Accurate interatomic energies and forces enable high-quality molecular dynamics simulations, torsion scans, potential energy surface mapping, and geometry optimization. Machine learning algorithms have enabled rapid estimates of energies and forces with high accuracy. Further development of machine learning algorithms holds promise for producing general potentials that support dozens of atomic species. I present my own Transformer Interatomic Potential (TrIP): a chemically sound potential based on the SE(3)-Transformer. TrIP's species-agnostic architecture--using continuous atomic representation and homogenous graph convolutions--encourages parameter sharing between atomic species for more general representations of chemical environments, keeps a reasonable number of parameters, serves as a form of regularization, and is a step towards accurate universal interatomic potentials. I introduce physical bias in the form of Ziegler-Biersack-Littmark-screened nuclear repulsion and constrained atomization energies to improve qualitative behavior for near and far interaction. TrIP achieves state-of-the-art accuracies on the COMP6 benchmark with an energy prediction error of just 1.02 kcal/mol MAE, outperforming all other models. An energy scan of a water molecule shows improved short- and long-range interactions compared to other neural network potentials, demonstrating its physical realism compared to other models. TrIP also shows stability in molecular dynamics simulations with a reasonable exploration of Ramachandran space.

京都大学 / 新制・課程博士 / 博士(工学) / 甲第23899号 / 工博第4986号 / 新制||工||1778(附属図書館) / 京都大学大学院工学研究科材料工学専攻 / (主査)教授 田中 功, 教授 中村 裕之, 教授 奥田 浩司 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

Este trabalho explora a utilização do algoritmo genético de minimização global por Evolução Diferencial (ED) como método de determinação de parâmetros de potenciais interatômicos (PIs) usados no cálculo de propriedades físicas de materiais. Dois compostos foram utilizados como estudo de caso: a berlinita (AlPO4) e a fase cúbica do tungstato de zircônio ( -ZrW2O8 ). Em ambos os casos, o potencial interatômico considerado foi uma combinação de potenciais de Buckingham, covalente exponencial e harmônico de três corpos, além do modelo casca-caroço de Dick-Overhauser para os átomos de oxigênio. Os parâmetros livres do potencial foram ajustados de modo a fornecer estimativas para os parâmetros de rede, posições atômicas e constantes elásticas de ambas as estruturas que mais se aproximassem dos valores experimentais. O algoritmo de evolução diferencial foi capaz de encontrar potenciais que melhor reproduzem as propriedades atérmicas em ambos os casos, quando comparados com PIs previamente publicados. Os potenciais encontrados para a fase cúbica do tungstato de zircônio foram aplicados à cálculos de dinâmica de rede para avaliar a influência da temperatura no seu parâmetro de rede. O algoritmo de ED encontrou um conjunto de parâmetros para potenciais com modelos analíticos relativamente simples, porém capaz de descrever com razoável precisão a expansão térmica negativa do -ZrW2O8 em baixas temperaturas. A evolução diferencial mostrouse um método capaz de explorar exaustivamente o espaço de parâmetros, o que indica que as limitações encontradas na descrição da estrutura possam ser superadas com a adição de termos ao PI ou com o uso de outra forma analítica. / This work explores the use of the genetic algorithm differential evolution (DE) for global minimization as a method for determining the interatomic potential (IP) parameters used in the calculation of physical properties of materials. Two compounds were used as a case study: Berlinite (AlPO4) and the cubic phase of zirconium tungstate ( -ZrW2O8 ). In both cases, the IP was built as a combination of Buckingham, covalent exponential, and three body harmonic potentials, together with the Dick-Overhauser core-shell model for the oxygen atoms. The free parameters of the potential were adjusted to estimate the lattice parameters, atomic positions and elastic constants of both structures that were closest to experimental values. The DE algorithm was able to find potentials that are better in describing the athermal properties for both compounds when compared to previously published IPs. The potentials found for the cubic phase of zirconium tungstate were applied in lattice dynamics calculations in order to assess the temperature influence in the lattice parameter. The DE found a relatively simple IP, but capable of describing the negative thermal expansion of -ZrW2O8 at low temperatures with reasonable precision. The DE has shown to be a method capable to exhaustively explore the parameter space of the PI, which indicates that the limitations found in describing the zirconium tungstate structure modifications as a function of temperature can be surpassed with additional terms in the potential or with another, more complex, analytical form.

