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Quantum de-trapping and transport of heavy defects in tungsten


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.

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Fig. 1: One-dimensional SIA cluster motion.
Fig. 2: Characterization of the motion frequency of SIA cluster de-trapping.
Fig. 3: Motion frequency of SIA cluster de-trapping versus temperature.

Data availability

The data generated and/or analysed within the current study will be made available on reasonable request to the corresponding author.


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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.

Author information




K.A., M.C.M. and L.P. designed the study. K.A., T.Y., T.A., S.A., Y.Y., K.H., N.T., H.Y., T.Y. and H.M. performed the experiments. M.C.M., S.F., L.P., D.N.M., A.M.G., S.L.D., P.W.M. and T.D.S. performed the theoretical works. K.A., M.C.M., S.F. and S.L.D. wrote the main draft. All authors discussed the results and commented on the manuscript.

Corresponding author

Correspondence to Kazuto Arakawa.

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Extended data

Extended Data Fig. 1 Suppression of the SIA cluster Peierls potential.

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).

Extended Data Fig. 2 Calculation of the SIA cluster binding energies.

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).

Extended Data Fig. 3 Average maximum hop distance per 10 hops vs temperature.

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.

Extended Data Fig. 4 Motion frequency vs irradiation time at 31 K, with beam energy 300 keV.

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.

Supplementary information

Supplementary Information

Supplementary Discussion

Supplementary Video 1

One-dimensional motion of nanoscale SIA clusters. Acceleration voltage, 1,000 kV; beam intensity, 2 × 1025 m−2 s−1 and temperature, 260 K. The frame width is 160 nm.

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Arakawa, K., Marinica, MC., Fitzgerald, S. et al. Quantum de-trapping and transport of heavy defects in tungsten. Nat. Mater. 19, 508–511 (2020).

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