Abstract: Significance Discovering rare earth (RE)–free magnets that can meet the performance and cost goals for advanced electromagnetic devices has been the dream of many scientists over several decades. We present the efficient discovery and synthesis of an RE-free magnetic Fe3CoB2 compound in this paper. Our machine learning (ML)–guided framework greatly reduces the complexity of high-throughput screening and makes ab initio calculations and further structure searches using an adaptive genetic algorithm much more effective than previous approaches. We demonstrate that our ML-guided framework enables the computational discovery and experimental synthesis of an Fe3CoB2 compound to be accomplished in days. Our ML-guided framework presents a paradigm for efficient materials design and discovery in the digital era. read less

Abstract: Fe-cluster-based crystal structures are predicted for chalcogenides Fe3X4 (X = S, Se, Te) using an adaptive genetic algorithm. Topologically different from the well-studied layered structures of iron chalcogenides, the newly predicted structures consist of Fe clusters that are either separated by the chalcogen atoms or connected via sharing of the vertex Fe atoms. Using first-principles calculations, we demonstrate that these structures have competitive or even lower formation energies than the experimentally synthesized Fe3X4 compounds and exhibit interesting magnetic and electronic properties. In particular, we show that Fe3Te4 can be a good candidate as a rare-earth-free permanent magnet and Fe3S4 can be a magnetic nodal-line topological material. read less

Abstract: Force matching is an established technique to generate effective potentials for molecular dynamics simulations from first-principles data. This method has been implemented in the open source code potfit. Here, we present a review of the method and describe the main features of the code. Particular emphasis is placed on the features added since the initial release: interactions represented by analytical functions, differential evolution as optimization method, and a greatly extended set of interaction models. Beyond the initially present pair and embedded-atom method potentials, potfit can now also optimize angular dependent potentials, charge and dipolar interactions, and electron-temperature-dependent potentials. We demonstrate the functionality of these interaction models using three example systems: phonons in type I clathrates, fracture of α-alumina, and laser-irradiated silicon. read less

Abstract: This thesis summarizes our efforts to study the structure and properties of materials computationally. The adaptive genetic algorithm (AGA) developed by us to predict crystal/surface/interface structures is presented. Applications of AGA to a variety of systems, such as non-rare earth magnetic materials, ultra-hard transition metal borides and SrTiO3 grain boundaries, are discussed. We demonstrated by AGA the capability of solving crystal structures with more than 100 atoms per unit cell and rapidly accessing the structures and phase stabilities of different compositions in multicomponent systems. We also introduced a motif-network scheme to study the complex crystal structures in silicate cathodes. In addition, we explored different computational methods for atomistic simulations of materials behavior, such as Monte Carlo modeling of the alnico magnets. read less

Abstract: Complex metallic alloys and quasicrystals show extraordinary physical properties relevant for technological applications, for example hardness at low density. In the study of these systems, atomistic simulation with classical interaction potentials is a very promising tool. Such simulations require classical effective potentials describing the cohesive energy as a function of the atomic coordinates. The quality of the simulation depends crucially on the accuracy with which this potential describes the real interactions. One way to generate physically relevant potentials is the force matching method, where the parameters of a potential are adjusted to optimally reproduce the forces on individual atoms determined from quantum-mechanical calculation. The programme package potfit developed as part of this thesis implements the force matching method efficiently. Potentials are generated for a number of complex metallic alloy systems. A potential for the decagonal basic Ni-rich Al-Co-Ni quasicrystal is used to simulate diffusion processes and melting. In the CaCd6 system built from multishelled clusters, the shape and orientation of the innermost cluster shell is studied. Finally, phonon dispersion in the Mg-Zn system is determined and compared to experiment. The programme potfit is shown to be an effective tool for generating physically justified effective potentials. Potentials created with potfit can greatly improve the understanding of complex metallic alloys through atomistic simulations. Komplexe intermetallische Verbindungen und Quasikristalle zeigen ausergewohnliche physikalische Eigenschaften, wie z.B. Harte bei geringer Dichte. Bei der Untersuchung dieser Systeme sind atomistische Simulationen mit klassischen Wechselwirkungspotenzialen ein wichtiges Werkzeug. Fur solche Simulationen benotigt man klassische effektive Potenziale, die die Bindungsenergie als eine Funktion der Atomkoordinaten beschreiben. Die Qualitat der Simulation hangt entscheidend von der Genauigkeit ab, mit der diese Potenziale die echten Wechselwirkungen wiedergeben. Eine Moglichkeit, physikalisch relevante Potenziale zu erzeugen, ist die Force-Matching-Methode. Dabei werden die Parameter eines Potenzials so angepasst, dass die mit quantenmechanischen Methoden bestimmten Krafte auf die einzelnen Atome bestmoglich reproduziert werden. Das als Teil dieser Arbeit entwickelte Programmpaket potfit implementiert die Force-Matching-Methode effizient. Fur einige komplexe intermetallische Verbindungen werden Potenziale bestimmt. In dekagonalen Al-Co-Ni-Quasikristallen werden mit Hilfe eines Potenzials Diffusionsprozesse und Schmelzvorgange simuliert. In der aus mehrschaligen Clustern bestehenden CaCd6-Verbindung wird die Struktur der innersten Clusterschale untersucht. Schlieslich wird die Phononendispersion im Mg-Zn-System bestimmt und mit experimentellen Ergebnissen verglichen. Es wird gezeigt, dass das Programm potfit ein effektives Werkzeug zur Erzeugung physikalisch gerechtfertigter Wechselwirkungen ist. Potenziale, die mit potfit erzeugt werden, konnen zum Verstandnis komplexer metallischer Verbindungen durch atomistische Simulationen viel beitragen. read less

