The diffusion of defects in crystalline materials1 controls macroscopic behaviour of a wide range of processes, including alloying, precipitation, phase transformation and creep2. In real materials, intrinsic defects are unavoidably bound to static trapping centres such as impurity atoms, meaning that their diffusion is dominated by de-trapping processes. It is generally believed that de-trapping occurs only by thermal activation. Here, we report the direct observation of the quantum de-trapping of defects below around one-third of the Debye temperature. We successfully monitored the de-trapping and migration of self-interstitial atom clusters, strongly trapped by impurity atoms in tungsten, by triggering de-trapping out of equilibrium at cryogenic temperatures, using high-energy electron irradiation and in situ transmission electron microscopy. The quantum-assisted de-trapping leads to low-temperature diffusion rates orders of magnitude higher than a naive classical estimate suggests. Our analysis shows that this phenomenon is generic to any crystalline material.
Subscribe to Journal
Get full journal access for 1 year
only $4.92 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
The data generated and/or analysed within the current study will be made available on reasonable request to the corresponding author.
Mehrer, H. Diffusion in Solids Vol. 155 (Springer, 2007).
Gupta, D. Diffusion Processes in Advanced Technological Materials (William Andrew Inc., 2005).
Was, G. S. Fundamentals of Radiation Materials Science (Springer, 2007).
Fu, C.-C., Torre, J. D., Willaime, F., Bocquet, J.-L. & Barbu, A. Multiscale modelling of defect kinetics in irradiated iron. Nat. Mater. 4, 68–74 (2005).
Arakawa, K. et al. Observation of the one-dimensional diffusion of nanometer-sized dislocation loops. Science 318, 956–959 (2007).
Bai, X.-M., Voter, A. F., Hoagland, R. G., Nastasi, M. & Uberuaga, B. P. Efficient annealing of radiation damage near grain boundaries via interstitial emission. Science 327, 1631–1634 (2010).
Kadono, R. et al. Quantum diffusion of positive muons in copper. Phys. Rev. B. 39, 23–41 (1989).
Sundell, P. G. & Wahnström, G. Activation energies for quantum diffusion of hydrogen in metals and on metal surfaces using delocalized nuclei within the density-functional theory. Phys. Rev. Lett. 92, 155901 (2004).
Ehrhart, P., Jung, P., Schultz, H. & Ullmaier, H. Atomic Defects in Metals 25 (Springer-Verlag, 1991).
Derlet, P. M., Nguyen-Manh, D. & Dudarev, S. L. Multiscale modeling of crowdion and vacancy defects in body-centered-cubic transition metals. Phys. Rev. B. 76, 054107 (2007).
Swinburne, T. D., Dudarev, S. L. & Sutton, A. P. Classical mobility of highly mobile crystal defects. Phys. Rev. Lett. 113, 215501 (2014).
Wollenberger, H. J. in Physical Metallurgy, Part II (eds R. W. Chan & P. Haasen) 1139 (North Holland Physics Publishing, 1983).
Pushkarov, D. I. Quantum theory of crowdions at low temperatures. Soviet Journal of Experimental and Theoretical Physics 37, 322–325 (1973).
Flynn, C. P. Resonance mode hopping and the stage I annealing of metals. Thin Solid Films 25, 37–43 (1975).
Swinburne, T. D., Ma, P.-W. & Dudarev, S. L. Low temperature diffusivity of self-interstitial defects in tungsten. N. J. Phys. 19, 073024 (2017).
Proville, L., Rodney, D. & Marinica, M.-C. Quantum effect on thermally activated glide of dislocations. Nat. Mater. 11, 845–849 (2012).
Ohresser, P. et al. Surface diffusion of Cr adatoms on Au(111) by quantum tunneling. Phys. Rev. Lett. 95, 195901 (2005).
Fitzgerald, S. P. & Nguyen-Manh, D. Peierls potential for crowdions in the bcc transition metals. Phys. Rev. Lett. 101, 115504 (2008).
