Quantum diffusion of heavy defects defies Arrhenius’ law – Physics World


Motion of defects (dislocation loops) in tungsten at low temperature. Courtesy: CEA

“Massively heavy” atoms can move quantum mechanically within a crystalline material at cryogenic temperatures. This result, from researchers in Japan, France and the UK, contradicts the generally-held notion that only hydrogen or helium atoms are light enough to migrate through materials in this way. The study, which was performed on defect clusters containing around 100 atoms of tungsten (atomic mass 184), represents a step forward in our understanding of the low-temperature dynamics of defects and could lead to new applications in materials science and engineering.

A perfect crystal is a purely theoretical concept. Real-world crystals contain defects that can severely degrade the mechanical properties of the materials in which they occur. Understanding the way these defects diffuse and interact is therefore important for a wide range of processes in materials science and metallurgy, including alloying, precipitation and phase transformations.

Defects are bound to so-called static trapping centres (often atoms of impurities within the crystal), and thus need to “de-trap” before they can travel. For elements heavier than hydrogen or helium, de-trapping is thought to occur by thermal activation, and defect diffusion rates typically obey Arrhenius’ law – a century-old empirical rule that describes how the rate of chemical reactions varies with temperature. In a material at very low temperatures, Arrhenius’ law implies that the transport of heavy-atom defects slows considerably and may even become “frozen”.

Studying self-interstitial defects

Experiments by a team of researchers at Shimane University, Nippon Steel, Nagoya University and Osaka University in Japan, the CEA and CNRS in France, and the University of Leeds and Culham Centre for Fusion Energy in the UK have now turned this idea on its head. The team studied a type of defect that occurs when excess atoms of the same type as the ones that make up the material’s crystal lattice become misplaced within the regular stack. These “self-interstitial atoms” (SIAs) cause distortions and stress in the lattice structure, and the researchers studied how clusters of them moved through a tungsten sample at cryogenic temperatures.

The team created both SIA defects and vacancies – that is, lattice sites with “missing” atoms, which are the counterparts of SIAs – by irradiating the tungsten with a high-energy (2000 keV) electron beam at 105 K. They then aged the sample at 300 K, which allowed the SIA clusters to nucleate, grow to nanometric sizes and bind to trapping centres.

At these temperatures, the researchers note that defects are thermally immobile and remain dispersed throughout the sample. Their next step was to illuminate the sample with a lower energy (100-1000 keV) electron beam. The energy of this second beam is too low to create additional SIAs but high enough to athermally move the vacancies around and cause trapped clusters of SIAs to become de-trapped. This de-trapping can occur via thermal and quantum-mechanical mechanisms.

Quantum transport of heavy defects

By measuring the clusters’ motion frequency using in situ transmission electron microscopy, the researchers say they could distinguish between purely thermal motion and movement caused by quantum-mechanical processes. To their surprise, they found that the quantum-assisted de-trapping of the defects leads to low-temperature diffusion rates that are orders of magnitude higher than that allowed by Arrhenius’ Law.

“Our results show that quantum transport, even of heavy defects, becomes dominant below around one-third of the Debye temperature (which is the approximate temperature below which quantum effects may be observed),” says study lead author Kazuto Arakawa. This behaviour, he explains, stems from the quantization of atomic vibrations of the crystal lattice. These quantized vibrations, known as phonons, drive the stochastic fluctuations of objects that are themselves too heavy to move quantum mechanically – a phenomenon that is likely to hold true for low-temperature defect transport in most crystalline materials.

The new finding will impact a wide range of fields across materials science and engineering – wherever low-temperature processes related to defect transport or diffusion are important, Arakawa says. The term “low temperature” is relative: beryllium, for example, has a Debye temperature of 1280 K, so even at room temperatures, the diffusion of beryllium defects is likely to be a predominantly quantum phenomenon.

Developing materials for extreme environments

Arakawa believes the team’s result could be important for understanding and developing microstructures that work in environments with high levels of radiation and/or mechanical shocks, both of which cause defects to form. It may also be relevant in processes such as the irradiation of semiconductors and superconductors, where defects are generated deliberately to manipulate material properties. Finally, Arakawa thinks it could pave the way for materials-processing techniques that exploit quantum-assisted transport and reactions between defects at temperatures close to absolute zero – something that has never been attempted, let alone achieved.

The work could have even more far-reaching consequences, he adds. Until now, most observations of atomic transport in crystals at cryogenic temperatures were interpreted using Arrhenius’ law. The fact that heavy defects move faster than expected at these low temperatures suggests that the materials-science community may need to revisit and reinterpret previous low-temperature experiments.

“Classic observations performed at cryogenic temperatures – for example, the recovery of electrical resistivity of materials exposed to irradiation near absolute zero, or low temperature internal friction studies – could now be analysed in a completely new light,” Arakawa tells Physics World.

The research is detailed in Nature Materials.

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