Atomistic modelling of precipitation in Ni-base superalloys

The presence of the ordered $\gamma^{\prime}$ phase ($\text{Ni}_{3}\text{Al}$) in Ni-base superalloys is fundamental to the performance of engineering components such as turbine disks and blades which operate at high temperatures and loads. Hence for these alloys it is important to optimize their microstructure and phase composition. This is typically done by varying their chemistry and heat treatment to achieve an appropriate balance between $\gamma^{\prime}$ content and other constituents such as carbides, borides, oxides and topologically close packed phases. In this work we have set out to investigate the onset of $\gamma^{\prime}$ ordering in Ni-Al single crystals and in Ni-Al bicrystals containing coincidence site lattice grain boundaries (GBs) and we do this at high temperatures, which are representative of typical heat treatment schedules including quenching and annealing. For this we use the atomistic simulation methods of molecular dynamics (MD) and density functional theory (DFT). In the first part of this work we develop robust Bayesian classifiers to identify the $\gamma^{\prime}$ phase in large scale simulation boxes at high temperatures around 1500 K. We observe significant \gamma^{\prime} ordering in the simulations in the form of clusters of $\gamma^{\prime}$-like ordered atoms embedded in a $\gamma$ host solid solution and this happens within 100 ns. Single crystals are found to exhibit the expected homogeneous ordering with slight indications of chemical composition change and a positive correlation between the Al concentration and the concentration of $\gamma^{\prime}$ phase. In general, the ordering is found to take place faster in systems with GBs and preferentially adjacent to the GBs. The sole exception to this is the $\Sigma3 \left(111\right)$ tilt GB, which is a coherent twin. An analysis of the ensemble and time lag average displacements of the GBs reveals mostly `anomalous diffusion' behaviour. Increasing the Al content from pure Ni to Ni 20 at.% Al was found to either consistently increase or decrease the mobility of the GB as seen from the changing slope of the time lag displacement average. The movement of the GB can then be characterized as either `super' or `sub-diffusive' and is interpreted in terms of diffusion induced grain boundary migration, which is posited as a possible precursor to the appearance of serrated edge grain boundaries. In the second part of this work we develop a method for the training of empirical interatomic potentials to capture more elements in the alloy system. We focus on the embedded atom method (EAM) and use the Ni-Al system as a test case. Recently, empirical potentials have been developed based on results from DFT which utilize energies and forces, but neglect the electron densities, which are also available. Noting the importance of electron densities, we propose a route to include them into the training of EAM-type potentials via Bayesian linear regression. Electron density models obtained for structures with a range of bonding types are shown to accurately reproduce the electron densities from DFT. Also, the resulting empirical potentials accurately reproduce DFT energies and forces of all the phases considered within the Ni-Al system. Properties not included in the training process, such as stacking fault energies, are sometimes not reproduced with the desired accuracy and the reasons for this are discussed. General regression issues, known to the machine learning community, are identified as the main difficulty facing further development of empirical potentials using this approach.EPSRC, Rolls-Royc

Elastic image registration using parametric deformation models

The main topic of this thesis is elastic image registration for biomedical applications. We start with an overview and classification of existing registration techniques. We revisit the landmark interpolation which appears in the landmark-based registration techniques and add some generalizations. We develop a general elastic image registration algorithm. It uses a grid of uniform B-splines to describe the deformation. It also uses B-splines for image interpolation. Multiresolution in both image and deformation model spaces yields robustness and speed. First we describe a version of this algorithm targeted at finding unidirectional deformation in EPI magnetic resonance images. Then we present the enhanced and generalized version of this algorithm which is significantly faster and capable of treating multidimensional deformations. We apply this algorithm to the registration of SPECT data and to the motion estimation in ultrasound image sequences. A semi-automatic version of the registration algorithm is capable of accepting expert hints in the form of soft landmark constraints. Much fewer landmarks are needed and the results are far superior compared to pure landmark registration. In the second part of this thesis, we deal with the problem of generalized sampling and variational reconstruction. We explain how to reconstruct an object starting from several measurements using arbitrary linear operators. This comprises the case of traditional as well as generalized sampling. Among all possible reconstructions, we choose the one minimizing an a priori given quadratic variational criterion. We give an overview of the method and present several examples of applications. We also provide the mathematical details of the theory and discuss the choice of the variational criterion to be used

Identifying Structure Transitions Using Machine Learning Methods

Methodologies from data science and machine learning, both new and old, provide an exciting opportunity to investigate physical systems using extremely expressive statistical modeling techniques. Physical transitions are of particular interest, as they are accompanied by pattern changes in the configurations of the systems. Detecting and characterizing pattern changes in data happens to be a particular strength of statistical modeling in data science, especially with the highly expressive and flexible neural network models that have become increasingly computationally accessible in recent years through performance improvements in both hardware and algorithmic implementations. Conceptually, the machine learning approach can be regarded as one that employing algorithms that eschew explicit instructions in favor of strategies based around pattern extraction and inference driven by statistical analysis and large complex data sets. This allows for the investigation of physical systems using only raw configurational information to make inferences instead of relying on physical information obtained from a priori knowledge of the system. This work focuses on the extraction of useful compressed representations of physical configurations from systems of interest to automate phase classification tasks in addition to the identification of critical points and crossover regions