Amino, T., Arakawa, K. & Mori, H. Detection of one-dimensional migration of single self-interstitial atoms in tungsten using high-voltage electron microscopy. Sci. Rep. 6, 26099 (2016).
Wirth, B. D., Odette, G. R., Maroudas, D. & Lucas, G. E. Dislocation loop structure, energy and mobility of self-interstitial atom clusters in bcc iron. J. Nucl. Mater. 276, 33–40 (2000).
Marian, J. et al. Dynamics of self-interstitial cluster migration in pure α-Fe and Fe-Cu alloys. Phys. Rev. B. 65, 144102 (2002).
Osetsky, Y. N., Bacon, D. J., Serra, A., Singh, B. N. & Golubov, S. I. One-dimensional atomic transport by clusters of self-interstitial atoms in iron and copper. Philos. Mag. 83, 61–91 (2003).
Dudarev, S. L. The non-Arrhenius migration of interstitial defects in bcc transition metals. Comptes Rendus Phys. 9, 409–417 (2008).
Swinburne, T. D., Dudarev, S. L., Fitzgerald, S. P., Gilbert, M. R. & Sutton, A. P. Theory and simulation of the diffusion of kinks on dislocations in bcc metals. Phys. Rev. B. 87, 064108 (2013).
Arakawa, K., Amino, T. & Mori, H. One-dimensional glide motion of ‘naked’ 1/2<111> prismatic dislocation loops in iron. ISIJ Int. 54, 2421–2424 (2014).
Dausinger, F. & Schultz, H. Long-range migration of self-interstitial atoms in tungsten. Phys. Rev. Lett. 35, 1773–1775 (1975).
Dausinger, F. Die Tieftemperaturerholung in elektronenbestrahltem Wolfram. Philos. Mag. A 37, 819–836 (1978).
Mizubayashi, H. & Okuda, S. Elastic after-effect studies of self-interstitials in tungsten after fast neutron irradiation at 5 K. Radiat. Eff. 54, 201–215 (1981).
Dudarev, S. L., Derlet, P. M. & Woo, C. H. Driven mobility of self-interstitial defects under electron irradiation. Nucl. Instrum. Methods Phys. Res. B. 256, 253–259 (2007).
Satoh, Y., Matsui, H. & Hamaoka, T. Effects of impurities on one-dimensional migration of interstitial clusters in iron under electron irradiation. Phys. Rev. B. 77, 94135 (2008).
Ashcroft, N. W. & Mermin, N. D. Solid State Physics (Holt, Rinehart and Winston, 1978).
Amino, T., Arakawa, K. & Mori, H. Activation energy for long-range migration of self-interstitial atoms in tungsten obtained by direct measurement of radiation-induced point-defect clusters. Philos. Mag. Lett. 91, 86–96 (2011).
Maury, F., Biget, M., Vajda, P., Lucasson, A. & Lucasson, P. Frenkel pair creation and stage I recovery in W crystals irradiated near threshold. Radiat. Eff. 38, 53–65 (1978).
Arakawa, K., Amino, T. & Mori, H. Direct observation of the coalescence process between nanoscale dislocation loops with different Burgers vectors. Acta Mater. 59, 141–145 (2011).
Hirsch, P. B., Howie, A., Nicholson, R. B., Pashley, D. W. & Whelan, M. J. Electron Microscopy of Thin Crystals (Butterworth, 1965).
Jenkins, M. L. & Kirk, M. A. Characterization of Radiation Damage by Transmission Electron Microscopy (Institute of Physics, 2001).
Kiritani, M. Electron radiation induced diffusion of point defects in metals. J. Phys. Soc. Jpn 40, 1035–1042 (1976).
Nguyen-Manh, D., Horsfield, A. P. & Dudarev, S. L. Self-interstitial atom defects in bcc transition metals: group-specific trends. Phys. Rev. B. 73, 020101 (R) (2006).