Abstract: Accurate equations of state (EOS) and plasma transport properties are essential for numerical simulations of warm dense matter encountered in many high-energy-density situations. Molecular dynamics (MD) is a simulation method that generates EOS and transport data using an externally provided potential to dynamically evolve the particles without further reference to the electrons. To minimize computational cost, pair potentials needed in MD may be obtained from the neutral-pseudoatom (NPA) approach, a form of single-ion density functional theory (DFT), where many-ion effects are included via ion-ion correlation functionals. Standard N-ion DFT-MD provides pair potentials via the force matching technique but at much greater computational cost. Here we propose a simple analytic model for pair potentials with physically meaningful parameters based on a Yukawa form with a thermally damped Friedel tail (YFT) applicable to systems containing free electrons. The YFT model accurately fits NPA pair potentials or the nonparametric force-matched potentials from N-ion DFT-MD, showing excellent agreement for a wide range of conditions. The YFT form provides accurate extrapolations of the NPA or force-matched potentials for small and large particle separations within a physical model. Our method can be adopted to treat plasma mixtures, allowing for large-scale simulations of multispecies warm dense matter. read less

Abstract: Fe, Mg, and O are among the most abundant elements in terrestrial planets. While the behavior of the Fe–O, Mg–O, and Fe–Mg binary systems under pressure have been investigated, there are still very few studies of the Fe–Mg–O ternary system at relevant Earth’s core and super-Earth’s mantle pressures. Here, we use the adaptive genetic algorithm (AGA) to study ternary Fe x Mg y O z phases in a wide range of stoichiometries at 200 GPa and 350 GPa. We discovered three dynamically stable phases with stoichiometries FeMg2O4, Fe2MgO4, and FeMg3O4 with lower enthalpy than any known combination of Fe–Mg–O high-pressure compounds at 350 GPa. With the discovery of these phases, we construct the Fe–Mg–O ternary convex hull. We further clarify the composition- and pressure-dependence of structural motifs with the analysis of the AGA-found stable and metastable structures. Analysis of binary and ternary stable phases suggest that O, Mg, or both could stabilize a BCC iron alloy at inner core pressures. read less

Abstract: Interaction potentials are critical to molecular dynamics simulations on fundamental mechanisms at atomic scales. Combination of well-developed single-element empirical potentials via cross interaction (CI) is an important and effective way to develop alloy embedded-atom method (EAM) potentials. In this work, based on neural-network (NN) models, firstly we proposed a framework to construct CI potential functions via utilizing single-element potentials. The framework contained four steps: (1) extracting characteristic points from single-element potential functions, (2) constructing CI functions by cubic spline interpolation, (3) evaluating the accuracy of CI functions by referring to first-principle (FP) data, and (4) searching for reasonable CI functions via NN models. Then with this framework, we developed a Zr–Nb alloy CI potential utilizing the MA-III (pure Zr potential developed by Mendelev and Ackland in 2007) and the Fellinger, Park and Wilkins (FPW) (pure Nb potential developed by FPW in 2010) potentials as single-element parts. The calculated results with this Zr–Nb alloy potential showed that: (1) the newly developed CI potential functions could simultaneously present the potential-function features of Zr and Nb; (2) the normalized energy–volume curves of L12 Zr3Nb, B2 ZrNb and L12 ZrNb3 calculated by this CI potential reasonably agreed with FP results; (3) the referred MA-III Zr and FPW Nb potentials can satisfactorily reproduce the priority of prismatic slip in Zr and the tension–compression asymmetry of 〈111〉{112} slip in Nb, while other ab initio developed Zr–Nb alloy potentials cannot. Our study indicates that, this NN based framework can take full advantage of single-element potentials, and is very convenient to develop EAM potentials of alloys; moreover, the new-developed Zr–Nb alloy EAM potential can reasonably describe the complicated deformation behaviors in Zr–Nb systems. read less

Abstract: We review recent results on discoveries of new magnetic compounds by combining experiments, adaptive genetic algorithm searches, and advanced electronic-structure computational methods. read less

