Here we describe the fitting and testing, via molecular dynamics simulation, of a bond-order potential for water with a unique force field parameterization. Most potentials for water, including some bond-order (reactive) potentials, are based on a traditional, many-body decomposition to describe water's structure with bond stretch, angle bend, electrostatics, and non-bonded terms. Our model uses an expanded version of the Bond Valence Model, the Valence Multipole Model, to describe all aspects of molecular structure using multibody, bond-order terms. Prior work successfully related these multibody, bond order terms to energy, provided the structures were close to equilibrium. The success of this equilibrium energy model demonstrated the plausibility of adapting its parameterization to a molecular dynamics force field. Further, we present extensive testing of ab initio methods to show that the ab initio data we obtained, using the CCSD(t)/cc-pwCVTZ level of theory, to augment the fitting set of our parameters is of the highest quality currently available for the OH system. While the force field is not yet finished, the model has demonstrated remarkable improvement since its initial testing. The test results and the insights gleaned from them have brought us significantly closer to adapting our unique parametrization to a fully functional molecular dynamics force field. Once the water potential is finished, it is our intent to develop and expand the Valence Multipole Model into a fully reactive alternative to CLAYFF, a non-reactive potential typically used to simulate fluid interfaces with clays and other minerals.

Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第14161号 / 工博第2995号 / 新制||工||1444(附属図書館) / 26467 / UT51-2008-N478 / 京都大学大学院工学研究科マイクロエンジニアリング専攻 / (主査)教授 立花 明知, 教授 榊 茂好, 教授 木村 健二 / 学位規則第4条第1項該当

Single crystal nickel-based superalloys are used in modern gas turbines because of their remarkable resistance to creep deformation at elevated temperatures, which is ensured by the addition of significant amounts of refractory elements. Too high concentrations of refractory elements can lead to the formation of topologically-close packed (TCP) phases during exposure to conditions of high temperature and stress which result in the degradation of the creep properties. The traditional methods for predicting the occurrence of TCP phases in Ni-based superalloys have been based on the PHACOMP and newPHACOMP methodologies which are well-known to fail with respect to new generations of alloys. In this work a novel two-dimensional structure map (Nbar, deltaV/V) for TCP phases where Nbar is the valence-electron count and deltaV/V is a compositional dependent size factor. This map is found to separate the experimental data on the TCP phases of binary, ternary and multi-component TCP phases into well-defined regions corresponding to different structure types such as A15, sigma, chi, delta, P, R, mu, and Laves. In particular, increasing size factor separates the A15, sigma and chi phases from the delta, P, R, mu phases. The structure map is then also used in conjunction with CALPHAD computations of sigma phase stability to show that the predictive power of newPHACOMP for the seven component Ni–Co–Cr–Ta–W–Re–Al system is indeed poor. In order to gain a microscopic understanding of the observed structural trends, namely the differences between the two groups of TCP structures with increasing deltaV/V and the trend from A15 to sigma to chi with increasing Nbar, the electronic structure is coarse-grained from density functional theory (DFT) to tight-binding to bond-order potentials (BOPs). First, DFT is used to calculate the structural energy differences across the elemental 4d and 5d transition metal series and the heats of formation of the binary alloys Mo-Re, Mo-Ru, Nb-Re, and Nb-Ru. These calculations show that the valence electron concentration stabilizes A15, sigma and chi but destablizes mu and Laves phases. The latter are shown to be stabilized instead by relative size difference. Second, a simple canonical TB model and in combination with the structural energy difference theorem is found to qualitatively reproduce the energy differences predicted by the elemental DFT calculations. The structural energy difference theorem rationalizes the importance of the size factor for the stability of the mu and Laves binary phases as observed in the structure map and DFT heats of formation. Finally, analytic BOP theory, is employed to identify the structural origins of the energetic differences between TCP structure-types that lead to the trends found within the two-dimensional structure map.

The development of interatomic potentials for magnetic transition metals, and particularly for iron, is difficult, yet it is also necessary for large-scale atomistic simulations of industrially important iron and steel alloys. The magnetism of iron is especially important as it is responsible for many of the element's unique physical properties -- its bcc ground state structure, its high-temperature phase transitions, and the mobility of its self-interstitial atom (SIA) defects. Yet an accurate description of itinerant magnetism within a real-space formalism is particularly challenging and existing interatomic potentials based on the Embedded Atom Method are suited only for studies of near-equilibrium ferritic iron, due to their restricted functional forms. For this work, the magnetic analytic Bond-Order Potential (BOP) method has been implemented in full to test the convergence properties in both collinear and non-collinear magnetic iron. The known problems with negative densities of states (DOS) are addressed by assessing various possible definitions for the bandwidth and by including the damping factors adapted from the Kernel Polynomial Method. A 9-moment approximation is found to be sufficient to reproduce the major structural energy differences observed in Density Functional Theory (DFT) and Tight Binding (TB) reference calculations, as well as the volume dependence of the atomic magnetic moments. The Bain path connecting bcc and fcc structures and the formation energy of mono- and divacancies are also described well at this level of approximation. Other quantities such as the high-spin/low-spin transition in fcc iron, the bcc elastic constants and the SIA formation energies converge more slowly towards the TB reference data. The theory of non-collinear magnetism within analytic BOP is extended as required for a practical implementation. The spin-rotational behaviour of the energy is shown to converge more slowly than the collinear bulk energy differences, and there are specific problems at low angles of rotation where the magnitude of the magnetic moment depends sensitively on the detailed structure of the local DOS. Issues of charge transfer in relation to magnetic defects are discussed, as well as inadequacies in the underlying d-electron TB model.

Silicon nitride is a bulk and a coating material exhibiting excellent mechanical properties. The understanding of the complex processes at the nanometre scale gained through experimental research will be enhanced by the existence of a computationally efficient and accurate model that is able to describe the mechanical properties of silicon nitride. Such a model has yet to be proposed. In this thesis we present a transferable reduced tight-binding (TB) model for the silicon nitride system. More precisely, this model consists of a reduced TB model for elemental silicon, a reduced TB model for elemental nitrogen, and a reduced TB model for silicon nitride. These models are developed within the framework of coarse-graining the electronic structure from density functional theory (DFT) to tight binding (TB) to bond-order potentials (BOPs), and can therefore be used in the future as the stepping stone to develop BOPs for the application in large scale simulations. The bond integrals employed in the reduced TB models are obtained directly from mixed-basis DFT projections of wave functions onto a minimal basis of atom-centred orbitals. This approach reduces the number of overall parameters to be fitted and provides models which are transferable through the different coarse-graining levels. We provide an example by using the same bond integrals in the reduced TB model for silicon and the preliminary bond-based BOP for silicon. DFT binding energies of ground state and metastable crystal structures are used as the benchmark to which the TB and BOP repulsive parameters are fitted. In addition to model development, we present an improved methodology when going from TB to reduced TB. By weighting all four σ TB bond integrals equally, we provide a new parameterisation (Eqs. (2.73) and (2.74)) and show that the quality of the silicon reduced TB model can be increased by choosing one of the reduced TB parameters to be distance invariant. The ingredients, the development methodology, and the quality of each of the four models are discussed in a separate chapter. The quality of the reduced TB models and BOP is demonstrated by comparing their predictions for the binding energies, heats of formation, elastic constants, and defect energies with DFT and experimental values.

No description available.