Oen, O. S. Cross Sections for Atomic Displacements in Solids by Fast Electrons (Oak Ridge National Laboratory, 1965).
Hänggi, P., Talkner, P. & Borkovec, M. Reaction-rate theory: fifty years after Kramers. Rev. Mod. Phys. 62, 251–341 (1990).
Dudarev, S. L. Coherent motion of interstitial defects in a crystalline material. Philos. Mag. 83, 3577–3597 (2003).
Benderskii, V., Makarov, D. & Wight, C. Chemical Dynamics at Low Temperature (Wiley, 1994).
Wang, C. Z., Chan, C. T. & Ho, K. M. Tight-binding molecular-dynamics study of phonon anharmonic effects in silicon and diamond. Phys. Rev. B. 42, 11276–11283 (1990).
This work was financially supported by JSPS KAKENHI (grant nos. 15H04244 and 18K18951), ImPACT Program of Council for Science, Technology and Innovation (Cabinet Office, Government of Japan), Q-LEAP Program (MEXT: Ministry of Education, Culture, Sports, Science and Technology—Japan), and the Iron and Steel Institute of Japan Research Promotion Grant. Part of this work was supported by the ‘Advanced Characterization Nanotechnology Platform, Nanotechnology Platform Programs’ of MEXT, at Institute of Materials and Systems for Sustainability (Nanotechnology Open Facilities) in Nagoya University and at Research Centre for Ultra-High Voltage Electron Microscopy (Nanotechnology Open Facilities) in Osaka University and TATARA Nanotechnology Project Centre in Shimane University. M.C.M., L.P. and A.M.G. acknowledge support from the GENCI-(CINES/CCRT) computer centre under grant no. A0070906973. A.M.G. and M.C.M acknowledge the financial support of the Cross-Disciplinary Program on Numerical Simulation of CEA, the French Alternative Energies and Atomic Energy Commission. S.P.F. acknowledges support from the UK EPSRC, grant no. EP/R005974/1. The work at CCFE has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2019–2020 under grant agreement no. 633053 and funding from the RCUK Energy Programme (grant no. EP/T012250/1). The views and opinions expressed herein do not necessarily reflect those of the European Commission.
The authors declare no competing interests.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Top: suppression of Peierls potential as delocalization increases (and μ decreases). Both the standard single-sine and more accurate double-sine Frenkel-Kontorova models predict a negligibly small barrier for cluster diffusion after escape from the traps. Bottom: atomic positions showing increased delocalization as μ decreases from 0.75 (open circles) through 0.5 (grey circles) to 0.25 (solid circles).
a, DFT calculation of the SIA-carbon binding energy vs. separation in plane transverse to the crowdion axis. b, Elastic calculation of the SIA cluster-dilatation centre binding energy (left) and cluster pressure field (right).
A range of binding energies exist, corresponding to different cluster-impurity separations. This means more impurities are effective traps at lower temperatures, leading to a reduced hop distance.
The decrease in motion frequency, attributed to the depletion of vacancies near the clusters, is still clear, and demonstrates that the direct mechanism (which would induce a motion frequency constant in time) is not wholly responsible for the cluster motion. Indeed, at short times the motion is dominated by the indirect mechanism, by at least a factor of 5.
Extended Data Fig. 5 The correspondence between the effective classical temperature Tc (our model) and the quantum (true) temperature Tq of perfect bulk bcc W.
The classical, DFT phonons and our model are shown in red, dark blue and light blue respectively.
About this article
Cite this article
Arakawa, K., Marinica, MC., Fitzgerald, S. et al. Quantum de-trapping and transport of heavy defects in tungsten. Nat. Mater. 19, 508–511 (2020). https://doi.org/10.1038/s41563-019-0584-0
Journal of Nuclear Materials (2021)
Physical Review Materials (2021)
Microstructure and mechanical properties of (TiB+TiC)/Ti composites fabricated in situ via selective laser melting of Ti and B4C powders
Additive Manufacturing (2020)