Semiempirical interatomic potentials have been developed for Al, $\alpha -\mathrm{Ti},$ and $\gamma -\mathrm{TiAl}$ within the embedded atom method (EAM) formalism by fitting to a large database of experimental as well as ab initio data. The ab initio calculations were performed by the linearized augmented plane wave (LAPW) method within the density functional theory to obtain the equations of state for a number of crystal structures of the Ti-Al system. Some of the calculated LAPW energies were used for fitting the potentials while others for examining their quality. The potentials correctly predict the equilibrium crystal structures of the phases and accurately reproduce their basic lattice properties. The potentials are applied to calculate the energies of point defects, surfaces, and planar faults in the equilibrium structures. Unlike earlier EAM potentials for the Ti-Al system, the proposed potentials provide a reasonable description of the lattice thermal expansion, demonstrating their usefulness for molecular-dynamics and Monte Carlo simulations at high temperatures. The energy along the tetragonal deformation path (Bain transformation) in $\gamma -\mathrm{TiAl}$ calculated with the EAM potential is in fairly good agreement with LAPW calculations. Equilibrium point defect concentrations in $\gamma -\mathrm{TiAl}$ are studied using the EAM potential. It is found that antisite defects strongly dominate over vacancies at all compositions around stoichiometry, indicating that $\gamma -\mathrm{TiAl}$ is an antisite disorder compound, in agreement with experimental data.

We construct an interatomic potential for the Ni-Al system within the embedded-atom method formalism. The potential is based on previously developed accurate potentials for pure Ni and Al. The cross-interactions are fitted to experimental cohesive energy, lattice parameter and elastic constants of B2-NiAl, as well as to ab initio formation energies of several real or imaginary intermetallic compounds with different crystal structures and chemical compositions. The potential accurately reproduces a variety of physical properties of the NiAl and Ni₃Al phases, and shows reasonable agreement with experimental and ab initio data for phase stability across the Ni-Al phase diagram. Most of the properties reproduced by the new potential were not involved in the fitting process, which demonstrates its excellent transferability. Advantages and certain weaknesses of the new potential in comparison with other existing potentials are discussed in detail. The potential is expected to be especially suitable for simulations of heterophase interfaces and mechanical behavior of Ni-Al alloys.

Large-scale atomistic computer simulations of materials heavily rely on interatomic potentials predicting the energy and Newtonian forces on atoms. Traditional interatomic potentials are based on physical intuition but contain few adjustable parameters and are usually not accurate. The emerging machine-learning (ML) potentials achieve highly accurate interpolation within a large DFT database but, being purely mathematical constructions, suffer from poor transferability to unknown structures. We propose a new approach that can drastically improve the transferability of ML potentials by informing them of the physical nature of interatomic bonding. This is achieved by combining a rather general physics-based model (analytical bond-order potential) with a neural-network regression. This approach, called the physically informed neural network (PINN) potential, is demonstrated by developing a general-purpose PINN potential for Al. We suggest that the development of physics-based ML potentials is the most effective way forward in the field of atomistic simulations.

An angular-dependent interatomic potential has been developed for the Al-Cu system based on existing embedded-atom method potentials for Al and Cu and fitting of the cross-interaction functions to experimental and first-principles data. The potential reproduces lattice parameters, formation energies, and elastic constants of the $\theta${} and $\theta${}$'${} phases of this system. It predicts the $\theta${}$'${} phase to be more stable than $\theta${} at 0 K but to become less stable at hight temperatures due to vibrational entropy. The temperate and entropy of this phase transformation are in good agreement with previous first-principles calculations [C. Wolverton and V. Ozoli\ifmmode \mbox{\c{n}}\else \c{n}\fi{}\ifmmode \check{s}\else \v{s}\fi{}, Phys. Rev. Lett. 86, 5518 (2001)]. The potential provides a reasonable description of the phase stability across the Al-Cu phase diagram, dilute heats of solution, and other thermodynamic properties. It has also been tested for generalized stacking fault energies in the presence of a copper layer embedded in Al. This configuration bears some resemblance to Guinier-Preston zones that strengthen Al-Cu alloys. The trends predicted by the potential for uniform shearing of this configuration are in agreement with results of first-principles density-functional calculations performed in this work. The potential is expected to be suitable for atomistic simulations of precipitation hardening of Al-Cu alloys.

The Frank–Bilby equation (FBE) can give many solutions for the dislocation content of a grain boundary (GB); most of them are considered to have little physical reality except in limited ranges of the angles which characterize low-angle GBs. We explore two such solutions, each of which is an accurate description for a different low-angle tilt GB with the same tilt axis. We develop a model that uses the two solutions to predict the coupling factor between normal motion and the shear strain produced by any (low- or high-angle) GB. Within this model, the two FBE solutions give rise to two possible modes of coupled GB motion which for the same GB under the same stress differ in direction of motion. Using molecular dynamics simulations we confirm our model. We find positive and/or negative coupled GB motion for all misorientation angles, and the model gives accurate predictions for the shear produced even by high-angle GBs where individual dislocations cannot be resolved. At low temperatures dual behaviour is observed for the same high-angle GB and applied stress: both coupling modes are found with a switch between them after some time. This switch signifies a change in the effective dislocation content. Dual behaviour indicates that both solutions for the dislocation content can be meaningful for the same GB. At higher temperatures only one mode is seen for each GB under the same shear stress, and the switch between the two modes seems to occur discontinuously at some high misorientation angle.