Nuclear fuel performance is highly affected by the behaviour of fission gases, particularly at elevated burnups, where large amounts of gas are produced and can potentially be released. The importance of fission gas release was the motivation for large efforts, both experimentally and theoretically, in order to increase our understanding of the different steps of the process, and to continuously improve our models. Extensions to higher burnups, together with the growing interest in novel types of fuels such as inert matrix fuels envisaged for the transmutation of minor actinides, make that one is still looking for a permanently better modelling, based on a physical understanding and description of all stages of the release mechanism. Computer simulations are nowadays envisaged in order to provide a better description and understanding of atomic-scale processes such as diffusion, but even in order to gain insight on specific processes that are inaccessible by experimental means, such as the fuel behaviour during thermal spikes. In the present work simulation techniques based on empirical potentials have been used, focusing in a first stage on pure uranium dioxide. The behaviour of point defects was at the core of this part, but also the estimation of elastic and melting properties. Then, in a second stage, the study has been extended to the behaviour of helium and xenon. For helium, the diffusion in different domains of stoichiometry was considered. The simulations enabled to determine the diffusion coefficient and the migration mechanism, using both molecular dynamics and static calculation techniques. Xenon behaviour has been investigated with the additional intention to model the behaviour of small intragranular bubbles, particularly their interaction with thermal spikes accompanying the recoil of fission fragments. For that purpose, a simplified description of these events has been proposed, which opens perspectives for further work. / Les performances du combustible nucléaire sont fortement affectées par le comportement des gaz de fission, et ce particulièrement lorsqu’un taux d’épuisement élevé est atteint, puisque d’importantes quantités de gaz sont alors produites et peuvent potentiellement être relâchées. Les enjeux, entre autre économiques, liés au relâchement de gaz de fission ont donné lieu à d’importants efforts, tant sur le plan expérimental que théorique, afin d’accroître notre compréhension des différentes étapes du processus, et d’améliorer sans cesse les mod`eles. Les extensions à des taux d’épuisements encore plus élevés ainsi que l’intérêt croissant pour de nouveaux types de combustible tels que les matrices inertes, envisages en vue de la transmutation des actinides mineures, font qu’à l’heure actuelle, le besoin permanent d’une meilleure modélisation, basée sur une compréhension et une description physique des différentes étapes du processus de relâchement de gaz de fission, est toujours de mise. Les simulations par ordinateur ont ainsi été considérée comme un nouvel angle de recherche sur les processus élémentaires se produisant à l’échelle atomique, à la fois afin d’obtenir une meilleure compréhension de processus tels que la diffusion atomique ; mais aussi afin d’avoir accès à certains processus qui ne sont pas observables par des voies expérimentales, tels que la le comportement du combustible lors de pointes thermiques. Dans ce travail, deux techniques, basées sur l’utilisation de potentiels interatomiques empiriques, ont permis d’étudier le dioxyde d’uranium, dans un premier temps en l’absence d’impuretés. Cette partie était principalement centrée sur le comportement des défauts ponctuels, mais a aussi concerné différentes propriétés élastiques, ainsi que le processus de fusion du composé. Ensuite l’étude a été étendue aux comportements de l’hélium de du xénon. Pour ce qui a trait à l’hélium, la diffusion dans différents domaines de stoechiométrie a été considérée. Les simulations ont permis de déterminer le coefficient de diffusion ainsi que le mécanisme de migration lui-même. Quant au xénon, outre les propriétés de diffusion, l’intention fut de se diriger vers la modélisation des petites bulles intragranulaires, et plus précisément vers leur interaction avec les pointes thermiques, créées lors du recul des fragments de fission. Une description simplifiée de ce processus a été proposée, qui offre de nouvelles perspectives dans ce domaine.

