By Shokirbek Shermukhamedov
The beginning of my life in Innsbruck coincided with the start of the pandemic. The week of my stay ended with self-isolation. At this time, I began to study a new field of science for myself. My research at the University of Innsbruck started with an introduction to the nuclear fusion field. I learned that nuclear fusion is a new experimental technology with the goal of developing a safe, abundant, sustainable energy source that could help curb greenhouse gas emissions and meet the increasing energy needs of future generations. To date, the main physical device in nuclear fusion is the International thermonuclear experimental reactor (ITER, "The Way" in Latin). Despite the fact that the reactor requires a constant external power source, it will be able to generate five times more heat energy than will be spent on plasma heating (and in peak modes, even ten times more). ITER is expected to demonstrate the first "burning fusion plasma" at a reactor scale by 2020. The ultimate challenge for fusion research is the demonstration of electricity generation from magnetic confinement fusion by 2050.
In the computational chemistry group of Prof. Probst at the University of Innsbruck and in cooperation with the Austrian Academy of Science (ÖAW), I have started my PhD project on the computational study of the properties of fusion-relevant materials. As physical objects were defined, materials containing beryllium, tungsten, and iron were identified. Since the first wall panels in ITER will use low-Z beryllium as armor material, while the divertor will be made of tungsten to withstand the high heat loads. We are interested in the particular plasma-wall interactions that deal with sputtering and retention processes. Sputtered atoms or molecules erode the blankets and the divertor, contaminate the plasma, and lead to radiative losses. Hydrogen (deuterium and tritium) and other plasma gases (helium, neon, argon, and nitrogen) can enter the wall material, lose their kinetic energy by successive collisions, diffuse in the material at higher temperatures, or bind chemically to beryllium or tungsten at lower temperatures.
In Prof. Probst's group, I began my work by studying the sputtering yields of the beryllium-tungsten alloys with Machine Learning Potentials (MLP). In the process, I learned to use Behler-Parrinello type high dimensional neural network potentials (HDNNPs) and high-performance computations on LEO and VSC clusters. As a consequence, I am convinced that the power of MLP is greater than that of more traditional (empirical or adjusted) potentials. Despite the fact that MLTs do not have a direct physical meaning but instead rely on flexible mathematical forms with many parameters, they are excellent tools for achieving quantum chemical precision at the atomic level. At the end of this tutorial, we were able to publish an article, of which I was a co-author [1].
Our next object was calculating the sputtering yields of pristine Be surfaces by hydrogen isotopes. In this case, the task was complicated many times over compared to the previous one. This time we considered the bombardment of beryllium with hydrogen, deuterium, and tritium atoms at different angles and different energies of incidence. To do this, quantum calculations were first carried out, and about 8000 structures were assembled for HDNNP training. As a result, fitted HDNNP enables us to perform atomic scale molecular dynamics (MD) simulation to compute beryllium surface sputtering yields. Also, we were able to greatly improve and expand the methods for analyzing the obtained MD trajectories. The results of these studies have been published in two papers [2].
Despite the good accuracy of fitted potential, the correlation between reference and fitted values was not perfect (Figure 1a). To achieve better results, we slightly modified the input parameters for the weighted atomic-centered symmetry functions of HDNNP, which allowed us to improve the correlation (Figure 1b). In further research, we used weighted atomic centered symmetry functions.
Figure 1. Correlation between the NNP and DFT energies for all configurations in the training and test sets: (a) input descriptors used in the beryllium-deuterium case and (b) modified “weighted” descriptors.
The next material studied was iron. Base-centered cubic lattice iron especially requires precise atomic potentials, which is an exceptional challenge in computational chemistry. During this work, we trained HDNNP for the deuterium bombardment of iron surfaces. The training set consisted of 8277 quantum-level computed structures. The final HDNNP were validated using deuterium adsorption curves on different iron surface sites. Despite the well-reproducible adsorption curves (an example is shown in Figure 2), the sputtering calculations showed a result different from the expected one. The calculated yields turned out to be lower than the theoretically predicted and experimentally measured values. A search in the literature points us to the complexity of such simulations at the quantum-mechanical level. This topic requires a more detailed study at the quantum level, with the inclusion of the magnetic properties of iron in the calculations.
At the time, we started studying the argon bombardment of tungsten surfaces. In this case, we were able to carry out all the calculations (quantum-chemical and MD levels) and get convincing results that are in good agreement with the experiment and theoretical data. In addition to the impact angles and impact energies, we investigated the effect of surface temperature on the sputtering yield of tungsten surfaces. The results of this research were published in our most recent article [3] .
Figure 2. Quantum-computed and NNP-predicted adsorption curve of deuterium on the "bridge" surface site of iron Subplots demonstrate an iron sample with deuterium in bridge position.
The last topic in which we also became involved was Monte Carlo (MC) simulations of sputtering processes. In contrast to the MD, the MC allows modeling systems with millions of atoms. In the fusion field, SDTrimSP is the most common package for such simulations. We got access to this package and were able to check some of the predictions from the MD simulations. More specifically, in all MD simulations, we have calculated surface binding energies, which are a key parameter in MC methods. Our calculations predict higher surface-binding energy compared to standard values. To verify these results, we performed our own calculations in SDTrimSP. In the case of beryllium (Figure 3a), our calculations proved to be better than in the case of tungsten (Figure 3b). The expected values in the second case turned out to be significantly higher than those calculated by us. Despite the results obtained, we have the opportunity to continue research in this direction because the potential of both MC and MD methods is great.
Figure 3. SDTrimSP calculated beryllium (a) and tungsten (b) sputtering yields vs. theoretically predicted (grey dashed-dotted lines) and MD calculated values (red filled circles). Calculations were performed for different impact angles (blank markers) and energies (x-axis).
In summary, computer simulations are of great interest in the field of material design in fusion. They can significantly aid in the study of the properties of materials. Our research shows the possibilities of machine learning methods and post-processing of modeling outputs. We have presented our results in several papers and at many conferences. We received positive feedback and interesting suggestions, some of which have been implemented and some of which will be implemented in the near future.
[1]L. Chen and others, ‘Sputtering of the Beryllium Tungsten Alloy Be2W by Deuterium Atoms: Molecular Dynamics Simulations Using Machine Learned Forces’, Nuclear Fusion, 61.1 (2021), 016031 <https://doi.org/10.1088/1741-4326/abc9f4>.
[2]Shokirbek Shermukhamedov and others, ‘Modelling the Sputtering of and Reflection from a Beryllium Surface: Atomistic Analysis’, Nuclear Fusion, 61.086013 (2021), 086013 https://doi.org/10.1088/1741-4326/ac044e;
S Shermukhamedov, L Chen, and Renat Nazmutdinov, ‘Sputtering and Reflection from a Beryllium Surface : Effects of Hydrogen Isotope Mass , Impact Position and Surface Binding Energy’, Nucl. Fusion, 62.1 (2022), 066024 https://doi.org/10.1088/1741-4326/ac592a.
[3] Shokirbek Shermukhamedov and Michael Probst, ‘Modelling the Impact of Argon Atoms on a Tungsten Surface’, The European Physical Journal D, 76.169 (2022), 169 <https://doi.org/10.1140/epjd/s10053-022-00495-3>.