Atomistic simulations of plasticity in topologically close-packed phases using machine learning potentials

Methods

In our workflow, we will employ the Nudged Elastic Band NEB method for investigating the movement of dislocations and their interactions with point defects in complex crystal structures like the Laves phase. To study the twin boundary structure in $\mu$-phases, we will utilize the classical MS method.
LAMMPS will be our primary tool. This code is widely used at simulating the non-relativistic motion of a vast number of atoms, from millions to trillions, using the Verlet algorithm. Due to the complexity of the crystal structures under study, we will use MLIP-2 and PACE. Both MLIP and PACE potentials are types of machine learning potential, which aim to deliver DFT-level accuracy with a much less computational load. Both MLIP and PACE potential is not significantly different from the classical empirical potentials, however, both use numerous DFT calculations and neural networks to fit the potential function in arbitrary target function to approximate the observed properties in DFT calculations.

Results

Dislocation behavior and defect interactions were studied across various Laves and $\mu$-phase intermetallic systems using a combination of atomistic simulations and advanced microscopy.

(Article submitted for review) In the C15 NbCr${}_2$ Laves phase, we elucidated the atomic-scale structure of dislocation cores at dislocation locks, which were shown to be decorated by point defects. Correlative simulations revealed site-specific occupancies and dislocation reaction mechanisms, including the formation of Lomer–Cottrell-type locks. These locks have implications for crack initiation and propagation under stress.

(Article in preparation) In parallel, a novel mechanism involving extrinsic stacking fault glide was uncovered in both C14 and C15 Nb-Cr Laves phases. This process, termed coupled synchro-shear, involves synchronized dislocation motion on multiple atomic layers and is critical for understanding polytype transformations and twinning behavior. High-resolution electron microscopy confirmed extended dislocation core structures and stacking faults, aligning well with NEB predictions.

(Article in preparation + Mini-thesis) The role of alloy chemistry was investigated in CaMg${}_2$-based C14 Laves phases. Deviations from stoichiometry, particularly with Al addition, significantly influenced elastic constants and stacking fault energies. Slip system analysis identified favorable deformation modes and revealed that point defects can soften the lattice depending on composition. NEB simulations further quantified energy barriers and indicated possible cross-slip pathways.

Lastly, in Ta-Fe $\mu$-phases, we modeled non-basal twin structures and fault energetics across a wide composition range. A transition from basal to pyramidal II twins with increasing Ta content was identified. Twin boundaries incorporating C14 Laves layers were observed experimentally and modeled using PACE potentials. While these simulations offered valuable insights, their results were not fully integrated into the final manuscript.

Discussion

Overall, the simulations reveals that grown-in defect structures—such as dislocation locks, intrinsic/extrinsic stacking faults, and twin boundaries—critically influence deformation in Laves phases. These defects hinder dislocation mobility, promote stress concentrations, and limit plasticity. At high temperatures, thermally activated coupled synchro-shear dislocations facilitate stacking fault propagation through the coupled synchroshear pathway, enabling the C15$\to$C36 phase transformation and twinning. Compositionally, off-stoichiometric NbCr${}_2$ phases exhibit Nb enrichment and vacancy decoration at dislocation cores, which reduce local stress and may suppress crack nucleation. These chemical effects align with experimental findings indicating that deviations from stoichiometry improve fracture toughness. Vacancy segregation further suggests dynamic strain aging behavior at elevated temperatures, revealing a complex interplay between point defects, dislocation interactions, and thermal activation in governing plasticity and toughness in Laves phases.

Furthermore, the simulation on $\mu$-phase non-basal twin boundaries contributes to understanding the defect landscape of the $\mu$-phase. This framework enables predictive control over defect populations by tuning composition. For example, altering the dominant planar fault type may modulate cleavage energies, thereby tailoring fracture resistance. Beyond mechanical response, the defect landscape offers a route to control functional properties such as thermal conductivity. Prior studies on intermetallic compounds like PbTe, Mg${}_2$Si, and AgSbTe${}_2$ demonstrate that thermal transport can be tuned via grain boundary misorientation, twin boundary density, and stacking fault density. These insights suggest that careful control of defect structures in $\mu$-phases through compositional tuning can enable property optimization for both mechanical and thermal applications.

In conclusion, we focused on specific material systems (Mg-Al-Ca, Nb-Cr, Nb-Ni). While we obtained generalizable insights to a certain extent, the generalization did not extend to the entire chemical space. Therefore, the next step is high-throughput calculation to complement the incomplete generalization effort from the first funding period. By using a custom-built MD high-throughput simulation framework, we will (i) explore the chemical space of Laves phase systems and (ii) seek opportunities to design ductile Laves phases through exploratory high-throughput simulations.

Additional Project Information

DFG classification: 406-03 Microstructural Mechanical Properties of Materials
Software: LAMMPS
Cluster: CLAIX

Publications

[1] On the atomic nature of complex dislocation locks in C15 Laves phases and their impact on cracking, G. Liu, S. Lee, C. H. Liebscher, S. Zhang, X. Zhou, J. Lee, S. Wei, M. Vega-Paredes, P. Schweizer, S. Korte-Kerzel, G. Dehm, Z. Xie, & F Stein, Article submitted for review, 2025.