The thermodynamics of three-dimensional, single-component elastic crystalline solids was developed by Slattery and Lagoudas (2005). Considering the in¯nitesimal deformations, the stress can be expressed as a function of the lattice vectors and density in the reference configuration and ¹(I;mn), which is defined as the derivative of specific Helmoholtz free energy with respect to the I(mn). Using the Cauchy - Born rule to connect the interatomic potential energy and the specific Helmholtz free energy, it is possible to calculate the elastic properties of both nano-scale materials such as carbon nanotubes and macro-scale materials such as diamond and silicon. In this study, we used Terso® (1988a) - Brenner (1990b) Potential, Terso® (1988b) potential and Finnis and Sinclair (1984) potential for carbon, silicon, and vanadium systems respectively. Using the interatomic potentials to describe the specific Helmholtz free energy, the elastic properties of graphite, diamond, silicon and vanadium were calculated. This method was also extended to the calculation of Young's modulus of single-walled carbon nanotubes (SWCNTs), which are composed of a two dimensional array of carbon atoms. For SWCNT, we get good agreement with the available experimental data. For diamond and silicon, C11 and C12 were consistent with both the superelastic model and the experimental data. The difference of C44 between the calculation and experimental data was due to accuracy of the potential functions.

Dissertation

The goal of this PhD research project is to devise a robust interatomic potential for large scale molecular dynamics simulations of carbon materials under extreme conditions. This screened-environment dependent reactive empirical bond order potential (SED-REBO) is specifically designed to describe carbon materials under extreme compressive or tensile stresses. Based on the original REBO potential by Brenner and co workers, SED-REBO includes reparametrized pairwise interaction terms and a new screening term, which serves the role of a variable cutoff. The SED-REBO potential overcomes the deficiencies found with the most commonly used interatomic potentials for carbon: the appearance of artificial forces due to short cutoff that are known to create erroneous phenomena including ductile fracture of graphene and carbon nanotubes, which contradicts the experimentally observed brittle character of these materials. SED-REBO was applied in large scale molecular dynamics simulations of nanoindentation of graphene membranes and shock-induced compression of diamond. It was shown in the first computational experiment that graphene membranes exhibit a non-linear response to large magnitude of indentation, followed by a brittle fracture in agreement with experiments. The strength of graphene was determined using the kinetic theory of fracture, and the crack propagation mechanisms in the material were identified. It was found in large-scale shock simulations that SED-REBO improves the predictive power of MD simulations of carbon materials at extreme conditions.

This thesis investigate the structure of cadmium sulfide (CdS) nanoparticles and its stabilization by a surfactant - cetyltrimethylamonnium cation CTA+ and further describe interactions among stabilized CdS nanoparticles and the surface of the layered clay mineral - montmorillonite with using the molecular simulation methods. Initial models of the CdS nanoparticles were build for both crystal structures (Greenockit (G) and Hawleyit (H)). The preferred orientations of the molecules of CTA+ for both crystal types of CdS nanoparticles were found with respect to minimum energy. Prefered orientation is monolayer for Greenockite and bilayer for Hawleyite. Models with the preferred orientation of the molecules of CTA+ were placed on the surface of montmorillonite and after optimization, adsorption energy of CdS nanoparticles with its envelope and montmorillonite surface was calculated. All results and used procedures were compiled in the form of practice for the subject Computational experiments in the theory of molecules I - NBCM100 taught at MFF UK in Prague.

Dissertation

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第20369号 / 工博第4306号 / 新制||工||1667(附属図書館) / 京都大学大学院工学研究科材料工学専攻 / (主査)教授 田中 功, 教授 酒井 明, 教授 中村 裕之 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM