An international team of researchers present new mathematical equations that with minimal increase in computational complexity allow for accurate and experimentally testable predictions.

Understanding the nature of radiation damage in materials is of paramount importance for controlling the safety of nuclear reactors, using ion implantation in semiconductor technology, and designing reliable devices in space.

The standard approach to estimating the radiation damage in materials analytically has been for more than 60 years a simple equation, known as “Kinchin-Pease”. However, the so called “displacements-per-atom” (dpa) number obtained from this equation does not in common metals usually correspond to any physically measurable quantity. This was established experimentally about 40 years ago, and computer simulations carried out during the last 25 years have firmly established the physical reason to this.

“The explanation is, in brief, that in metals, irradiation produces on picosecond time scales a liquid-like zone, which during the cooling-down phase recombines much of the initially produced damage, leading to a factor of 1/3 reduction in damage”, says Professor Kai Nordlund who was in lead of the team on search for more accurate predictions of usability of materials in nuclear environments, that now present their results freshly in Nature Communications.

“On the other hand, the formation of the transient liquid leads to a massive amount of atoms in the crystal, about a factor of 30 more than the dpa value, being replaced by others after the liquid has cooled down”, he says.

Formulating two new equations to correct the problem

Even though these issues are well established, there has until now been no attempt to correct the problems of the standard dpa equations.

In their article “Improving atomic displacement and replacement calculations with physically realistic damage models” published in Nature Communications, the scientists present the outcome of a reconsideration of the issue. It lead to the formulation of two new equations, the “athermal recombination-corrected dpa” (arc-dpa) and the replacements-per-atom (rpa) functions, that with a minimal increase in computational complexity allows for accurate and experimentally testable predictions of damage production and radiation mixing in materials.

Usable lifetime of materials in nuclear reactors

The researchers expect that the new equations will be a basis for formulating more reliable and efficient predictions of the usable lifetime of materials in nuclear reactors and other environments with high levels of ionizing radiation. This is especially important for formulating fusion and new kinds of fission nuclear power plants.

Improving atomic displacement and replacement calculations with physically realistic damage models,, DOI 10.1038/s41467-018-03415-5, Nature Communications, 14.3.2018

Image text
Left: Illustration of the number of defects in materials predicted by the old “Kinchin-Pease” equation; Right: Illustration of the actual number of remaining damage, consistent with the prediction of the new model.

Professor Kai Nordlund, University of Helsinki, +358 50 415 6815, @kai_nordlund,
Press Officer Minna Meriläinen-Tenhu, +358 50 415 0316, @MinnaMeriTenhu,