Abstract: The Open Knowledgebase of Interatomic Models (OpenKIM) is a framework intended to facilitate access to standardized implementations of interatomic models for molecular simulations along with computational protocols to evaluate them. These protocols include tests to compute material properties predicted by models and verification checks to assess their coding integrity. While housing this content in a unified, publicly available environment constitutes a major step forward for the molecular modeling community, it further presents the opportunity to understand the range of validity of interatomic models and their suitability for specific target applications. To this end, OpenKIM includes a computational pipeline that runs tests and verification checks using all available interatomic models contained within the OpenKIM Repository at https://openkim.org. The OpenKIM Processing Pipeline is built on a set of Docker images hosted on distributed, heterogeneous hardware and utilizes open-source software to automatically run test-model and verification check-model pairs and resolve dependencies between them. The design philosophy and implementation choices made in the development of the pipeline are discussed as well as an example of its application to interatomic model selection. read less

Abstract: Effective potentials are an essential ingredient of classical molecular dynamics (MD) simulations. Little is understood of the consequences of representing the complex energy landscape of an atomic configuration by an effective potential or force field containing considerably fewer parameters. The probabilistic potential ensemble method has been implemented in the potfit force matching code. This introduces uncertainty quantification into the interatomic potential generation process. Uncertainties in the effective potential are propagated through MD to obtain uncertainties in quantities of interest (QoI), which are a measure of the confidence in the model predictions. We demonstrate the technique using three potentials for nickel: two simple pair potentials, Lennard-Jones and Morse, and a local density dependent embedded atom method potential. A potential ensemble fit to density functional theory (DFT) reference data is constructed for each potential to calculate the uncertainties in lattice constants, elastic constants and thermal expansion. We quantitatively illustrate the cases of poor model selection and fit, highlighted by the uncertainties in the quantities calculated. This shows that our method can capture the effects of the error incurred in QoI resulting from the potential generation process without resorting to comparison with experiment or DFT, which is an essential part to assess the predictive power of MD simulations. read less

Abstract: We performed a systematic search for low-energy structures of binary iron silicide over a wide range of compositions using the crystal structure prediction method based on adaptive genetic algorithm. 36 structures with formation energies within 50 meV/atom (11 of them are within 20 meV) above the convex hull formed by experimentally known stable structures are predicted. Magnetic properties of these low-energy structures are investigated. Some of these structures can be promising candidates for rare-earth-free permanent magnet. read less

Abstract: Two-dimensional molybdenum disulfide (MoS2) is a promising material for the next generation of switchable transistors and photodetectors. In order to perform large-scale molecular simulations of the mechanical and thermal behavior of MoS2-based devices, an accurate interatomic potential is required. To this end, we have developed a Stillinger-Weber potential for monolayer MoS2. The potential parameters are optimized to reproduce the geometry (bond lengths and bond angles) of MoS2 in its equilibrium state and to match as closely as possible the forces acting on the atoms along a dynamical trajectory obtained from ab initio molecular dynamics. Verification calculations indicate that the new potential accurately predicts important material properties including the strain dependence of the cohesive energy, the elastic constants, and the linear thermal expansion coefficient. The uncertainty in the potential parameters is determined using a Fisher information theory analysis. It is found that the parameters are... read less

Abstract: Fitted interatomic potentials are widely used in atomistic simulations thanks to their ability to compute the energy and forces on atoms quickly. However, the simulation results crucially depend on the quality of the potential being used. Force matching is a method aimed at constructing reliable and transferable interatomic potentials by matching the forces computed by the potential as closely as possible, with those obtained from first principles calculations. The potfit program is an implementation of the force-matching method that optimizes the potential parameters using a global minimization algorithm followed by a local minimization polish. We extended potfit in two ways. First, we adapted the code to be compliant with the KIM Application Programming Interface (API) standard (part of the Knowledgebase of Interatomic Models project). This makes it possible to use potfit to fit many KIM potential models, not just those prebuilt into the potfit code. Second, we incorporated the geodesic Levenberg–Marquardt (LM) minimization algorithm into potfit as a new local minimization algorithm. The extended potfit was tested by generating a training set using the KIM environment-dependent interatomic potential (EDIP) model for silicon and using potfit to recover the potential parameters from different initial guesses. The results show that EDIP is a ‘sloppy model’ in the sense that its predictions are insensitive to some of its parameters, which makes fitting more difficult. We find that the geodesic LM algorithm is particularly efficient for this case. The extended potfit code is the first step in developing a KIM-based fitting framework for interatomic potentials for bulk and two-dimensional materials. The code is available for download via https://www.potfit.net. read less

Abstract: Using a combination of adaptive genetic algorithm search, motif-network search scheme and first-principles calculations, we have systematically studied the low-energy crystal structures of Na2FeSiO4. We show that the low-energy crystal structures with different space group symmetries can be classified into several families based on the topologies of their Fe-Si networks. In addition to the diamond-like network which is shared by most of the low-energy structures, another three robust Fe-Si networks are also found to be stable during the charge/discharge process. The electrochemical properties of representative structures from these four different Fe-Si networks in Na2FeSiO4 and Li2FeSiO4 are investigated and found to be strongly correlated with the Fe-Si network topologies. Our studies provide a new route to characterize the crystal structures of Na2FeSiO4 and Li2FeSiO4 and offer useful guidance for the design of promising cathodes for Na/Li ion batteries. read less

