# Multiscale modelling of material properties

In the multiscale modelling approach different modelling methods are being linked to each other by exchanging the relevant data and parameters. By doing so it is, in principle, possible to bridge the scales from atomistic to continuum methods. Heat capacities and enthalpies of formation can be calculated by DFT which are taken as input parameters in the CALPHAD method to model the phase diagrams. | |

Technical data | |
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- 3 work stations with a total of 38 cores within the research group
- Access to the cluster JURECA of the Jülich Supercomputing Centre (JSC)
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CALPHAD | |

CALculation of PHAse Diagrams refers to a type of semi-empirical modelling method designed for the calculations of phase diagrams from thermodynamic data. All phase diagrams are a projection of the underlying thermodynamics which is being parametrized within the CALPHAD approach and saved in data bases. The central property is the Gibbs energy as a function of temperature, pressure and composition, which needs to be known for each respective phase. The calculation of a phase diagram of a phase equilibrium is carried out by minimizing the Gibbs energy. To be able to run a calculation the thermodynamic approach has to be determined with a phase diagram optimization. This optimization is an elaborate data fit by including the experimental phase diagram data, calorimetric data and with increasing impact also DFT data, which have to be chosen with care and need to be evaluated (assessment). The thermodynamic data is also needed as input for other modelling methods e.g. for the calculation of the chemical potential in the phase field method, the calculation of thermo-physical properties (surface tension and viscosity) or diffusion coefficients. | |

Employed software packages: | |

- ThermoCalc
- FactSage
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Density-functional theory – ab initio modelling | |

The density-functional theory (DFT ) is built upon a theorem stating that the energy of a system is a functional of the electron density. More specifically it states the existence of an electron density distribution which minimizes the system’s energy. Consequently, by minimizing the energy with respect to atomic/ionic & electronic degrees of freedom the ground-state energy can be obtained. By employing DFT -codes molecules and solids can be investigated with minimal input from experiments. In the context of multiscale modelling DFT methods can be used to obtain parameters which are experimentally difficult or impossible to access. Moreover, it is possible to model hypothetical compounds which are actually non-existent (as being done in the sublattice model in CALPHAD). This provides a physical basis and avoids the necessity of plain estimates. | |

Employed software packages: | |

- VASP (Vienna ab initio simulation package)
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Cluster expansion method | |

When it comes to the modelling of systems in which two or more atomic species occupy the same lattice sites (substitutional solid solutions) one is faced with a combinatorial problem of a vast amount of possible atomic arrangements and the main question to answer is which of the atomic arrangements represent the ground state configuration with the lowest energy possible. In essence, when looking at a solid with N atomic sites which can be occupied by either the element A or B (whereas B can also be a vacancy) then the number of possible atomic arrangements is 2N. It would be a futile task to calculate the energies for all of these configurations. The so-called cluster expansion is a method to alleviate this problem by providing a formalism for enabling the prediction of the energies of an arbitrary configuration based on the knowledge of a finite set of configurations (structures). The formalism is based on an expansion series constructed from specific arrangements (clusters) of two to four specific atoms in a range of crystal structures. The power of the cluster expansion is that it converges quickly so that only relatively small clusters need to be included and therefore only a finite set of crystal structures which contain these specific clusters have to be calculated. Eventually, one obtains the energy of a solid solution in dependence of the atomic configuration. | |

Employed software: | |

• ATAT (Alloy Theoretic Automated Toolkit) |