On the Hardness of Energy Minimisation for Crystal Structure Prediction

Crystal Structure Prediction (csp) is one of the central and most challenging problems in materials science and computational chemistry. In csp, the goal is to find a configuration of ions in 3D space that yields the lowest potential energy. Finding an efficient procedure to solve this complex optimisation question is a well known open problem. Due to the exponentially large search space, the problem has been referred in several materials-science papers as "NP-Hard and very challenging" without a formal proof. This paper fills a gap in the literature providing the first set of formally proven NP-Hardness results for a variant of csp with various realistic constraints. In particular, we focus on the problem of removal: the goal is to find a substructure with minimal potential energy, by removing a subset of the ions. Our main contributions are NP-Hardness results for the csp removal problem, new embeddings of combinatorial graph problems into geometrical settings, and a more systematic exploration of the energy function to reveal the complexity of csp. In a wider context, our results contribute to the analysis of computational problems for weighted graphs embedded into the three-dimensional Euclidean space.Comment: Short version published in SOFSEM 2020, full version to be published in Fundamenta Informatica

Modified deformation behaviour of self-ion irradiated tungsten : A combined nano-indentation, HR-EBSD and crystal plasticity study

Predicting the dramatic changes in mechanical and physical properties caused by irradiation damage is key for the design of future nuclear fission and fusion reactors. Self-ion irradiation provides an attractive tool for mimicking the effects of neutron irradiation. However, the damaged layer of self-ion implanted samples is only a few microns thick, making it difficult to estimate macroscopic properties. Here we address this challenge using a combination of experimental and modelling techniques. We concentrate on self-ion-implanted tungsten, the frontrunner for fusion reactor armour components and a prototypical bcc material. To capture dose-dependent evolution of properties, we experimentally characterise samples with damage levels from 0.01 to 1 dpa. Spherical nano-indentation of grains shows hardness increasing up to a dose of 0.032 dpa, beyond which it saturates. Atomic force microscopy (AFM) measurements show pile-up increasing up to the same dose, beyond which large pile-up and slip-steps are seen. Based on these observations we develop a simple crystal plasticity finite element (CPFE) model for the irradiated material. It captures irradiation-induced hardening followed by strain-softening through the interaction of irradiation-induced-defects and gliding dislocations. The shear resistance of irradiation-induced-defects is physically-based, estimated from transmission electron microscopy (TEM) observations of similarly irradiated samples. Nano-indentation of pristine tungsten and implanted tungsten of doses 0.01, 0.1, 0.32 and 1 dpa is simulated. Only two model parameters are fitted to the experimental results of the 0.01 dpa sample and are kept unchanged for all other doses. The peak indentation load, indent surface profiles and damage saturation predicted by the CPFE model closely match our experimental observations. Predicted lattice distortions and dislocation distributions around indents agree well with corresponding measurements from high-resolution electron backscatter diffraction (HR-EBSD). Finally, the CPFE model is used to predict the macroscopic stress-strain response of similarly irradiated bulk tungsten material. This macroscopic information is the key input required for design of fusion armour components.Peer reviewe

Substituent interference on supramolecular assembly in urea gelators: synthesis, structure prediction and NMR

Eighteen N-aryl-N'-alkyl urea gelators were synthesised in order to understand the effect of head substituents on gelation performance. Minimum gelation concentration values obtained from gel formation studies were used to rank the compounds and revealed the remarkable performance of 4-methoxyphenyl urea gelator 15 in comparison to 4-nitrophenyl analogue 14, which could not be simply ascribed to substituent effects on the hydrogen bonding capabilities of the urea protons. Crystal structure prediction calculations indicated alternative low energy hydrogen bonding arrangements between the nitro group and urea protons in gelator 14, which were supported experimentally by NMR spectroscopy. As a consequence, it was possible to relate the observed differences to interference of the head substituents with the urea tape motif, disrupting the order of supramolecular packing. The combination of unbiased structure prediction calculations with NMR is proposed as a powerful approach to investigate the supramolecular arrangement in gel fibres and help understand the relationships between molecular structure and gel formation

Development of an evolutionary algorithm for crystal structure prediction

Die vorliegende Dissertation befasst sich mit der theoretischen Vorhersage neuer Materialien. Ein evolutionärer Algorithmus, der zur Lösung dieses globalen Optimierungsproblems Konzepte der natürlichen Evolution imitiert, wurde entwickelt und ist als Programmpaket EVO frei verfügbar. EVO findet zuverlässig sowohl bekannte als auch neuartige Kristallstrukturen. Beispielsweise wurden die Strukturen von Germaniumnitrofluorid, einer neue Borschicht und mit dem gekreuzten Graphen einer bisher unbekannte Kohlenstoffstruktur gefunden. Ferner wurde in der Arbeit gezeigt, dass das reine Auffinden solcher Strukturen der erste Teil einer erfolgreichen Vorhersage ist. Weitere aufwendige Berechnungen sind nötig, die Aufschluss über die Stabilität der hypothetischen Struktur geben und Aussagen über zu erwartende Materialeigenschaften liefern

Computer simulations of the interactions of the (012) and (001) surfaces of jarosite with Al, Cd, Cu2+ and Zn

Jarosite is an important mineral on Earth, and possibly on Mars, where it controls the mobility of iron, sulfate and potentially toxic metals. Atomistic simulations have been used to study the incorporation of Al3+, and the M2+ impurities Cd, Cu and Zn, in the (0 1 2) and (0 0 1) surfaces of jarosite. The calculations show that the incorporation of Al on an Fe site is favorable on all surfaces in which terminal Fe ions are exposed, and especially on the (0 0 1) [Fe3(OH)3]6+ surface. Incorporation of Cd, Cu or Zn on a K site balanced by a K vacancy is predicted to stabilize the surfaces, but calculated endothermic solution energies and the high degree of distortion of the surfaces following incorporation suggest that these substitutions will be limited. The calculations also suggest that incorporation of Cd, Cu and Zn on an Fe site balanced by an OH vacancy, or by coupled substitution on both K and Fe sites, is unfavorable, although this might be compensated for by growth of a new layer of jarosite or goethite, as predicted for bulk jarosite. The results of the simulations show that surface structure will exert an influence on uptake of impurities in the order Cu > Cd > Zn, with the most favorable surfaces for incorporation being (0 1 2) [KFe(OH)4]0 and (0 0 1) [Fe3(OH)3]6+

The use of microstructural evolution in a coated nickel base superalloy, IN738, as a time–temperature recorder

Nickel base superalloys are used for turbine blades in gas turbine engines, and are required to operate at very high temperatures (≈900°C) for long periods of time in an aggressive environment. A particular problem is that although the operating times of such blades are generally well-known, their effective operating temperatures are less well defined due to variations in position and metal-gas temperature. The microstructure of this material is known to evolve as a function of time and temperature. The aim of this research is to develop a model that will enable the microstructure to act as a time temperature recorder for IN738LC industrial gas turbine blades. [Continues.