The path to a clean energy future relies on our ability to tailor the flow of heat in next-generation energy materials.
Linu Malakkal

Heat transfer is essential to our daily life—from heating a pot of water to complex carbon-free energy technologies that aim to achieve zero carbon emissions. Examples of these technologies include concentrated solar power generation, thermoelectric generation, and nuclear power generation. Approximately 20 percent of America's carbon-free energy comes from nuclear energy. A nuclear reactor is very similar in principle to a fossil energy plant in which the thermal energy is used to generate steam, which is then converted to electricity using a turbine.  The primary difference involves the heat source.  In a nuclear fuel, a fissile nuclide absorbs a neutron, becomes unstable, and splits, creating at least two new atoms, imparting sufficient kinetic energy to these new atoms to displace thousands of adjacent atoms from their equilibrium positions.  The kinetic energy transfer to the crystalline lattice generates heat that must be conducted through the fuel for eventual conversion to electricity.  The violent transfer of energy also produces crystalline defects, which degrade the thermal conductivity of the fuel (the ability to conduct heat).  The degradation of thermal conductivity results in the early retirement of fuel, which decreases plant efficiency and increases waste generation.

Over the lifetime of the fuel in a reactor, the thermal conductivity decreases by as much as 70 percent. However, researchers are now finding that thermal conductivity degradation can be mitigated by specially designing the chemistry and microstructure of nuclear fuels.  Examples include using dopants to control defect concentrations, modifying crystallite size to improve fission gas retention, and directly adding other materials to raise the baseline thermal conductivity.  To best utilize these mitigation measures, it is imperative to fundamentally understand how heat is transported on an atomic scale.  At this scale, electrons and lattice vibrations or phonons are responsible for thermal energy transfer (see Figure 1).

Figure 1: Nuclear fission generates heat and fission fragments. Fission fragments create defects in crystal structure. In oxide fuels, heat is carried by collective vibrations of atoms (phonons).

It was from this perspective that the Center for Thermal Energy Transport under Irradiation (TETI), led by Idaho National Laboratory, was formed in 2018. The Center’s mission is to accurately predict thermal energy transport in actinide materials in extreme environments. Since the Center’s inception, the scientists at TETI have been using cutting-edge computational and experimental tools to develop the foundational work necessary to accurately model and ultimately control thermal energy transport in advanced nuclear fuels [1].

Selected major accomplishments:

During TETI’s first four years, scientists provided critical new insights into accurately resolving phonon lifetimes using inelastic neutron scattering (INS) measurements. Phonon lifetimes are a key component to theories of thermal transport, yet lifetimes predicted using principles of quantum mechanics are rarely compared to INS results. TETI researchers demonstrated that a proper comparison between the theoretical and the experimental phonon linewidth requires the theoretical predictions based on quantum mechanics to explicitly consider the finite region in the reciprocal space (q-voxel) used in the INS data analysis instead of just a single point (q-point) in the reciprocal space [2].  Accurately resolving phonon linewidths is essential to the phonon transport research community and will be central to fully understanding thermal transport in nuclear fuel. TETI scientists also started work on tuning empirical interatomic potentials (EIPs) to reproduce phonon structure accurately. Computing thermal transport properties of crystals in the presence of complex defects often necessitates using EIPs, which are typically not well characterized for perfect crystals. TETI’s approach, which uses a minimum representation of the interatomic force constants, provides a means to rapidly train EIPs for predicting phonons and related properties [3]. This newly developed EIP represents a significant advancement for phonon transport and applied fuels communities. Regarding thermal transport under irradiation, TETI scientists have thoroughly treated thermal transport in oxide fuels from atomistic models to mesoscale transport measurements [1]. This comprehensive treatment of thermal transport provides the necessary basis to investigate thermal transport under irradiation in more complex systems.

Sneak peek of TETI’s new direction:

After making significant advancements during the first four-year term, the Center currently focuses on two thrust areas: (a) advanced oxide fuels and (b) advanced nitride fuels. In the oxide thrust, we extend the computational and experimental framework to the temperature extremes crucial for developing the fundamental understanding of fuels at operating temperatures. In oxide fuels, heat transfer is primarily by phonons. Phonon transport, in turn, is governed by the interatomic potential. The interatomic potential is written as a series expansion of mathematical functional terms that depends on the position of atoms. At high temperatures, the higher-order terms in the series must be included, presenting non-trivial computational and experimental challenges. A central challenge for the nitride thrust involves accurately capturing the scattering of electrons by phonons. This scattering mechanism is primarily responsible for limiting thermal conductivity in nitride fuels. However, the interactions between electrons and phonons are challenging to model and unambiguously observe. TETI’s emphasis here will be on using multiple investigative methods spanning different aspects of the solution space to accurately gauge the impact of electron–phonon coupling. Meeting these challenges will give the fuel community the tools to develop advanced fuels with superior thermal transport properties. Moreover, developing a comprehensive understanding of thermal energy transport can offer opportunities for energy-related technologies beyond nuclear energy.

More Information

[1] Hurley et al. “Thermal Energy Transport in Oxide Nuclear Fuel”, Chem. Rev2022, 122, 3, 3711–3762.

[2] Xiao et al. “Validating first-principles phonon lifetimes via inelastic neutron scattering”, PhysRevB.106.144310.

[3] Zhou et al. “Improving empirical interatomic potentials for predicting thermophysical properties by using an irreducible derivatives approach: The case of thorium dioxide”, arXiv:2204.13685.


This newsletter and the work cited in the newsletter were supported from the Center for Thermal Energy Transport under Irradiation (TETI), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences. The author also acknowledges that this research made use of the resources of the High-Performance Computing Center at Idaho National Laboratory, which is supported by the Office of Nuclear Energy of the U.S. Department of Energy and the Nuclear Science User Facilities under Contract No. DE-AC07-05ID14517.

About the author(s):

Linu Malakkal is a computational material scientist in the Computational Mechanics and Materials department at the Idaho National Laboratory working in the Thermal Energy Transport under Irradiation (TETI) EFRC and performs atomistic scale simulations for the United States High-Performance Research Reactor Program. He also serves as the U.S. DOE Basic Energy Sciences Early Career Network (BES – ECN) Representative for TETI. ORCID ID # 0000-0003-4895-0323.