord MP (1992) Macmillan’s chemical and physical data. Macmillan, Basingstoke
Jonsson H, Mills G, Jacobsen KW (1998) Nudged elastic band method for finding minimum energy paths of transitions. In: Berne BJ, Ciccotti G, Coker DF (eds) Classical and quantum dynamics in condensed phase simulations. World Scientific, Singapore
Henkelman G, Jonsson H (2000) Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. J Chem Phys 113:9978
See Supplemental Material with the movies of the different migration processes: movie1 shows the tetrahedral to octahedral migration in Cu, movie2 shows the tetrahedral to tetrahedral movement in Cu, movie3/movie4 show the movement of the HeV complex in Cu/W, and movie5/movie6 show the same for the complex HeV 2
Balluffi RW (1978) Vacancy defect mobilities and binding energies obtained from annealing studies. J Nucl Mater 69–70:240
Ullmaier H, Schilling W (1980) Radiation damage in metallic reactor materials, in physics of modern materials, vol I. IAEA, Vienna
Wilson WD, Johnson RD (1972) Rare gases in metals. In: Gehlen PC, Beeler JR Jr, Jaffee RI (eds) Interatomic potentials and simulation of lattice defects. Plenum, New York, p 375
Kornelsen EV, Van Gorkum AA (1990) A study of bubble nucleation in tungsten using thermal desorption spectrometry: clusters of 2 to 100 helium atoms. J Nucl Mater 92:79–88
Samaras M (2009) Multiscale modelling: the role of helium in iron. Mater Today 12:46–53
Becquart CS, Domain C (2012) Solutepoint defect interactions in bcc systems: focus on first principles modelling in W and RPV steels. Curr Opin Solid State Mater Sci 16:115–125
You YW, Kong XS, Wua XB, Fang QF, Chen JL, Luo GN, Liu CS (2013) Effect of vacancy on the dissolution and diffusion properties of hydrogen and helium in molybdenum. J Nucl Mater 433:167–173
Was GS (2007) Fundamentals of radiation materials science. Springer, New York 356
Mundy JN, Ockers ST, Smedskjaer LC (1987) Vacancy migration enthalpy in tungsten at high temperatures. Philos Mag A 56:851–860
Dai Y, Odette GR, Yamamoto T (2012) The effects of helium in irradiated structural alloys in Konings RJM in comprehensive nuclear materials. Elsevier, Amsterdam 141
Trocellier P, Agarwal S, Miro S (2014) A review on helium mobility in inorganic materials. J Nucl Mater 445:128–142
Caturla MJ, Soneda N, Alonso E, Wirth BD, Perlado JM (2000) Comparative study of radiation damage accumulation in Cu and Fe. J Nucl Mater 276:13–21
Caturla MJ, Soneda N, Fluss M (2006) Kinetic Monte Carlo simulations applied to irradiated materials: the effect of cascade damage in defect nucleation and growth. J Nucl Mater 351:78–87
Akbarzadeh AR, Chen ZZ, Kioussis N (2009) Crucial role of surface in stability and mobility of vacancy clusters in metals. Phys Rev B 79:195404
Ullmaier H (1991) In: Landolt-Bornstein Numerical Data and Functional Relationships in Science and Technology, New Series, vol III/25. Springer, Berlin. p 381
Derlet PM, Nguyen-Manh D, Dudarev SL (2007) Multiscale modeling of crowdion and vacancy defects in body-centered-cubic transition metals. Phys Rev B 76:054107
Hu W, Shu W, Zhang B (2002) Point-defect properties in body-centered cubic transition metals with analytic EAM interatomic potentials. Comput Mater Sci 23:175–189
Zinkle SJ, Busby JT (2008) Structural materials for fission and fusion energy. Mater Today 12:12–19
van Veen A (1987) Thermal helium desorption spectrometry (THDS) as a tool for the study of vacancies and self-interstitials. Mater Sci Forum 15–18:3–24
Acknowledgement
This work has been supported by the FP7 project RADINTERFACES and the Spanish Ministry of Economy and Competitiveness project NANO-EXTREM, Ref. MAT2012-38541. Angel Gutiérrez at the UNIOVI Scientific Modelling Cluster is gratefully acknowledged for technical help and CPU time. Some calculations have been performed thanks to the support provided by the Spanish Supercomputing Network (RES) through the Project FI-2014-1-0008.
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Below is the link to the electronic supplementary material.
Supplementary material 4 (MPG 952 kb)
Rights and permissions
About this article
Cite this article
González, C., Iglesias, R. Migration mechanisms of helium in copper and tungsten. J Mater Sci 49, 8127–8139 (2014). https://doi.org/10.1007/s10853-014-8522-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10853-014-8522-7