Abstract: Simulating laser ablation on an atomistic scale is a demanding task which requires millions to billions of atoms for sample sizes in the nano- to micrometer range. read less

Abstract: Both quantum mechanical and molecular-dynamics (MD) simulations of α-boron are done at this work. Angular dependent interatomic potential (ADP) for boron is obtained using force-matching technique. Fitting data are based on ab initio results within  −20..100 GPa pressure range and temperatures up to 2000 K. Characteristics of α-boron, obtained using ADP potential such as bond lengths at equilibrium condition, bulk modulus, pressure-volume relations, Gruneisen coefficient, thermal expansion coefficient are in good agreement with both ab initio data, obtained in this work and known experimental data. As an example of application, the propagation of shock waves through a single crystal of α-boron is also explored by large-scale MD simulations. read less

Abstract: Information about the atomic structures at solid–solid interfaces is crucial for understanding and predicting the performance of materials. Due to the complexity of the interfaces, it is very challenging to resolve their atomic structures using either experimental techniques or computer simulations. In this paper, we present an efficient first-principles computational method for interface structure prediction based on an adaptive genetic algorithm. This approach significantly reduces the computational cost, while retaining the accuracy of first-principles prediction. The method is applied to the investigation of both stoichiometric and nonstoichiometric SrTiO3 Σ3(112)[110] grain boundaries with unit cell containing up to 200 atoms. Several novel low-energy structures are discovered, which provide fresh insights into the structure and stability of the grain boundaries. read less

Abstract: We present a genetic algorithm (GA) for structural search that combines the speed of structure exploration by classical potentials with the accuracy of density functional theory (DFT) calculations in an adaptive and iterative way. This strategy increases the efficiency of the DFT-based GA by several orders of magnitude. This gain allows a considerable increase in the size and complexity of systems that can be studied by first principles. The performance of the method is illustrated by successful structure identifications of complex binary and ternary intermetallic compounds with 36 and 54 atoms per cell, respectively. The discovery of a multi-TPa Mg-silicate phase with unit cell containing up to 56 atoms is also reported. Such a phase is likely to be an essential component of terrestrial exoplanetary mantles. read less

Abstract: A new interatomic potential for a uranium–molybdenum system with xenon is developed in the framework of an embedded atom model using a force-matching technique and a dataset of ab initio atomic forces. The verification of the potential proves that it is suitable for the investigation of various compounds existing in the system as well as for simulation of pure elements: U, Mo and Xe. Computed lattice constants, thermal expansion coefficients, elastic properties and melting temperatures of U, Mo and Xe are consistent with the experimentally measured values. The energies of the point defect formation in pure U and Mo are proved to be comparable to the density-functional theory calculations. We compare this new U–Mo–Xe potential with the previously developed U and Mo–Xe potentials. A comparative study between the different potential functions is provided. The key purpose of the new model is to study the atomistic processes of defect evolution taking place in the U–Mo nuclear fuel. Here we use the potential to simulate bcc alloys containing 10 wt% of intermetallic Mo and U2Mo. read less

Abstract: We have studied the dependence of metal oxide properties in molecular dynamics (MD) simulations on the polarizability of oxygen ions. We present studies of both liquid and crystalline structures of silica (SiO2), magnesia (MgO) and alumina (Al2O3). For each of the three oxides, two separately optimized sets of force fields were used: (i) long-range Coulomb interactions between oxide and metal ions combined with a short-range pair potential; (ii) extension of force field (i) by adding polarizability to the oxygen ions. We show that while an effective potential of type (i) without polarizable oxygen ions can describe radial distributions and lattice constants reasonably well, potentials of type (ii) are required to obtain correct values for bond angles and the equation of state. The importance of polarizability for metal oxide properties decreases with increasing temperature. read less

Abstract: A novel embedded atom method (EAM) potential for the Ξ phases of Al-Pd-Mn has been determined with the force-matching method. Different combinations of analytic functions were tested for the pair and transfer part. The best results are obtained if one allows for oscillations on two different length scales. These potentials stabilize structure models of the Ξ phases and describe their energy with high accuracy. Simulations at temperatures up to 1200 K show very good agreement with ab initio results with respect to stability and dynamics of the system. read less

Abstract: We extend the program potfit, which generates effective atomic interaction potentials from ab initio data, to electrostatic interactions and induced dipoles. The potential parametrization algorithm uses the Wolf direct, pairwise summation method with spherical truncation. The polarizability of oxygen atoms is modeled with the Tangney-Scandolo interatomic force field approach. Due to the Wolf summation, the computational effort in simulation scales linearly in the number of particles, despite the presence of electrostatic interactions. Thus, this model allows to perform large-scale molecular dynamics simulations of metal oxides with realistic potentials. Details of the implementation are given, and the generation of potentials for SiO(2) and MgO is demonstrated. The approach is validated by simulations of microstructural, thermodynamic, and vibrational properties of liquid silica and magnesia. read less

