Complete thermodynamic description of alloys to extreme pressure and temperature

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The aim of the proposed PhD is to develop a first-principles theoretical and computational scheme that provides a complete thermodynamic description of alloys from ambient to extreme conditions. This is in collaboration with the Atomic Weapons Establishment. We propose to develop a workflow that will be easily adaptable to arbitrary materials and require little human intervention. The scheme will deliver the required thermodynamic properties at a modest computational cost while retaining ab initio accuracy, with any uncertainties strictly quantified. In order to realise this requirement, we propose to include surrogate interatomic potential models for ab initio calculations in the workflow. This can be achieved in the form of using machine learning interatomic potentials (MLIP). After the generation, refinement and validation of such models, the calculation of free energies will follow, using thermodynamic integration and the nested sampling method [2,3], allowing the derivation of any equilibrium thermodynamic properties.In more detail, we propose the following workflow. For the ab initio calculations, we plan to use Density Functional Theory (DFT), as it has been established as a reliable, transferable and accurate first principles methodology to study metallic systems and alloys.1.Generation of a database of atomic configurations. MLIPs are typically fitted on a database of atomic configurations, which includes ab initio energetics, such as total energies, forces and stresses. When the stable phases of a material are known, these can be used to "bootstrap" the database, but in a general case, and especially at extreme conditions, these are not necessarily available in advance. Therefore, we propose to use the Ab Initio Random Structure Search (AIRSS) [4,5] method, which automatically generates stable and metastable crystalline polymorphs in an unbiased way at broad and tuneable range of pressure conditions.2.Fitting a MLIP. We propose to use the Gaussian Approximation Potential (GAP) framework, which has been shown to achieve first principles accuracy at a significantly lower computational cost. Using the generated database, a GAP model will be fitted and validated. It is anticipated that the database will need to be extended in an iterative, or "active learning" fashion, especially to provide an adequate coverage of high-temperature crystalline and disordered phases.3.Calculation of the temperature-pressure phase diagram. To obtain a general picture of phase stability at a broad range of temperature and pressures, we first propose to run a series of nested sampling (NS) calculations using the GAP model. NS has been shown to be able to automatically identify thermodynamically stable phases and generate phase diagrams. In order to refine the thermodynamic information obtained from NS, thermodynamic integration calculations will be performed using the Einstein crystal as the reference and GAP as the endpoint. It will be established if additional free energy perturbation calculations are required to achieve DFT accuracy. Thermodynamic properties such as the melting line, equation of state, latent heat, temperature-dependent elastic properties will be derived from the free-energies.