Results on a possible new nuclear fuel

In my project “Heat transport in novel nuclear fuels“, as mentioned in the previous blogs, it is studied the influence of carbon atoms in uranium and thorium compounds in their heat transport. So, in the last weeks of this Summer of HPC, I had the opportunity to put my hands on a possible novel nuclear fuel, U₂C₃. You can see the complicated structure of this crystals in the feature image of this blog. There are 40 atoms in the most simple cube that you can cut from the entire solid! So many atoms and a big supercomputer that can handle them! To do all the calculations I used the Barbora cluster in the IT4I supercomputing center in Ostrava. It consist of 201 compute nodes, totaling more than 7000 compute cores!

To calculate the electronic properties, I first found the equilibrium distance of the ions, the so called lattice parameter. The procedure to find it is quite intuitive. You fix the volume of your solid, you ran the VASP code that calculates the total energy of the system, then you “press” or “dilate” the structure, you repeat the calculation and so on. At the end you will find an energy-volume curve. The minimum of this curve is exactly the position in which the crystal is at the equilibrium.

An important feature of uranium atoms is their big charge so electrons around them can move very fast! Therefore relativistic effects (the so-called Spin-Orbit Coupling) on this compound may not be negligible. Luckily, in the VASP module, there is the possibility to take it into account (with the effect of slowing down the calculations). Having this in mind I calculated the electronic properties with and without this correction. What it is showed in the figure below is the electronic band structure. What is it? To understand that we have to think about how do we solve the the crystal structure. Since we are dealing with microscopic matter, quantum mechanics is needed. At the end we have to solve a Schrodinger-like equation that will eventually give as all the quantized energy of the system. Another feature that a crystal has is the ordered structure. Just from this fact it exist a relation between the momenta of the electrons and the periodicity of the solid. So, at the end, what are these bands? Simply the plot of the quantized energies over this sort of momenta.

As you can see both from the bands and from the energy-volume curve, the SOC is sensibly not negligible! We cannot exclude the SOC in further calculation and unfortunately it will slow down the codes. But problems never ends! Uranium has also a magnetic moment and we have to include it. To understand thermal properties, we need to ask: how many electron states are available for the heat transport? Let’s look at the Density of States, more specifically at the projected DOS. This will tell us what kind of electrons are involved in the thermal conductivity. As you can see in the graph below, mainly localized electrons (f-orbitals are localized) from uranium are available (only electrons around zero energy matters!). Further calculations can be done to compute phonon and thermal properties.

And now we are at the conclusion of this SoHPC. I really enjoyed this experience and I hope that I have passed on to you my passion for physics and computational science. Goodbye everyone, it’s been a pleasure!