Abstract: We propose three new phases of H2O under ultrahigh pressure. Our structural search was performed using an adaptive genetic algorithm which allows an extensive exploration of crystal structure. The new sequence of pressure-induced transitions beyond ice X at 0 K should be ice X! Pbcm ! Pbca ! Pmc21 ! P21 ! P21=c phases. Across the Pmc21-P21 transition, the coordination number of oxygen increases from 4 to 5 with a significant increase of density. All stable crystalline phases have nonmetallic band structures up to 7 TPa. read less

Abstract: In i-ScZn, like other quasicrystals of the i-CaCd class, the innermost shell of the icosahedral cluster is a Zn4 tetrahedron, which thus breaks the symmetry of the outer cluster shells. We investigate theoretically the dynamics of individual tetrahedra, using interatomic pair potentials, fitted from an ab initio database, and molecular dynamics (MD). This includes the formulation of an effective Hamiltonian written in terms of a rigid-body rotation representing the state of each tetrahedron. We characterize the minimum-energy orientations of a tetrahedron, as well as the paths of the transitions between minima (reorientations). The velocity autocorrelations were evaluated for the tetrahedral atoms in the MD dynamics; the corresponding spectral density S(ω) is fairly well fitted by a simplified model in which each atom hops in a double well. read less

Abstract: Force matching is a method for parameterizing empirical potentials in which the empirical parameters are fitted to a reference potential energy surface (PES). Typically, training data are sampled from a canonical ensemble generated with either the empirical potential or the reference PES. In this Communication, we show that sampling from either ensemble risks excluding critical regions of configuration space, leading to fitted potentials that deviate significantly from the reference PES. We present a hybrid ensemble which combines the Boltzmann probabilities of both potential surfaces into the fitting procedure, and we demonstrate that this technique improves the quality and stability of empirical potentials. read less

Abstract: Large-scale simulations of plastic deformation and phase transformations in alloys require reliable classical interatomic potentials. We construct an embedded-atom method potential for niobium as the first step in alloy potential development. Optimization of the potential parameters to a well-converged set of density-functional theory (DFT) forces, energies, and stresses produces a reliable and transferable potential for molecular dynamics simulations. The potential accurately describes properties related to the fitting data, and also produces excellent results for quantities outside the fitting range. Structural and elastic properties, defect energetics, and thermal behavior compare well with DFT results and experimental data, e.g., DFT surface energies are reproduced with less than 4% error, generalized stacking-fault energies differ from DFT values by less than 15%, and the melting temperature is within 2% of the experimental value. read less

Abstract: We present a program called potfit which generates an effective atomic interaction potential by matching it to a set of reference data computed in first-principles calculations. It thus allows one to perform large-scale atomistic simulations of materials with physically justified potentials. We describe the fundamental principles behind the program, emphasizing its flexibility in adapting to different systems and potential models, while also discussing its limitations. The program has been used successfully in creating effective potentials for a number of complex intermetallic alloys, notably quasicrystals. read less

Abstract: We introduce a simple local atomic structure optimization algorithm which is significantly faster than standard implementations of the conjugate gradient method and often competitive with more sophisticated quasi-Newton schemes typically used in ab initio calculations. It is based on conventional molecular dynamics with additional velocity modifications and adaptive time steps. The surprising efficiency and especially the robustness and versatility of the method is illustrated using a variety of test cases from nanoscience, solid state physics, materials research, and biochemistry. read less

Abstract: Molecular dynamics simulations of crack propagation are performed for two extreme cases of complex metallic alloys. In a model quasicrystal the structure is determined by clusters of atoms, whereas the model C15 Laves phase is a simple periodic stacking of a unit cell. The simulations reveal that the basic building units of the structures also govern their fracture behaviour. Atoms in the Laves phase play a comparable role with the clusters in the quasicrystal. Although the latter are not rigid units, they have to be regarded as significant physical entities. read less

Abstract: Cadmium-based quasicrystals (Cd--Ca and Cd--Yb) were the first binary alloys discovered to form thermodynamically stable quasicrystals. As binary alloys, and with a strong size difference between atomic species, they are ideal systems for structural and thermodynamic analysis. Observed quasicrystal approximants with crystallographically determined structures can be interpreted as decorations of Henley's canonical cells. We use first-principles total energy calculations to resolve details of the most favourable decorations. read less

