Plutonium is considered a fascinating element. It was first chemically isolated in 1941 at the University of California, but its discovery was hidden until after the Second World War. There are six distinct allotropic phases of plutonium with very different properties. At ambient pressure, continuously increasing the temperature converts the room-temperature, simple monoclinic a phase through five phase transitions, the final one occurring at approximately 450°C.

The delta (δ) phase is perhaps the most interesting allotrope of plutonium. δ-plutonium is technologically important, has a very simple crystal structure, but its electronic structure has been debated for decades. Researchers have attempted to understand its anomalous behaviour and how the properties of δ-plutonium are connected to the 5f electrons.

The 5f electrons are found in the actinide group of elements which includes plutonium. Their behaviour is counterintuitive. They are sensitive to temperature, pressure and composition, and behave in both a localised manner, staying close to the nucleus and in a delocalised (itinerant) manner, more spread out and contributing to bonding. Both these states can support magnetism depending on actinide element. The 5f electrons contribute to δ-phase stability, anomalies in the material’s volume and bulk modulus, and to a negative thermal expansion where the δ-phase reduces in size when heated.

In this work, the researchers present a comprehensive model to predict the thermodynamic behaviour of δ-plutonium, which has a face-centred cubic structure. They use density functional theory, a computational technique that explores the overall electron density of the system and incorporate relativistic effects to capture the behaviour of fast-moving electrons and complex magnetic interactions. The model includes a parameter-free orbital polarization mechanism to account for orbital-orbital interactions, and incorporates anharmonic lattice vibrations and magnetic fluctuations, both transverse and longitudinal modes, driven by temperature-induced excitations. Importantly, it is shown that negative thermal expansion results from magnetic fluctuations.

This is the first model to integrate electronic effects, magnetic fluctuations, and lattice vibrations into a cohesive framework that aligns with experimental observations and semi-empirical models such as CALPHAD. It also accounts for fluctuating states beyond the ground state and explains how gallium composition influences thermal expansion. Additionally, the model captures the positive thermal expansion behaviour of the high-temperature epsilon phase, offering new insight into plutonium’s complex thermodynamics.

Do you want to learn more about this topic?

Pu 5f population: the case for n = 5.0 J G Tobin and M F Beaux II (2025)