Abstract
In the present work, we present a free energy derivation of the multi-component phase-field crystal model [1] and illustrate the capability to simulate dendritic and eutectic solidification in ternary alloys. Fast free energy minimization by a simulated annealing algorithm of an approximated crystal is compared with the free energy of a fully simulated phase field crystal structure. The calculation of ternary phase diagrams from these free energies is described. Based on the free energies related to the ternary Al–Cu–Mg system, we show phase field crystal simulations of both, ternary dendritic growth as well as lamellar eutectic growth of three distinct solid phases.
Highlights
In the last years, simulations of atomistic effects have become an important field in materials research
We write the free energy as a sum of the ideal energy density DFid comprising entropy contributions for an K-component system and the excess energy density DFex, which is based on the interactions of the atoms
For the construction of a ternary phase diagram, the free energies of the single phases depending on c2CD are required
Summary
Simulations of atomistic effects have become an important field in materials research. Elder et al [3,4] introduce a continuous field of the probability density of atomic presence, by adapting the SwifteHohenbergeEquation [5] and later approximating the functional of DFT. In line of these approaches, the phase field crystal (PFC) method is able to reproduce results of DFT and MD such as the physics of grain boundaries [6], elastic and plastic deformations [4] and thermodynamics of iron [7].
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