Abstract: 15 Deutsche Zusammenfassung 18 I. Theoretical background 27 read less

Abstract: Metal oxides belong to the most important material classes in industrial technology. These high-tech ceramics are irreplacable in lots of modern microelectronic devices due to their excellent insulating properties, high melting points and high degrees of hardness. In the theoretical study of these systems, the atomistic modelling with molecular dynamics simulations and classical effective interaction force fields is a very powerful tool. There, fundamental properties can be uncovered and understood due to the atomic resolution. Both force field generation and simulation of oxide systems are computationally much more demanding than those of metals or covalent materials due to long-range electrostatic interactions. Furthermore, it is often not sufficient to only take Coulomb interactions into account, but to include electrostatic dipole moments. The latter can be integrated with the Tangney Scandolo polarizable force field model, where dipole moments are determined by a self-consistent iterative solution during each simulation time step. Applying the direct, pairwise Wolf summation to interactions between charges and its extension to dipole moments avoids high computational effort due to its linear scaling properties in the number of particles. Three relevant metal oxides have been selected to apply the new high-performance force field generation model. Therewith, a detailed investigation of crack propagation was possible. Both crack propagation insights and the influence of cracks on the dipole field are shown. Finally, the coupling of strain and – even more meaningful – strain gradient with the dipole moments is presented, which gives rise to flexoelectric effects in non-piezoeletric materials. Die vorliegende Arbeit vertieft die breit angelegte Modellierungs-Studie dreier wichtiger Metalloxide. Detaillierte Untersuchungen durch Molekulardynamik- Simulationen mit Kraftfeldern fur Siliziumdioxid, Magnesiumoxid und Alpha-Aluminiumoxid werden dargestellt. Speziell angepasste Visualisierungs-Techniken erweitern die numerischen Einblicke und verhelfen zu neuen Erkenntnissen in den untersuchten ionischen Systemen. Im Wesentlichen leistet die Arbeit einen dreistufigen Beitrag zur numerischen Erforschung ionischer kondensierter Materie: 1. Zunachst wird die neue Art der Kraftfelderstellung dargestellt, welche das Potenzial-Modell von Tangney und Scandolo mit der direkten Wolfsummation verknupft. Gezeigt wird die gewissenhafte Prufung, dass die Vereinigung der Vorteile des TS Modells, welches elektrostatische Dipolmomente mit einbezieht, mit den linearen Skalierungs-Eigenschaften der Wolfsumme gelungen ist. Die Implementierung der Kraftfelderstellung in potfit durch den Autor gibt anderen Simulations-Gruppen die Moglichkeit, diese prazise, effiziente und flexible Methode fur ihre individuellen Studien ionischer Materie einzusetzen. 2. Weiterhin werden die mithilfe der neuen Methodik generierten Kraftfelder fur Siliziumdioxid, Magnesiumoxid und Alpha-Aluminiumoxid vorgestellt. Neben ihrer Erstellung wird in jedem Einzelfall die sorgfaltige Validierung gezeigt. Die neuen Kraftfelder werden nicht nur fur eigene Simulationen eingesetzt, sondern anderen Gruppen offentlich zuganglich gemacht. Dadurch konnen nun vielerorts Simulationen durchgefuhrt werden, die bisher aufgrund von Beschrankungen bezuglich Zeit-, Langenskalen oder Randbedingungen nicht annehmbar realisierbar waren. 3. Unter Einsatz der neuen Kraftfelder wurden verschiedene Simulationen durchgefuhrt, die – auch mithilfe der speziell angepassten Visualisierung der fraktionalen Anisotropie – zu neuen Entdeckungen und grundlegenden Erkenntnissen gefuhrt haben: • Das fur Alpha-Aluminiumoxid erstellte Kraftfeld wurde zur MD Simulation von sich ausbreitenden Rissen verwendet, welche die vor zwei Jahren elektronenmikroskopisch untersuchten Verlaufs-Richtungen von in verschiedenen kristallinen Ebenen existierenden Rissen vollstandig reproduzieren konnte. Daruberhinaus konnte – erstmalig in atomistischen Simulationen von Metalloxiden – der Einfluss von sich ausbreitenden Rissen auf die Orientierung der elektrostatischen Dipolmomente beobachtet und analysiert werden. • Derartige flexoelektrische Phanomene wurden schlieslich sowohl in MD Simulationen als auch mithilfe der Darstellungstheorie untersucht. Die Kombination liefert eine konsistente Vorhersage flexoelektrischen Verhaltens in Alpha-Aluminiumoxid und auch in Periklas, obwohl beide Materialien aufgrund ihrer inversionssymmetrischen Kristallstruktur keine Piezoelektrizitat aufweisen. Die analytisch angenommene und experimentell vorhergesagte lineare Kopplung zwischen Spannungsgradient und flexoelektrischer Polarisation wurde von MD Simulationen bestatigt. Erstmalig wurde flexoelektrische Domanenausbildung modelliert. In Periklas zeigt sich, dass flexoelektrische Domanen exakt von Neel-Wanden abgetrennt werden. read less

