Periodic Reporting for period 1 - MAPAA (MULTISCALE ANALYSIS OF PRECIPITATE IN Al-Cu ALLOYS)
Reporting period: 2020-03-01 to 2022-02-28
The equilibrium phase diagrams are at the core of novel design strategies to discover new materials or to optimize existing ones through integrated computational material engineering. So far, the determination of phase diagrams has been achieved through the CALPHAD (CALculation of PHAse Diagrams) method. Notwithstanding the huge success of the CALPHAD methodology, the accuracy of the predicted phase diagrams is not always as good as required because of the difficulties imposed by kinetics and metastability to determine experimentally accurate thermodynamics and thermochemical parameters, together with the inherent approximations of the CALPHAD method. This is the main problem being addressed in MAPPA project.
Advanced materials are involved in everyday life of the general public and the applications of computational strategies involving artificial intelligence are of interest to the general public. The activities carried out in MAPPA project will promote and create awareness among the widest possible audience of the the application of computational strategy, especially the virtually discovery of new alloys.
The objective of the MAPAA project was to develop a novel methodology to determine the precipitate structure resulting from high temperature aging and the resulting precipitate strength of the alloys from first principles calculations. The strategy was applied to Al alloys (with particular emphasis in the Al-Cu system) and it was based in two main pillars. The first one is the determination of the phase diagram by means the construction of effective cluster expansion Hamiltonians that can extrapolate first-principles calculations in combination with statistical mechanics approaches based on Monte Carlo simulations to include the entropic contributions, enabling parameter-free predictions of the phase diagram. The second one was the combination of this information with phase field modeling to predict the homogeneous and heterogeneous nucleation and growth of precipitates during high temperature aging and the application of molecular dynamics and dislocation dynamics simulations to predict the strengthening provided by the precipitates.
Advanced materials are involved in everyday life of the general public and the applications of computational strategies involving artificial intelligence are of interest to the general public. The activities carried out in MAPPA project will promote and create awareness among the widest possible audience of the the application of computational strategy, especially the virtually discovery of new alloys.
The objective of the MAPAA project was to develop a novel methodology to determine the precipitate structure resulting from high temperature aging and the resulting precipitate strength of the alloys from first principles calculations. The strategy was applied to Al alloys (with particular emphasis in the Al-Cu system) and it was based in two main pillars. The first one is the determination of the phase diagram by means the construction of effective cluster expansion Hamiltonians that can extrapolate first-principles calculations in combination with statistical mechanics approaches based on Monte Carlo simulations to include the entropic contributions, enabling parameter-free predictions of the phase diagram. The second one was the combination of this information with phase field modeling to predict the homogeneous and heterogeneous nucleation and growth of precipitates during high temperature aging and the application of molecular dynamics and dislocation dynamics simulations to predict the strengthening provided by the precipitates.
In MAPPA project, the DFT simulation of atomic configurations was first carried out, aimed at obtaining the formation energy of different atomic configurations, i.e. possible arrangements of atomic species on lattice. The calculations were performed using the open-source code Quantum Espresso and the cut-off energy, k-point sampling and smearing were decided from convergence tests.
Then the cluster expansion Hamiltonians formulation was fitted based on the DFT energy information. The optimum cluster terms and dominant configurations were obtained by machine-learning algorithms. At the end of fitting, the predictions of the cluster expansion Hamiltonians were validated against the DFT results. The metrics were the cross-validation score and the comparison of the fitted and calculated formation energy of each configuration, especially the ones on the convex hull.
Then Monte Carlo simulations based on the fitted cluster expansions were performed. The phase diagrams were determined from the calculated free energy.
Then the thermodynamics properties from the constructed phase diagram were combined with the elastic strain energies and interface energies of precipitates to predict the size and shape of these precipitates during high temperature aging. To this end, the critical size for homogeneous precipitation was determined while the growth of the precipitate from the critical nucleus were computed using the phase-field method.
Then the cluster expansion Hamiltonians formulation was fitted based on the DFT energy information. The optimum cluster terms and dominant configurations were obtained by machine-learning algorithms. At the end of fitting, the predictions of the cluster expansion Hamiltonians were validated against the DFT results. The metrics were the cross-validation score and the comparison of the fitted and calculated formation energy of each configuration, especially the ones on the convex hull.
Then Monte Carlo simulations based on the fitted cluster expansions were performed. The phase diagrams were determined from the calculated free energy.
Then the thermodynamics properties from the constructed phase diagram were combined with the elastic strain energies and interface energies of precipitates to predict the size and shape of these precipitates during high temperature aging. To this end, the critical size for homogeneous precipitation was determined while the growth of the precipitate from the critical nucleus were computed using the phase-field method.
Starting from quantum mechanical calculations, the results in MAPPA proved that we are able to predict, without any adjustable parameters, the formation energy and phase diagrams of binary and ternary structures. In the case of binary alloys, the type of analysis we are doing has the highest accuracy in the world. And regarding ternary alloys, we are really one of the few centers anywhere that have demonstrated the ability to conduct this kind of modeling.
The whole project (including the calculation of the phase diagram from first principles and its combination with the multiscale modeling strategies for precipitation and precipitation hardening) will have a large scientific impact, but it will also be very valuable for industry, because it provides a very valuable strategy for computational materials design and optimization. At the end of the project, the computational strategy was available for precipitation strengthened Al-Cu, Al-Li alloys but it could be easily extended to other Al alloys and, with more effort, to other metallic systems.
The whole project (including the calculation of the phase diagram from first principles and its combination with the multiscale modeling strategies for precipitation and precipitation hardening) will have a large scientific impact, but it will also be very valuable for industry, because it provides a very valuable strategy for computational materials design and optimization. At the end of the project, the computational strategy was available for precipitation strengthened Al-Cu, Al-Li alloys but it could be easily extended to other Al alloys and, with more effort, to other metallic systems.