Abstract: In this work, a method for computer simulations of laser ablation in metals is presented. The ambitious task to model the physical processes, that occur on different time and length scales, is overcome to some extent by the combination of two techniques: Molecular dynamics and finite differences. The former is needed to achieve atomistic resolution of the processes involved. Material failure like melting, vaporization or spallation occur on the atomic scale. Light absorption and electronic heat conduction, which plays the major role in metals, is described by a generalized heat conduction equation solved by the finite differences method. From the so-called Two-Temperature Model temperature, density and pressure evolution - both in time and space - can be derived. With this, various studies on laser heated metals were done. For reasons discussed in more detail later, aluminum was chosen as a model system for most simulations on isotropic materials. As a more complex structure, the metallic alloy Al13Co4 was used because of its special material properties. As an approximant to the decagonal phase of Al-Ni-Co, the alloy shows an anisotropy in its transport properties, e.g. an anisotropic heat conduction. It will be shown, that the model is able to describe the physics in laser heated solids on time scales from 100 fs up to the ns-scale properly. Great insight was gained about the processes occuring during and shortly after the laser pulse. Many of the quantities interesting for experimentalists can be predicted by the theory. From the simulations relevant parameters like the electron-cooling time or the important ablation threshold were calculated. All values match their experimental counterpart very well. Die vorliegende Arbeit beschaftigt sich mit der Laserablation in Metallen. Ziel ist es, mit Hilfe von numerischen Simulationen das Verhalten von Metallen nach der Bestrahlung mit intensiven Laserpulsen vorherzusagen. Die Arbeit ist inhaltlich in zwei Teile gegliedert. In der ersten Halfte werden theoretische Grundlagen, eine qualitative Beschreibung der Ablation und die Implementierung des Modells gegeben. Im zweiten Teil folgen Ergebnisse sowie, falls vorhanden, Vergleiche mit Experimenten. Die Arbeit schliest mit einer Zusammenfassung und einem Ausblick. read less

Abstract: An introduction is presented to numerical methods, by which the behavior of complex metallic alloys can be simulated. We primarily consider the molecular dynamics (MD) technique as implemented in our software package IMD, where Newton’s equations of motion are solved for all atoms in a solid. After a short discourse on integration algorithms, some possible types of interactions are addressed. Already simple model potentials, as for example the Lennard-Jones-Gauss potential, can give rise to complex structures, where the characteristic length scales of the order by far exceed the range of the pair interaction. Realistic interactions are modelled by highly parametrized effective potentials, like the EAM (Embedded Atom Method) potential. Our program potfit allows to fit the parameters such that data from experiment or from ab-initio calculations are well reproduced. Several applications of the methods are outlined, notably the simulation of aluminium diffusion in quasicrystalline d-Al-Ni-Co, the computation of the phonon dispersion via the dynamical structure factor of MgZn2, the propagation of cracks in NbCr2, and an order-disorder phase transition in CaCd6. read less

Abstract: Die etwa 25 Jahre zuruckliegende Entdeckung der Quasikristalle erweiterte das Gebiet der Festkorperphysik um einen neuen Strukturtyp. In der Erforschung dieser geordneten, jedoch nicht periodischen Strukturen wurden seither bedeutende Erfolge erzielt. Von verschiedenen Quasikristalltypen konnten zunehmend detaillierte Strukturmodelle erstellt werden. Zunachst wurden in der numerischen Simulation einfache binare Modellsysteme untersucht, inzwischen sind realistische ternare Strukturen Gegenstand der numerischen Forschung. Fur die Molekulardynamiksimulation solcher Strukturen ist, neben einem geeigneten Strukturmodell, eine gute Modellierung der atomaren Wechselwirkungen erforderlich. Besonders fur Simulationen nahe der Schmelztemperatur besteht Bedarf nach einem realistischen Wechselwirkungspotential. Da herkommliche Potentiale ublicherweise an Parameter der Grundzustandsstruktur angepasst wurden, tendieren diese dazu, bei hohen Temperaturen zu versagen. Die numerische Exploration in diesem Temperaturbereich kann einen wichtigen Beitrag zum Verstandnis der Quasikristalle liefern. Diffusionsprozesse, die bedeutend fur die Entstehung von quasikristallinen Hochtemperaturphasen sind, konnen im Fall von Aluminium nur in der Simulation erforscht werden, weil fur das ubliche Messverfahren kein geeignetes Radioisotop existiert. Da Aluminium ein wesentlicher Bestandteil vieler Quasikristalle ist, ist das Verstandnis der Aluminiumdiffusion von groser Bedeutung. Ziel dieser Arbeit ist die Untersuchung der Aluminiumdiffusion in den dekagonalen Quasikristallen AlNiCo und AlCoCu mittels Molekulardynamiksimulation. Dazu werden zunachst, durch Anpassung an Ab-initio-Daten, Wechselwirkungspotentiale fur die Strukturen entwickelt. Mit diesen Potentialen werden Simulationen bei hohen Temperaturen durchgefuhrt. Die dabei auftretende Diffusion wird ausgewertet und mit Daten aus Ab-initio-Rechnungen verglichen. Die in der vorliegenden Arbeit konstruierten EAM-Potentiale fur Hochtemperatursimulationen an dekagonalen Quasikristallen erwiesen sich als geeignet, um grundlegende Eigenschaften der Systeme richtig zu modellieren. Der Vergleich mit der Ab-initio-Rechnung lieferte fur alle Atomsorten eine sehr gute Ubereinstimmung in den aus der thermischen Bewegung resultierenden Atomaufenthaltswahrscheinlichkeiten der Strukturen. Auch einzelne mit den EAM-Potentialen untersuchten Al-Diffusionsprozesse konnten in der Ab-initio-MD-Simulation bestatigt werden. In den quasikristallinen Strukturen wurde in der klassischen Molekulardynamiksimulation weit reichende Aluminiumdiffusion beobachtet. Die durch Ab-initio-Rechnungen bestatigten Al-Diffusionsprozesse wurden detailliert untersucht. Dabei wurde deutlich, dass die Diffusion in der dekagonalen Ebene uber quasikristallspezifische Mechanismen verlauft. Bedeutend ist hierbei die Besonderheit, dass Gebiete existieren, die zur Atomabgabe neigen, wahrend andere ein zusatzliches Atom aufnehmen konnen. Es finden Kettenprozesse statt, an deren Start- und Endpositionen sich diese Regionen befinden. Charakterisch fur diese Gebiete ist, dass die Al-Positionen nicht scharf lokalisiert sind, sondern innerhalb eines Bereichs eine kontinuierliche Al-Aufenthaltswahrscheinlichkeit besteht. In der periodischen Richtung existieren durchgangige Kanale kontinuierlicher Al-Aufenthaltswahrscheinlichkeit. Durch diese Kanale verlauft die Al-Diffusion in periodischer Richtung. Der Diffusionsmechanismus ist hierbei die direkte, synchron verlaufende, Bewegung innerhalb einer Reihe von Atomen. Dabei befinden sich immer drei Atome pro Schicht im Kanal. Bei mehr als drei Schichten findet meist eine Kopplung mit einem Prozess der dekagonalen Ebene statt, wobei ein Atom aus der dekagonalen Ebene in den Diffusionskanal springt, wahrend ein anderes diesen verlasst. In diesem Fall diffundieren nur die sich dazwischen befindenden Atome entlang des Kanals. Zur Diffusion in der dekagonalen Ebene konnen deutlich mehr Al-Atome beitragen als zu jener in der periodischen Richtung, welche auf die Diffusionskanale beschrankt ist. Da jedoch die Mobilitat der Al-Atome in den Diffusionskanalen deutlich hoher ist, liegen die Diffusionskoeffizienten fur die periodische Richtung uber jenen der dekagonalen Ebene. Die geringe Energiebarriere innerhalb der Diffusionskanale wurde mit Ab-initio-Rechnungen bestatigt. With the discovery of quasicrystals in 1982, condensed matter physics was extended by a new kind of structure. Since then, the exploration of these ordered, but nonperiodic structures has lead to significant new results. There was an increase of detailed structure models of several quasicrystals. For a long time, in numerical simulations only binary model systems were studied, but real quasicrystals are mostly ternary or even quaternary. Nowadays these structures can be explored in numerical simulations. Molecular dynamics simulations of such realistic structures require, apart from an appropriate model of the structure, a well adjusted model of the atomic interactions. Especially for simulations at temperatures near the melting point, there is demand for realistic potentials. Since conventional potentials were usually constructed by adjustment to the ground state structure, these potentials tend to fail at high temperatures. Simulations at high temperatures provide an important contribution to the understandig of quasicrystals. Diffusion processes are fundamental in the formation of high temperature phases and the motion of defects. In the case of aluminium the diffusion cannot be measured experimentally, due to the lack of suitable radiotracers. Therefore numerical simulation is the sole possibilty to study the Al diffusion processes. Since aluminium is a basic component of many quasicrystals, the understanding of aluminum diffusion is of great importance. The goal of this thesis is the exploration of diffusion in the decagonal AlNiCo and AlCoCu quasicrystals via molecular dynamics simulation. For this purpose, atomic interaction potentials for these structures are developed by adjusting them to ab initio data. The newly developed EAM potentials for molecular dynamics simulations at high temperatures in AlNiCo and AlCoCu quasicrystals turned out to be well adapted for modelling the basic properties of these decagonal quasicrystals. The comparison with ab initio calculations shows very good agreement in the atom density maps of both structures. Similarly some specific diffusion processes, which were found in the simulations with EAM potentials, were validated in ab initio calculations. In the molecular dynamics simulation, long range Al diffusion was observed in both decagonal quasicrystal structures. Al diffusion processes, which were validated by ab initio calculations, were studied in detail. It was found that the diffusion in the decagonal plane proceeds via mechanisms which are specific to quasicrystals. Of great importance are sites which tend to emit atoms, whereas other sites can absorb atoms. Chain processes occur, where the initial and the final positions are at these sites. The important characteristic of these sites is that the Al positions are not localized, but there is a continuous Al density in these regions. In the periodic direction, channels of continuous Al density extend through the structure. The diffusion in this direction runs via such channels. The diffusion mechanism is a synchronous motion of atoms within a column. In each layer there are three atoms which are part of this column. With more than three layers there is usually a coupling with a jump process in the decagonal plane. An atom of the decagonal plane jumps into the diffusion channel, whereas another atom leaves the channel. In this case, only the atoms in-between diffuse along the channel. There are clearly more Al atoms which contribute to the diffusion in the decagonal plane than in the periodic direction, in which the diffusion is limited to the channels. However, since the mobility of Al atoms in the diffusion channels is significantly higher, the diffusion coefficients in the periodic direction are larger than those in the decagonal plane. The small energy barriers in the diffusion channels were validated in ab inito calculations. read less